Deck 2: Equations and Inequalities

Question 1

The sum of two consecutive numbers is $253$ . Which of the following equations describes this situation?

A) $3 n - 1 = 253$
B) $2 n + 1 = 253$
C) $2 n = 253$
D) $2 n + 2 = 253$
E) $n + 2 = 253$

Answer 1

$2 n + 1 = 253$

Question 2

Translate the following statement into an algebraic expression. $\text { "The speed of an automobile that travels } d \text { miles in } t \text { hours" }$

A) $d t$
B) $\frac { t } { d }$
C) $d + t$
D) $\frac { d } { t }$
E) $\frac { d t } { t }$

Answer 2

$\frac { d } { t }$

Question 3

Find two consecutive integers whose product is 7 more than the square of the smaller number.

A) $5,6$
B) $6,7$
C) $7,8$
D) $8,9$
E) $9,10$

Answer 3

$7,8$

Question 4

Solve: $7 ( x + 7 ) = 9 ( 2 - x ) - 2$

A) $x = \frac { 9 } { 8 }$
B) $x = - \frac { 65 } { 2 }$
C) $x = - \frac { 33 } { 8 }$
D) $x = \frac { 65 } { 16 }$
E) $x = - \frac { 33 } { 16 }$

Question 5

Solve the following equation. $9 ( 15 w + 13 ) = 13 ( 7 w + 35 )$

A) $\frac { 170 } { 23 }$
B) $\frac { 57 } { 8 }$
C) $\frac { 169 } { 22 }$
D) $\frac { 172 } { 25 }$
E) $\frac { 173 } { 26 }$

Question 6

Solve: $\frac { 1 } { x - 6 } + \frac { 2 } { x + 2 } = \frac { 3 } { x ^ { 2 } - 4 x - 12 }$

A) $x = \frac { 7 } { 3 }$
B) $x = - \frac { 4 } { 3 }$
C) $x = - \frac { 5 } { 3 }$
D) $x = \frac { 13 } { 3 }$
E) $x = \frac { 1 } { 3 }$

Question 7

Solve: $\frac { x } { 8 } - \frac { x } { 2 } = 7 + \frac { 7 x } { 16 }$

A) $x = - \frac { 112 } { 13 }$
B) $x = - \frac { 8 } { 3 }$
C) $x = - 16$
D) $x = - \frac { 3 } { 8 }$
E) $x = \frac { 112 } { 3 }$

Question 8

Solve the equation below. $( x + 4 ) ^ { 2 } + ( x + 2 ) = ( x + 4 ) ( x + 2 )$

A) $x = 1 \frac { 1 } { 3 }$
B) $x = - 3 \frac { 1 } { 3 }$
C) $x = - 2 \frac { 2 } { 3 }$
D) $x = - \frac { 1 } { 3 }$
E) $x = 4 \frac { 2 } { 3 }$

Question 9

Your weekly paycheck is 20% more than your coworker's. Your two paychecks total $1034. Find the amount of your paycheck.

A)$529
B)$470
C)$434
D)$481
E)$564

Question 10

Determine which of the following values of x is a solution to the equation $5 + \frac { 1 } { x + 4 } = 6$ .

A) $x = - 3$
B) $x = - \frac { 3 } { 5 }$
C) $x = - 4$
D) $x = 5$
E) $x = 3$

Question 11

Suppose a lunch consisting of a large hamburger, large fries and large soft drink at a fast food chain contains 1280 calories. A lunch consisting of a small hamburger, small fries and a small soft drink at the same fast food chain contains 740 calories. Find the percent change in calories from the smaller to the larger lunch. Round to the nearest hundredth of a percent.

A)72.97% increase
B)42.19% increase
C)42.19% decrease
D)72.97% decrease
E)57.81% increase

Question 12

The length of a rectangle is 8 feet less than 3 times the width of a rectangle. If the perimeter of the rectangle is $184$ feet, find the width and the length.

A) $w = 74 ; l = 92$
B) $w = 18 ; \quad l = 46$
C) $w = 28 ; l = 64$
D) $w = 28 ; l = 76$
E) $w = 25 ; l = 67$

Question 13

You accept a new job with a starting salary of $36,000. You receive a 4.4% raise at the start of your second year, a 7.3% raise at the start of your third year, and a 9.3% raise at the start of your fourth year. Find your salary for the fourth year.

