if sin0<0 and cos>0, then the terminal point is determined by 0 is in:

If Sin0&lt;0 And Cos&gt;0, Then The Terminal Point Is Determined By 0 Is In:

Answers

Answer 1

the terminal point of the angle determined by sin(0) < 0 and cos(0) > 0 is in the fourth quadrant.

why it is and what is trigonometry?

If sin(0) < 0 and cos(0) > 0, then we know that the angle 0 is in the fourth quadrant of the unit circle.

In the unit circle, the x-coordinate represents cos(θ) and the y-coordinate represents sin(θ). Since cos(0) > 0, we know that the terminal point of the angle is to the right of the origin. And since sin(0) < 0, we know that the terminal point is below the x-axis.

The fourth quadrant is the only quadrant where the x-coordinate is positive and the y-coordinate is negative, so that is the quadrant where the terminal point of the angle lies.

Therefore, the terminal point of the angle determined by sin(0) < 0 and cos(0) > 0 is in the fourth quadrant.

Trigonometry is a branch of mathematics that deals with the relationships between the sides and angles of triangles. It focuses on the study of the functions of angles and their applications to triangles, including the measurement of angles, the calculation of lengths and areas of triangles, and the analysis of periodic phenomena.

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Related Questions

6TH GRADE MATH, What is the y intercept in the equation y= 4x - 8??

Answers

the y intercept is -8

Part A
Use GeoGebra to graph points A, B, and C to the locations shown by the ordered pairs in the table. Then join each pair of
points using the segment tool. Record the length of each side and the measure of each angle for the resulting triangle.

Location
A(3,4), B(1,1).
C(5.1)
A(4.5), B(2.1).
C(7.3)
—————-
AB=
BC=
AC=

Answers

Answer:

Step-by-step explanation:

Answer:

[tex]\begin{array}{|c|c|c|c|}\cline{1-4}\vphantom{\dfrac12}\sf Location&AB&BC&AC\\\cline{1-4}\vphantom{\dfrac12} A(3,4),\;B(1,1),\;C(5,1)&3.61&4&3.61\\\cline{1-4}\vphantom{\dfrac12} A(4,5),\;B(2,1),\;C(7,3)&4.47&5.39&3.61\\\cline{1-4}\end{array}[/tex]

[tex]\begin{array}{|c|c|c|c|}\cline{1-4}\vphantom{\dfrac12}\sf Location&m \angle A&m \angle B&m \angle C\\\cline{1-4}\vphantom{\dfrac12} A(3,4),\;B(1,1),\;C(5,1)&67.38^{\circ}&56.31^{\circ}&56.31^{\circ}\\\cline{1-4}\vphantom{\dfrac12} A(4,5),\;B(2,1),\;C(7,3)&82.87^{\circ}&41.63^{\circ}&55.49^{\circ}\\\cline{1-4}\end{array}[/tex]

Step-by-step explanation:

Step 1

Place points A, B and C on the coordinate grid.

Alternatively, type the following into the input field as 3 separate inputs:

Triangle 1

A = (3, 4)B = (1, 1)C = (5, 1)

Triangle 2

A = (4, 5)B = (2, 1)C = (7, 3)

Step 2

Use the Segment tool to join each pair of points.

Alternatively, type Segment( <Point>, <Point> ) into the input field (replacing <Point> with the letter name of the point) to create a segment between two points.

Record the length of each side.

[tex]\begin{array}{|c|c|c|c|}\cline{1-4}\vphantom{\dfrac12}\sf Location&AB&BC&AC\\\cline{1-4}\vphantom{\dfrac12} A(3,4),\;B(1,1),\;C(5,1)&3.61&4&3.61\\\cline{1-4}\vphantom{\dfrac12} A(4,5),\;B(2,1),\;C(7,3)&4.47&5.39&3.61\\\cline{1-4}\end{array}[/tex]

Step 3

Use the Angle tool to measure each angle in the resulting triangle.

Alternatively, type Angle(Polygon(A, B, C)) into the input field to create all interior angles.

Record the measure of each angle.

[tex]\begin{array}{|c|c|c|c|}\cline{1-4}\vphantom{\dfrac12}\sf Location&m \angle A&m \angle B&m \angle C\\\cline{1-4}\vphantom{\dfrac12} A(3,4),\;B(1,1),\;C(5,1)&67.38^{\circ}&56.31^{\circ}&56.31^{\circ}\\\cline{1-4}\vphantom{\dfrac12} A(4,5),\;B(2,1),\;C(7,3)&82.87^{\circ}&41.63^{\circ}&55.49^{\circ}\\\cline{1-4}\end{array}[/tex]

Note: All measurements have been given to the nearest hundredth (2 decimal places).

