How to evaluate rational expressions - SAT Math

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Question

Answer

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Question

If √(ab) = 8, and _a_2 = b, what is a?

Answer

If we plug in _a_2 for b in the radical expression, we get √(_a_3) = 8. This can be rewritten as a_3/2 = 8. Thus, log_a 8 = 3/2. Plugging in the answer choices gives 4 as the correct answer.

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Question

If $\frac{b+c}{c}=\frac{14}{15}$ , then which of the following must be also true?

Answer

$\frac{b+c}{c}=\frac{14}{15}$

$\frac{b}{c}+\frac{c}{c}=\frac{14}{15}$

$\frac{b}{c}+1=\frac{14}{15}$

$\frac{b}{c}+1\ {\color{Red} -1}=\frac{14}{15}\ {\color{Red} -1}$

$\frac{b}{c}=\frac{14}{15}-\frac{15}{15}$

$\frac{b}{c}=-\frac{1}{15}$

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Question

If Jill walks $100:\text{ft}$ in $20:\sec$ , how long will it take Jill to walk $1500:\text{ft}$ ?

Answer

To solve this, we need to set a proportion.

$\frac{100:\text{ft}}{20\sec}=\frac{1500:\text{ft}}{x}$

Cross Multiply

$100\cdot x=1500\cdot 20$

$x=\frac{30000}{100}=300$

So it will take Jill $300 \sec$ to walk $1500: \text{ft}$

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