A)$44,078.10
B)$43,214.60
C)$43,732.70
D)$44,423.50
E)$44,768.90

Question 14

Solve for x, rounding your answer to the nearest thousandth. $2.709 - 1.091 ( 4.193 x - 1.134 ) = 4.812 x - 3$

A)0.101
B)0.740
C)0.163
D)-29.255
E)6.436

Question 15

Determine which of the following values of x is a solution to the equation $x ^ { 2 } + 9 x + 20 = 0$ .

A) $x = 4 , x = - 5$
B) $x = - 4$
C) $x = - 4 , x = - 5$
D) $x = - 4 , x = 5$
E) $x = 5$

Question 16

Which of the following equations is not an identity equation?

A) $- 2 + \frac { 1 } { x + 1 } = \frac { - 2 x - 1 } { x + 1 }$
B) $- 2 ( x + 1 ) = - 2 x + 1$
C) $- ( - 2 - x ) = x + 2$
D) $\frac { 2 } { x } + \frac { 1 } { x } = \frac { 3 x } { x ^ { 2 } }$
E) $x ^ { 2 } - 2 ( x + 2 ) = x ^ { 2 } - 2 x - 4$

Question 17

The relationship between the length of an adult's femur (thigh bone) and the height of the adult can be approximated by the linear equations $y = 0.432 x - 10.44$ Female $y = 0.449 x - 12.15$ Male where $y$ is the length of the femur in inches and x is the height of the adult in inches (see figure). An anthropologist discovers a femur belonging to an adult human male. The bone is 12 inches long. Estimate the height of the male. Round to the nearest tenth of an inch.

A)52.6 inches
B)54.4 inches
C)53.8 inches
D)55.0 inches
E)56.9 inches

Question 18

Solve the equation below. $3 x + 6 = 18$

A)4
B)10
C)7
D)-2
E)-9

Question 19

Which of the following equations is not a conditional equation?

A) $- 9 ( x - 7 ) = - 16 x + 49$
B) $- 9 ( x - 7 ) = - 9 x - 7$
C) $x ^ { 2 } - 16 x + 63 = ( x - 9 ) ( x - 7 ) + 3$
D) $x ^ { 2 } - 18 x + 81 = ( x - 9 ) ^ { 2 } + 4 x$
E) $x ^ { 2 } - 9 ( - 7 x + 9 ) = x ^ { 2 } + 63 x - 81$

Question 20

Solve the following equation. $2 x + 13 = 4 x + 12$

A) $\frac { 25 } { 6 }$
B) $\frac { 1 } { 2 }$
C) $- \frac { 1 } { 6 }$
D) $- \frac { 25 } { 2 }$
E)-1

Question 21

The price of a computer fell 10% this year. If the computer now costs $621, how much did it cost last year?

A)$700
B)$650
C)$690
D)$700.0
E)$660

Question 22

Solve the quadratic equation below by factoring. $x ^ { 2 } + x = 72$

A) $x = - 1,8$ .
B) $x = - 9,8$ .
C) $x = - 1,8$
D) $x = - 8,9$
E) $x = 8,9$

Question 23

How much water must be added to 3 liters of a 47% saline solution to dilute it to a 32% saline solution? Round answer to nearest tenth of a liter.

A)1.2 liters
B)1.4 liters
C)1.6 liters
D)1.8 liters
E)2.0 liters

Question 24

Solve $( x - 4 ) ^ { 2 } = 25$ by any convenient method.

A) $x = 7,1$
B) $x = 7 , - 4$
C) $x = 9 , - 1$
D) $x = 10 , - 3$
E) $x = 6,0$

Question 25

To determine the height of a tree, you measure its shadow and the shadow of a five-foot lamppost. The shadow of the lamppost is 4 feet and the shadow of the tree is 45 feet. Assuming both the tree and the lamppost are standing next to each other and perpendicular to the ground, how tall is the tree? Round to the nearest tenth of a foot.

