A pair of linear equations is shown: y = −3x + 5 y = x + 2 Which of the following statements best explains the steps to solve the pair of equations graphically? On a graph, find the point of intersection of two lines; the first line has y-intercept = 5 and slope = −3, and the second line has y-intercept = 2 and slope = 1. On a graph, find the point of intersection of two lines; the first line has y-intercept = −3 and slope = 5, and the second line has y-intercept = 1 and slope = 2. On a graph, find the point of intersection of two lines; the first line has y-intercept = −5 and slope = 3, and the second line has y-intercept = −2 and slope = −1. On a graph, find the point of intersection of two lines; the first line has y-intercept = 3 and slope = −5, and the second line has y-intercept = −1 and slope = −2

The median or the middle value of 42 48 52 54 59 61 61 64 65 67 68 70 72 75 80 is 64.

It is the middle value of the given set of numbers after arranging the given set of numbers in order.

We have,

42 48 52 54 59 61 61 64 65 67 68 70 72 75 80

The given set of numbers is in ascending order.

There are 15 numbers.

The middle number will be the 8th number.

8th number = 64

Thus,

The median is 64.

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Answer:

This is an irrational number.

Step-by-step explanation:

If you see the decimal, it has the values of 1 and 0, but are not constant.

If it were to be 0.010101010... it would be rational.

But this decimal does not look like that, so its irrational.

Hope this helps.

Answer:

The value of the ratio of crisp wheat cereal to crisp rice cereal is 1/4 to 1 1/2, which can be simplified to 1/4 to 3/2. This means that for every 4 parts of crisp wheat cereal, there are 3 parts of crisp rice cereal. The amount of crisp wheat cereal is therefore less than the amount of crisp rice cereal. Specifically, the amount of crisp wheat cereal is 1/4 * the amount of crisp rice cereal.

Step-by-step explanation:

Answer: x = 14/5 or x = 2.8

Step-by-step explanation:

Step 1: Divide both sides of the equation by five: a common nonzero real number.

(5x)/5= 14/5

Step 2: Simplify

x = 14/5

Answer:

y ≤ -3x - 3

Step-by-step explanation:

The graph crosses the y axis at -3.  The slope is -3.  (0, -3) .  From that point do down vertical 3 spaces and horizontally 1 space.  You will be at the point (1,-6)  Draw a line to join those 2 points.  The inequality is ≤ that means the solutions are the points on the line and below the line.  This is shown in the pink shading.

y ≤ -3x - 3

Step-by-step explanation:

The graph crosses the y-axis at -3.  The slope is -3.  (0, -3) .  From that point do down vertical 3 spaces and horizontally 1 space.  You will be at the point (1,-6) Draw a line to join those 2 points.  

The inequality is ≤ which means the solutions are the points on the line and below the line.  This is shown in the pink shading.

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The probability that the sample mean is greater than 18 as calculated  is 0.8413.

Given data,

n = 36, sample size

μ = 17, population mean

σ = 6, population standard deviation

when x = 18

z = (18 - 17)/1 = 1

P(x <18) = 0.8413

Therefore , the probability = 0.8413

A population's standard deviation serves as a gauge for how widely distributed its individual data points are. It's a way to express how dispersed from the mean the data is.

While a large standard deviation indicates that the data is more spread, a small standard deviation indicates that the data points are often close to the mean.

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The equation that is equivalent to quadratic equation x^ 2-8x+19=0 is

(x-4)^ 2+k = 0 using quadratic equation properties .

What is quadratic equation ?

A quadratic equation is a second order equation written as ax2 + bx + c = 0 where a, b, and c are coefficients of real numbers and a ≠ 0.

Properties of graph of quadratic equation :

1. The shape of curve y = f(x) is a parabola.

2. If a>0, the parabola opens upwards.

3. If a<0, the parabola opens downwards.

4.The coordinates of vertex of parabola in all these cases is

(-b/2a , -D/4a).

The given equation is x^ 2-8x+19=0

a  = 1,

b = -8,

c = 19.

As a>0, 2nd property is correct i.e. no maximum value , only minimum value can be find that will be at vertex.

So, the vertex = (4,3)

The minimum value = 3 at 4.

So, the value of k = 3,

Given equation can be written as x^ 2-8x+16+3 = 0.

                                                      = (x-4)^ 2 +3 = 0.