HELP Whats the Answer to this Stand Deviation Question?

Answers

Answer: he would be 2 standard deviations above the

Step-by-step explanation:

A salesperson earns 4% commission on furnace sales.

What is the commission that the salesperson earns on the sale of $33,000 worth of furnaces.

Answers

The commission earned 4 percentage on the salesperson on the sale of furnaces is $1320.

What is percentage?

In mathematics, a percentage is a number or ratio that can be expressed as a fraction of 100. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100. The percentage therefore refers to a part per hundred. The word per cent means per 100. The letter "%" stands for it. The term "percentage" was adapted from the Latin word "per centum", which means "by the hundred". Percentages are fractions with 100 as the denominator.

by the question.

the commission that the salesperson earns on the sale of $33,000 worth of furnaces= 4% of 33,000 = 4× 330 = $1320

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If r and s are constants and r² +rx + 12 is equivalent to (x+3)(x + 5), what is the value of r?

F.:3
H. 7
J. 12
K. Cannot be determined from the given information

Answers

Answer:

H. 7

Step-by-step explanation:

Given x² + rx + 12 is equivalent to (x + 3)(x + s), equate the two expressions and expand the right side of the equation:

[tex]\begin{aligned}x^2+rx+12&=(x + 3)(x + s)\\ x^2+rx+12&=x^2 + sx + 3x + 3s\\x^2+rx+12&=x^2 + (s+3)x + 3s\end{aligned}[/tex]

To find the value of r, first find the value of s.

The constant term of the right-hand side must be equal to the constant term of the left-hand side. Therefore:

[tex]\implies 3s = 12[/tex]

Solve for s by dividing both sides of the equation by 3:

[tex]\implies s = 4[/tex]

Compare the coefficients of the terms in x:

[tex]\implies r = s + 3[/tex]

Substitute the value of s into the equation and solve for r:

[tex]\begin{aligned} \implies r &= s + 3\\&= 4 + 3\\&= 7\end{aligned}[/tex]

Therefore, the value of r is 7.

Answer:

[tex]\large\boxed{\sf r = 7 }[/tex]

Step-by-step explanation:

Correct question:- If r and s are constants and r² +rx + 12 is equivalent to (x+3)(x + s), what is the value of r?

Here we are given that , the expression (x+3)(x+s) is equal to r² + rx + 12 .

Firstly, expand the expression (x+3)(x+s) as ,

[tex]\implies (x+3)(x+s) \\[/tex]

[tex]\implies x(x+s)+3(x+s) \\[/tex]

[tex]\implies x^2 + xs + 3x + 3s \\[/tex]

Take out x as common,

[tex]\implies x^2 + (3+s)x + 3s \\[/tex]

Now according to the question,

[tex]\implies x^2 + (3+s)x + 3s = r^2 + rx + 12\\[/tex]

On comparing the respective terms , we get,

[tex]\implies r = 3 + s \\[/tex]

[tex]\implies 3s = 12 \\[/tex]

Solve the second equation to find out the value of s , so that we can substitute that in equation 1 to find "r" .

[tex]\implies 3s = 12 \\[/tex]

[tex]\implies s =\dfrac{12}{3}=\boxed{4} \\[/tex]

Now substitute this value in equation (1) as ,

[tex]\implies r = 3 + s \\[/tex]

[tex]\implies r = 3 + 4 \\[/tex]

[tex]\implies \underline{\underline{ \red{ r = 7 }}} \\[/tex]

and we are done!

Which operation do you use to simplify a ratio after finding the greatest common factor (GCF)?
division
addition
multiplication
subtraction

Answers

Answer:

hey baby

Step-by-step explanation:

hi thwrw honey i love you lol

The operation we use to simplify a ratio after finding the greatest common factor (GCF) is division.

Option A is the correct answer.

What is an expression?

An expression contains one or more terms with addition, subtraction, multiplication, and division.

We always combine the like terms in an expression when we simplify.

We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.

Example:

1 + 3x + 4y = 7 is an expression.

3 + 4 is an expression.

