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3 years ago

9

What integer is equivalent to

rmula1" title=" {9}^{ \frac{3}{2} } " alt=" {9}^{ \frac{3}{2} } " align="absmiddle" class="latex-formula">

1 answer:

Leokris [45]3 years ago

8 0

Answer:

27

Step-by-step explanation:

${9}^{ \frac{3}{2} } = \sqrt{ {9}^{3} } = \sqrt{ {( {3}^{2} )}^{3} } =\sqrt{ {( {3}^{3} )}^{2} } = {3}^{3} = 3 \times 3 \times 3 = 27$

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when I double my number, add four, and then subtract my number and subtract 3, I get my number plus 1

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3 years ago

The drama club at Central sells hot chocolate and coffee at the high school football games. At the last game, they had sales of

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3 years ago

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Answer:

3√5 or ≈ 6.71

Step-by-step explanation:

The Distance Formula is d = √((x2-x1)² + (y2-y1)²)

<u>Given Points:</u> (-3, 2) and (0, -4)

<u>Points:</u> (x1, y1) and (x2, y2)

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(x2 - x1) = (0 - (-3)) = 3

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3 years ago

What values of a and b make the equation true? StartRoot 648 EndRoot = StartRoot 2 Superscript a Baseline times 3 Superscript b

kramer

Option C: $a=3, b=4$ is the value of a and b

Explanation:

Given that the expression $\sqrt{648}=\sqrt{2^a\times3^b}$

We need to determine the value of a and b

Let us consider the term $\sqrt{648}$ and take the prime factorization of the term 648

Thus, we have,

648 divides by 2,

$648=2 \cdot 324$

324 divides by 2,

$648=2 \cdot 2 \cdot 162$

162 divides by 2,

$648=2 \cdot 2 \cdot 2 \cdot 81$

81 divides by 3,

$648=2 \cdot 2 \cdot 2 \cdot 3 \cdot 27$

27 divides by 3,

$648=2 \cdot 2 \cdot 2 \cdot 3 \cdot 3 \cdot 9$

9 divides by 3,

$648=2 \cdot 2 \cdot 2 \cdot 3 \cdot 3 \cdot 3 \cdot 3$

Thus, we have,

$\sqrt{648}=\sqrt{2^{3} \cdot 3^{4}}$

Therefore, equating the powers of 2 and 3, we get,

$a=3, b=4$

Hence, the value of a and b is 3 and 4

Thus, Option C is the correct answer.

4 0

3 years ago

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