If a + b = 3 and ab = 2, find the value of a² + b²​

Answers

Answer 1

Answer:

Through observation, a=2, b=1 or vice versa .

Step-by-step explanation:

If a=2 and b=1

a² +b²=?

2² +1² =4+1=5

a²+b²=5


Related Questions

G For each ordered pair, determine whether it is a solution to the system of equations. 9x+2y=-5 2x-3y=-8 (x, y) (1, -7) (0, -4) (5,6) (-1,2) Is it a solution? Yes No X 5​

Answers

Answer:

Math Quotient Verification

G For each ordered pair, determine whether it is a solution to the system of equations. 9x+2y=-5 2x-3y=-8 (x, y) (1, -7) (0, -4) (5,6) (-1,2) Is it a solution? Yes No X 5

To check if an ordered pair is a solution to a system of equations, we substitute the values of x and y into both equations and see if both equations are satisfied.

Let's check each ordered pair one by one:

(1, -7):

9x + 2y = -5 becomes 9(1) + 2(-7) = -5, which is false.

2x - 3y = -8 becomes 2(1) - 3(-7) = -8, which is true.

Therefore, (1, -7) is not a solution to the system of equations.

(0, -4):

9x + 2y = -5 becomes 9(0) + 2(-4) = -8, which is false.

2x - 3y = -8 becomes 2(0) - 3(-4) = 12, which is false.

Therefore, (0, -4) is not a solution to the system of equations.

(5, 6):

9x + 2y = -5 becomes 9(5) + 2(6) = 41, which is false.

2x - 3y = -8 becomes 2(5) - 3(6) = -8, which is true.

Therefore, (5, 6) is not a solution to the system of equations.

(-1, 2):

9x + 2y = -5 becomes 9(-1) + 2(2) = -11, which is false.

2x - 3y = -8 becomes 2(-1) - 3(2) = -8, which is true.

Therefore, (-1, 2) is not a solution to the system of equations.

Therefore, the answer is "No" for all the ordered pairs given in the problem.

(please mark my answer as brainliest)

The weight of a small Starbucks coffee is a normally distributed random variable with a mean of 360 grams and a standard deviation of 9 grams find the weight that corresponds to each event(use excel or appendix c to calculate the z value round your final answers to 2 decimal places

Answers

Answer:

Step-by-step explanation:

We'Re looking at a normal distribution here- let's start by drawing it out to the mean me- is 315 grams standard. Deviation is 16 point. We want to know the weight corresponding to each of these events and we can use either the appendix which i assume is a z, school table or excel so the first 1. We want the highest 20 percent up here somewhere. This is what we would call the 80 percent. It separates the bottom 80 percent from the highest 20 percent. So how do we work the well? We need to start by getting the z score for it. So how do we get that, while in excel you're going to use the norm inverse function which looks like this? So it's calls norm and then in here you just put in x, where x is your percentage and that will spit out the z score and i'm using this rather than a table, because it will give me a more exact value. So we're going to do that, and so here the percent is the 80, so it's not .8 and that spits out the z score of nort .8416 to 4 decimal places. But i'm always going to this exact score, because we now have to turn it from a z score to a piece of real data. Z score is a measure of how many standard deviations away from the mean a value is so we're. Looking for the value not .84 standard deviations, above the mean or if we write it like this x, is equal to z, sigma plus mu. So here we take our exact zedscore, because we can still just use excels, multiply it by 16 and add it on to the mean and we'll get our value of 328.447328 .47 grams to 2 decimal places for part b. We want to be middle 60 percent. Now we need to cut off points and within here where, in this interval we have 60 percent of values, which means we have 40 percent of values, not in here. So we can label our 3 sections. These 2 add up to 40 percent, so they have to be 20 percent. Each are called nor .2 and not .2, and then this middle bit here is nor .6 for the total of 100 percent point. So we need these cut off points when you, the z, scores first, and because these are equal distances away from a mine they're going to have the same z score. Just 1 is going to be positive or negative, so z is going to be equal to plus and minus. Let'S look at the lower 1. This is the 20 percent here so into this excel command. We put 20 percent nor .2 and out of it we get the z score of minus, not .8416. So it's actually very similar to the top question, because the top question asked you for the 80 percent be 80 percent. Is the upper cut off point here? 20? Is below cutoff point, so we already have the up 1, let's just calculate below 1, so we've got to be minus, nor .8416 multiplied by 16, but the standard deviation and on to the mean- and we get 301.53 and the upper cut off point is from part A so that's the middle 60 percent makes more space a part c. We want to be highest 80 percent. So now what we want is the cut off between the lowest 20 and the highest 80, which we've just got from part c part b. It'S this lower 1, here, 301.53 grams. That'S an easy! 1! Now we want the lowest 15 percent, so the lowest 15 percent is the 15 percent. So we go to our exylgamant put in the 15 for percent, so that would be no .15 and it's a z score of minus 1.036 keeping the exact value put into this formula. We multiply our z by 16, as on 315, to get 298.42 grams.

The weight that corresponds to this event are approximately 344.03 grams and 375.97 grams.

What is normal distribution?

To find the weight that corresponds to each event, we need to use the standard normal distribution, which has a mean of 0 and a standard deviation of 1. We can convert the given mean and standard deviation to z-scores using the formula:

z = (x - μ) / σ

where x is the weight we want to find, μ is the mean (360 grams), and σ is the standard deviation (9 grams).

Then, we can use a standard normal distribution table or calculator to find the probability of each event, and convert it back to a weight using the inverse of the z-score formula:

x = μ + z * σ

where z is the z-score that corresponds to the desired probability.

Event 1: The weight is less than 345 grams.

z = (345 - 360) / 9 = -1.67

Using a standard normal distribution table or calculator, we find that the probability of a z-score less than -1.67 is approximately 0.0475.

x = 360 + (-1.67) * 9 = 344.03 grams

Therefore, the weight that corresponds to this event is approximately 344.03 grams.

Event 2: The weight is between 355 and 365 grams.