2 x 4 + 6 x 7 – 9 is an expression.

33 + 77 – 88 is an expression.

We have,

To simplify a ratio after finding the greatest common factor (GCF), we use division.

We divide both terms of the ratio by the GCF.

This reduces the ratio to its simplest form.

Thus,

The operation we use to simplify a ratio after finding the greatest common factor (GCF) is division.

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write an algebraic expression to represent the phrase twelve dollars less than the original price. let p represent the unknown.

Answers

Answer:

p=O-12

Step-by-step explanation:

original price:O

12 less than O is "O-12"

therefore p=O-12

Graph the function.

f(x) = 3/5x -5


Use the Line tool and select two points to graph.

Answers

Answer:

  see attached

Step-by-step explanation:

You want to graph the function f(x) = 3/5x -5.

Graph

For graphing purposes, it is convenient to choose values of x that result in integer values of y. In this case, the multiplier of x (the slope) has a denominator of 5, so it is convenient to choose x-values that are multiples of 5.

For x = 0, y = 3/5·0 -5 = -5

For x = 5, y = 3/5·5 -5 = 3 -5 = -2

Suitable points for your plot are (0, -5) and (5, -2). These are shown in the attachment.

Find the standard normal area for each of the following (LAB)Round answers to 4 decimals

Answers

The answer of the standard normal area for each of the following questions are given below respectively.

What is standard normal area?

Standard normal area refers to the area under the standard normal distribution curve, which is a normal distribution with a mean of 0 and a standard deviation of 1.

a. P(1.24<Z<2.14) = 0.0912

b. P(2.03 <Z<3.03) = 0.0484

c. P(-2.03 <Z<2.03) = 0.9542

d. P(Z > 0.53) = 0.2977

Note: The standard normal distribution is a continuous probability distribution with mean 0 and standard deviation 1. The area under the curve represents probabilities and can be calculated using a standard normal distribution table or a calculator with a normal distribution function.

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Find the distance from Link to the Octorok so Link can attack

Answers

The distance  from Link to the Octorok  is 10.63 units.

How to find the distance?

We know that the distance between two points (x₁, y₁) and (x₂, y₂) is given by the formula below:

distance = √( (x₂ - x₁)² + (y₂ - y₁)²)

Here we want to find the distance from Link to the Octorok so Link can attack, so we need to get the distance between the points (-4, -5) and (3, 3).

The distance will be:

distance = √( (3 + 4)² + (3 + 5)²)

distance = √( (7)² + (8)²)

distance = √113

distance = 10.63

The distance is 10.63 units.

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Is this figure a polygon dont answer if you don’t know the answer

Polygon - a plane figure with at least three straight sides and angles, and typically five or more.

Answers

Answer:

No

Step-by-step explanation:

Since a polygon has straight sides, with 3 or more, it cannot be a polygon since one side is curved.

Cant figure out the surface area

Answers

Answer:

[tex]96 \: {m}^{2} [/tex]

The correct answer is B

Step-by-step explanation:

First, we have to find the area of one side of the cube:

[tex]a(side) = 4 \times 4 = 16[/tex]

Now multiply this number by 6 (since the cube has 6 sides in total):

[tex]a(surface) = 16 \times 6 = 96[/tex]

Answer: B - 96 sq m

Step-by-step explanation:

The surface area is the area of all the squares added up. To find the area of one square, you multiply 4 x 4, which equals 16. Then, count the number of sides on the cube. There are 6 sides on this cube. So, you multiply        16 x 6. 96 is your total. And you can eliminate C because it says meters instead of square meters.

Pls help !! I will mark brainilest

Answers

Answer:

m = -1

Step-by-step explanation:

may not be accurate, I haven't done this in a while

Answer:

-1y−y1=m(x−x1)

y−6=−1(x+5)

y−6=−1x+(−1×5)

y−6=−1x+−5

y−6=−1x−5

y=−1x−5+6

y=−1x+1

y=−x+1

m=−1

b=1

Step-by-step explanation: Hope this helps!! Mark me brainliest!

Complete the recursive formula of the arithmetic s -17,-8, 1, 10, .... a(1) = -17 a(n) = a(n − 1)+​

Answers

Answer:

The common difference between consecutive terms in the sequence is 8 (since -17 + 8 = -9, -9 + 8 = -1, -1 + 8 = 7, and so on). Therefore, the recursive formula for this arithmetic sequence is:

a(1) = -17

a(n) = a(n-1) + 8 for n >= 2

This formula says that the first term in the sequence is -17, and each subsequent term is found by adding 8 to the previous term.

