if y varies directly as x, find the constant of variation if y= 32 when x= 8

Answer:

y=-3/2x+5

Step-by-step explanation:

3x + 2y = -4

2y=-4-3x /:2

y=-4/2-3x/2

y=-3/2x-2

Slope=-3/2(=m) , because this line is parallel slope is the same, then

y-y1=m(x-x1) ,where

A(4,-1).... x1 =4, y1 =-1

y-(-1)=-3/2(x-4)

y+1=-3/2x+3/2*4

y+1=-3/2x+6

y=-3/2x+6-1

y=-3/2x+5

Answer:

Note from question, Let K be any integer.  Integer = 1

θ = πk

  θ = 3.142 * 1

  θ = 3.142 in three decimal places

θ = sin⁻¹ (2/3) + 2kπ

   θ = sin⁻¹0.667 + 2*1*3.142

   θ = 0.718 + 6.284

   θ = 7.002 in three decimal places

∴ 7.002 , 3.142

Step-by-step explanation:

Considering the equation

3 tan(θ) sin(θ) − 2 tan(θ) = 0

The objective is to solve the equation.

First solve the equation in one period.

3 tan(θ) sin(θ) − 2 tan(θ) = 0

( 3sinθ − 2 ) tanθ = 0

Therefore, 3sinθ − 2 = 0    also   tanθ = 0

            =>  sinθ = 2/3        ,        tanθ = 0

Pick the right equation.

tanθ = 0

    θ = tan⁻¹ 0

    θ = 0

Using the unit circle, the period of tangent functions is π

Then the general solution of the equation is θ = 0 + πk ==> θ = πk

Pick the left equation.

3sinθ − 2 = 0

3sinθ = 2

sinθ = 2/3

    θ = sin⁻¹ (2/3)

As the sine function has period 2π

Then the general solution is θ = sin⁻¹ (2/3) + 2kπ

Answer: OPTION A.

Step-by-step explanation:

A dilation is defined as a transformation in which the Image (The figure obtained after the transformation) and the Pre-Image (The original figure before the transformation) have the same shape, but they have different sizes.

In this case you know that the dilation is centered at the origin and the scale factor is:

[tex]k=0.5[/tex]

Therefore, the rule is the following:

[tex]Q(kx,ky)[/tex]

You can identify in the figure attached that the point Q is:

[tex]Q(1,5)[/tex]

Therefore, you must multiply its coordinates by the scale factor 0.5 in order to get its Image Q'. This is:

[tex]Q'=(1*0.5,5*0.5)\\\\Q'=(0.5.2.5)[/tex]

Final answer:

The image of point Q for a dilation with a scale factor of 0.5 and center (0,0) is (option A) (0.5, 2.5).

Explanation:

To find the image of point Q, we need to apply the dilation equation: (x', y') = (k * x, k * y), where (x, y) are the coordinates of the original point and k is the scale factor.

In this case, the center of dilation is (0, 0) and the scale factor is 0.5. So, for point Q which has coordinates (x, y), the image coordinates (x', y') will be:

(x', y') = (0.5 * x, 0.5 * y)

Therefore, the image of point Q will be (option A) (0.5, 2.5).

The type of transformation that moves P (3,-7) to P'' (3,7) is a reflection. The point has been flipped over the x-axis.

The type of transformation which moves point

P (3,-7)

to

P'' (3,7)

is a

reflection

. It appears that point P has simply been flipped over the x-axis. The x-coordinate remains unchanged at 3, but the y-coordinate has been reflected to the opposite side of the x-axis, changing it from -7 to 7. So, a reflection over the x-axis is the correct transformation in this case. The transformation that moves point P (3,-7) to P'' (3,7) is a reflection over the x-axis. When a point is reflected in the x-axis, the y-coordinate changes sign while the x-coordinate remains the same. In this case, when the y-coordinate of P changes from -7 to 7, it means that P was reflected over the x-axis.

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Answer:

The distribution positively skewed

Step-by-step explanation:

We have the mean of a distribution to be 276, while the median is 231.

When compare the mean and median,

we gave

276>231

Since the mean is greater than the median, the distribution is skewed to the right.

In other words, the the distribution is positively skewed.

Answer:

Positively skewed

Step-by-step explanation:

The  arc MPN is a major arc, and the length of arc MPN is 79/9π

The given parameters are:

Ф = 360 - 44

Radius, r = 5

The arc length is then calculated using:

[tex]L = \frac{\theta}{360} * 2\pi r[/tex]

So, we have:

[tex]L = \frac{360 - 44}{360} * 2\pi * 5[/tex]

[tex]L = \frac{316}{360} * 2\pi * 5[/tex]

Evaluate the product

[tex]L = \frac{3160}{360} \pi[/tex]

Divide

[tex]L = \frac{79}9 \pi[/tex]

Hence, the length of arc MPN is 79/9π

Read more about arc lengths at:

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The length around the rug is the circumference.