First, we need to find the z-scores that correspond to the two boundaries:

z1 = (355 - 360) / 9 = -0.56

z2 = (365 - 360) / 9 = 0.56

Using a standard normal distribution table or calculator, we find that the probability of a z-score less than -0.56 is approximately 0.2123, and the probability of a z-score less than 0.56 is approximately 0.7123. Therefore, the probability of a z-score between -0.56 and 0.56 is:

0.7123 - 0.2123 = 0.5

x1 = 360 + (-0.56) * 9 = 355.16 grams

x2 = 360 + (0.56) * 9 = 364.84 grams

Therefore, the weight that corresponds to this event is any weight between 355.16 and 364.84 grams.

Event 3: The weight is greater than 375 grams.

z = (375 - 360) / 9 = 1.67

Using a standard normal distribution table or calculator, we find that the probability of a z-score greater than 1.67 is approximately 0.0475.

x = 360 + (1.67) * 9 = 375.97 grams

Therefore, the weight that corresponds to this event is approximately 375.97 grams.

To know more about Normal distribution visit:

brainly.com/question/29509087

#SPJ2

Question 2 of 3
Which subtraction equation shows how to subtract
4
2
12

2
8
12
using equivalent fractions? i need help​

Answers

Answer:

Step-by-step explanation:

your given is not cleared repost it then post

Find the error. Select choice options are step 1, 2, 3 and x-coordinates and y-coordinates​

Answers

Therefore, the slope of the line that passes through (-2, 8) and (4, 6) is -1/3.

What is the slope?

In mathematics, the slope is a measure of the steepness of a line.

The solution provided involves three steps to find the slope of the line that passes through two points: (-2, 8) and (4, 6).

Step 1 involves finding the change in y-coordinates, which is the difference between the y-coordinate of the second point and the y-coordinate of the first point. In this case, the second point has a y-coordinate of 6 and the first point has a y-coordinate of 8.

Therefore, the change in y-coordinates is 6 - 8 = -2.

Step 2 involves finding the change in x-coordinates, which is the difference between the x-coordinate of the second point and the x-coordinate of the first point. In this case, the second point has an x-coordinate of 4 and the first point has an x-coordinate of -2.

Therefore, the change in x-coordinates is 4 - (-2) = 6.

Step 3 involves dividing the change in y-coordinates by the change in x-coordinates to find the slope of the line. In this case, the change in y-coordinates is -2 and the change in x-coordinates is 6, so the slope is -2/6 or -1/3.

Since all the steps are correct and properly executed, there is no error.

Therefore, the slope of the line that passes through (-2, 8) and (4, 6) is -1/3.

To learn more about slope from the given link:

https://brainly.com/question/3605446

#SPJ1

show that the properties of a probability distribution for a discrete random variable are satisfied.

Answers

The properties of a probability distribution for a discrete random variable ensure that the probabilities assigned to each possible value of the variable are consistent with the axioms of probability and allow for meaningful inference and prediction.

The properties of a probability distribution for a discrete random variable are.

The probability of each possible value of the random variable must be non-negative.

The sum of the probabilities of all possible values must equal 1.

The probability of any event A is the sum of the probabilities of the values in the sample space that correspond to A.

These properties are satisfied because the probabilities of each possible value of a discrete random variable are defined in such a way that they are non-negative and sum to 1. Additionally, any event A can be expressed as a collection of possible values of the random variable, and the probability of A is then computed as the sum of the probabilities of those values.

To know more about probability distribution:

https://brainly.com/question/14210034

#SPJ4

in the right triangle what is the value of X? 30 24 X

Answers

Answer:

x = 21

Step-by-step explanation:

Given the angle measurements of two angles, we can deduce that this is a 30-60-90 triangle. The formula for side lengths of this type of triangle is given by s → s√3 → 2s with s being the shortest side (the side opposite the 30° angle).

We are looking for the side length represented by s[tex]\sqrt{3}[/tex]. We can see that the hypotenuse is represented by 2s, so...

2s = 24

s = 12

The side length of the shortest side is 12. Therefore, we can say that

x = s  [tex]\sqrt{3}[/tex]

x = 12 * [tex]\sqrt{3}[/tex]

x = 20.785

The question asks for our answer to the nearest whole number, so

x = 21

What are the values of the interior angles?

Round each angle to the nearest degree.
A) m∠X = 131º, m∠Y = 16º, m∠Z = 33º
B) m∠X = 120º, m∠Y = 15º, m∠Z = 30º
C) m∠X = 145º, m∠Y = 18º, m∠Z = 36º

Answers

We can see here the values of the interior angles will be: A) m∠X = 131º, m∠Y = 16º, m∠Z = 33º.

What is interior angle?

An interior angle is an angle created between two adjacent sides of a polygon. To put it another way, it is the angle created by two polygonal sides that have a shared vertex.

Sum of interior angles of a triangle = 180°

[tex]2p + \frac{1}{4} p + \frac{1}{2} p = 180[/tex]

11p/4 = 180°

p = 720°/11

m∠X = 2p = 2 ×  720°/11 = 130.9 ≈ 131°

m∠Y = [tex]\frac{1}{4} p[/tex] = 1/4 × 720°/11 = 16.3 ≈ 16°

m∠Z = [tex]\frac{1}{2} p[/tex] = 1/2 × 720°/11 = 32.7 ≈ 33°

Learn more about interior angle on https://brainly.com/question/24966296

#SPJ1

The cost of manufacturing a molded part is related to the quantity produced during a production run. When 100 parts are produced, the cost is $300. When 104 parts are
produced, the cost is $324. What is the average cost per part?
OA $0.23 per part
B. $6 per part
OC. $0.17 per part
OD. $7 per part

Answers

Answer:

B. $6 per part

Step-by-step explanation:

The average cost per part can be computed as follows

Average Cost = (324-300)/(104-100)

= 24/4

=$6

Answer: B. $6 per part

Find the inverse of the function

Answers

Answer:

g(y) = √(3/2 y)

Step-by-step explanation:

To find the inverse of a function, we need to solve for x in terms of y and interchange x and y. That is, we need to write the given function f(x) = 2/3x^2 in the form y = 2/3x^2 and then solve for x in terms of y.y = 2/3x^2

Multiplying both sides by 3/2, we get:

3/2 y = x^2

Taking the square root of both sides, we get:x = ± √(3/2 y)

Note that we have two possible values of x for each value of y, because the square root can be either positive or negative. However, for a function to have an inverse, it must pass the horizontal line test, which means that each value of y can only correspond to one value of x.Therefore, we need to restrict the domain of the original function to ensure that it is one-to-one. The simplest way to do this is to take the range of the function and use it as the domain of the inverse function.The range of f(x) = 2/3x^2 is all non-negative real numbers, or [0, ∞). Therefore, we can define the inverse function g(y) as:

g(y) = ± √(3/2 y)

where we choose the positive square root to ensure that the function is one-to-one.Thus, the inverse of the function f(x) = 2/3x^2 is:

g(y) = √(3/2 y)

with domain [0, ∞).

Let me know if this helped by hitting brainliest! If you have a question, please comment below and I'll get back to you ASAP!

Which is the solution to the inequality?

One-fourth + x less-than StartFraction 5 over 6 EndFraction
x less-than StartFraction 7 over 12 EndFraction
x greater-than StartFraction 7 over 12 EndFraction
x less-than 1 and StartFraction 1 over 12 EndFraction
x greater-than 1 and StartFraction 1 over 12 EndFraction

Answers

To satisfy the inequality x less-than StartFraction 7 over 12 EndFraction.

What is an Inequality?

Inequalities are called as the mathematical expressions in which both sides are nonequal. Unlike to equations, we compare two values in inequality. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs can be used in place of the equal sign in between.

The inequality is 1/4 + x < 5/6 in order to solve this inequality we need to isolate the value of x, that is our variable of interest. This is shown bellow:

1/4 + x < 5/6

x < 5/6 - 1/4

LMC is used to subtract the fractions we have as follows:

x < (2*5 - 3*1)/12

x < (10 - 3)/12

x< 7/12

The inequality must be satisfied for x to be smaller than 7/12.

to know more about equation, visit:

https://brainly.com/question/10413253

#SPJ1

Answer:  x < 7/12

Step-by-step explanation:

What is this question asking? What does it mean by floor plan? A step-by-step explanation would be very much appreciated. ​

Answers

Answer:

this is when you want to draw a sketch of a building

Determine the length of HK

Answers

Step-by-step explanation:

that height splits GK (32) into 2 parts :

8 and 32-8 = 24

then we use the geometric mean theorem for right-angled triangles

height = sqrt(p×q)

with p and q being the parts of the Hypotenuse.

so,

height = sqrt(8×24) = sqrt(192)

and now we can use Pythagoras

c² = a² + b²

with c being the Hypotenuse (the side opposite of the 90° angle), a and b are the legs,

to get HK.

HK² = height² + 24² = 192 + 576 = 768

HK = sqrt(768)

let be the space spanned by the two functions and . find the matrix of the linear transformation from into itself with respect to the basis .

Answers

When space is spanned by the two functions of linear transformation from into itself with respect to the basis we need to apply T to each basis vector vi to get the column vectors T(vi) = [T(vi)]B.

where [T(vi)]B is the coordinate vector of T(vi) with respect to the basis B. Arrange the column vectors [T(v1)]B, [T(v2)]B, ..., [T(vn)]B into a matrix. This matrix is the matrix of T with respect to the basis B.

In this case, you have two functions that span a vector space, so you need to specify the basis B. Once you have chosen the basis, you can apply the above steps to find the matrix of the linear transformation.

To learn about linear transformation visit:

https://brainly.com/question/30585642

#SPJ4

A school has 1800 pupils. 55% of the pupils are girls. 30% of the girls
and 70% of the boys travel by bus.
a) How may girls travel by bus?
b) How many boys travel by bus?
c) What percentage of the pupils travel by bus?

Answers

In linear equation, 65.625% of the pupils travel by bus.

What is  linear equation?

A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept. The variables in the previous sentence, y and x, are referred to as a "linear equation with two variables" at times.

A) 1800 * 0.55 * 0.3 = 297 Girls.

B)  1800 * 0.45 * 0.7 = 567 boys

C)  Girl

      297/864 * 100%  = 34.375%

  boy -

       567 ÷ (297 + 567 ) * 100%  = 65.625%

         864 = 297 + 567

Learn more about linear equation

brainly.com/question/11897796

#SPJ1

For the graph, find the average rate of change on the intervals given

See attached picture b

Answers

We cannot determine the actual value of the average rate of change without knowing the function f(x) or having a graph of the function.

Define the term graph?

The visual representation of mathematical functions or data points on a Cartesian coordinate system is an x-y axis graphic. The vertical or dependent variable is represented by the y-axis, while the horizontal or independent variable is represented by the x-axis. The difference between the change in output values and the change in input values is known as the average rate of change of a function over a period.

Let's assume that the function is denoted by f(x). Then, the average rate of change on the interval (a, b) can be calculated as

average rate of change = (f(b) - f(a)) / (b - a)

Using this formula, we can calculate the average rate of change on the given intervals as follows:

For the interval (-3, -2):

average rate of change = [tex]\frac{[f(-2) - f(-3)]}{[-2 - (-3)]}[/tex]

For the interval (1, 3):

average rate of change = [tex]\frac{(f(3) - f(1))}{(3 - 1)}[/tex]

For the interval (-1, 1):

average rate of change = [tex]\frac{(f(1) - f(-1))}{ (1 - (-1))}[/tex]

Note that we cannot determine the actual value of the average rate of change without knowing the function f(x) or having a graph of the function. If you provide the function or the graph, I can help you find the actual values of the average rate of change on these intervals.

To know more about plot, visit:

https://brainly.com/question/30195492

#SPJ1

find the sum of the series 1 12 13 14 16 18 19 112 where the terms are reciprocals of the positive integers whose only prime factors are 2s and 3s.

