Q: Which of the following is the correct equation for the line passing through the points $$(5, 3)$$ and $$(-1, 8)$$?

$$y = -rac{5}{6}x + rac{43}{6}$$

Question 1

Which of the following is the correct equation for the line passing through the points $$(5, 3)$$ and $$(-1, 8)$$?

Accepted Answer

$$y = -rac{5}{6}x + rac{43}{6}$$

Question 2

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 3

Solve the equation $$x^3$$ - $$2x^2$$ + \frac{3}{2}x + 4 = 0$$ to two decimal places. Which of the following is a solution?

Accepted Answer

$$x \approx -2.13$$

Question 4

A rock falls from a height of $$20$$ meters. Its height after $$t$$ seconds is given by $$y = 20 - 4.9t^2$. When does the rock hit the ground? (Round to two decimal places)

Accepted Answer

$$t \approx 2.02$$ seconds

Question 5

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

Accepted Answer

$$x 
eq -6, x 
eq 2$$

Question 6

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 7

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

Accepted Answer

$$60 mL$$

Question 8

An electric company charges a flat monthly fee of $$\12.76$ plus 0.18$ per kilowatt-hour. Which equation gives the monthly charge C$ for x$ kilowatt-hours?

Accepted Answer

$$C = 12.76 + 0.18x$$

Question 9

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

Accepted Answer

$$V = 450 cm$^3$$

Question 10

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

Accepted Answer

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

Question 11

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

Accepted Answer

$$x = 3, y = 1$$

Question 12

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

$$9 in by$$ $$12 in$$

Question 13

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

Accepted Answer

$$14.29 oz$$

Question 14

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

Accepted Answer

$$21$$ mph

Question 15

Find the domain of $$h(x) = \sqrt{2 + 5x}.$$

Accepted Answer

$$x \geq -0.4$$

Question 16

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? (Round to two decimal places)

Accepted Answer

$$131.25$$ ohms

Question 17

Which of the following is the equation of a line parallel to $$3x + 4y = 2$$ and passing through $$(4, 1)$$?

Accepted Answer

$$3x + 4y = 16$$

Question 18

Solve for $$x$$: $$\sqrt{x - 3} = 0$$

Accepted Answer

$$x = 3$$

Question 19

Find the equation of a line with undefined slope passing through $$(5, 7).$$

Accepted Answer

$$x = 5$$

Question 20

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

Accepted Answer

$$x 
eq 0, x 
eq 4$$

College Algebra Study Guide: Equations, Functions, and Applications

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