The formula is C = 2 x PI x r

C = 2 x 3.14 x 5 = 31.4 feet

For this case we must find the perimeter of the circular carpet.

By definition, the perimeter of a circle is given by:

[tex]P = 2 \pi * r[/tex]

Where:

r: It is the radius of the circle

According to the statement we have:

[tex]r = 5 \ ft[/tex]

Substituting:

[tex]P = 2 * 3.14 * 5\\P = 2 * 3.14 * 5\\P = 31.4 \ ft[/tex]

So, you need[tex]31.4 \ ft[/tex]

Answer:

[tex]31.4 \ ft[/tex]

Answer:

[tex]2\pi \times \: r = 150 \\ 6.2831r = 150 \\ \frac{6.2831r}{6.2831} = \frac{150}{6.2831} \\ r = 23.87cm[/tex]

Answer:

23.9

Step-by-step explanation:

circumference = Diameter · Pie

150 = X · pie

divide both sides by pie(use the accrual symbol on a calc) and you get 47.7 as the diameter then divide 47.7 by 2 and you get 23.9 as you radius

The answer is n= -4. It shows the work to get -4

Answer: i think the answer is -22 which is A

Step-by-step explanation:

Answer:

-22

Step-by-step explanation:

I put it in decimal form so it would be like this.2.20 dived by -.10 and got -22

Solution:

Given system of equations are:

[tex]\frac{1}{4}x + \frac{1}{8}y =2 ---------- eqn\ 1\\\\\frac{1}{3}x + \frac{1}{2}y = 4 -------------- eqn\ 2[/tex]

We have to find value of y

From eqn 1,

[tex]\frac{1}{4}x + \frac{1}{8}y =2 \\\\2x + y = 2 \times 8\\\\2x + y = 16 ---- eqn\ 3[/tex]

From eqn 2,

[tex]\frac{1}{3}x + \frac{1}{2}y = 4\\\\2x + 3y = 4 \times 6\\\\2x + 3y = 24 ------ eqn\ 4[/tex]

Subtract eqn 3 from eqn 4

2x + 3y = 24

2x + y = 16

( - ) -----------------

2y = 8

y = 4

Thus value of y is 4

Answer:

Vertical translations would affect the horizontal asymptote.

Answer:

900

Step-by-step explanation:

ANSWER: y

=

125

+

900

50

=

$

20.5

Step-by-step explanation: Cost of each puppet =  

$

20.5

Explanation:

The number of puppets :  

50

-------(given)

Let cost of each puppet be  

y

So, total cost will be  

50

y

He brought all string needed for  

$

125

He needs to invest  

$

18

for EACH puppet for the remaining material, i.e.

18

×

50

=

$

900

is the total extra investment to be done.

So total cost will be :  

125

+

900

=

50

y

#therefore cost of each puppet will be :

Answer:

the answer is d.) the runner stopped

Step-by-step explanation:

because the distance is staying the same but the time is changing wich means the runner isn't moving for a period of time.

Answer:

the answer is 1/4

Step-by-step explanation:

1/2 *3/6=1/4

Without knowing the type of triangle or the values of the angles, we can only provide a possible range of values for side AC of triangle ABC, which is between 9 inches (in case of an acute triangle) and 47 inches (in case of an obtuse or right angled triangle). For accurate calculation, more detail is necessary.

The question pertains to determining the length of the side AC in a triangle ABC. Given are the lengths AB and BC so without additional details such as the angle values or the nature of the triangle, we cannot definitively determine the length of side AC. Such a calculation usually requires the use of trigonometric calculations or the Pythagorean theorem which applies only to right triangles. However, we can establish a range for the possible length of side AC.

If the triangle ABC is obtuse or a right triangle with the right angle at point B, the length of AC (AB+BC) could be up to 47 inches (19 inches + 28 inches). On the other hand, if it is an acute triangle, the length of AC (BC-AB) would be a minimum of 9 inches (28 inches - 19 inches). Please provide more details or check if it's a right triangle for a more specific calculation.

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The correct option is D (52 inches) satisfies all conditions of the triangle inequality theorem.