Answers

the sum of the series is 8/3. The series consists of reciprocals of positive integers whose only prime factors are 2s and 3s.

In other words, each term of the series can be expressed as a fraction of the form 1/n, where n is a positive integer that can be factored into only 2s and 3s. For example, the first term of the series is 1/1, the second term is 1/2, and the fourth term is 1/4.

To find the sum of the series, we can first list out the terms and their corresponding values:

1/1 = 1

1/2 = 0.5

1/3 = 0.333...

1/4 = 0.25

1/6 = 0.166...

1/8 = 0.125

1/9 = 0.111...

1/12 = 0.083...

and so on.

We can see that the terms of the series decrease in value as n increases, so we can use this fact to estimate the sum of the series. For example, we can take the sum of the first few terms to get an idea of how large the sum might be:

1 + 0.5 + 0.333... + 0.25 = 2.083...

We can see that the sum is greater than 2, but less than 3. To get a more accurate estimate, we can add a few more terms:

2.083... + 0.166... + 0.125 + 0.111... = 2.486...

We can continue adding terms in this way to get a more and more accurate estimate of the sum. However, it is not easy to find a closed-form expression for the sum of the series.

Alternatively, we can use a formula for the sum of a geometric series to find the sum of the series. A geometric series is a series of the form a + ar + ar^2 + ... + ar^n, where a is the first term and r is the common ratio between terms. In our series, the first term is 1 and the common ratio is 1/2 or 1/3, depending on whether n is even or odd. Therefore, we can split the series into two separate geometric series:

1 + 1/2 + 1/8 + 1/32 + ... = 1/(1 - 1/2) = 2

1/3 + 1/12 + 1/48 + 1/192 + ... = (1/3)/(1 - 1/2) = 2/3

The sum of the two geometric series is the sum of the original series:

2 + 2/3 = 8/3

Therefore, the sum of the series is 8/3.

To know more about geometric series click here:

brainly.com/question/21087466

#SPJ4

Please help!

To prove the converse of the Pythagorean theorem, we can define a right triangle, [FILL WITH ANSWER], with sides a, b, and x. Then, we will show that if ​△ABC​ is a triangle with sides a, b, and c where a² + b² = c², then it is congruent to △DEF and therefore a right triangle.

By the Pythagorean theorem, because ​△DEF​ is a right triangle, a² + b² = x².

If ​​a² + b² = x² and a² + b² = c² ​​, then c² = x². Further, since sides of triangles are positive, then we can conclude that ​c = x​. Thus, the two triangles have congruent sides and are congruent.

If ​△ABC​ is congruent to a right triangle, then it must also be a right triangle.

Answers:
right triangle
[tex]a^{2}[/tex] + [tex]b^{2}[/tex] = [tex]x^{2}[/tex]
[tex]a^{2}[/tex] + [tex]b^{2}[/tex] = [tex]c^{2}[/tex]
​△ABC
​△DEF

Answers

If △ABC is congruent to △DEF, then it must also be a right triangle. Thus, the two triangles have congruent sides and are congruent.

what is pythagoras theorem ?

A key idea in geometry known as the Pythagorean theorem explains the relationship between the sides of a right triangle. The square of the hypotenuse, or side opposite the right angle, is said to be equal to the sum of the squares of the other two sides. It can be expressed mathematically as: a² + b² = c²

given

By defining a right triangle, DEF, with sides a, b, and x, we can demonstrate the opposite of the Pythagorean theorem. Then, we'll demonstrate that if ABC is a triangle with sides a, b, and c where a2 + b2 = c2, it is congruent to DEF and is thus a right triangle because a2 + b2 = c2.

By the Pythagorean theorem, because △DEF is a right triangle, a² + b² = x².

When a2 + b2 = c2 and a2 + b2 = x2, c2 equals x2.

If △ABC is congruent to △DEF, then it must also be a right triangle.Thus, the two triangles have congruent sides and are congruent.

To know more about Pythagoras theorem visit :-

https://brainly.com/question/14461977

#SPJ1

If △ABC is congruent to △DEF, then it must also be a right triangle. Thus, the two triangles have congruent sides and are congruent.

What is Pythagoras theorem?

A key idea in geometry known as the Pythagorean theorem explains the relationship between the sides of a right triangle. The square of the hypotenuse, or side opposite the right angle, is said to be equal to the sum of the squares of the other two sides. It can be expressed mathematically as: a² + b² = c²

By defining a right triangle, DEF, with sides a, b, and x, we can demonstrate the opposite of the Pythagorean theorem. Then, we'll demonstrate that if ABC is a triangle with sides a, b, and c where [tex]a^2 + b^2 = c^2[/tex], it is congruent to DEF and is thus a right triangle because a2 + b2 = c2.

By the Pythagorean theorem, because △DEF is a right triangle, a² + b² = x².

When[tex]a^2 + b^2 = c^2[/tex] and [tex]a^2 + b^2 = x^2[/tex], [tex]c^2[/tex] equals [tex]x^2[/tex].

If △ABC is congruent to △DEF, then it must also be a right triangle. Thus, the two triangles have congruent sides and are congruent.

To know more about Pythagoras theorem visit :-

brainly.com/question/14461977

#SPJ1

you are computing a confidence interval for the difference in 2 population proportions. which of the following could be negative? select all.OP1Op 1 - 2Standard errorCritical valueLower bound of the confidence intervalUpper bound of the confidence interval

Answers

For the computation of confidence interval for the difference in two population proportions following are negative,

p₁(cap) - p₂(cap)

Lower bound of the confidence interval

Upper bound of the confidence interval

For the computation of confidence interval,

The difference in two population proportions,

p₁ - p₂, can be negative or positive.

This implies,

The sample estimate of the difference in proportions,

p₁(cap) - p₂(cap), can also be negative or positive.

The standard error and critical value are always positive values and cannot be negative.

The lower and upper bounds of the confidence interval can be negative or positive.

Depending on the sample estimate and the margin of error.

So, both the lower and upper bounds can be negative.