(please mark my answer as brainliest)

5 Mrs. Newsome bought a piece of fabric 142 centimeters long to make a quilt for her son's bedroom. She bought a piece of fabric 2 meters long for curtains. How could Mrs. Newsome find the total length, in centimeters, of both pieces of fabric? Multiply 2 by 2,000, then add 142. Add 2 and 142, then multiply by 100. Divide 142 by 100, then add 2,000. O Multiply 2 by 100, then add 142. B C​

Answers

Answer:

Step-by-step explanation:

To find the total length of both pieces of fabric in centimeters, we need to add the length of the first piece of fabric (142 cm) and the length of the second piece of fabric (2 meters).

However, we need to make sure that the units are consistent before we add the lengths. We can convert the length of the second piece of fabric from meters to centimeters by multiplying by 100. Therefore, the total length in centimeters is:

142 cm + 2 meters * 100 cm/meter = 142 cm + 200 cm = 342 cm

The option that correctly gives the answer is "Multiply 2 by 100, then add 142" (Option C).

performed 100 trials of a simulation to see what difference in proportions would occur due to chance variation

Answers

Performing a simulation with 100 trials is a common technique used to assess the impact of chance variation on the results of an experiment or study. The simulation can help you understand how likely it is to see certain results due to chance variation alone, rather than any underlying difference in proportions.

To perform this simulation, you would first need to define the two proportions that you want to compare. For example, you might want to compare the proportion of people who prefer brand A to brand B in a survey.

Next, you would randomly assign each trial to either brand A or brand B based on the defined proportions. For example, if the proportion of people who prefer brand A is 0.6, you would assign 60 out of the 100 trials to brand A and 40 trials to brand B.

After assigning each trial, you would then calculate the difference in proportions between the two groups. This would give you a distribution of differences that you would expect to see due to chance variation alone.

If the observed difference falls within the range of differences expected due to chance variation, you can conclude that the difference in proportions you observed is not statistically significant and may be due to chance.

However, if the observed difference is larger than what you would expect to see due to chance variation, you can conclude that the difference is statistically significant and likely due to an underlying difference in proportions.

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HELP ME ASAP!!! YOU WILL BE BRAINLIEST

Answers

We can conclude that Maya's experimental probabilities fluctuate around the theoretical probability, but over a larger number of trials, the experimental probabilities should converge towards the theoretical probability.

What is probability?

Probability is simply how likely something is to happen. Whenever we're unsure about the outcome of an event, we can talk about the probabilities of certain outcomes—how likely they are. The analysis of events governed by probability is called statistics.

The theoretical probability of rolling a 5 on a fair die is 1/6, which means that if the die is rolled many times, we would expect to see a 5 about 1/6 of the time.

For the first 100 trials, Maya rolled a 5 on 25 of those trials. The experimental probability of rolling a 5 in this case is:

experimental probability = number of 5's rolled / number of trials

experimental probability = 25/100

experimental probability = 0.25

So, in the first 100 trials, Maya's experimental probability of rolling a 5 was 0.25.

For the first 200 trials, Maya rolled a 5 on 30 of those trials. The experimental probability of rolling a 5 in this case is:

experimental probability = number of 5's rolled / number of trials

experimental probability = 30/200

experimental probability = 0.15

So, in the first 200 trials, Maya's experimental probability of rolling a 5 was 0.15.

Comparing these experimental probabilities to the theoretical probability, we see that after 100 trials, Maya's experimental probability of rolling a 5 (0.25) is higher than the theoretical probability (1/6 ≈ 0.167). This suggests that Maya's sample of 100 trials was somewhat biased in favor of rolling a 5.

On the other hand, after 200 trials, Maya's experimental probability of rolling a 5 (0.15) is lower than the theoretical probability (1/6 ≈ 0.167). This suggests that Maya's sample of 200 trials was somewhat biased against rolling a 5.

Overall, we can conclude that Maya's experimental probabilities fluctuate around the theoretical probability, but over a larger number of trials, the experimental probabilities should converge towards the theoretical probability. This is known as the law of large numbers, which states that as the number of trials or observations increases, the experimental probability will tend to approach the theoretical probability.