To determine which length of side AC could form a triangle with sides AB = 19 inches and BC = 28 inches, we apply the triangle inequality theorem:

1. Triangle Inequality Theorem:

  - For any triangle with sides [tex]\( a \), \( b \),[/tex] and [tex]\( c \)[/tex]:

    - [tex]\( a + b > c \)[/tex]

    - [tex]\( a + c > b \)[/tex]

    - [tex]\( b + c > a \)[/tex]

2. Checking the options:

  - Option A: 42 inches

    - [tex]\( 19 + 42 = 61 > 28 \)[/tex]

    - [tex]\( 19 + 28 = 47 > 42 \)[/tex]

    - [tex]\( 42 + 28 = 70 > 19 \)[/tex]

    - Valid

  - Option B: 7 inches

    - [tex]\( 19 + 7 = 26 < 28 \)[/tex]

    - Invalid (Does not satisfy [tex]\( AB + AC > BC \)[/tex])

  - Option C: 49 inches

    - [tex]\( 19 + 49 = 68 > 28 \)[/tex]

    - [tex]\( 19 + 28 = 47 < 49 \)[/tex]

    - Invalid (Does not satisfy [tex]\( AB + BC > AC \)[/tex])

  - Option D: 52 inches

    - [tex]\( 19 + 52 = 71 > 28 \)[/tex]

    - [tex]\( 19 + 28 = 47 < 52 \)[/tex]

    - [tex]\( 52 + 28 = 80 > 19 \)[/tex] Valid

3. Conclusion:

  - The lengths of side AC that satisfy the triangle inequality theorem and can form a triangle with sides AB = 19 inches and BC = 28 inches are 42 inches and 52 inches.

The complete question is:

In triangle ABC, the length of side AB is 19 inches and the length of side BC is 28 inches. Which of the following could be the length of side AC? A. 42 inches B. 7 inches C. 49 inches D. 52

Answer:

D) 27

Step-by-step explanation:

1. add 4 on both sides to leave 4/3x by itself

2. subtract x on both sides to cancel x on the right side

3. multiply 3 ton both sides to cancel out fraction

Answer:

d(27)

Step-by-step explanation:

Answer:

[tex]f(g( - 4)) = 196[/tex]

Step-by-step explanation:

The functions are;

[tex]f(x) = {x}^{2} [/tex]

and

[tex]g(x) = 3x - 2[/tex]

We want to find

[tex]f(g( - 4))[/tex]

First we find g(-4) to get:

[tex]g( - 4) = 3 \times - 4 - 2[/tex]

[tex]g( - 4) = - 12- 2[/tex]

[tex]g( - 4) = - 14[/tex]

Now

[tex]f(g( - 4)) = f( - 14)[/tex]

This implies that,

[tex]f(g( - 4)) = {( - 14)}^{2} [/tex]

[tex]f(g( - 4)) = {( - 14)} \times - 14[/tex]

[tex]f(g( - 4)) = 196[/tex]

Answer:   x + 4

                5x

Step-by-step explanation:

The first one is "x + 4" because you are adding 4 to the 1st number

The second one is "5x" because you are multiplying 5 to the 2nd number.

Answer:

The slope of the equation is:   [tex]m=\frac{2}{3}x[/tex]

Step-by-step explanation:

Given the equation

[tex]y=\frac{2}{3}x-1[/tex]

As the equation in slope intercept form

[tex]\:y=mx+b[/tex]

Here:

Comparing the equation in slope intercept form

[tex]y=\frac{2}{3}x-1[/tex]

so

[tex]m=\frac{2}{3}x[/tex]

Therefore, the slope of the equation is:   [tex]m=\frac{2}{3}x[/tex]

Answer:

X = 4

Step-by-step explanation:

Solve for x.

-3x + 4 = -8

Make sure to subtract both sides.

-3x (+4 -4) = -8 - 4

-3x= -12

Divide by -3 on both sides.

-3x/-3 = -12/-3

Answer:

4

Step-by-step explanation:

-3x + 4 = -8

Subtract 4 from both sides

-3x + 4 - 4 = -8 - 4

-3x = -12

Divide both sides by by -3

x = -12/-3

x = 4

First, subtract 24 from 31.

31 - 24 = 7

Now divide 7 by 2.

7 ÷ 2 = 3.5

Plug 3.5 into the equation to check.

24 + (3.5 × 2) = 31

x = 3.5

Answer:

Kevin needs 96 points on his last test to raise his mean test score to 90 points.

Step-by-step explanation:

we know that

The mean score is the total of all scores divided by the total number of tests.

