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3 years ago

6

Diego is building a kitchen table and a coffee table. The legs of a kitchen table must be twice the height of a coffee table and

there are 4 legs on each table. He writes the expression 4(2x) + 4(x) to model his building plans. What does the coefficient of 4 represent?
A. 4 represents the height of one kitchen table leg.
B. 4 represents the number of legs on each table.
C. 4 represents the height of one coffee table leg.
D. 4 represents the total number of table legs.

2 answers:

jek_recluse [69]3 years ago

8 0

Given : The legs of a kitchen table must be twice the height of a coffee table and there are 4 legs on each table Diego is building.The expression he wrote to model his building plans is 4(2x) + 4(x).

The question is asking us to write what the 4 in the expression represent.

The 4 is representing the number of legs of each table .

Among all the given options :B. 4 represents the number of legs on each table is the right answer.

muminat3 years ago

6 0

The answer is B as the coefficient represents the number of legs

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$(3^{-2} \cdot 4^{-5} \cdot 5^0)^{-3} \cdot (4^{-\frac{4}{3^3} })\cdot 3^3$

Note that

$\boxed{a^{-b} = \dfrac{1}{a^b}, a\neq 0 }$

The denominator can't be 0 because it would be undefined.

So, we can solve the expression inside both parentheses.

$\left(\dfrac{1}{3^2} \cdot \dfrac{1}{4^5} \cdot 5^0 \right)^{-3} \cdot \left(\dfrac{1}{4^{\frac{4}{3^3} } }\right)\cdot 3^3$

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$\left(\dfrac{1}{9216} \right)^{-3} \cdot \left(\dfrac{1}{4^{\frac{4}{27} } }\right)\cdot 27$

$\left(\dfrac{1}{9216} \right)^{-3} \cdot \left(\dfrac{27}{4^{\frac{4}{27} } }\right)$

$\left( \dfrac{1}{\left(\dfrac{1}{9216}\right)^3} \right)\cdot \left(\dfrac{27}{4^{\frac{4}{9} } }\right)$

$\left( \dfrac{1}{\left(\dfrac{1}{9216}\right)^3} \right)\cdot \left(\dfrac{27}{4^{\frac{4}{27} } }\right)$

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Once

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We have

$\left(\dfrac{ 2^{30} \cdot 3^6\cdot 27}{2^{\frac{8}{27} } }\right)$

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$2^{30-\frac{8}{27}} \cdot 3^6\cdot 27 = 2^{\frac{802}{27}} \cdot 3^6 \cdot 3^3$

$2^{\frac{802}{27}} \cdot 3^9$

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