Question 1

Factor the trinomial $$x^2 - 2x - 48$. Which of the following is correct?

Accepted Answer

$$x^2 - 2x - 48 = (x + 6)(x - 8$$)$$

Question 2

Solve the equation $$5x^2 - 9x - 2 = 0$ by factoring. What is the solution set?

Accepted Answer

$$x = -\frac{1}{5},\ 2$$

Question 3

Solve the equation $$x^2 + 2x = 80$ by completing the square. What are the solutions?

Accepted Answer

$$x = 8,\ -10$$

Question 4

Find the real solutions of $$x^2 - 6x - 4 = 0$ using the quadratic formula.

Accepted Answer

$$x = 3 \pm \sqrt{13}$$

Question 5

Solve the equation $$6 + \frac{1}{4x - 12} = x. $$What is the real solution?

Accepted Answer

$$x = 12$$

Question 6

A store manager wants to mix 400 pounds of tea blend to sell at $$2.50 per pound. Earl Grey sells for 4 $$per pound and Orange Pekoe for $2 per pound. How many pounds of each should be used to ensure no change in revenue?

Accepted Answer

100 pounds of Earl Grey and 300 pounds of Orange Pekoe

Question 7

A nut store mixes 60 pounds of peanuts ($$1.50/lb) with cashews (4.00/lb) to $$sell the mixture at $2.00/lb. How many pounds of cashews should be mixed to ensure no change in revenue?

Accepted Answer

15 pounds of cashews

Question 8

A motorboat travels upstream at 29 mph and downstream at 38 mph, taking 20 minutes each way. What is the speed of the current?

Accepted Answer

$$9$$ miles per hour

Question 9

The length of a rectangle is 2 meters less than twice its width. If the area is $$220$$ square meters, what are the dimensions?

Accepted Answer

Width $$= 11$$ meters, Length $$= 20$$ meters

Question 10

Solve the inequality $$4 - 3(1 - x) \leq 3. $$Express the solution in interval notation.

Accepted Answer

$$(-\infty, \frac{2}{3}]$$

Question 11

Solve the inequality $$\frac{x}{4} \geq 1 - \frac{x}{8}. $$Express the solution in interval notation.

Accepted Answer

$$[\frac{8}{3}, \infty)$$

Question 12

Solve the compound inequality $$2 \u003c 5 - \frac{x}{15} \u003c 7. $$Express the solution in interval notation.

Accepted Answer

$$(-10, 15)$$

Question 13

A gardener has 97 feet of fencing to enclose a rectangular garden with a 2-foot border. If the length is twice the width, what are the garden's dimensions?

Accepted Answer

Length $$= 27$$ feet, Width $$= 13.5$$ feet

Question 14

Trent can deliver newspapers in 60 minutes, Lois in 40 minutes. How long would it take them together?

Accepted Answer

24 minutes

Question 15

How much water should be added to 1 gallon of pure antifreeze to obtain a $$15\%$$ antifreeze solution?

Accepted Answer

$$\frac{5}{2}$$ gallons

Question 16

Find the equation of the line parallel to $$x - 2y = -5$$ and passing through $$(0,0).$$

Accepted Answer

$$y = \frac{1}{2}x$$

Question 17

Find the equation of the line perpendicular to $$y = -\frac{1}{3}x - 1$$ and passing through $$(1,3).$$

Accepted Answer

$$y = 3x$$

Question 18

What is the distance between the points $$P_1 = (5$$, -4)$$ and P_2$ = (2, 2)$$?

Accepted Answer

$$\sqrt{45}$$

Question 19

Find the midpoint of the segment joining $$P_1 = (-3$$, 8)$$ and P_2$ = (6, 0).$$

Accepted Answer

$$(1.5, 4)$$

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

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