The option A is correct.

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The absolute error and the percent error of the police officer’s estimate will be 4.29%.

The amount of any product is given as though it was a proportion of a hundred. The ratio can be expressed as a quarter of 100. The phrase % translates to one hundred percent. It is symbolized by the character '%'.

The percentage is given as,

Percentage (P) = [Final value - Initial value] / Initial value x 100

A cop is assessing the separation from one side of a road to the next. The genuine distance is 13.4 m. The cop's gauge is 14 m.

The absolute error and the percent error of the police officer’s estimate are calculated as,

%error = [(14 - 13.4) / 14] x 100

%error = (0.60 / 14) x 100

%error = 4.29%

The outright mistake and the percent blunder of the cop's gauge will be 4.29%.

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The formula for the cumulative probability of a Poisson distribution can be used to calculate the likelihood that there will be at most 2 reported car accidents over the course of a month:

Cumulative probability is equal to (number of events * e)/(average number of events per time period).

(Number of events / (-average number of events per time period)!)

In this instance, there are typically 0.05 events per time period (the likelihood that a car accident is reported at the intersection on any given day), and there are typically between 0 and 2 events per time period (at most 2 car accidents). With these values entered into the formula, we obtain:

Cumulative probability is equal to (0.05 * e(-0.05)) / 0, (0.05 * e(-0.05)) / 1, and (0.05 * e(-0.05)) / 2, respectively.

That amounts to:

Probability total = 1 + 0.05 + 0.0025

which translates to 1.0525 percent, or 105.25%. It's crucial to keep in mind that this probability exceeds 1, which is impossible. This is because the formula for cumulative probability makes the assumption that each event is independent, which means that the occurrence of one event has no bearing on the probability of the occurrence of another. The cumulative probability calculated using this formula may not accurately reflect the probability of at most 2 car accidents occurring throughout a month because in reality, the probability of a car accident occurring on a given day may be influenced by the number of car accidents that have already occurred. You would need to account for the dependencies between the events in order to calculate this probability precisely.

answer : 26

steps

get hypotenuse

a² + b² = c²

7² + 8² = c²

49 + 64 = c²

113 = c²

square root of c is √113 which 10.63

7 + 8 + 10.63 = 25.63

There are $21.5 money was spent on a pass and lunch for each student.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that:

The amount spent by school on pass of 40 students and 3 teachers = $546.53

And, the amount spent for the lunch only for students = $351.60

Now,

The money spent for pass of 43 person = $546.53

Then, The amount of pass for each person  = 546.53/43

                                = $12.71

Since, there are 40 student then amount of lunch for each students = ⇒ 351.60/40

⇒ $8.79

Therefore, amount of pass and lunch for each student = 12.71 + 8.79

                              = $21.5

Thus, $21.5 is the required answer.

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The values of x = 19.5, y= 17, and z=30.6 is not valid for the parallelogram.

What are the Properties of Angles of a Parallelogram?

A parallelogram is a quadrilateral with equal and parallel opposite sides. There are some special properties of a parallelogram that make it different from the other quadrilaterals.

The consecutive angles are supplementary then,

5y + 7y - 24 = 180

12y = 180 + 24

12y = 204

y = 204/12

y = 17

The opposite angles of a parallelogram are congruent (equal) then,

5y = 4x + 7

5(17) = 4x + 7

85 = 4x + 7

85 -7 = 4x

4x = 78

x = 78/4 = 19.5

x = 19.5

the consecutive angles are supplementary, then

4x + 7 + 3z = 180

4(19.5) + 7 + 3z = 180

78 + 7 + 3z = 180

85 + 3z = 180

3z = 180 - 88

3z = 92

z = 92/3

z = 30.6

All the angles of a parallelogram add up to 360°, then:

4x + 7 + 3z + 5y +7y - 24 = 360

To check is this a parallelogram? put the values of x, y, and z in the above equation:

4(19.5) + 7 + 3(30.6) + 5(17) +7(17) - 24 = 360

356.8 ≠ 360

hence, the values of x = 19.5, y= 17, and z=30.6 is not valid for the parallelogram.

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yes, z can lie between x and y but z can also lie on another side of x in Number lines.

With an example, define number line?

Number lines in mathematics are horizontal straight lines on which numbers are arranged in equal intervals.

