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3 years ago

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Which expression is equivalent to the given expression after using the distributive property? 6 · 13 + 6 · 7 A. 6 (13 + 7) B. 6

· 7(13 + 6 ) C. 6(13 + 6) + 7 D. 6 · (13 + 6) · 7

1 answer:

Sauron [17]3 years ago

3 0

Answer:

A

Step-by-step explanation:

6*13+6*7

because 6 in both side

6(13+6)

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Which of the following pairs of functions are inverses of each other?

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A or C

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Which expression is equivalent to (16 x Superscript 8 Baseline y Superscript negative 12 Baseline) Superscript one-half?.

loris [4]

To solve the problem we must know the Basic Rules of Exponentiation.

<h2>Basic Rules of Exponentiation</h2>

$x^ax^b = x^{(a+b)}$
$\dfrac{x^a}{x^b} = x^{(a-b)}$
$(a^a)^b =x^{(a\times b)}$
$(xy)^a = x^ay^a$

$x^{\frac{3}{4}} = \sqrt[4]{x^3}= (\sqrt[3]{x})^4$

The solution of the expression is $\dfrac{4x^4}{y^6}$ .

<h2>Explanation</h2>

Given to us

$(16x^8y^{12})^{\frac{1}{2}}$

Solution

We know that 16 can be reduced to $2^4$ ,

$=(2^4x^8y^{12})^{\frac{1}{2}}$

Using identity $(xy)^a = x^ay^a$ ,

$=(2^4)^{\frac{1}{2}}(x^8)^{\frac{1}{2}}(y^{12})^{\frac{1}{2}}$

Using identity $(a^a)^b =x^{(a\times b)}$ ,

$=(2^{4\times \frac{1}{2}})\ (x^{8\times\frac{1}{2}})\ (y^{12\times{\frac{1}{2}}})$

Solving further

$=2^2x^4y^{-6}$

Using identity $\dfrac{x^a}{x^b} = x^{(a-b)}$ ,

$=\dfrac{2^2x^4}{y^6}$

$=\dfrac{4x^4}{y^6}$

Hence, the solution of the expression is $\dfrac{4x^4}{y^6}$ .

Learn more about Exponentiation:

brainly.com/question/2193820

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2 years ago

Without drawing the graphs, find the points of intersection of the lines: a 7x+4y=23 and 8x–10y=19

emmainna [20.7K]

Answer:

(3,0.5)

Step-by-step explanation:

The given system has equations:

$7x + 4y = 23 \\ 8x - 10y = 19$

Let us multiply the second equation by 4 and the first equation by 10.

$70x + 40y = 230 \\ 32x - 40y = 76$

We add both new equations to get:

$102x = 306 \\ x = \frac{306}{102} = 3$

Put x=3 into the first equation and solve for y.

$7(3) + 4y = 23 \\ 21 + 4y = 23 \\ 4y = 23 - 21 \\ 4y = 2 \\ y = \frac{1}{2}$

The point of intersection is the solution to the system of equation which is (3,0.5)

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3 years ago