A)56.3 feet
B)42.8 feet
C)49.5 feet
D)36.0 feet
E)59.6 feet

Question 26

Write $x ( x - 5 ) = - 2 x ^ { 2 } + 8$ in general form.

A) $- 3 x ^ { 2 } + 13 = 0$
B) $- x ^ { 2 } - 5 x + 8 = 0$
C) $- x ^ { 2 } + 5 x - 8 = 0$
D) $- 3 x ^ { 2 } + 5 x + 8 = 0$
E) $- 3 x ^ { 2 } - 5 x - 8 = 0$

Question 27

Solve the quadratic equation by any convenient method. $( 4 x - 5 ) ^ { 2 } - 25 = 0$

A) $\frac { 4 } { 5 }$ and $- \frac { 4 } { 5 }$
B) $- \frac { 4 } { 5 }$ and $- \frac { 5 } { 2 }$
C) $- \frac { 4 } { 5 }$ and $0$
D) $- \frac { 5 } { 2 }$ and $0$
E) $\frac { 5 } { 2 }$ and $0$

Question 28

Two friends fly from from one city to another (a distance apart of 2930 miles). It takes 2 hours and 45 minutes to fly the first 1350 miles. At this rate, how long is the entire flight? Round to the nearest hundredth of an hour.

A)5.57 hours
B)5.97 hours
C)5.17 hours
D)6.76 hours
E)4.77 hours

Question 29

The price of a home theater system has been discounted 14%. The sale price is $269. Find the original price of the system.

A)$318.92
B)$316.88
C)$306.66
D)$312.79
E)$323.01

Question 30

Solve $( x - 4 ) ^ { 2 } = 9$ by extracting square roots.

A) $x = 5,3$
B) $x = 5 , - 2$
C) $x = 7,1$
D) $x = 8 , - 1$
E) $x = 4,2$

Question 31

A rectangular pool is 40 feet wide and 65 feet long. It is surrounded on all four sides by a wooden deck of fixed width. The total area enclosed within the perimeter of the deck is 2794 square feet. What is the width of the deck?

A)8 feet
B)3 feet
C)4 feet
D)11 feet
E)9 feet

Question 32

The demand equation for a product is $p = 60 - 0.005 x,$ where $p$ is the price per unit and $x$ is the number of units sold. The total revenue $R$ for selling $x$ units is given by $R = x p = x ( 60 - 0.005 x ).$ How many units must be sold to produce a revenue of $180,000?

A)12,000 units
B)6000 units
C)18,000 units
D)24,000 units
E)30,000 units

Question 33

How many liters of a 27% acid solution should be mixed with 5 liters of a 19% acid solution to produce a 26% solution?

A)6 liters
B)35 liters
C)17 liters
D)4 liters
E)15 liters

Question 34

An investment adviser invested $\$ 120,000$ in two accounts. One investment earned 8% annual simple interest, and the other investment earned 10.5% annual simple interest. The amount of interest earned for 1 year was $\$ 10,850.$ How much was invested in each account?

A) $\$ 97,500$ @ 8%; $\$ 22,500$ @ 10.5%
B) $\$ 77,500$ @ 8%; $\$ 42,500$ @ 10.5%
C)$70,000 @ 8%; $50,000 @ 10.5%
D) $\$ 63,000$ @ 8%; $\$ 57,000$ @ 10.5%
E) $\$ 65,000$ @ 8%; $\$ 55,000$ @ 10.5%

Question 35

Solve $9 + 16 x ^ { 2 } + 24 x = 0$ by factoring.