Learn more about confidence interval here

brainly.com/question/15049116

#SPJ4

The above question is incomplete, the complete question is:

You are computing a confidence interval for the difference in 2 population proportions. which of the following could be negative?

Select all.

a. p₁

b. p₁(cap) - p₂(cap)

c. Standard error

d. Critical value

e. Lower bound of the confidence interval

f. Upper bound of the confidence interval

Find the derivative of f(x) = -2x^3 by the limit process…

Answers

Answer:

f'(x) = -6x^2

f'(-5) = -150

f'(0) = 0

f'(√17) = -102

. If h> 3 and h - 2g= 0, which of
the following must be true?
A. g> 2.5
B. g> 1.5
C. g <0.5
D. g <1.5
E. g>2

Answers

By linear equality , g >1.5 is must be true.

What are equality and inequality along a line?

Equal (=) is the symbol used in linear equations. Example. Using the inequality symbols (>,, is greater than or equal to, and is less than or equal to), linear inequalities are expressed.

                          x - 5 > 3x - 10 is an illustration of a linear inequality. As the larger than symbol is employed in this inequality, the LHS is strictly greater than the RHS. After being solved, the inequality appears as 2x 5 x (5/2).

If h> 3 and h - 2g= 0

H=2g

2g>3

g >1.5

Learn more about linear equality

brainly.com/question/11874554

#SPJ1

Line AB contains point A(1, 2) and point B (−2, −1). Find the coordinates of A′ and B′ after a dilation with a scale factor of 5 with a center point of dilation at the origin

Answers

The coordinates of A' and B' after a dilation with a scale factor of 5 and a center point of dilation at the origin are A'(5, 10) and B'(-10, -5), respectively.

How to find dilated coordinate of A and B?

To find the coordinates of the points A' and B' after a dilation with a scale factor of 5 and a center point of dilation at the origin, we can use the following formula:

[tex]$$(x', y') = (5(x - 0), 5(y - 0)) = (5x, 5y)$$[/tex]

where (x, y) are the original coordinates of the point, and (x', y') are the new coordinates after the dilation.

For point A(1, 2), the new coordinates A' are:

[tex]$$(x_A', y_A') = (5(1), 5(2)) = (5, 10)$$[/tex]

Therefore, the coordinates of point A' are (5, 10).

For point B(-2, -1), the new coordinates B' are:

[tex]$$(x_B', y_B') = (5(-2), 5(-1)) = (-10, -5)$$[/tex]

Therefore, the coordinates of point B' are (-10, -5).

Therefore, the coordinates of A' and B' after a dilation with a scale factor of 5 and a center point of dilation at the origin are A'(5, 10) and B'(-10, -5), respectively.

To know more about Dilation factor visit:

brainly.com/question/10617018

#SPJ1

If y= cos x - sin x /cos x + sin x then dy /dx is :​

Answers

Answer:

Step-by-step explanation:

We can find dy/dx by differentiating y with respect to x using the quotient rule.

First, we need to rewrite y using the trigonometric identity for the tangent of the difference of two angles:

y = (cos x - sin x)/(cos x + sin x) = [(cos x - sin x)/(cos x + sin x)] * [(cos x - sin x)/(cos x - sin x)]

y = (cos^2 x - 2cos x sin x + sin^2 x)/(cos^2 x - 2sin x cos x + sin^2 x)

y = (cos 2x - sin 2x)/(cos 2x + sin 2x)

Now we can apply the quotient rule:

dy/dx = [(-sin 2x - cos 2x)(cos 2x + sin 2x) - (cos 2x - sin 2x)(-sin 2x + cos 2x)]/(cos 2x + sin 2x)^2

dy/dx = (-sin^2 2x - cos^2 2x - 2sin 2x cos 2x + sin^2 2x + cos^2 2x + 2sin 2x cos 2x)/(cos 2x + sin 2x)^2

dy/dx = 0/(cos 2x + sin 2x)^2

Therefore, dy/dx = 0.

Let Vector r = LeftAngleBracket 4, negative 2, 1 RightAngleBracket.and Vector r = LeftAngleBracket 3, 4, negative 1 RightAngleBracket.. Select the graph that shows the correct representation of Vector r + vector s. and select the correct magnitude of the resulting vector. Check all that apply.

Answers

Use the vector law of addition to get the resulting vector is [tex](7i+2j-k)[/tex] and magnitude of resulting vector is [tex]3\sqrt{6}[/tex].

What is the resulting vector and its magnitude?

Vector addition can be defined as the sum of two or more vectors of corresponding components.

It is given that,

[tex]\vec{r}= < 4, -2 > \\\vec{s}= < 3,4,-1 >[/tex]

Given vectors can also be written as,

[tex]\vec{r}=4i-2j\\\vec{s}=3i+4j-k[/tex]

Add above vectors as follows:

[tex]\vec{r}+\vec{s}=(4i-2j)+(3i+4j-k)\\\\=(7i+2j-k)[/tex]

Therefore,

[tex]\vec{r}+\vec{s}= < 7,2,-1 >[/tex]

Show the resulting vector as follows:

Now calculate the magnitude of the vector [tex](\vec{r}+\vec{s})[/tex]

[tex]|\vec{r}+\vec{s}|=\sqrt{(7)^2+(2)^2+(-1)^2}\\=\sqrt{49+4+1}\\=\sqrt{54}\\=3\sqrt{6}[/tex]

Hence the resulting vector is [tex](7i+2j-k)[/tex] and magnitude of resulting vector is [tex]3\sqrt{6}[/tex].

To know more about vector visit:

https://brainly.com/question/29740341

#SPJ1

93. Electricity Usage The graph shows
the daily megawatts of electricity used
on a record-breaking summer day in
Sacramento, California.
(a) Is this the graph of a function?
(b) What is the domain?
(c) Estimate the number of megawatts
used at 8 A.M.
(d) At what time was the most electric-
ity used? the least electricity?
(e) Call this function f. What is f(12)?
Interpret this answer.
(f) During what time intervals is usage
increasing? decreasing?

