Question 1

Solve the equation $$\frac{3}{x+5} + \frac{2}{2x+1} = \frac{4}{x-2}. $$What is the solution for $$x$$?

Accepted Answer

$$x = -46, x = 47$$

Question 2

Solve the equation by factoring: $$x(x - 11) + 30 = 0. $$What are the solutions?

Accepted Answer

$$x = 5, x = 6$$

Question 3

Solve the equation by completing the square: $$x^2 + 12x + 27 = 0$. What are the solutions?

Accepted Answer

$$x = -3, x = -9$$

Question 4

Find the real solutions, if any, of the equation $$2x^2 = -10x - 4$ using the quadratic formula.

Accepted Answer

$$x = -5 \pm \frac{17}{2}$$

Question 5

Write the expression $$4(7 - 9i) in $$the standard form $$a + bi.$$

Accepted Answer

$$28 - 36i$$

Question 6

Multiply $$(5 + 8i)(3 + 9i)$$ and write the result in the form $$a + bi.$$

Accepted Answer

$$-57 + 69i$$

Question 7

Divide $$\frac{7 + 3i}{3 - 2i}$$ and write the result in the form $$a + bi.$$

Accepted Answer

$$\frac{15}{13} + \frac{23}{13}i$$

Question 8

Solve the equation $$|6x + 4| + 7 = 12. $$What are the solutions?

Accepted Answer

$$x = \frac{1}{6}, x = -\frac{3}{2}$$

Question 9

A candy store wants to mix 50 pounds of chocolate-covered raisins ($$3 per pound) with chocolate-covered macadamia nuts (8 $$per pound) to sell the mixture for $6 per pound. How many pounds of nuts should they mix with the barrel of raisins?

Accepted Answer

75 lb

Question 10

A boat heads upstream 30 miles on a river with a current of 5 mph. The return trip takes an hour less. What was the speed of the boat in still water (rounded to two decimal places)?

Accepted Answer

18.03 mph

Question 11

Find the midpoint of the line segment joining the points $$P_1 = (0.3$$, -0.1)$$ and P_2$ = (-2.4, -1.4).$$

Accepted Answer

$$(-1.05, -0.75)$$

Question 12

List the intercepts for the graph of $$y = x^2$ + 14x + 48.$$

Accepted Answer

$$(-6, 0), (-8, 0), (0, 48)$$

Question 13

Determine whether the graph of $$y = x^2$ - \frac{81}{9x^4$} is $$symmetric with respect to the x-axis, y-axis, and/or the origin.

Accepted Answer

y-axis

Question 14

Find the center $$(h, k)$$ and radius $$r of $$the circle with equation $$x^2$$ + $$y^2 - 4x + 18y + 85 = 36$.

Accepted Answer

$$(2, -9); r = 6$$

Question 15

Find the domain of the function $$g(x) = \frac{2x}{x^2$ - 36}.$$

Accepted Answer

$$\{x | x 
eq -6, 6\}$$

Question 16

For the function $$f(x) = x^2$ - 2x$$, find the average rate of change from $$x = 1 to$$ $$x.$$

Accepted Answer

$$x - 1$$

Question 17

Bob wants to fence in a rectangular garden with 70 feet of fencing. If the garden is $$x$$ feet wide, express the area as a function of $$x.$$

Accepted Answer

$$A(x) = 35x - x^2$

Question 18

The manufacturer of a CD player has found that the revenue $$R (in $$dollars) is $$R(p) = -4p^2$ + 1280p. $$What is the maximum revenue to the nearest whole dollar?

Accepted Answer

$$102,400$$

Question 19

Find the domain of the function $$f(x) = \log(x - 4).$$

Accepted Answer

$$(4, \infty)$$

College Algebra Final Exam Review – Step-by-Step Guidance

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