Question 1

A car is listed at $18,500. If a dealership offers a 15% discount, what is the final price of the car after the discount?

Accepted Answer

$$ \15$$,725 $

Question 2

Solve the equation $$ 2(x+3) = 4x - 2 $$ for $$ x .$$

Accepted Answer

$$ x = 3 $$

Question 3

Find the slope of the line that passes through the points $$ (4, 5) $$ and $$ (8, 1) .$$

Accepted Answer

$$ m = -2 $$

Question 4

A solution contains 20% copper. How much of this solution should be mixed with 300 ounces of an alloy that is 50% copper to get an alloy that is 30% copper?

Accepted Answer

$$ 150 $$ ounces

Question 5

Given the function $$ f(x) = x^2$ - 4x + 5 $$, what is the vertex of the parabola?

Accepted Answer

$$ (2, 1) $$

Question 6

If $$ y $$ varies inversely as $$ x $$, and $$ y = 10 $$ when $$ x = 4 $$, what is the inverse variation equation?

Accepted Answer

$$ y = \frac{40}{x} $$

Question 7

A ball with a radius of $$ 2 $$ inches weighs $$ 2.4 $$ pounds. If the weight of a similar ball varies directly with the cube of its radius, what is the weight of a ball with a $$ 3 $$ inch radius?

Accepted Answer

$$ 8.1 $$ pounds

Question 8

Solve the system of equations using any method:
$$ \begin{cases} 2x + y = 4 \ 3x - y = 7 \end{cases} $$

Accepted Answer

Question 9

Simplify the expression $$ (2x + 3)(x - 5) .$$

Accepted Answer

Question 10

A city with a population of $$ 500,000  is $$growing at a rate of $$ 3\% $$ per year. What will the population be in $$ 12 $$ years? (Round to the nearest person.)

Accepted Answer

$$ 712,986 $$

Question 11

Find the domain of the rational function $$ f(x) = \frac{x+2}{x^2$-9} .$$

Accepted Answer

$$ x 
eq -3, x 
eq 3 $$

Question 12

Solve the quadratic equation $$ x^2$ - 4x + 4 = 0 $$ using the square root property.

Accepted Answer

$$ x = 2 $$

Question 13

If the eighth term of an arithmetic sequence is $$ 26 $$ and the first term is $$ 12 $$, what is the common difference?

Accepted Answer

$$ 2 $$

Question 14

Simplify the expression $$ \sqrt{50} .$$

Accepted Answer

$$ 5\sqrt{2} $$

Question 15

Write the exponential equation for $$ \log_2$ x = 5 .$$

Accepted Answer

$$ x = 2^5$ $$

Question 16

A manufacturer needs to mix a solution that is $$ 30\% $$ acid. How many liters of $$ 20\% $$ acid solution must be mixed with $$ 600 $$ liters of $$ 40\% $$ acid solution to get the desired concentration?

Accepted Answer

$$ 600 $$ liters

Question 17

Find the inverse of the function $$ f(x) = \frac{2x-2}{5} .$$

Accepted Answer

Question 18

Solve the exponential equation $$ 64^x = 16 .$$

Accepted Answer

$$ x = \frac{1}{3} $$

Question 19

If $$ y $$ varies directly as $$ x $$, and $$ y = 12 $$ when $$ x = 3 $$, what is the constant of variation?

Accepted Answer

$$ 4 $$

Question 20

Find the sixth term of the geometric sequence whose first term is $$ 5 $$ and whose common ratio is $$ 2 .$$

Accepted Answer

$$ 160 $$

College Algebra Final Exam Review: Comprehensive Study Notes

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