All of the edges of a regular triangular pyramid have length 12. A frustum of the pyramid has height half of that of the pyramid. What is the:

1) Volume of the frustum?

2) Surface area of the frustum?

Answers

Answer 1

Answer:

1) The volume of the frustum is 27·(√3)·h

2) The surface area the frustum is 24·h + 54·√3

Step-by-step explanation:

1) A frustum of the regular triangular prism is a portion of the triangular prism

The length of the edge of the triangle prism = 12

The area of the triangular face, A = (√3/4)·a²

∴ A = (√3/4)·12² = 36·√3

When

The volume of the triangular prism, V = A·h = (36·√3)·h

By triangle proportionality theorem, the cross sectional area of the top half of the triangular prism =  (√3/4)·6² = 9·(√3)

The volume of the top half, V₂ = 9·(√3)·h

The volume of the frustum = V - V₂ = (36·√3)·h - 9·(√3)·h = 27·(√3)·h

The volume of the frustum = 27·(√3)·h

2) The surface area of the triangular side of the frustum is given as follows;

A = 36·√3- 9·(√3) = 27·(√3)

The surface area the frustum, [tex]F_A[/tex] = 2×27·(√3) + 2 ×6 ×h + 12×h = 24·h + 54·√3

The surface area the frustum = 24·h + 54·√3


Related Questions

7th grade math
plz help asap
the picture is attached
10 POINTS

Answers

Answer:

1. A, C, and E

2. 13.5

3. -3

4. $3.39

5. 9 1/4 miles

Step-by-step explanation:


Directions: Tell whether each set of ordered pairs satisfies an exponential function. Write yes
or no.
{(-1-1),(0,0),(1,-1).12.-4)}
. 4
{(0,1),(1,4),(216),(3,64)}
{(-11.5),(0,3).(16) (2.12)}
()/(
{(-1-9).(1,9),(3,27).(5,45)}

Answers

Answer:

1_9

Step-by-step explanation:

Directions: Underline the prepositional phrase in each sentence. Highlight the preposition. (There may be more than one.)

Can someone plz help real quick?

Answers

1 cm: 3 m. you just have to divide the 15 by the 5 :)

Answer:

1 Cm - 3 Meters

Step-by-step explanation:

Just do 15 (meters) divided by 5 centimeters. 15 divided by 5 is 3.

4x^2+9x+10+3x^2+7x+2​

Answers

Answer:

7x2+16x+12

Step-by-step explanation:

=4x2+9x+10+3x2+7x+2

=(4x2+3x2)+(9x+7x)+(10+2)

=7x2+16x+12

Find the midpoint of the line segment with end coordinates of:
(−4,8) and (4,−2)

Answers

Answer:

(0, 3 )

Step-by-step explanation:

Given endpoints (x₁, y₁ ) and (x₂, y₂ ) then midpoint is

( [tex]\frac{x_{1}+x_{2} }{2}[/tex], [tex]\frac{y_{1}+y_{2} }{2}[/tex] )

Here (x₁, y₁ ) = (- 4, 8) and (x₂, y₂ ) = (4, - 2) , then

midpoint = ( [tex]\frac{-4+4}{2}[/tex], [tex]\frac{8-2}{2}[/tex] ) = ( [tex]\frac{0}{2}[/tex], [tex]\frac{6}{2}[/tex] ) = (0, 3 )

Help!!!!!!!!!!!!!!!!!!!!

Answers

Answer:

4

Step-by-step explanation:

What is 3.00 - 2.50 explain your work

Answers

Answer:

0.5

Step-by-step explanation:

Subtract 2.5 from 3

Option A
Option B
Option C
Option D​

Answers

Answer:

It's B

... because if you evaluate it it'll be 9x - 6xy, and 2xy + 2x^2

-6xy and 2xy are like terms

g(n) = 20(x+15) What is g(10)?

Answers

Answer:

500

Step-by-step explanation:

g (10) = 20(x+15)

= 20 (10+15)

= 20 (25)

= 500

Elianna studied data collected on the school hockey team for one season. She noticed that a player on the team had 13 successful shots out of a total of 50 attempted shots. To find the percentage of the total shots attempted by this player that were successful, Elian set up the equivalent ratios below.