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We might say that Maya's experimental probabilities oscillate about the theoretical probability, but after more trials, the experimental probabilities ought to converge to the theoretical probability.

What is probability?

Simply put, probability is the likelihood that something will occur. When we don't know how an event will turn out, we can discuss the likelihood or likelihood of several outcomes. Statistics is the study of events that follow a probability distribution.

A fair die has a theoretical probability of rolling a 5 of 1/6, therefore if the die is rolled several times, we can anticipate seeing a 5 roughly 1/6 of the time.

For the first 100 trials, Maya rolled a 5 on 25 of those trials. The experimental probability of rolling a 5 in this case is:

experimental probability = number of 5's rolled / number of trials

experimental probability = 25/100

experimental probability = 0.25

So, in the first 100 trials, Maya's experimental probability of rolling a 5 was 0.25.

For the first 200 trials, Maya rolled a 5 on 30 of those trials. The experimental probability of rolling a 5 in this case is:

experimental probability = number of 5's rolled / number of trials

experimental probability = 30/200

experimental probability = 0.15

So, in the first 200 trials, Maya's experimental probability of rolling a 5 was 0.15.

Comparing these experimental probabilities to the theoretical probability, we see that after 100 trials, Maya's experimental probability of rolling a 5 (0.25) is higher than the theoretical probability (1/6 ≈ 0.167). This suggests that Maya's sample of 100 trials was somewhat biased in favor of rolling a 5.

On the other hand, after 200 trials, Maya's experimental probability of rolling a 5 (0.15) is lower than the theoretical probability (1/6 ≈ 0.167). This suggests that Maya's sample of 200 trials was somewhat biased against rolling a 5.

Overall, we can conclude that Maya's experimental probabilities fluctuate around the theoretical probability, but over a larger number of trials, the experimental probabilities should converge towards the theoretical probability. This is known as the law of large numbers, which states that as the number of trials or observations increases, the experimental probability will tend to approach the theoretical probability.

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Please help me solve this my head hurts

Answers

a. Nοne οf these measure οf central tendency dοn't exist fοr this data set. Optiοn d) is cοrrect

b. As the sum οf all οbservatiοns wοuld chance, the mean wοuld be affected by the change. Optiοn a) is cοrrect

What is central tendency?

In statistics, the central tendency is the descriptive summary οf a data set. Thrοugh the single value frοm the dataset, it reflects the centre οf the data distributiοn. Mοreοver, it dοes nοt prοvide infοrmatiοn regarding individual data frοm the dataset, where it gives a summary οf the dataset. Generally, the central tendency οf a dataset can be defined using sοme οf the measures in statistic.

c.

Suppοse that, the largest measurement 97 is remοved.

The number οf οbservatiοns as well as the sum οf all οbservatiοns wοuld change.

Therefοre, the median and the mean wοuld be changed and οptiοn a) and b) are cοrrect.

d.

Since there are three mοdes, the mean, median and mοde must nοt be cοmpared tο each οther fοr skewness.

Instead, it is required tο grοup data in intervals and οbserve the pattern οf classes versus frequencies, as displayed in histοgram.

Therefοre, the distributiοn appears rοughly symmetric and οptiοn c) is cοrrect.

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4. A pet store has eight dogs and cats. Three are dogs. What fraction represents the number of cats?

A. 1/4
B. 3/8
C. 1/2
D.5/8

Answers

D.5/8

There are 3 dogs out of 8 pets
Dogs=3/8
1-3/8=5/8
Cats=5/8

Answer:

Step-by-step explanation:

Number of cats = 8 - 3 = 5

Fraction that are cats [tex]=\frac{5}{8}[/tex]

please help me with 4 math questions

Answers

Using linear negative association, According to the  all four parts correct options are D ;A ;D ;D respectively

What is linear negative association?

The slope of a line expresses a great deal about the linear relationship between two variables. If the slope is negative, there is a negative linear relationship, which means that as one variable increases, the other variable decreases. If the slope is zero, one increases while the other remains constant.

The first answer to the question is option D

The second answer to the question must be option A  

Option D must be chosen for the third question.

Option D  must be selected for Question 4.

Solution:

1.

square of 3 is 9

3 to the power of negative 2 is 1/ 9

cube of 3 is 27

3 to the negative power 3 is 1/27

2.

cylinder  volume =πr²h

Given value

pi =3.14

r=5

h=10

Volume=3.14×5²×10

cylinder volume =785m³

3.

