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Arada [10]
1 year ago
8

Which arrangement shows −275 , −4.1 , −535 , and −3 in order from least to greatest?

Mathematics
1 answer:
vodomira [7]1 year ago
6 0

Answer:

-535, -275, -4.1, -3

Step-by-step explanation:

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PLEASE HELP ASAP<br> Prove that x+a is a factor of (x+a)^5 + (x+c)^5 + (a-c)^5
Brums [2.3K]

P(x)=(x+a)^5 + (x+c)^5 + (a-c)^5

If x+a is a factor of P(x), then -a is a root of P(x).

Therefore

(-a+a)^5+(-a+c)^5+(a-c)^5=0\\\\0^5+(-1(a-c))^5+(a-c)^5=0\\\\(-1)^5(a-c)^5+(a-c)^5=0\\\\-(a-c)^5+(a-c)^5=0\\\\0=0

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Which expression is equivalent to x Superscript negative five-thirds? StartFraction 1 Over RootIndex 5 StartRoot x cubed EndRoot
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Option B : \frac{1}{\sqrt[3]{x^{5} } } is the expression equivalent to x^{-\frac{5}{3}

Explanation:

The given expression is x^{-\frac{5}{3}

Rewriting the expression x^{-\frac{5}{3} using the exponent rule, $a^{-b}=\frac{1}{a^{b}}$

Hence, we get,

\frac{1}{x^{\frac{5}{3} } }

Simplifying, we get,

\frac{1}{\left(x^{5}\right)^{\frac{1}{3}}}

Applying the rule, a^{\frac{1}{n}}=\sqrt[n]{a}

Thus, we have,

\frac{1}{\sqrt[3]{x^{5} } }

Now, we shall determine from the options that which expression is equivalent to x^{-\frac{5}{3}

Option A: \frac{1}{\sqrt[5]{x^{3} } }

The expression \frac{1}{\sqrt[5]{x^{3} } } is not equivalent to simplified expression  \frac{1}{\sqrt[3]{x^{5} } }

Thus, the expression \frac{1}{\sqrt[5]{x^{3} } } is not equivalent to x^{-\frac{5}{3}

Hence, Option A is not the correct answer.

Option B: \frac{1}{\sqrt[3]{x^{5} } }

The expression \frac{1}{\sqrt[3]{x^{5} } } is equivalent to the simplified expression  \frac{1}{\sqrt[3]{x^{5} } }

Thus, the expression \frac{1}{\sqrt[3]{x^{5} } } is equivalent to x^{-\frac{5}{3}

Hence, Option B is the correct answer.

Option C: -\sqrt[3]{x^5}

The expression -\sqrt[3]{x^5} is not equivalent to the simplified expression \frac{1}{\sqrt[3]{x^{5} } }

Thus, the expression -\sqrt[3]{x^5} is not equivalent to x^{-\frac{5}{3}

Hence, Option C is not the correct answer.

Option D: -\sqrt[5]{x^3}

The expression -\sqrt[5]{x^3} is not equivalent to the simplified expression \frac{1}{\sqrt[3]{x^{5} } }

Thus, the expression -\sqrt[5]{x^3} is not equivalent to x^{-\frac{5}{3}

Hence, Option D is not the correct answer.

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