Answers

Answer: See explanation

Step-by-step explanation:

Your question isn't complete but based on the information given in the question, since she noticed that a player on the team had 13 successful shots out of 50 attempted shots.

The percentage of the total shots attempted by this player that were successful will be:

= 13/50 × 100

= 26%

Which expression is equivalent to the area of square A, in square inches?
A
10 in.
24 in.
(10)(24)
o
10(24)
Saun and Exit

Answers

Answer:

10^2+24^2

Step-by-step explanation:

got 100% on the quiz

Sara simplified an expression as shown.

image

What property of operations did Sara use to get from Step 3 to Step 4?

A.
Subtracting a number is the same as adding its inverse.

B.
Associative Property of Addition

C.
Commutative Property of Addition

D.
The opposite of a sum is the sum of its opposites.







Sara simplified an expression as shown.

image

What property of operations did Sara use to get from Step 3 to Step 4?

A.
Subtracting a number is the same as adding its inverse.

B.
Associative Property of Addition

C.
Commutative Property of Addition

D.
The opposite of a sum is the sum of its opposites.

Answers

Answer:

B. Associative Property of Addition

Step-by-step explanation:

Explain what the (0,0) represents in the table.

Answers

Answer:

0,0

Step-by-step explanation:

0,0 on a graph would represent the origin.

the origin ​​​​ㅤㅤㅤㅤㅤㅤ

which number is a zero of f(x) = 2x (x + 7) ( x-4)​

Answers

Answer:

0, -7, 4

Step-by-step explanation:

Zeros of a function are values that make the function = 0

So, f(x) = 2x(x + 7)(x - 4) = 0

                x = 0 or x + 7= 0  or x - 4 = 0

                                   x = -7           x = 4

Note:  If you were to graph f(x), the graph would intercept the x-axis at 0, -7, and 4

someone help ME PLZZZZ

Answers

Answer:

a+b

Step-by-step explanation:

Solve the system of linear equations.
Check your solution, if possible.
2x + 3y = 5
2x + 3y = 7

Answers

Answer:

there is no solution, meaning the lines would be parallel

Step-by-step explanation:

i hope this helps :)

FUDGEE help pleasee

. Question Category: Solving Quadratic Equations by Factoring Select the correct answer. Find the solution(s) for x in the equation below. x^2 + 10x + 21 = 0 x = 3; x = -7 x = -3; x = -7 x = 3; x = 7 x = -3; x = 7

Answers

Answer:

x= -7 and x= -3

Step-by-step explanation:

(x+7)(x+3)=0 (Think about the numbers that will add to 10 and multiply to 21)

x= -7 and x= -3

Answer:

x = −3 or x = −7

Step-by-step explanation:

Let's solve your equation step-by-step.

x^2 +  10x + 21 = 0

Step 1: Factor left side of equation.

(x+3) (x+7) = 0

Step 2: Set factors equal to 0.

x + 3 = 0 or x + 7 = 0

x = −3 or x = −7

I hope this helps you with your assignment and have a fantastic day! :D

one cookie at the bakery cost $0.65 two cookies cost $1.20 and three cookies cost $1.75 how much will half a dozen cookies cost

Answers

Answer:

half a dozen cookies would cost  $3.90

Step-by-step explanation:

Your teacher gave you 45 of a bag of candy, but she only gave your friend 23 of a bag.

How much more of the bag did your teacher give you than your friend?

Answers

Answer:

you got 12 more then your friend, 45-23

Step-by-step explanation:

Give the product in simplest form:

Answers

Answer:

5 15/48

Step-by-step explanation:

5 times 3 is 15,  8 times 6 is 56, and 5 times 1 is 5....you can not simplify 15/48 so the final answer is 5 15/48

DO,-2(x, y)(3, 5). The point (x, y) is (1, 3) (-3/2, -5/2) (-6, -10)

Answers

Answer: -6, -10.

The question is asking you to make the coordinates negative and then multiply the negative numbers by 2, thus, -6, -10.

The coordinate of (x, y) is (-3/2, -5/2) if the -2(x, y) → (3, 5) option second is correct.

What is an ordered double?

It is defined as a representation of coordinates in a two-dimensional coordinate plane. It has a list of two elements in it, such as (x, y).