Answers

The graph that shows the electricity usage on a record-breaking summer day is Sacramento, California is a function.

The domain is 24 hours of a day.

The number of megawatts used at 8 am is 1, 200 megawatts.

The time with the most electricity used was 4 pm to 6 pm and least used was 4 am.

f ( 12 ) would be 1, 900 megawatts.

Usage is increasing from 4 am to 5 pm and decreasing from 5 pm to 4 am.

What does the graph show ?

The graph is a function because each point on the graph represents a distinct megawatt usage. The domain would be 24 hours of a day as this graph of electricity usage shows the usage per day.

The megawatts used at 8 am is:

= 1, 300 - ( 200 / 2 )

= 1, 200 megawatts

From 4 am to 5 pm, we see that electricity usage is increasing as people are getting ready for work and going to work, but from 5 pm to 4 am, electricity usage decreases.

Find out more on graphs at https://brainly.com/question/21444630

#SPJ1

How do you write 0.048 as a percentage?

Write your answer using a percent sign (%).

Answers

Answer:

0.048 in %

Step-by-step explanation:

firstly: remove the decimal point

= 48/1000

secondly : Simplify

48/1000*100

=48/10

=4.8%

Use the Chain Rule to find dz/dt. z = cos(x + 8y), x = 7t^5, y = 5/t

Answers

Answer:

We need to find dz/dt given:

z = cos(x + 8y), x = 7t^5, y = 5/t

Using the chain rule, we can find dz/dt by taking the derivative of z with respect to x and y, and then multiplying by the derivatives of x and y with respect to t:

dz/dt = dz/dx * dx/dt + dz/dy * dy/dt

First, let's find dz/dx and dz/dy:

dz/dx = -sin(x + 8y)

dz/dy = -8sin(x + 8y)

Now, let's find dx/dt and dy/dt:

dx/dt = 35t^4

dy/dt = -5/t^2

Substituting these values, we get:

dz/dt = (-sin(x + 8y)) * (35t^4) + (-8sin(x + 8y)) * (-5/t^2)

Simplifying this expression, we get:

dz/dt = -35t^4sin(x + 8y) + 40sin(x + 8y)/t^2

Substituting x and y, we get:

dz/dt = -35t^4sin(7t^5 + 40/t) + 40sin(7t^5 + 40/t)/t^2

Therefore, dz/dt is given by -35t^4sin(7t^5 + 40/t) + 40sin(7t^5 + 40/t)/t^2.

What the values of angles B and C?

Answers

The value of b is 73° as opposite angles of congruent sides are equal in an isosceles triangle.

What dοes a math angle mean?  

An angle is created by cοmbining twο rays (half-lines) that have a cοmmοn terminal. The angle's vertex is the latter, while the rays are alternately referred tο as the angle's legs and its arms.

What is fundamental angle?

An angle within a shape that has the shape's base as οne οf its sides is knοwn as the base angle οf a shape in geοmetry. Cοnsider the triangle in the image as an example. We can οbserve that the triangle's base side is made up οf an angle B side and an angle C side. As a result, the triangle's base angles are angles B and C.

To know more about complimentary angles visit:-

brainly.com/question/20693383

#SPJ1

help plsss


Mitsugu has one quiz each week in math class. The table gives the probability of having a quiz on each day of the week. What is the probability that Mitsugu will have a quiz Wednesday, Thursday, or Friday? Express your answer as a percentage.

Answers

The likelihood that Mitsugu will have a quiz on Wednesday, Thursday, or Friday is 0.57, or 57%, based on the facts given.

What does arithmetic probability mean?

To determine how probable something is to occur, use probability. Many things are difficult to forecast with absolute precision. Using it, we can only make predictions about how probable an occurrence is to happen, or its chance of happening.

Let's first examine each day's specific probabilities:

Wednesday: 0.16Thursday: 0.21Friday: 0.20

Now, all we have to do to determine the overall chance is combine the partial probabilities that were previously provided, as shown below:

0.16 + 0.21 + 0.20 = 0.57

Finally, to determine the chance as a percentage, multiply this figure by 100:

0.57 x 100 = 57%

To know more about Probability visit:

https://brainly.com/question/13604758

#SPJ1

need some help on some questions

Answers

For the triangle ABC, the given trigonometric ratios are -

a. sin A = 8/17

b. cos A = 15/17

c. tan A = 8/15

d. tan B = 8/15

What is trigonometric ratio?

Triangle side length ratios are known as trigonometric ratios. In trigonometry, these ratios show how the ratio of a right triangle's sides to each angle. Sine, cosine, and tangent ratios are the three fundamental trigonometric ratios.

For a right-angled triangle ABC, the hypotenuse AB is given as 17.

The base CB is given as 15 and the perpendicular AC is given as 8.

The angle C is given to be 90°.

Using the given values of the sides of the right triangle ABC, we can calculate the trigonometric ratios as follows -

a. sin A = opposite/hypotenuse = AC/AB = 8/17 (reduced fraction)

b. cos A = adjacent/hypotenuse = CB/AB = 15/17 (reduced fraction)

c. tan A = opposite/adjacent = AC/CB = 8/15 (reduced fraction)

d. tan B = opposite/adjacent = AC/CB = 8/15 (reduced fraction)

Note that since angle C is 90°, angles A and B are acute angles, so their tangent ratios are equal to each other.

Therefore, the ratios expressed as reduced fractions are -

a. sin A = 8/17

b. cos A = 15/17

c. tan A = 8/15

d. tan B = 8/15

To learn more about trigonometric ratio from the given link

https://brainly.com/question/13276558

#SPJ1

Find the area of each shape (Please don’t give me the formula to find the area of each shape, that won’t help.)

Answers

To find the area of the triangle with vertices (9,-1), (6,1), and (6,3), we can use the formula:

[tex]$A = \frac{1}{2} \left| x_1 (y_2 - y_3) + x_2 (y_3 - y_1) + x_3 (y_1 - y_2) \right|$[/tex]

where (x1, y1), (x2, y2), and (x3, y3) are the coordinates of the three vertices.

