Q: Find the domain of the function $$f(x) = \frac{2x^2$ + 3x}{4x - 12}.$$

$$x \in \mathbb{R},\ x \neq 3$$

Q: Find the domain of $$g(x) = \frac{x^2$ + 9}{16x - 4}.$$

$$x \in \mathbb{R},\ x \neq \frac{1}{4}$$

Question 1

A car dealer reduces the list price of its vehicles by 14%. If one vehicle has a sale price of $28,809.99, what was its original list price to the nearest cent?

Accepted Answer

$$\33$$,489.53$

Question 2

If a rock falls from a height of 20 meters on earth, the height $$s in $$meters after $$t$$ seconds is given by $$s = 20 - 4.9t^2$. When does the rock strike the ground? (approximate to two decimal places)

Accepted Answer

$$2.02$$ seconds

Question 3

Solve the equation algebraically: $$4(x + 2) - 3(5x - 2) = 6x + 2$$

Accepted Answer

$$x = 2$$

Question 4

Donna invested $$33,000 and received a total of 970 in $$interest after one year. If part of the money returned $$4\%$$ interest and the rest returned $$2.25\%$$ interest, how much did she invest at each rate?

Accepted Answer

$$20,000 at$$ $$4\%$$, $$13,000 at$$ $$2.25\%$$

Question 5

A motorboat travels on a river that has a current of $$3$$ mph. The trip upstream takes $$5$$ hours and the return trip downstream takes $$2.5$$ hours. What is the speed of the boat in still water?

Accepted Answer

$$8$$ mph

Question 6

The resistance $$R of a $$wire varies directly with its length $$L$$ and inversely with the square of its diameter $$d. If a $$wire $$1.2$$ meters long and $$0.5$$ centimeters in diameter has a resistance of $$140$$ ohms, what is the resistance of a wire made from the same material that is $$3$$ meters long and has a diameter of $$0.8$$ centimeters? (approximate to two decimal places)

Accepted Answer

$$131.25$$ ohms

Question 7

Find the domain of the function $$f(x) = \frac{2x^2$ + 3x}{4x - 12}.$$

Accepted Answer

$$x \in \mathbb{R},\ x 
eq 3$$

Question 8

An electric company charges a flat monthly fee of $$\12.76$ plus an additional 18$ cents for every kilowatt-hour of usage. Write a linear equation that gives the monthly charge C$ for a customer who uses x$ kilowatt-hours in a month.

Accepted Answer

$$C = 0.18x + 12.76$$

Question 9

Two cyclists leave a city at the same time, one going east and the other going west. The westbound cyclist bikes $$5$$ mph faster than the eastbound cyclist. After $$6$$ hours they are $$246$$ miles apart. How fast is each cyclist riding?

Accepted Answer

Eastbound: $$17$$ mph, Westbound: $$22$$ mph

Question 10

If the area of a rectangle is $$108$$ square inches and the perimeter is $$42$$ inches, what are the dimensions of the rectangle?

Accepted Answer

$$9$$ inches by $$12$$ inches

Question 11

How much water should be added to $$300$$ milliliters of a $$60\%$$ acid solution to make a $$50\%$$ acid solution?

Accepted Answer

$$60$$ milliliters

Question 12

An $$8\%$$ solution and a $$15\%$$ solution are to be mixed in order to obtain $$20$$ ounces of a $$10\%$$ solution. How much of the $$8\%$$ and the $$15\%$$ solutions should be used? (Round answers to 2 decimal places)

Accepted Answer

$$15.71 oz of$$ $$8\%$$, $$4.29 oz of$$ $$15\%$$

Question 13

The volume $$V of a $$gas in a closed container varies inversely with its pressure $$P. If $$the volume is $$600$$ cubic centimeters when the pressure is $$150 mm Hg$$, what is the volume when the pressure is $$200 mm Hg$$?

Accepted Answer

$$450$$ cubic centimeters

Question 14

Find the equation of the line parallel to $$3x + 4y = 2$$ and passing through the point $$(4, 1). $$Express your answer in slope-intercept form.

Accepted Answer

$$y = -\frac{3}{4}x + 4$$

Question 15

Find and simplify $$(f \circ g)(x)$$ for $$f(x) = 8x - 5$$ and $$g(x) = 2x^2$ - x.$$

Accepted Answer

$$16x^2 - 8x - 5$

Question 16

Solve the system of equations: $$\begin{cases} 2x + 5y = 3 \ 3x - y = 9 \end{cases}$$

Accepted Answer

$$x = 2.5$$, $$y = -0.6$$

Question 17

If a rock falls from a height of $$25$$ meters on earth, the height $$s in $$meters after $$t$$ seconds is given by $$s(t) = 25 - 4.9t^2$. When is the height of the rock 10$ meters? (approximate to two decimal places)

Accepted Answer

$$1.74$$ seconds

Question 18

Find the intercepts of the line $$5x - 2y = 8.$$

Accepted Answer

x-intercept: $$\frac{8}{5}$$, y-intercept: $$-4$$

Question 19

Find the domain of $$g(x) = \frac{x^2$ + 9}{16x - 4}.$$

Accepted Answer

$$x \in \mathbb{R},\ x 
eq \frac{1}{4}$$

College Algebra Exam 1 Review – Step-by-Step Guidance

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