A) $x = - \frac { 3 } { 4 }$
B) $x = - 4 , - 3$
C) $x = - \frac { 3 } { 4 } , \frac { 3 } { 4 }$
D) $x = 3,4$
E) $x = - \frac { 4 } { 3 } , \frac { 4 } { 3 }$

Question 36

Solve the quadratic equation below by extracting square roots. Round to two decimal places. $3 x ^ { 2 } - 2 \left( x ^ { 2 } - 3 \right) = 15$

A) $\pm 2.05$
B) $\pm 0.33$
C) $\pm 0.22$
D) $\pm 3.00$
E) $\pm 1.41$

Question 37

Solve: $20 x ^ { 2 } + 37 x + 15 = 0$

A) $x = - \frac { 4 } { 5 } , - \frac { 5 } { 3 }$
B) $x = \frac { 3 } { 5 } , - \frac { 4 } { 5 }$
C) $x = \frac { 5 } { 4 } , \frac { 3 } { 5 }$
D) $x = \frac { 5 } { 4 } , - \frac { 5 } { 3 }$
E) $x = - \frac { 5 } { 4 } , - \frac { 3 } { 5 }$

Question 38

Assume that air resistance is negligible, which implies that the position equation $s = - 16 t ^ { 2 } + v _ { 0 } t + s _ { 0 }$ is a reasonable model. A rock is dropped from the top of a 180-foot cliff that overlooks the ocean. How long will it take for the rock to hit the water? Round to the nearest hundredth of a second.

A)7.30 seconds
B)3.35 seconds
C)5.99 seconds
D)4.67 seconds
E)11.25 seconds

Question 39

Use the discriminant to determine the number of real solutions of the quadratic equation below. $4 x ^ { 2 } + 9 x + 3 = 0$

A)no real solutions
B)three real solutions
C)four real solutions
D)one real solution
E)two real solutions

Question 40

Variable costs depend on the number of units produced. Fixed costs are the same regardless of how many units are produced. A company has fixed monthly costs of $11,000 and variable monthly costs of $7.00 per unit. The company has $75,000 available each month to cover costs. Find the greatest number of units the company can produce each month.

A)9142 units per month
B)9146 units per month
C)9149 units per month
D)9152 units per month
E)9135 units per month

Question 41

Solve $0 = 64 x ^ { 2 } + 80 x + 15$ using the quadratic formula.

A) $x = \frac { 5 \pm \sqrt { 10 } } { 8 }$
B) $x = \frac { \pm \sqrt { 10 } } { 8 }$
C) $x = \frac { - 8 \pm \sqrt { 10 } } { 5 }$
D) $x = \frac { - 5 \pm \sqrt { 10 } } { 8 }$
E) $x = \frac { 5 } { 8 }$

Question 42

Find the real solutions of the radical equation. $\sqrt { - 6 - y } = 5$

A)11
B)25
C)121
D)-31
E)-1

Question 43

Use the Quadratic Formula to solve the quadratic equation below. $( y + 2 ) ^ { 2 } = - 2 y$

A) $3 \pm \sqrt { 3 }$
B) $- 3 \pm \sqrt { 3 }$
C) $3 \pm \sqrt { 5 }$
D) $- 3 \pm \sqrt { 5 }$
E) $1 \pm \sqrt { 3 }$

Question 44

Determine the number of real solutions of $36 x ^ { 2 } - 12 x + 61 = 0$ by using the discriminant.

A)2
B)1
C)none

Question 45

Find the real solutions of the polynomial equation below. $x ^ { 6 } - 729 = 0$

A) $x = \pm 6$
B) $x = \pm 2$
C) $x = \pm 3$
D) $x = \pm 4$
E) $x = \pm 1$

Question 46

Solve $- 0.9 x ^ { 2 } + 3 x + 0.5 = 0$ using the quadratic formula. Round answers to nearest thousandth.

A) $x = - 1.071,3.622$
B) $x = - 0.609,3.162$
C) $x = - 0.159,3.492$
D) $x = - 0.036,2.492$
E) $x = 0.309,3.583$

Question 47

A square piece of cardboard is formed into a box by cutting out 2-inch squares from each of the corners and folding up the sides. If the volume of the box needs to be 112.5 cubic inches, what size square piece of cardboard is needed?

