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

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

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

Question 4

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

$$9$$ mph

Question 5

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 6

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 7

An electric company charges a flat monthly fee of $$\12.76$ plus an additional 0.18$ for every kilowatt-hour of usage. Which equation models the monthly charge C$ for x$ kilowatt-hours?

Accepted Answer

$$C = 0.18x + 12.76$$

Question 8

The volume of a gas in a closed container varies inversely with its pressure. If the volume is $$600 cm$^3 at$$ $$150 mm Hg$$, what is the volume when the pressure is $$200 mm Hg$$?

Accepted Answer

$$450 cm$^3$$

Question 9

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 $$0.5 cm in $$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 $$0.8 cm$$? (approximate to two decimal places)

Accepted Answer

$$131.25$$ ohms

Question 10

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 11

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 12

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

Accepted Answer

$$(-\infty, 3) \cup (3, \infty)$$

Question 13

If $$f(x) = 8x - 5$$ and $$g(x) = 2x^2$ - x$$, what is $$(f \circ g)(x)$$?

Accepted Answer

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

Question 14

Solve the inequality $$3x - 2 \u003c 9$$ and $$3x - 2 \leq -3. $$Express your answer in interval notation.

Accepted Answer

$$(-\infty, 0]$$

Question 15

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 16

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

$$14.29 oz of 8$$\%$$, 5.71$ oz of 15\%$$

Question 17

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

Accepted Answer

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

Question 18

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

Accepted Answer

$$x = 0$$, $$y = 0.6$$

Question 19

Find the equation of the line perpendicular to $$3x + 4y = 2$$ and passing through $$(-6, 0). $$Express your answer in slope-intercept form.

Accepted Answer

$$y = \frac{4}{3}x + 8$$

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

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