Which expression represents the volume of the pyramid? One-thirdn(n − 1) units3 One-thirdn(n − 1)2 units3 One-thirdn2(n − 1) units3 One-thirdn3(n − 1) units3

Answer:

Step-by-step explanation:

This is because only a reduction can be 0-1, as it will shrink, while if you multiply a number by a number greater than 1, is will largen.

The dilation is an enlargement with a scale factor greater than 1. Thus, the correct option is D.

(SCALING ZOOMING SIMILAR FIGURES)

Suppose a figure (pre image) is dilated (dilated image) by scale factor of k.

So, if a side of the figure is of length L units, and that of its similar figure is of M units, then:

L = k × M

where 'k' will be called as scale factor.

The linear things grow linearly like length, height etc.

The quantities which are squares or multiple of linear things twice grow by square of scale factor. Thus, we need to multiply or divide by k² to get each other corresponding quantity from their similar figures' quantities.

So area of first figure = k² × area of second figure

Similarly, Volume of first figure = k³ × volume of second figure.

It is because we will need to multiply 3 linear quantities to get volume, which results in k getting multiplied 3 times, thus, cubed.

As it can be seen in the image below that the red rectangle is the pre-image therefore, it is the original figure.

The blue rectangle is the image of the original figure.

Now, as it can be seen that the pre-image is a smaller rectangle, while the image is a large rectangle, therefore, the dilation made is of enlargement.

Also, it can be observed that the ratio of any corresponding sides of the two rectangles is more than 1.

Hence, the dilation is an enlargement with a scale factor greater than 1. Thus, the correct option is D.

Learn more about Dilation:

https://brainly.com/question/27212783

#SPJ2

Answer:

10x + 210 = 25x

Step-by-step explanation:

Plan A

Annual fee = $210

Payment per lesson = $10

If 'x' lessons to be taken, total cost = 10x + 210

Plan B

Annual fee = 0

Payment per lesson = $25

Total cost for 'x' lessons = $25x

Equation for the equal payments in both the plans for 'x' lessons,

10x + 210 = 25x

Step-by-step explanation:

Classroom A has n students.

Since Classroom B has 4 less students, they have (n - 4) students.

Also Classroom C has double the students in B, so they have 2(n - 4) students.

We have A + B + C = 40.

=> n + (n - 4) + 2(n - 4) = 40

=> n + n - 4 + 2n - 8 = 40

=> 4n - 12 = 40

=> 4n = 52, n = 13.

Hence there are 13 students in Classroom A.

Answer:

C y>2/3x+3

Step-by-step explanation:

Use y=mx+b format. The B is the y-intercept. From the y-intercept (3), go up two then to the right 3. That gives you the slope, or mx which is 2/3. The area shaded is above so it would be the greater than symbol.  

Answer:

y = 320,000 ( 1.048 ) ^x

x = number of years

(the  ^  before the x symbolizes "to the power of," but I can't do that on my keyboard)

Step-by-step explanation:

formula i used:

A = amount that you start with

t = amount of years / time

%increase: you must convert your percent (4.8%) to a decimal (0.048)

A ( 1 + %increase ) ^t

Answer:

y = 320,000(1.048)^t  

Step-by-step explanation:

4.8% = 0.048.

The population grows by 1.048 per year.

The required equation is:

y = 320,000(1.048)^t

Answer:

i think 5

Step-by-step explanation:

Answer:

$9.18

Step-by-step explanation:

45.92/20%

=$9.18

Answer:

47

Step-by-step explanation:

Answer:

27 because you have to multipli and then divide

Answer:

about 93 weeks

Step-by-step explanation:

divide 1200 by 13 to get your answer which is 92.3076923077 so then you just instead of rounding to 92 you would round to 93 because it would take her more then 92 weeks so the answer would be about 93 weeks

Picture relating to question has been attached below

Answer:

x = 10 ; y = 15

Step-by-step explanation:

The values for which the park is a parallelogram :

