Graph the image of QRS after a rotation 270º counterclockwise around the origin.

The volume is 201√2 and the surface area is 274.

To solve the problem, we need to calculate both the volume and the surface area of the frustum of a regular square pyramid with given dimensions.

First, let's find the volume of the frustum. The volume V of a frustum of a pyramid can be calculated using the formula:

[tex]\[ V = \frac{1}{3}h(B_1 + B_2 + \sqrt{B_1B_2}) \][/tex]

where h is the height of the frustum, [tex]\( B_1 \)[/tex] is the area of the smaller base, and [tex]\( B_2 \)[/tex] is the area of the larger base.

Given that the edges of the bases are 5 and 9, the areas of the bases are:

[tex]\[ B_1 = 5^2 = 25 \] \[ B_2 = 9^2 = 81 \][/tex]

To find the height , we can use the Pythagorean theorem on the right triangle formed by the slant height, half of the difference of the base edges, and the height of the frustum:

[tex]\[ h = \sqrt{s^2 - \left(\frac{a_2 - a_1}{2}\right)^2} \][/tex]

where s is the slant height, [tex]\( a_1 \)[/tex] is the edge of the smaller base, and [tex]\( a_2 \)[/tex] is the edge of the larger base. Plugging in the given values:

[tex]\[ h = \sqrt{6^2 - \left(\frac{9 - 5}{2}\right)^2} = \sqrt{36 - 4} = \sqrt{32} = 4\sqrt{2} \][/tex]

Now we can calculate the volume:

[tex]\[ V = \frac{1}{3} \cdot 4\sqrt{2} \cdot (25 + 81 + \sqrt{25 \cdot 81}) \] \[ V = \frac{1}{3} \cdot 4\sqrt{2} \cdot (106 + \sqrt{2025}) \] \[ V = \frac{1}{3} \cdot 4\sqrt{2} \cdot (106 + 45) \] \[ V = \frac{1}{3} \cdot 4\sqrt{2} \cdot 151 \] \[ V = \frac{1}{3} \cdot 604\sqrt{2} \] \[ V = 201\sqrt{2} \][/tex]

Next, let's calculate the surface area of the frustum. The surface area \( A \) of a frustum is the sum of the areas of the two bases and the area of the lateral surface:

[tex]\[ A = B_1 + B_2 + A_{\text{lateral}} \][/tex]

The lateral surface area [tex]\( A_{\text{lateral}} \)[/tex] can be found using the formula:

[tex]\[ A_{\text{lateral}} = \frac{1}{2}(P_1 + P_2)s \][/tex]

where [tex]\( P_1 \)[/tex] and [tex]\( P_2 \)[/tex] are the perimeters of the smaller and larger bases, respectively, and s is the slant height. Since the pyramid is regular and square:

[tex]\[ P_1 = 4a_1 = 4 \cdot 5 = 20 \] \[ P_2 = 4a_2 = 4 \cdot 9 = 36 \][/tex]

Now we can find the lateral surface area:

[tex]\[ A_{\text{lateral}} = \frac{1}{2}(20 + 36) \cdot 6 \] \[ A_{\text{lateral}} = \frac{1}{2} \cdot 56 \cdot 6 \] \[ A_{\text{lateral}} = 28 \cdot 6 \] \[ A_{\text{lateral}} = 168 \][/tex]

Adding the areas of the bases:

[tex]\[ A = 25 + 81 + 168 \] \[ A = 274 \][/tex]

Therefore, the volume and surface area of the frustum are:

[tex]\[ {V = 201\sqrt{2}} \] \[ {A = 274} \][/tex]

Answer:

Step-by-step explanation:

part A. area = L X H

9 x 8/9 = 72/9 = 8 square feet

Part B. Draw a line diagonally either between Point A & C or B & D, this would make 2 triangles.

the area of the triangle would be half of the full area so 8 / 2 = 4 feet square

Question:

Triangle ABC is a right triangle

The length of BC is 5 units.