                  A number line can be used to visualize all the numbers in a succession. The endpoints of this line go on forever.

What does the math number line mean?

A horizontal line with uniformly spaced numerical increments is called a number line. How the number on the line can be answered will depend on the numbers that are provided.

                               How a number is used—for example, to plot a point—depends on the question that goes with it.

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Answer: 9.8

Step-by-step explanation:

Answer:

$103

Step-by-step explanation:

In order to determine how much money Sonny has, we need to write a mathematical equation to solve for x. We know how much money Sonny and Allan each have in terms of x, and we can add the two expressions together to equal a total amount of $407. This will be represented and simplified as follows:

Now we can solve the equation for x.

We know that x is equal to 50, so we can plug it back into Sonny's expression to find out how much money she has.

We can check our work by solving for the amount of money Allan has and then adding up the two amounts to make sure the total is $407.

The equation of the line is 3y = -4x + 18 and the Graph can draw as given in the picture.

The slope-intercept form a line is given by  

where m is the slope of a line and c is the y-intercept.

Here we use the Slope intercept form to find the line of the equation by using the equation we will draw the graph of the line

Here we have

Slope of line = -4/3

The point of the line

As we know y = mx + c is the line Here m is the slope of the line

From the given data, m = -4/3

=> y = (-4/3)x + c

=> 3y = -4x + 3c

Given that the point on the line is (-6, 2)

=> 3(2) = -4(-6) + 3c

=> 6 = 24 + 3c

=>  3c = 18

=> c = 6

Therefore,

The equation of the line is 3y = -4x + 18 and the Graph can draw as given in the picture.

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Answer:

please tell me if you get the answer. I need it too!

Answer: (x+1)(x+4)

Step-by-step explanation:

Step 1: Use the sum-product pattern

x^2 + 5x + 4

x^2 + 4x + x + 4

Step 2: Common factor from the two pairs

x(x+4) + x+4

Step 3: Rewrite in factored form

(x+1)(x+4)

Answer:

f^-1(x) = 2(x-2)^2 + 1

f^-1(x) = (x+3)^3

Step-by-step explanation:

The inverse of a function is found by switching the roles of the dependent and independent variables. In other words, we can find the inverse of a function by interchanging the x and y values in the equation. So, the inverse of the function f(x) = 2(x-2)^2 + 1 can be written as f^-1(x) = 2(x-2)^2 + 1.

1. To find the inverse function explicitly, we can use the following steps:

2. Replace f(x) with y in the original function to obtain y = 2(x-2)^2 + 1.

3. Solve for x in terms of y to obtain x = +/- sqrt((y-1)/2) + 2.

The inverse function f^-1(x) can then be written as f^-1(x) = +/- sqrt((x-1)/2) + 2.

Note that this inverse function is not a one-to-one function, because for some values of x (namely, x < 1), the function has two possible values of y (i.e. it has two solutions). Therefore, the inverse function is not a function in the strict mathematical sense, but it is still a useful concept in certain contexts.

To find the inverse of a function, we switch the roles of the dependent and independent variables, so the inverse function can be written as x = ^3√y-3.

1. To find the inverse function explicitly, we can use the following steps:

2. Replace y with x in the original function to obtain x = ^3√y-3.

3. Solve for y in terms of x to obtain y = (x+3)^3.

The inverse function can then be written as f^-1(x) = (x+3)^3.

Note that this inverse function is a one-to-one function, meaning that for every value of x, there is only one corresponding value of y. Therefore, the inverse function is a function in the strict mathematical sense.

The large percentage obtained above will still not be a cause for celebration, because the observations demand a higher precision in the calculation results being obtained after running a logistic reg-session.

A precise calculation can be referred to or considered as a type of calculation, wherein the final results obtained are completely true and correct. Unlike approximate results, there is no scope of true and fair results in a precise calculation. Usually, rounding-off shall be avoided to obtained precise solutions at the end.

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The side measures that could form a right triangle are B (24 in, 34 in, 28 in) and C (55 ft, 45 ft, 35 ft).

What is the right triangle is triangle?

