QUESTION 1

Use function notation to write the equation of the line.

From 18 wolves to 27 wolves, what was the increase? 27 - 18 is 9, so the increase was 9.

How much of 18 is 9? 9 / 18 is equal to 1 / 2, which is 0.5. To make 0.5 a percent we multiply by 100.

0.5 times 100 is 50%.

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:

[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.

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

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

These are the dilations

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:x=7 y=5

Step-by-step explanation:

I just took it, sorry I'm not good at math and just guessed until I got it right for this answer.

Answer:

-4

Step-by-step explanation:

magic

Answer:

The dimensions are lenght = 15 units

And width = 4 units

Step-by-step explanation:

Kindly refer to the attached image for explanations

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

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:

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 answer is D

Step-by-step explanation:

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

Step-by-step explanation:

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:

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:

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

Answer:

45√q^5

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:d

Step-by-step explanation:

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 median is 5.5.

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)

64 - (3y + 8y + y) / 40 = 37

Simplify 3y + 8y + y

64 - 12y / 40 = 37

Add 12y / 40 to both sides and subtract 37

27 = 12y / 40

Multiply both sides by 40

1080 = 12y

Divide both sides by 12

90 = y

Answer:

y=90

Step-by-step explanation:

Collect the like terms first (3y, 8y, and y) and add them together, which gives you 12y. Equation looks like this so far 64-12y/40=37

Divide the -12 by 40, which can be reduced to -3/10.Equation so far: 64-3/10y=37

Multiply each side by 10 to cancel out the 10 in -3/10y. Equation so far: 640-3y=370

Use inverse operations to move the 640 with the 370. Equation so far: 3y=370-640

Subtract 640 from 370, which gives you -270. Then you'll have -3y=-270 and divide both sides by -3.

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:

A. $16,500

Step-by-step explanation:

82500/5

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:

3 MIN AND 46 SECONDS. ITHINK BUT DONT QUOTE ME

Step-by-step explanation:

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