The area of ABC is ______ square units.

Cordinates are given below.

A(-9, 10)

B(7, -2)

C(4,-6)

Answer:

50 square units

Step-by-step explanation:

Image to question is attached.

Given:

Length of BC = 5 units

Coordinates:

A = (-9, 10)

B= (7, -2)

C = (4, -6)

Let's take BC as base, and AB as height.

Since we know length of BC, let's find length of AB.

Length of AB =

[tex] \sqrt{(-9 - 7)^2 +(10 + 2)^2 [/tex]

[tex] = \sqrt{(256)+(144) [/tex]

= 20.

Therefore, the area of triangle ABC [tex] = \frac{1}{2} b*h [/tex]

[tex] = \frac {1}{2} * 5 * 20 [/tex]

= 50 square units.

Answer: 50

Step-by-step explanation:

Answer:

$14.04

Step-by-step explanation:

19.50 - 28%·19.50 =

= 19.50 - 28·19.50/100

= 19.50 - 546/100

= 19.50 - 5.46

= $14.04

Answer:

A. $16,500

Step-by-step explanation:

82500/5

Question:

Parallelogram f"g"h"j" is the final image after the rule ry-axis • t1,2(x, y) was applied to parallelogram fghj.  The coordinates are f''(3,4), g''(2,2), h''(4,2) and j''(5,4)

what are the coordinates of vertex f of parallelogram fghj?

(–2, 2)

(–2, 6)

(–3, 4)

(–4, 2)

Given:

Given that the the coordinates of the parallelogram f''g''h''j'' is the final image after the rule ry-axis • t1,2(x, y) was applied to parallelogram fghj.

The coordinates are f''(3,4), g''(2,2), h''(4,2) and j''(5,4)

We need to determine the coordinates of vertex f of parallelogram fghj.

Reflection across y - axis:

The general rule to reflect the coordinate across y - axis is given by

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

Substituting the coordinate f''(3,4), we get;

[tex](3,4)\rightarrow (-3,4)[/tex]

Thus, the coordinates of f'' of reflection across the y - axis is (-3,4)

Translation  T1,2(x, y):

The translation can be performed using the rule,

[tex]T_{1,2}(x,y)=(x+1,y+2)[/tex]

Now, substituting the coordinate (-3,4), we get;

[tex]T_{1,2}(-3,4)=(-3+1,4+2)[/tex]

[tex]T_{1,2}(-3,4)=(-2,6)[/tex]

Thus, the coordinates of vertex F is (-2,6)

Hence, Option b is the correct answer.

The answer is D) (-4,2) on Edge 2020

Answer:

(-1/2,1/2)

Step-by-step explanation:

We have  the two endpoints

(-3,-2) and ( 2,3)

To find the x coordinate of the midpoint, add the x coordinates of the endpoints and divide by 2

(-3+2)/2 = -1/2 =-1/2

To find the y coordinate of the midpoint, add the y coordinates of the endpoints and divide by 2

(-2+3)/2 = 1/2

The midpoint is (-1/2,1/2)

Answer:

we know that the most repeated value is mode and here we can see that the most repeated value is 11 that is 20 times so it's mode is 11.

Hope you understood

Answer:

The volume of the cylinder in feet is

V= 9.43ft³

Step-by-step explanation:

Step one

The formula for the volume of a cylinder is given as

V=πr²h

Where r= radius

h= height

Step two

Given Data

Radius = 1foot

Height = 3 feet

Substituting in our formula we have

V=3.142*1²*3

V= 9.43ft³

Answer:

i just got this question... It was B

3pie ft^3

​​Step-by-step explanation:

Answer:

The median is 5.5.

Answer:d

Step-by-step explanation:

Answer:

the range is 492

Step-by-step explanation:

to find range you have to subtract the smallest number from the largest number so you would subtract 120 from 612 which gets you 492

Answer:

The range in the following data set is 470.

Step-by-step explanation:

It's easy, you just have to subtract the highest number from the data set with the lowest number.