We have:

-2(x, y)  →  (3, 5)

The coordinate (x, y) changes after multiplication by factor 2

New coordinate = (3, 5)

-2x = 3

x = -3/2

-2y = 5

y = -5/2

Thus, the coordinate of (x, y) is (-3/2, -5/2) if the -2(x, y) → (3, 5) option second is correct.

Learn more about the ordered double here:

https://brainly.com/question/10757890

#SPJ2

What’s the slope? I need help pls

Answers

Answer:

The slope is -2/-3

Step-by-step explanation:

Look at the X-axis and go up to the point

Answer:

4/-2

Four over -2

Is your slope.

Your y-intercept is -1

Step-by-step explanation:

70% of x is 63. Write an equation to find the value of x, and solve the equation. What is the value of x?

Answers

Answer:

70%of x = 63

70/100 × x = 63

x=63×100/70

x=90

Step-by-step explanation:

find an ordered pair of 5x + y = 3

Answers

Answer:

Step-by-step explanation:

Find an ordered pair that satisfies the equation 5x + y = 3.  

There are infinitely many ordered pairs that satisfy this equation.

If we were to choose y = 0, then 5x = 3, and x = 3/5, leading to the ordered pair (3/5, 0).

If we were to choose x = 1, then 5(1) + y = 3, or y = -2.  The ordered pair would be (1, -2).

And so on.

There are 10 marbles in a paper bag, 6 of which are red. The rest are blue. You play a game with your friend. If you draw a red marble, you win. If you draw a blue marble she wins. Is this a fair game?

Answers

No, because you have 1 more marble than her. While you have 6 marbles in the bag, she has 4; there’s a 3/5 chance that you’ll win, and a 2/5 chance that she’ll win.

Please help with these 3 pretty easy problems and explain how you got it!!! 100 POINTS AND BRAINLIEST!!!! Serious answers please..

Answers

Answer:

Step-by-step explanation:

1)

(x-3)/18=12/9, cross multiply

9(x-3)=18(12)

9x-27=216, add 27 to each side

9x=243, divide each side by 9

x=27

2)

(x-16)/(x+6)=3/5, cross multiply

5(x-16)=3(x+6)

5x-80=3x+18, subtract 3x from each side

2x-80=18, add 80 to each side

2x=98, divide each side by 2

x=49

3)

Since the triangles are similar we can say that

25/(4x-1)=10/(x+5), cross multiply

25(x+5)=10(4x-1)

25x+125=40x-10, subtract 40x from each side

-15x+125=-10, subtract 125 from each side

-15x=-135, divide each side by -15

x=9

here are the answers!

1)

(x-3)/18=12/9, cross multiply

9(x-3)=18(12)

9x-27=216, add 27 to each side

9x=243, divide each side by 9

x=27

2)

(x-16)/(x+6)=3/5, cross multiply

5(x-16)=3(x+6)

5x-80=3x+18, subtract 3x from each side

2x-80=18, add 80 to each side

2x=98, divide each side by 2

x=49

3)

Since the triangles are similar we can say that

25/(4x-1)=10/(x+5), cross multiply

25(x+5)=10(4x-1)

25x+125=40x-10, subtract 40x from each side

-15x+125=-10, subtract 125 from each side

-15x=-135, divide each side by -15

x=9

Can the sides of a triangle have lengths of 19,24 and 43? If so, what kind of triangle is it?

Answers

Answer:

Yes Isosceles Triangle

Step-by-step explanation:

Im not a 100% sure but they all add up to 84 so good luck

Simplify the expression.



-21k - 3 + 4 - 7k

Answers

Step-by-step explanation:

I hope it is helpful to you

A fair spinner has 9 equal sections: 3 red, 4 blue and 2 green.
It is spun twice.
What is the probability of getting red both times?

Answers

Answer:

9/81

Step-by-step explanation:

Too long for me to explain it

Can someone help me pls :(

Answers

The answer is C
30x-10

Answer:

30x-10

Step-by-step explanation:

6(5x−2)+2

Distribute:

=(6)(5x)+(6)(−2)+2

=30x+−12+2

Combine Like Terms:

=30x+−12+2

=(30x)+(−12+2)

=30x+−10

Answer:

=30x−10

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