When a point is rotated 90 degrees anticlockwise about the origin, it becomes the point (x,y) (-y,x).

The coordinates of Point N are (4, 3)

N' will be the new coordinates (-3, 4)

As a result, the y-coordinate of N' is 4.

4.

Option D must be selected for Question 4.

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6.) The sum of two numbers is 45.
The larger number y is 6 less than twice the smaller number
a.
Write a system of linear equations.
What is the smaller number?

Answers

Answer:

x= 13 =smaller number

Step-by-step explanation:

let x=smaller number

y=2x-6=larger number

x+y=45

x+2x-6=45 (equation)

3x=39

x=13

Answer:

[tex]x = 13[/tex] ..... smaller number

and

[tex]y = 32[/tex] ....... larger number

Step-by-step explanation:

Greetings!!!

Let the two numbers be X and Y

[tex]x + y = 45........ \:equation \: 1[/tex]

The larger number is y and is 6 less than twice the smaller number. which means:-

[tex](y - 6) = 2x........... \: equation \: 2[/tex]

so, now solve for y. from equation 2

[tex]y - 6 = 2x \\ y = 2x + 6[/tex]

Substitute equation 1 into equation 2

[tex]x + y = 45 \\ x + (2x + 6) = 45 \\ 3x + 6 = 45 \\ 3x = 45 - 6 \\ 3x = 39....divide \: both \: sides \: by \: 3 \\ x = 13[/tex]

To solve for y substitute x into the first equation

[tex](13) = + y = 45 \\ y = 45 - 13 \\ y = 32[/tex]

Finally, to be more sure make a cross check

[tex]y - 6 = 2x \\ 32 - 6 = 2(13) \\ 26 = 26[/tex]

If you have any questions tag it on comments

Hope it helps!!!

Does the expression 56x+40y-48z=8(7x+5y-6z)

Answers

For all values of x, y, and z, the expression 56x + 40y - 48z = 8(7x + 5y - 6z) holds true.

Explain expression using an example.

As an illustration, the phrase x + y is one where x and y are terms with an addition operator in between. There are two sorts of expressions in mathematics: numerical expressions, which only contain numbers, and algebraic expressions, which also include variables.

Indeed, for all values of x, y, and z, the expression 56x + 40y - 48z = 8(7x + 5y - 6z) holds true.

We can simplify both sides of the equation to understand why:

56x + 40y - 48z = 8(7x + 5y - 6z)

56x + 40y - 48z = 56x + 40y - 48z

As we can see, the equation is true for all values of x, y, and z because both sides are identical.

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What value of Y and Z will make DEF correspond to JKI?

Answers

[tex]\bold{Solution:}[/tex]

[tex]\Delta[/tex][tex]DE[/tex][tex]F[/tex] congruent to [tex]\Delta[/tex][tex]JKI[/tex]

[tex]\bold{FD=JI} \text{(corresponding angles of congruent triangles)}[/tex]

[tex]z + 22 = 3z[/tex]

[tex]\text{or,} \ z-3 z= -22[/tex]

[tex]\text{or,} \ -2z = -22[/tex]

[tex]\text{or,} \ z = \bold{11}[/tex]

[tex]\bold{EF=KI} \text{(corresponding angles of congruent triangles)}[/tex]

[tex]5y+13=6y[/tex]

[tex]\bold{y=13}[/tex]

In the inequality, x (< with line underneath) 8, represents the number of books on a shelf.

How do you know if 8 is a possible value of x?

Answers

Answer:

The numbers 8 and lower are possible values of x.

Step-by-step explanation:

The inequality [tex]x\leq 8[/tex] means x is less than or equal to 8. Therefore, 8 is a possible value of x.

Really Need help asap!

Answers

Step-by-step explanation:

h(-2) = 25

h(-1) = 5

h(0) = 1

h(1) = 1/5

h(2) = 1/25

Use the gradient to find the directional derivative of the function at P in the direction of PQ. f(x, y) = 3x2 - y2 + 4, P(1, 5), 2(4,2)

Answers

The directional derivative of f(x,y) at point P(1,5) in the direction of PQ is -2√2.

Find the directional derivative of the function f(x,y) = 3x² - y² + 4 at point P(1,5) in the direction of PQ, where P(1,5) as well as Q(4,2), we need to first calculate the gradient of f(x,y) at point P.