So the highest value in this data set would be 590 and the lowest number in the list is 120.

So:

Range: 590 - 120 = 470

~hope this helps~

Answer:

no

Step-by-step explanation:

cant mult. by power of 10

Answer:

no

Step-by-step explanation:

Answer:

Hope this helps!!

Step-by-step explanation:

2ya and 2yb where a and b have no common factors and a and b are polynomaals

a=(x+2)(x+3)

b=(x+4)(x+5)

no common factors betwen a and b

so

2ya=2y(x+2)(x+3)=2yx²+10xy+12y

2yb=2y(x+4)(x+5)=2yx²+18xy+40y

the 2 polynomials  are  2yx²+18xy+40y and 2yx²+10xy+12y

Answer:

The GCF of a polynomial is the greatest factor which is common to all the terms of the polynomial.

Thus, an example of a polynomial with a GCF of 2y is

The above polynomial can also be rewritten as

This form of the polynomial is obtained by factoring out the GCF of the polynomial.

Answer:

41.43%

Step-by-step explanation:

Change:

99 - 70 = 29

% change:

29/70 × 100

= 41.42857143%

Answer:

The answer is D

Step-by-step explanation:

Answer: The answer is (3, One-half) or option D

Step-by-step explanation:

Answer:

B: (-1, 1) and (-6, -1)

D: (1, 0) and (6, 2)

E: (3, 0) and (8, 2)

Step-by-step explanation:

Hope this helps! :D

Answer:

there' yo answer. B,D,E

Answer:

3 MIN AND 46 SECONDS. ITHINK BUT DONT QUOTE ME

Step-by-step explanation:

Answer: 111.72 m^2 if they want round its 112

Is from O to C 14m

A=pixr^2

3.14x14^2= 615.44 m/2 half circle = 307.72

Area of triangle A= 1/2bh. .5x28x14=196

307.72-98=196= 111.72 m^2

Step-by-step explanation:

Answer:

[tex]5\,x\,y\,(-x+2-3y)[/tex]

Step-by-step explanation:

Always proceed by first extracting all common factors to all terms:

Notice that the factors: 5, x, and y are present in all terms, so we can extract them from the trinomial:

[tex]-5x^2y+10xy-15xy^2\\5\,x\,y\,(-x+2-3y)[/tex]

Now, the trinomial left (-x+2-3y) cannot be factored out, so then factoring is complete.

Answer: 54 minutes

Step-by-step explanation: Given that Tom spent 1/10 hour less time than normal exercising.

Let the normal exercising hour = H

Tom spent 1/10 hour less time than normal exercisin. That is

Tom spent = H - 1/10H

Tom spent = 9/10 hours

The much time Tom spent exercising last week will be

9/10 × 60 = 54 minutes

Answer:

I´m pretty sure its all real numbers

Step-by-step explanation:

Well I already know that y=0,and the domain would be (-∞,∞)

hope this helps!

Answer: d. all real numbers!!

Step-by-step explanation:

Edge

Can you give us the options so we can try to help you?

These are the dilations

B is the correct answer.

Answer:

B.

Step-by-step explanation:

Answer:

B. x= -1, x=3

Step-by-step explanation:

4x²-8x -12 =0 /:4

x² - 2x -3=0

x² - 3x + x -3 = 0

x(x-3) + 1(x-3)=0

(x-3)(x+1)=0

x-3 =0 or x+1 =0

x=3 and x = -1

Answer:

4(3+3)=3(3(3)-1)

Step-by-step explanation:

1) plug in the three

2) distribute

3)  see if the answers gotten are the same if not than the statement is wrong

I know it looks a bit complicated but its not once you get the hang of it

Answer:

The dimensions are lenght = 15 units

And width = 4 units

Step-by-step explanation:

Kindly refer to the attached image for explanations

Answer:

1/3

Step-by-step explanation:

Take the model size and divide by the original size by using the length

7/21 = 1/3

The scale factor is 1/3

We check by using the width

5/15 = 1/3