A right triangle is a triangle in which one angle measures 90 degrees. The sides of a right triangle can be used to determine if a triangle is a right triangle using the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

Using this information, we can determine which of the given sets of side measures could form a right triangle:

A. 61 m, 60 m, 11 m: We can use the Pythagorean theorem to see if these sides could form a right triangle. We'll let the hypotenuse be the side with a length of 61 m, and the other two sides are the ones with lengths of 60 m and 11 m. Plugging these values into the Pythagorean theorem, we get:

(61 m)² = (60 m)² + (11 m)²

61² = 60² + 11²

61² ≠ 60² + 11²

Since the left side does not equal the right side, these sides cannot form a right triangle.

B. 24 in, 34 in, 28 in: Using the Pythagorean theorem, we can see that these sides could form a right triangle:

(34 in)² = (24 in)² + (28 in)²

34² = 24² + 28²

34² = 24² + 28²

The left side equals the right side, so these sides could form a right triangle.

C. 55 ft, 45 ft, 35 ft: Using the Pythagorean theorem, we can see that these sides could form a right triangle:

(55 ft)² = (45 ft)² + (35 ft)²

55² = 45² + 35²

55² = 45² + 35²

The left side equals the right side, so these sides could form a right triangle.

D. 48 cm, 46 cm, 15 cm: Using the Pythagorean theorem, we can see that these sides could not form a right triangle:

(48 cm)² ≠ (46 cm)² + (15 cm)²

48² ≠ 46² + 15²

Since the left side does not equal the right side, these sides cannot form a right triangle.

Hence, The side measures that could form a right triangle are B (24 in, 34 in, 28 in) and C (55 ft, 45 ft, 35 ft).

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The expected value for the given problem is E(x) = 1.4.

What is expected value?

The expected value is a generalization of the weighted average in probability theory. Informally, the expected value is the arithmetic mean of a significant number of outcomes of a random variable that were independently chosen.

A projected average value for an investment at some point in the future is known as the expected value (EV).

Investors use expected value to gauge an investment's merit, frequently in relation to how risky the investment is.

The formula for to find the expected value is given as,

E ( X ) = μ = ∑ x P ( x ) .

E(x) =  0*0.30 + 1*0.25 + 2*0.25 + 3*0.15 + 4*0.05

E(x) = 1.4

Hence, the expected value for the given problem is E(x) = 1.4.

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Answer:

Step-by-step explanation:

Answer:

(sqrt3)/2

Step-by-step explanation:

Sin(x)=opposite/hypotenuse

30, 60, 90 right triangle.

ratio of sides are 1, sqrt3, and 2.

Locate the 60 degree angle on the triangle

The opposite side is sqrt3

The hypotenuse is 2

so its (sqrt3)/2

Answer:

√3/2 or 0.866

Step-by-step explanation:

Answer:

find my dad

Step-by-step explanation:

Answer:  BD = 5

Step-by-step explanation:

[tex]a^{2} +12^{2} =13^{2}[/tex]

[tex]a^{2} =13^{2}-12^{2}[/tex]

[tex]a = \sqrt{25}[/tex]

[tex]a = 5[/tex]

Therefore BD = 5

The graph of the function f(x) = x(x - 5)(x - 3) is given by the image shown at the end of the answer.

To draw the sketch of the graph, we need to consider these three following features:

The function in this problem is defined as follows:

f(x) = x(x - 5)(x - 3).

From the factor theorem, the x-intercepts are taken from the linear factors, as follows:

The y-intercept is the value of y when the graph of the function crosses the y-axis, that is, the value of y when x = 0, hence:

f(0) = 0(0 - 5)(0  -3) = 0.

In the problem, we have a cube function, hence:

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Answer:

Step-by-step explanation:

You want to find the effect of compounding 2% annual interest on $1000 at different intervals for a year. The intervals are ...

The attached calculator display shows the result:

If a point is on the bisector of an angle, then it is equidistant from the two sides of the angle. Explanation is given.

Lines that cross the angle under investigation are known as angle bisectors. To "bisect" is to split into two sections of equal size. Therefore, the bisected halves divide the considered angle in half.

According to the angle bisector theorem;

An angle bisector divides the opposing side of a triangle into two portions that are proportionate to the other two sides, according to the angle bisector theorem.

a point is equally far from both sides of an angle if it is on the angle's bisector.

According to the inverse of the angle bisector theorem, a point is on the angle's bisector if it is both in the interior of the angle and equally far from its sides.

The explanation with diagram is given in the image.

Therefore, If a point is on the bisector of an angle, then it is equidistant from the two sides of the angle.

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