For the quadrilateral to be a parallelogram ; the diagonals will bisect each other such as :

VT = RV and UV = VS

From the diagram :

VT = 3x + 5y

RV = 6x + 3y

UV = 11y + 33 m

VS = 14y - 12 m

VT = RV and UV = VS

3x + 5y = 6x + 3y

3x - 6x = 3y - 5y

-3x = - 2y

3x = 2y

11y + 33 = 14y - 12

11y - 14y = - 12 - 33

-3y = - 45

y = 45/3

y = 15

From ;

3x = 2y

3x = 2*15

3x = 30

x = 30/3

x = 10

Answer:

kisses -A

Step-by-step explanation:

Answer: 5/2

Step-by-step explanation: Use the slope formula

Answer:

C.) 32

Step-by-step explanation:

2^5 = 32

Answer:

(-6, 4)

Step-by-step explanation

translation rule: (x+1,y-3)

(-7+1, 7-3)

(-6, 4)

Step-by-step explanation:

jejnddndmkkdksjsjdenekekeej

Answer:

i think the answer is 3 I dont know if i'm right tho

Step-by-step explanation:

^-^ sorry if this is wrong but for me i did 3 on edge 2021

Given:

[tex]OA=3[/tex] units

[tex]OA'=9[/tex] units

To find:

The scale factor of the dilation.

Solution:

From the given figure it is clear that the center of dilation is point O. Point A' is the image of point A. So,

[tex]\text{Scale factor}=\dfrac{OA'}{OA}[/tex]

Putting the given values, we get

[tex]\text{Scale factor}=\dfrac{9}{3}[/tex]

[tex]\text{Scale factor}=3[/tex]

Therefore, the scale factor of the dilation is 3.

Answer:

C

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

A

Answer:

poop=pee

Step-by-step explanation:

Answer:

Option D: 1 is the correct answer.

Step-by-step explanation:

Given that:

n(x) = 7x+4        

n(x) = 11

Putting n(x) = 11 in first function.

11 = 7x + 4

Now, we will subtract 4 from both sides

11 - 4 = 7x + 4 - 4

7 = 7x

7x = 7

Dividing both sides by 7

[tex]\frac{7x}{7}=\frac{7}{7}[/tex]

x = 1

Hence,

Option D: 1 is the correct answer.

Answer:

im not too sure but i think the answer is c

Step-by-step explanation:

Answer: use desmos to graph them

Step-by-step explanation:

Answer:

140

Step-by-step explanation:

7- Cranberry

2:Grape = 40 so 40/2 = 1

3:Pineapple

1= 20 juices

7+2+3 is 12

20 x 12 is 140

Answer:

A' = ( 0,4 )

B' = ( -3,6 )

C' = ( -4,3 )

Step-by-step explanation:

Transformation involves changing the coordinates of a shape.

The coordinates of △ABC after the glide transformation are [tex]A' = ( 0,4 )[/tex], [tex]B' = ( -3,6 )[/tex] and  [tex]C' = ( -4,3 )[/tex]

The coordinates of triangle ABC is given as:

[tex]A = (1,3)[/tex]

[tex]B = (4,5)[/tex]

[tex]C = (5,2)[/tex]

The glide reflection is given as: T⟨−1, 1⟩° Ry-axis

So, we start by translating the shape by (x - 1, y + 1).

The coordinate ABC becomes

[tex]A = (1 - 1, 3 + 1) = (0,4)[/tex]

[tex]B = (4 - 1, 5 + 1) = (3,6)[/tex]

[tex]C = (5 - 1, 2 + 1) = (4,3)[/tex]

Next, we reflect the coordinates across the y-axis.

The rule of this reflection is:

[tex](x,y) \to (-x,y)[/tex]

So, we have:

[tex]A' = ( 0,4 )[/tex]

[tex]B' = ( -3,6 )[/tex]

[tex]C' = ( -4,3 )[/tex]

Read more about transformation at:

https://brainly.com/question/1616371