Use the data in the table to write a multiplication or a division story for each number fact.Solve.

Find the volume of the prism.

umka21 [38]

Answer:

C = 210cm^3

Step-by-step explanation:

We can get an estamate when we use the equation L x H x W = x/2

This shows 8 x 8 x 7, then divide by 2 = 224cm^3

The reason it is slightly less could be the facts the teachers want you to remember this one.

For right side prism the equation is (1/2)b x h x H

which means;

The volume of a triangular prism can be found by multiplying the base times the height. Both of the pictures of the Triangular prisms below illustrate the same formula. The formula, in general, is the area of the base (the red triangle in the picture on the right) times the height,h.

We use the side and base that surrounds the right side as (1/2)base and as side to find area then use the H as the height being the 7.

3 0

3 years ago

Read 2 more answers

The formula for the slant height of a cone is , where S is surface area of the cone. Use the formula to find the slant height, l

liq [111]

we know that

The formula of the surface area of the cone is equal to

$SA=\pi r^{2}+\pi rl$

where

SA is the surface area

r is the radius of the cone

l is the slant height

in this problem we have

$SA=500\pi\ ft^{2}\\r=15\ ft\\l=?$

Solve the formula for l

$SA=\pi r^{2}+\pi rl\\ \\\pi rl=SA-\pi r^{2} \\ \\l=\frac{SA-\pi r^{2} }{\pi r}$

substitute the values

$l=\frac{500\pi -\pi 15^{2} }{\pi15}\\ \\l=\frac{275}{15}\ ft\\ \\l=\frac{55}{3}\ ft\\ \\l=18\frac{1}{3}\ ft$

therefore

<u>the answer is</u>

The slant height is $18\frac{1}{3}\ ft$

7 0

3 years ago

Read 2 more answers

Write the sum using summation notation, assuming the suggested pattern continues. -9 - 4 + 1 + 6 + ... + 66

Ipatiy [6.2K]

Answer:

Summation notation is:

$\sum_{n=1}^{16}[5(x-1)-9]$

If you prefer it a little more simplified:

$\sum_{n=1}^{16}(5x-14)$

Step-by-step explanation:

First my favorite part, finding a pattern between the consecutive terms.

This is an arithmetic series because the terms are going up by 5 each time.

So arithmetic sequence, think linear equations:

x | y

1 -9

2 -4

3 1

4 6

..................

n 66

We are going to have to find that n but will will eventually...

The equation for a line in point slope form is $y-y_1=m(x_x_1)$ where $(x_1,y_1)$ is a point on the line and m is the slope.

We are already have the slope is 5 (the slope is the common difference in arithmetic sequence).

I'm going to use the first point (1,-9).

So the equation in point slope form is $y-(-9)=5(x-1)$

Subtract 9 on both sides:

$y=5(x-1)-9$

Now we need to know how many terms we are adding so what is x if y=66.

$66=5(x-1)-9$

Add 9 on both sides:

$75=5(x-1)$

Divide both sides by 5:

$15=x-1$

Add 1 on both sides:

$16=x$

We have 16 terms in this sequence where the 16th term is 66.

Summation notation is:

$\sum_{n=1}^{16}[5(x-1)-9]$

You could simplify the 5(x-1)-9.

Distribute: 5x-5-9

Add like terms: 5x-14

3 0

3 years ago

Read 2 more answers

ASAP! GIVING BRAINLIEST! Please read the question THEN answer CORRECTLY! NO guessing. Show your work OR give an explaination.

alexandr402 [8]

Answer:

A

Step-by-step explanation:

all of them are positive✔︎

all of them are real numbers✔︎

5 0

3 years ago

Which ordered pair is a solution to this equation? 2x + 6y = 10 (4, 1) (3, 1) (2, 1) (12, 2)

gizmo_the_mogwai [7]

2, 1 because 2 x 2 is 4 + 6 x 1 is 10

4 0

3 years ago

Read 2 more answers