Plugging in the coordinates, we get:

[tex]$A = \frac{1}{2} \left| 9(1-3) + 6(3-(-1)) + 6((-1)-1) \right|$[/tex]

[tex]$A = \frac{1}{2} \left| -6 + 24 - 12 \right| = \frac{1}{2} \cdot 6 = 3$[/tex]

Therefore, the area of the triangle is 3 square units.

To find the area of the triangle with vertices (0,-8), (0,-10), and (7,-10), we can again use the formula:

[tex]$A = \frac{1}{2} \left| x_1 (y_2 - y_3) + x_2 (y_3 - y_1) + x_3 (y_1 - y_2) \right|$[/tex]

Plugging in the coordinates, we get:

[tex]$A = \frac{1}{2} \left| 0((-10)-(-10)) + 0((7)-0) + 7((-8)-(-10)) \right|$[/tex]

$A = \frac{1}{2} \cdot 14 = 7$

Therefore, the area of the triangle is 7 square units.

To find the area of the triangle with vertices (6,-7), (3,-1), and (-1,4), we can again use the formula:

[tex]$A = \frac{1}{2} \left| x_1 (y_2 - y_3) + x_2 (y_3 - y_1) + x_3 (y_1 - y_2) \right|$[/tex]

Plugging in the coordinates, we get:

[tex]$A = \frac{1}{2} \left| 6((-1)-4) + 3(4-(-7)) + (-1)((-7)-(-1)) \right|$[/tex][tex]$A = \frac{1}{2} \cdot 55 = \frac{55}{2}$[/tex]

Therefore, the area of the triangle is $\frac{55}{2}$ square units.

To find the area of the quadrilateral with vertices (-6,1), (-9,1), (-6,-4), and (-9,-4), we can divide it into two triangles and find the area of each triangle using the determinant method. The area of the quadrilateral is the sum of the areas of the two triangles.

First, we find the coordinates of the diagonals:

$D_1=(-6,1)$ and $D_2=(-9,-4)$

The area of the quadrilateral can be calculated as:

\begin{align*}

\text{Area}&=\frac{1}{2}\left|\begin{array}{cc} x_1 & y_1 \ x_2 & y_2 \end{array}\right| + \frac{1}{2}\left|\begin{array}{cc} x_2 & y_2 \ x_3 & y_3 \end{array}\right|\

&=\frac{1}{2}\left|\begin{array}{cc} -6 & 1 \ -9 & -4 \end{array}\right| + \frac{1}{2}\left|\begin{array}{cc} -9 & -4 \ -6 & -4 \end{array}\right|\

&=\frac{1}{2}\cdot 21 + \frac{1}{2}\cdot 9\

&=\frac{15}{2}\

\end{align*}

Therefore, the area of the quadrilateral is $\frac{15}{2}$ square units.

To find the area of the pentagon with vertices (0,3), (-3,3), (-5,1), (-3,-3), and (-1,-2), we can divide it into three triangles and find the area of each triangle using the determinant method. The area of the pentagon is the sum of the areas of the three triangles.

First, we find the coordinates of the diagonals:

$D_1=(0,3)$ and $D_2=(-1,-2)$

The area of the pentagon can be calculated as:

\begin{align*}

\text{Area}&=\frac{1}{2}\left|\begin{array}{cc} x_1 & y_1 \ x_2 & y_2 \end{array}\right| + \frac{1}{2}\left|\begin{array}{cc} x_2 & y_2 \ x_3 & y_3 \end{array}\right| + \frac{1}{2}\left|\begin{array}{cc} x_3 & y_3 \ x_4 & y_4 \end{array}\right|\

&=\frac{1}{2}\left|\begin{array}{cc} 0 & 3 \ -3 & 3 \end{array}\right| + \frac{1}{2}\left|\begin{array}{cc} -3 & 3 \ -5 & 1 \end{array}\right| + \frac{1}{2}\left|\begin{array}{cc} -5 & 1 \ -3 & -3 \end{array}\right|\

&=\frac{1}{2}\cdot 9 + \frac{1}{2}\cdot (-6) + \frac{1}{2}\cdot (-8)\

&=\frac{5}{2}\

\end{align*}

Therefore, the area of the pentagon is $\frac{5}{2}$ square units.

Area of triangle whose vertices are (6,1), (9,-1) and (6,-3) is 6 square units and the area of triangle whose vertices are (0,-8), (7,-10) and (0,-10) is 7 square units.

What is Triangle?

A polygon having 3 edges and 3 vertices is called a triangle. It is one of the fundamental geometric forms.

Lets find the area of triangle ( Pink Colour) whose vertices are (6,1), (9,-1) and (6,-3), [tex]Area = \frac{1}{2} [x_{1}(y_{2} -y_{3}) + x_{2}(y_{3}-y_{1}) + x_{3}(y_{1}-y_{2} ) ][/tex]

Area = 1/2 [ 6 ( -1 - (-3) ) + 9( -3 -1 ) + 6( 1 - ( -1 ) ) ]

Area = 1/2 [6 * 2 + 9 * (-4) + 6 * 2]

Area = 1/2 [12-36+12] = 1/2 (-12) = -6

Therefore , Area of Triangle is 6 square units.

Now, Lets find the area of triangle ( Brown Colour ) whose vertices are (0,-8), (7,-10) and (0,-10),

[tex]Area = \frac{1}{2} [x_{1}(y_{2} -y_{3}) + x_{2}(y_{3}-y_{1}) + x_{3}(y_{1}-y_{2} ) ][/tex]

Area = 1/2 [  0( -10 - ( -10 )) + 7 ( -10 - ( -8 ) ) + 0 ( -8 - ( -1- ) ) ]

Area = 1/2 [ 0 + 7 * (-2) + 0]

Area = 1/2 ( -14 ) = -7

Therefore, Area of Triangle is 7 square units.

Now. Lets find the area of Rectangle( Blue Colour ) whose length is 5 unit and Breadth is 3 unit.

