Quadrilateral DEFG is a rectangle. If DF = 2(x+5)-7 and EG = 3(x-2), find EG

Mathematics

1 answer:

marishachu [46]4 years ago

5 0

The answer is EG = 21
Hope I helped :)

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Which expression is equivalent to (r Superscript negative 7 Baseline) Superscript 6? r Superscript 42 StartFraction 1 Over r Sup

vodomira [7]

Power rule of exponents says that the power of the power of a exponent is equal to the multiplying both the powers. The expression which is equal to the given expression is,

$\dfrac{1}{(r)^{42}}$

The option B is the correct option.

Given information-

The given expression in the problem is,

$[(r)^{-7}]^5$

<h3>Power rule of exponents</h3>

Power rule of exponents says that the power of the power of a exponent is equal to the multiplying both the powers.

Suppose<em> </em><em>x</em> is a number with power <em>a. </em>The power is power of the power of number <em>x. </em>Then by the power rule of the exponents,

$(x^a)^b=x^{ab}$

Using the power rule of the exponents given expression can be written as,

$[(r)^{-7}]^6=(r)^{-7\times 6} 
$

$[(r)^{-7}]^6=(r)^{-42}$

<h3>Negative exponents rule</h3>

Negative exponents rule says that when a power of a number is negative, then write the number in the denominator with the same power with positive sign.Thus,

$[(r)^{-7}]^6=\dfrac{1}{(r)^{42}}$