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2 years ago

Rewrite the expression with the given base. 125^2x with a base of 5

1 answer:

6 0

We should know that
$(a^{m} )^{n} = a^{m*n}$
125 = 5 * 5 * 5

so, the given expression can be rewritten as following 
$125^{2x} = (5*5*5)^{2x} = ( 5^{3} )^{2x} = 5^{3*2x} =5^{6x}$

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A pyramid has a square base with sides of length s. The height of the pyramid is equal to - of the length of a side on the base.

Vera_Pavlovna [14]

<h3>Question:</h3>

A pyramid has a square base with sides of length s. The height of the pyramid is equal to 1/2 of the length of a side on the base. Which formula represents the volume of the pyramid?

<h3>Answer:</h3>

The formula represents the volume of the pyramid is:

$V=\frac{1}{6}s^3$

<h3>Solution:</h3>

The volume of square pyramid is given by formula:

$V = \frac{1}{3} a^2h$

Where, "h" is the height of pyramid

"a" is the length of side of base

Here given that, pyramid has a square base with sides of length s

Therefore,

a = s

The height of the pyramid is equal to 1/2 of the length of a side on the base

$h = \frac{1}{2} \times s\\\\h = \frac{s}{2}$

Thus the volume of pyramid becomes:

$V = \frac{1}{3} \times s^2 \times \frac{s}{2}\\\\V = \frac{s^3}{6}$

$\boxed{V=\frac{1}{6}s^3}$

Thus the formula represents the volume of the pyramid is $\frac{s^3}{6}$

5 0

3 years ago

ALI. calonades i TONS QUESTIONS 1 begun bow PORT RT pod is 8.1.1Give a reason why P2=70

kolbaska11 [484]

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6 0

3 years ago

What is the value of x enter your answer in the Box

Dimas [21]

61.4 is the value of x

7 0

3 years ago

You spend $20 total on tubes of paint and disposable brushes for an art project. Tubes of paint cost $4.00 each and paintbrushes

hram777 [196]

You are buying 2 items so let's use two different variables to represent each:
p = number of tubes of paint
b = number of disposable brushes
cost = price per item × number of items
Equations from information given:
4p + 0.50b = 20 ← from the first 2 sentences
2p = b ← if there are twice as many brushes as paint tubes you need 2 times paint tubes to equal number of brushes
Solve the problem by using substitution... 1b equals 2p so replace b with that:
4p + 0.50(2p) = 20
4p + 1p = 20 ← 0.50 is half so half of 2p is 1p
5p = 20 ← combine like terms
p = 4 ← divide both sides of the equation by 5
Recall the equation 2p = b replace p with 4
2(4) = b
8 = b
ANSWER:
You purchased 4 tubes of paint and 8 disposable brushes.

8 0

2 years ago

There are 96 girls and 72 boys who want to participate in 6th grade intramurals.

Gekata [30.6K]

Answer:

i) 24

ii) 4 girls, 3 boys

Step-by-step explanation:

The GCF is 24

96= 24*4

72= 24*3

I hope this helps!

5 0

2 years ago