1. Solve each equation.
a.4(-5x + 1) = 6 - (2x - 4)
b.(1/15)(2x + 5) = (x+2) / 9
2. Solve each formula for the individual variable. Assume that the denominator is not 0 if variables appear in the denominator.
a. I = Prt, for P (simple interest)
b. A = ½h(B+b), for h (area of a trapezoid)
3. Simple interest- Levada Qualls borrows $30,900 from her bank to open a florist shop. She agrees to repay the money in 18 months with simple annual interest of 5.5%.
a. How much must she pay the bank in 18 months?
b. How much of the amount in part (a) is interest?
4. Convert to Celsius [C= (5/9)(F - 32)].
77oF
5. Perform mentally- If 120 L of an acid solution is 75% acid, how much pure acid is in the mixture?
6. Solve- The world's largest ice cream cake, made at the Baxy ice cream factory in Beijing, China, on January 16, 2006, had a length 5.9 ft greater than its width. Its perimeter was 51 ft. What were the length and width of this 8-ton cake?
7. Which one or more of the following cannot be a correct equation to solve a geometry problem, if x represents the length of a rectangle?
a. 2x + 2(x-1) = 14
b. -2x + 7(5-x)= 52
c. 5(x+2) + 5x = 10
d.2x + 2(x-3) = 22
8. Distance between cities- On a vacation, Elwyn averaged 50 mph traveling from Denver to Minneapolis.
Returning by a different route that covered the same number of miles, he averaged 55 mph. What is the distance between the two cities if his total traveling time was 32 hr?
9. Speed of a plane- Two planes leave Los Angeles at the same time. One heads south to San Diego, while the other heads north to San Francisco. The San Diego plane flies 50 mph slower than the San Francisco plane. In hr, the planes are 275 mi apart. What are their speeds?
10. Alcohol mixture- How many gallons of pure alcohol should be mixed with 20 gal of a 15% alcohol solution to obtain a mixture that is 25% alcohol?
11. Cooking royalties- Becky Schantz earned $48,000 from royalties on her cookbook. She paid a 28% income tax on these royalties. The balance was invested in two ways, some of it at 3.25% interest and some at 1.75%. The investments produced $904.80 interest per year. Find the amount invested at each rate.
12. Determine whether each statement is true or false. If false, tell why.
a. No real number is a pure imaginary number.
b. A complex number might not be a pure imaginary number.
13. Identify the number as real, complex, pure imaginary, or nonreal complex. (More than one of these descriptions may apply.)
-6 -2i
14. Find the sum or difference. Write the answer in standard form.
3√7 - (4√7 - i) - 4i + (-2√7 + 5i)
15. Find each product. Write the answer in standard form.
a.i(2+7i) (2 - 7i)
b.-5i(4-3i)2
16. Find the quotient. Write the answer in standard form a + bi.
(4-3i) / (4+3i)
17. Solve the equation by the zero-factor property.
x2 + 2x - 8 = 0
18. Solve the equation by completing the square.
x2 - 7x + 12 = 0
19. Francesca claimed that the equation x2 - 19 = 0 cannot be solved by the quadratic formula since there is no value for b. Is she correct?
20. Solve each equation using the quadratic formula.
a.x2 - 4x = -1
b.x2 = 2x -10
21. Solve the equation for the indicated variable. Assume no denominators are 0.
A = πr2, for r
22. Evaluate the discriminant for the equation. Then use it to predict the number of distinct solutions and whether they are rational, irrational, or nonreal complex. Do not solve the equation.
3x2 = 4x - 5
23. Dimensions of a garden- An ecology center wants to set up an experimental garden using 300 m of fencing to enclose a rectangular area of 5000 m2. Find the dimensions of the garden.
24. Width of flower border- A landscape architect has included a rectangular flower bed measuring 9 ft by 5 ft in her plans for a new building. She wants to use two colors of flowers in the bed, one in the center and the other for a border of the same width on all four sides. If she has enough plants to cover 24 ft2 for the border, how wide can the border be?
25. Height of a kite- Grady is flying a kite on 50 ft of string. Its vertical distance from his hand is 10 ft more than the horizontal distance from his hand. Assuming that the string is being held 5 ft above ground level, find the distance from Grady and its vertical distance from the ground.
26. Height of a projectile- A projectile is launched from ground level with an initial velocity of v0 feet per second. Neglecting air resistance, its height in feet t seconds after launch is given by
s = -16t2 + v0t
Find the time(s) that the projectile will (a) reach a height of 80 ft and (b) return to the ground for the given value of v0. Round answers to the nearest hundredth if necessary.
v0 = 16
27. Solve each equation.
a. √(4x + 13) = 2x - 1
b. √2x - x + 4 = 0
c. √2x = √(3x + 12) - 2
d. √(2x - 5) = 2 + √(x - 2)
28. Solve the equation.
3x4 + 10x2 -25 = 0
29. Solve the equation for the indicated variable. Assume all denominators are nonzero.
x2/3 + y2/3 = a2/3, for y
30. Match the following inequality with its equivalent interval notations (a-d).
a. (-∞, -6]
b. (-∞, -6)
c. [-6, -∞)
d. (-∞, 6]
31. The three-part inequality a < x < b means "a is less than x and x is less than b." Which one of the following inequalities is not satisfied by some real number x?
a. -3 < x < 10
b. 0 < x < 6
c. -3 < x < -1
d. -8 < x < -10
32. Solve each inequality. Write each solution set in interval notation.
a.-4x + 3≥-2 + x
b. (2x - 5) / (-8) ≤ 1 -x
33. Break-even interval-Find all intervals where the product will at least break even.
The cost to produce x units of baseball caps is C = 1000x + 6000, while the revenue isR = 500x.
34. Which of the following inequalities has solution set Φ?
a. (x-3)2 ≥0
b. (5x-6)2 ≤ 0
c. (6x+4)2 > 0
d.(8x + 7)2 < 0
35. Solve the following rational inequality. Write the solution set in interval notation.
-6 / (3x-5) ≤ 2
36. Solve each equation.
a.|7 - 3x| = 3
b.|2x+3) / (3x-4)| = 1
37. The equation |5x - 6| = 3x cannot have a negative solution. Why?
38. Determine the solution set of each equation by inspection.
a. -|x| = |x|
b. |-x| = |x|
c. |x2| = |x|
d. -|x| = 9
39. Solve the inequality. Give the solution set using interval notation.
|(3/5) + x| < 1
40. Write the statement as an absolute value equation or inequality.
z is no less than 5 units from 4.