Let

x_1 ----> the score in the first math test

x_2 ----> the score in the second math test

x_3 ----> the score in the third math test

x_4 ----> the score in the fourth math test

we have

After taking the first 3 tests, his mean test score is 88 points

so

[tex]\frac{x_1+x_2+x_3}{3} =88[/tex]

[tex]x_1+x_2+x_3=264[/tex] ----> equation A

How many points does he need on his last test to raise his mean test score to 90 points?

so

[tex]\frac{x_1+x_2+x_3+x_4}{4} =90[/tex]

[tex]x_1+x_2+x_3+x_4=360[/tex] ----> equation B

substitute equation A in equation B

[tex]264 + x_4 = 360[/tex]

solve for x_4

[tex]x_4 = 360-264[/tex]

[tex]x_4 = 96[/tex]

Therefore

Kevin needs 96 points on his last test to raise his mean test score to 90 points.

Answer:

345.

Step-by-step explanation:

Just divide 407.10 by 1.18 and you'll get your answer.

Answer: she is jogging 2.25 i think

Step-by-step explanation:

im sorry im not sure i just divided 135 by 60 but i dont think its right:(

Answer:

48 yards

Step-by-step explanation:

we know that

The circumference of a circle is equal to

[tex]C=2\pi r[/tex]

we have

[tex]r=7.6\ yd\\\pi=3.14[/tex]

substitute

[tex]C=2(3.14)(7.6)=48\ yd[/tex]

Answer: 48 yards

Step-by-step explanation:

The circumference of a circle can be calculated with the following formula:

[tex]C=2\pi r[/tex]

Where "C" is the circumference of the circle and "r" is the radius of the circle.

In this case you know that the radius of the circular track is the following:

[tex]r=7.6\ yd[/tex]

Knowing tha radius, you can substitute it into the formula (According to the information given in the exercise, you need to use [tex]\pi =3.14[/tex])

[tex]C=2(3.14)(7.6\ yd)[/tex]

Finally, you need to evaluate.

Therefore, you get that the whole yards of fencing that they need to purchase to enclose the track is:

[tex]C\approx48\ yd[/tex]

Answer:

0.33333333333

Step-by-step explanation:

Typing 1/3 in a calculator gives 0.333333333333

Answer: 150 miles

Step-by-step explanation:

The distance between Chicago and Indianapolis is approximately 150 miles.

To find the distance between Chicago and Indianapolis using their latitude and longitude coordinates, we can apply the Pythagorean theorem. The distance between two points on the Earth's surface can be approximated by considering the Earth as a flat plane, which is reasonable for relatively short distances like the one between these two cities.

The difference in latitude (north-south distance) between Chicago and Indianapolis is:

[tex]\[ 42N - 40N = 2N \][/tex]

The difference in longitude (east-west distance) between the two cities is  [tex]\[ 86W - 88W = 2W \][/tex]

Since each degree is approximately 53 miles, we can calculate the north-south distance and the east-west distance:

North-south distance in miles:

[tex]\[ 2N \times 53 \text{ miles/degree} = 106 \text{ miles} \][/tex]

East-west distance in miles:

[tex]\[ 2W \times 53 \text{ miles/degree} = 106 \text{ miles} \][/tex]

Now, we can use the Pythagorean theorem to find the straight-line distance (the hypotenuse of the right triangle formed by the north-south and east-west distances):

Let [tex]\( d \)[/tex] be the distance between the two cities, then:

[tex]\[ d^2 = (106 \text{ miles})^2 + (106 \text{ miles})^2 \] \\[/tex]

[tex]\[ d^2 = 11236 \text{ miles}^2 + 11236 \text{ miles}^2 \] \\[/tex]

[tex]\[ d^2 = 22472 \text{ miles}^2 \] \\[/tex]

[tex]\[ d = \sqrt{22472 \text{ miles}^2} \] \\[/tex]

[tex]\[ d \approx 150 \text{ miles} \][/tex]

Answer:

I don't know but I have the equations. (also Im going to assume you know a bit of trig)

Step-by-step explanation:

You have to use law of cosines.

a=11

b=15

take these equations and plug in the variables

a^2=b^2+c^2-2bc cos(a)

b^2=a^2+c^2-2ac cos (b)

c^2=a^2+b^2-2ab cos(c)

you will get something along the lines of

something=cos a

something=cos b

something=cos c

then in a calculator you push inverse cos or cos-1(x) and input the "something" into as x and that answer should be one angle, and repeat it for the rest of the three values.

The greatest number of DVDs that Tony can pack in each box is 6, which is the greatest common divisor of 12, 24, and 30.

To find the greatest number of DVDs that Tony can pack in each box, we need to determine the greatest common divisor (GCD) of the quantities of each type of DVD. The GCD is the largest number that can evenly divide all the given numbers without leaving a remainder. The numbers of DVDs are 12 (comedy), 24 (animated), and 30 (musical).

Here are the steps to find the GCD:

Thus, the greatest number of DVDs Tony can pack in each box is 6.