The gradient of f(x,y) at P is:

∇f(x,y) = [∂f/∂x, ∂f/∂y] = [6x, -2y]

Evaluating this at point P(1,5), we get:

∇f(1,5) = [6(1), -2(5)] = [6, -10]

Now, we need to find the unit vector in the direction of PQ. This can be calculated as follows:

u = PQ/|PQ|

where PQ = Q - P = [4 - 1, 2 - 5] = [3, -3] and |PQ| = √(3² + (-3)²) = √18 = 3√2

So, u = PQ/|PQ| = [3/3√2, -3/3√2] = [1/√2, -1/√2]

The directional derivative of f(x,y) at P in the direction of PQ is then given by:

D_u f(P) = ∇f(P) · u

where · represents the dot product.

Substituting the values we obtained earlier, wehave:

D_u f(P) = [6, -10] · [1/√2, -1/√2]

D_u f(P) = (6/√2) + (-10/√2)

D_u f(P) = -2√2

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for autonomous equations, find the equilibria, sketch a phase portrait, state the stability of the equilibria.

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Understanding the equilibria, sketching a phase portrait, and determining the stability of equilibria for autonomous equations are important tools for analyzing and understanding the behavior of systems over time.

Autonomous equations are differential equations that do not depend explicitly on time. To find the equilibria of an autonomous equation, we set the derivative of the function to zero and solve for the values of the independent variable that satisfy the equation. These values represent points at which the function does not change over time and are known as equilibrium points.

To sketch a phase portrait for an autonomous equation, we plot the slope field of the function and then draw solutions through each equilibrium point. The resulting graph shows the behavior of the function over time and helps us understand how the solutions behave near each equilibrium point.

The stability of an equilibrium point is determined by examining the behavior of nearby solutions. If nearby solutions move toward the equilibrium point over time, the equilibrium point is stable. If nearby solutions move away from the equilibrium point over time, the equilibrium point is unstable. Finally, if the behavior of nearby solutions is inconclusive, further analysis is needed.

Here is the sketch for [tex]dx/dt = x - x^3[/tex]

       / <--- (-∞)  x=-1  (+∞) ---> \

      /                                \

  <--0-->       x=-1       x=1        0-->

      \                                /

       \ <--- (-∞)  x=1   (+∞) --->  /

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Given the coefficient of correlation in the relationship to be - 0.73 , what percentage of the variation in hours of sleep cannot be explained by the time spent on social media?

Answers

The coefficient of correlation, denoted by r, represents the strength and direction of a linear relationship between two variables. The value of r ranges from -1 to +1. The closer the absolute value of r is to 1, the stronger the linear relationship between the variables.

The coefficient of determination, denoted by r^2, represents the proportion of the variation in one variable that can be explained by the other variable in a linear regression model.

The proportion of the variation in hours of sleep that cannot be explained by the time spent on social media is equal to 1 - r^2.

Given the coefficient of correlation, r = -0.73, we can find the coefficient of determination:

r^2 = (-0.73)^2 = 0.5329

So, the proportion of the variation in hours of sleep that can be explained by the time spent on social media is 0.5329.

Therefore, the proportion of the variation in hours of sleep that cannot be explained by the time spent on social media is:

1 - 0.5329 = 0.4671

Multiplying this by 100, we get:

0.4671 x 100 = 46.71%

So, approximately 46.71% of the variation in hours of sleep cannot be explained by the time spent on social media.

can you help me to solve this question?

Answers

The asymptotes of the function f(x) = (2x² - 5x + 3)/(x - 2) are given as follows:

Vertical asymptote at x = 2.Oblique asymptote at: y = 2x - 3/2.

How to obtain the asymptotes of the function?

The function for this problem is defined as follows:

f(x) = (2x² - 5x + 3)/(x - 2)

The vertical asymptote is the value of x for which the function is not defined, hence it is at the zero of the denominator, and thus it is given as follows:

x - 2 = 0

x = 2.

The oblique asymptote is at the quotient of the two functions, hence:

(mx + b)(x - 2) = 2x² - 5x + 3

mx² + (b - 2m) - 2b = 2x² - 5x + 3.

Hence the values of m and b are given as follows:

m = 2.-2b = 3 -> b = -3/2.

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6TH GRADE MATH IS THIS CORRECT??

Answers

Answer:

Step-by-step explanation:

y2-y1/x2-x1

-7-(-19)/-2-1

12/-2

-6

The slope is -6

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