A cone has volume 36 pi. IF the cone's radius is 1, what is its height?

ABC is dilated by a scale factor of 3 with the origin as the center of dilation, resulting in the image A'B'C'. If the slope of

uysha [10]

Answer:

The slope of A'B' = -1.2 ⇒ answer A

Step-by-step explanation:

* Lets talk about dilation

- A dilation is a transformation that changes the size of a figure.

- It can become larger or smaller, but the shape of the

figure does not change.

- The scale factor, measures how much larger or smaller

the image will be

- If the scale factor greater than 1, then the image will be larger

- If the scale factor between 0 and 1, then the image will be smaller

- If the center of the dilation is the origin then multiply each coordinate

by the scale factor

* In the problem

∵ Δ ABC is dilated by a scale factor of 3 with the origin as the center

of dilation

- Let point A is (a , b) and point B is (c , d)

∵ The slope of the line which passes through points (x1 , y1) and (x2 , y2)

is m = (y2 - y1)/(x2 - x1)

∴ The slope of AB = (d - b)/(c - a) = -1.2

∵ Point A' is (3a , 3b) and point B' is (3c , 3d)

∴ The slope of A'B' = (3d - 3b)/(3c - 3a)

- Take 3 as a common factor from up and down

∴ The slope of A'B' = 3(d - b)/3(c - a) ⇒ cancel 3 up with 3 down

∴ The slope of A'B' = (d - b)/(c - a) = the slope of AB

∵ The slope of AB = -1.2

∴ The slope of A'B' = -1.2

* The slope of A'B' = -1.2

3 0

3 years ago

Sketch the graph of each line y= -2

Inessa [10]

The graph of y = -2 is shown below;

Please observe that y is always -2 for any value of x. Hence the graph is a straight line at the point where you have negative 2 on the vertical axis (y-axis).

8 0

1 year ago

. Center at (-4,-1), radius = 2

valkas [14]

Consider we need to find the equation of the circle.

Given:

The Center at (-4,-1), radius = 2.

To find:

The equation of the circle.

Solution:

The standard form of a circle is

$(x-h)^2+(y-k)^2=r^2$

Where, (h,k) is the center of the circle and r is the radius of the circle.

Putting h=-4, k=-1 and r=2, we get

$(x-(-4))^2+(y-(-1))^2=(2)^2$

$(x+4)^2+(y+1)^2=4$

Therefore, the equation of the circle is $(x+4)^2+(y+1)^2=4$ .

6 0

3 years ago

Patrica scored 80% on a math test. She missed 4 problems. How many problems were on the test?

svet-max [94.6K]

Answer:

20

Step-by-step explanation:

Patrica got 80% correct. She missed 4 problems, so that must have been the remaining 20% of the test.

Therefore:

4 = 20% x

Percent means out of 100, so:

4 = (20/100) x

4 = 1/5 x

x = 20

There were 20 problems on the test.

3 0

3 years ago

Given the function f(x)=x^2+7x+6f(x)=x

Sonbull [250]

The average rate of change of the function f( x ) = x² + 7x + 6 at the interval of −4 ≤ x ≤ −1 is 2

<h3>What is the average rate of change the function?</h3>

The average rate of change the function is simply the change in y-values of the two points divided by the change in x-values of the two points.

It is expressed as;

Given the data in the question;

f( x ) = x² + 7x + 6
Interval: −4 ≤ x ≤ −1 ⇒ [-4.-1]

Average rate of change = ( f(-1) - f(-4) ) / ( (-1) - (-4) )

Average rate of change = ( (-1)² + 7(-1) + 6 ) - ( (-4)² + 7(-4) + 6 ) ) / ( (-1) - (-4) )

Average rate of change = ( (1 + -7 + 6 ) - ( 16 - 28 + 6 ) ) / (-1 + 4 )

Average rate of change = ( ( 0 ) - ( -6 ) ) / (-1 + 4 )

Average rate of change = ( 0 + 6 ) / ( 3 )

Average rate of change = 6 / 3

Average rate of change = 2

Therefore, the average rate of change of the function is 2.

Learn more about average rate of change here: brainly.com/question/28744270

#SPJ1

8 0

1 year ago