What is the value of A when we rewrite ((5)/(2))^(x)+((5)/(2))^(x+3) as A*((5)/(2))^(x) ? A=

Factor out common term: Question_prompt: What is the value of A when we rewrite ((5)/(2))^(x)+((5)/(2))^(x+3) as A*((5)/(2))^(x)?Calculate exponent: First, let's factor out ((5)/(2))^(x) from both terms. ((5)/(2))^(x) * (1 + ((5)/(2))^3)Substitute back: Now, calculate ((5)/(2))^3. ((5)/(2))^3 = (5^3)/(2^3) = 125/8Add fractions: Substitute 125/8 back into the factored expression. ((5)/(2))^(x) * (1 + 125/8)Find final value: Add 1 to 125/8 to get a common denominator. (8/8) + (125/8) = (8 + 125)/8 = 133/8Now, we have A as 133/8. A = 133/8

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What is the value of
A when we rewrite
((5)/(2))^(x)+((5)/(2))^(x+3) as
A*((5)/(2))^(x) ?

A=

What is the value of $A$ when we rewrite $\left(\frac{5}{2}\right)^{x}+\left(\frac{5}{2}\right)^{x+3}$ as A. $\left(\frac{5}{2}\right)^{x}$ ? $\newline$ $A=$

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Math Problems

Algebra 1

Compare linear and exponential growth

Full solution

Q. What is the value of

A

when we rewrite

\left(\frac{5}{2}\right)^{x}+\left(\frac{5}{2}\right)^{x+3}

as A.

\left(\frac{5}{2}\right)^{x}

\newline

A=

Factor out common term: Question_prompt: What is the value of $A$ when we rewrite $\left(\frac{5}{2}\right)^{x}+\left(\frac{5}{2}\right)^{x+3}$ as $A\cdot\left(\frac{5}{2}\right)^{x}$ ?
Calculate exponent: First, let's factor out $\left(\frac{5}{2}\right)^x$ from both terms. $\left(\frac{5}{2}\right)^x \cdot \left(1 + \left(\frac{5}{2}\right)^3\right)$
Substitute back: Now, calculate $\left(\frac{5}{2}\right)^3$ . $\left(\frac{5}{2}\right)^3 = \frac{5^3}{2^3} = \frac{125}{8}$
Add fractions: Substitute $\frac{125}{8}$ back into the factored expression. $\newline$ $\left(\frac{5}{2}\right)^{x} \times \left(1 + \frac{125}{8}\right)$
Find final value: Add $1$ to $\frac{125}{8}$ to get a common denominator. $\newline$ $(\frac{8}{8}) + (\frac{125}{8}) = \frac{8 + 125}{8} = \frac{133}{8}$
Find final value: Add $1$ to $125/8$ to get a common denominator. $\newline$ $(8/8) + (125/8) = (8 + 125)/8 = 133/8$ Now, we have $A$ as $133/8$ . $\newline$ $A = 133/8$