So, Area of Rectangle = Length * Breadth

= 5 * 3 square units

= 15 square units.

To Learn more about Triangle, visit:

https://brainly.com/question/1058720

#SPJ1

Other Questions
Classify the items with the appropriate cell type. Squamous alveolar cells Engulf microorganisms Dust cells Septal cells Involved in the diffusion of gases Secrete surfactant Alveolar Type 1 Cells Alveolar Type Il Cells Alveolar Macrophages if an increase in the price of pineapple juice of 20% results in an increase in the demand for grape juice of 4%, the cross-price elasticity of demand between pineapple juice and grape juice isa. -5b.0,20c.-0,20d.5 true/false. effectiveness of recruiters is often the main reason for applicants to select one organization over another. Essay "The pandemics hero and heroine in white gowns" SOMEONE HELP PLEASE!!!Find P(C|Y) from the information in the table.To the nearest tenth, what is the value of P(C|Y)?A. 0.4B. 0.5C. 0.7D. 0.8 if burler corp. pays an annual dividend on its common stock that is expected to grow by 4.47 percent per year forever, the next dividend is due in 1 year, and the next dividend is expected to be $2.76, then what is the dividend expected to be in 6 years?(round the value to 100th decimal) consumer confidence is . a.) a comprehensive indicator and good predictor of the economy b.) immune to time lags c.) not sensitive to media reports d.) sensitive to marketing campaigns which of the following is in proper order starting as you inhale air through the nose down to the lungs? A, nasal cavity>larynx>pharynx>trachea>main bronchi>segmental bronchi>bronchiole>terminal bronchiole>respiratory bronchiole>alveolus B. nasal cavity>pharynx>larynx>trachea>main bronchi>segmental bronchi>bronchiole>terminal bronchiole>respiratory bronchiole>alveolus C. nasal cavity>pharynx>trachea>larynx>main bronchi>segmental bronchi>bronchiole>terminal bronchiole>respiratory bronchiole>alveolus D. nasal cavity>pharynx>larynx>trachea>main bronchi>segmental bronchi> bronchiole>respiratory bronchiole>terminal bronchiole>alveolus The nurse is educating a parent of a toddler with Down syndrome. Which statement by the parent indicates teaching was effective?a. "I hope my child does well with the various therapies we have arranged."b. "I am aware my child needs to be immunized on a delayed schedule."c. "I will continue to offer my child low fiber foods for meal and snacks."d. "I know my child will meet developmental milestones earlier than my other children." write the method computewages. assume that itemssold has been filled appropriately, and there are at least three employees in the array. assume also that the wages array and the itemssold array have the same length. your solution must call computebonusthreshold appropriately to receive full credit. /** computes employee wages as described in part (b) * and stores them in wages. * the parameter fixedwage represents the fixed amount each employee * is paid per day. * the parameter peritemwage represents the amount each employee * is paid per item sold. */ public void computewages(double fixedwage, double peritemwage) in each of the following independent cases, indicate the amount (1) deductible for AGI, (2) deductible from AGI, and (3) neither deductible for nor deductible from AGI before considering income limitations or the standard deduction. 1) Fran spent $97 for uniforms for use on her job. Her employer reimbursed her for $9 of this amount under an accountable plan (and did not report the reimbursement as wages). 2) Timothy, a plumber employed by ACE Plumbing, spent $101 for small tools to be used on his job, but he was not reimbursed by ACE. 3) Jake is a perfume salesperson. Because of his high pay, he receives no allowance or reimbursement from his employer for advertising expenses even though his position requires him to advertise frequently. During the year, he spent $2,650 on legitimate business advertisements. 4) Trey is a self-employed special-duty nurse. He spent $460 for uniforms. 5) Mary, a professor at a community college, spent $465 for magazine subscriptions. The magazines were helpful for her research activities, but she was not reimbursed for the expenditures. 6) Wayne lost $440 on the bets he made at the race track, but he won $62 playing slot machines cos(1+tan)=cos+sin lysogeny can result in all of the following except A) Acquisition of new characteristics by the host cell B) Transduction of specific genes C) Immunity to reinfection by the same phage. D) Immunity to reinfection by any phage can someone explain interval and set notation (algebra 2) In the textbook, a section of material on genetic and environmental factors in the development of disorder describes a study by Caspi and colleagues. The Caspi and colleagues study was conducted to investigate the role of genes and the environment in shaping antisocial behavior. What did they find?A. a single gene causes antisocial behavior, and there in otsentially no role for (that is no influence of) environmental factorsB. an environmental factor, childhood mistreatment, causes antisocial behavior, and there is essentially no role for that is, no influence of) genetic factors C. variations in genes and in childhood maltreatment combined to predict antisocial behavior (that is, there was an interaction between genetic and environmental factors). D. everyone in the study displayed about the same level of antisocial behavior, with the result that individual differences in genes and environmental experiences were not related to antisocial behavior significantly (that is, to a statistically significant degree) The general manager of a large, mid-market hotel wants to hire off-duty police officers as part-time security staff. Which of the following statements about off-duty police officers is false?A.They may be better able to identify known criminals. B.They are oriented more toward crime prevention than the apprehension of criminals. C.They may have superior training in dealing with emergencies. D.They might be fatigued after already working a full duty shift. Three softball players discussed their batting averages after a game.ProbabilityPlayer 1 four seventhsPlayer 2 five eighthsPlayer 3 three sixthsBy comparing the probabilities and interpreting the likelihood, which statement is true? The lack of face-to-face contact in online communication often causes ________, which may make it easy to respond aggressively, without considering the consequences. What is the quotient of 6. 208 10^9 and 9. 7 10^4 expressed in scientific notation? Consider the rainfall event having 5-min cumulative rainfall record given below: a) What is the duration of the entire rainfall event and the corresponding total rainfall amount? b) Find the rainfall depth hyetograph (in tabular form) with 10-min time interval for the storm event. c) Find the maximum 10-min and 20-min average rainfall intensities (in mm/hr) for the storm event.