A)14.5 inches by 14.5 inches
B)15.0 inches by 15.0 inches
C)5.5 inches by 5.5 inches
D)9.5 inches by 9.5 inches
E)11.5 inches by 11.5 inches

Question 48

Find the real solutions of the polynomial equation below. $x ^ { 3 } - x ^ { 2 } - 36 x + 36 = 0$

A) $x = \pm 6,1$
B) $x = \pm 1,6$
C) $x = \pm 1 , - 6$
D) $x = \pm 6 , - 1$
E) $x = \pm 1$

Question 49

Solve the quadratic equation below using any convenient method. $x ^ { 2 } + 7 x + 3 = 0$

A) $\frac { 7 } { 2 } \pm \frac { \sqrt { 61 } } { 2 }$
B) $- \frac { 7 } { 2 } \pm \frac { \sqrt { 61 } } { 2 }$
C) $- \frac { 7 } { 2 } \pm \frac { \sqrt { 37 } } { 2 }$
D) $\frac { 7 } { 2 } \pm \frac { \sqrt { 37 } } { 2 }$
E) $- \frac { - 9 } { 2 } \pm \frac { \sqrt { 37 } } { 2 }$

Question 50

A veterinarian wishes to use 132 feet of chain-link fencing to enclose a rectangular region and subdivide the region into two smaller rectangular regions, as shown below. If the total enclosed area is 702 square feet, find the dimensions of the enclosed area.

A) $18 \mathrm { ft } \times 39 \mathrm { ft }$ or $13 \mathrm { ft } \times 54 \mathrm { ft }$
B) $9 \mathrm { ft } \times 78 \mathrm { ft }$ or $26 \mathrm { ft } \times 27 \mathrm { ft }$
C) $26 \mathrm { ft } \times 27 \mathrm { ft }$ or $13 \mathrm { ft } \times 54 \mathrm { ft }$
D) $9 \mathrm { ft } \times 78 \mathrm { ft }$ or $18 \mathrm { ft } \times 39 \mathrm { ft }$
E) $18 \mathrm { ft } \times 39 \mathrm { ft }$ or $26 \mathrm { ft } \times 27 \mathrm { ft }$

Question 51

Use the quadratic formula to solve the equation. $- 42 x ^ { 2 } + 61 x - 14 = 0$

A) $x = \frac { 6 } { 7 } , \frac { 7 } { 2 }$
B) $x = - \frac { 2 } { 7 } , \frac { 6 } { 7 }$
C) $x = - \frac { 7 } { 6 } , - \frac { 2 } { 7 }$
D) $x = - \frac { 7 } { 6 } , \frac { 7 } { 2 }$
E) $x = \frac { 7 } { 6 } , \frac { 2 } { 7 }$

Question 52

Use the cost equation $C = 2100 + 0.08 x + 0.004 x ^ { 2 }$ to find the number of units x that a manufacturer can produce when $C = 2600$ . Round answer to the nearest whole unit.

A)365 units
B)357 units
C)344 units
D)336 units
E)330 units

Question 53

Find the real solutions of the polynomial equation. $q ^ { 4 } - 17 q ^ { 2 } + 16 = 0$

A) $1,16$
B) $1 , - 4$
C) $\pm 1 , \pm 16$
D) $\pm 1 , \pm 4$
E) $- 1,16$

Question 54

The demand equation for a product is $p = 40 - 0.0008 x$ where $p$ is the price per unit and $x$ is the number of units sold. The total revenue $R$ for selling $x$ units is given by $R = x p.$ How many units must be sold to produce a revenue of $200,000?

A)5635 units or 54,580 units
B)44,365 units or 74,090 units
C)4580 units or 74,090 units
D)5635 units or 44,365 units
E)5635 units or 74,090 units

Question 55

Solve the following polynomial equation by factoring and using the zero factor property. $x ^ { 4 } - 81 x ^ { 2 } = 0$

A) $0 , \pm 9$
B) $\pm 9 , \pm 81$
C) $0,81$
D) $0,9,81$
E) $\pm 9$

Question 56

A windlass is used to tow a boat to a dock. The figure shows a situation in which there are $y$ feet of rope extended to the boat $x + b$ feet away from the dock. How far is the boat from the dock if $y = 75$ feet and $b = 54$ feet? Round to the nearest tenth of a foot.

A)29.4 feet
B)7.8 feet
C)72.6 feet
D)18.6 feet
E)61.8 feet

Question 57

Find the real solutions of the radical equation. $v = \sqrt { - 9 - v } - 9$

A)-81
B)-9
C)99
D)-18
E)41

Question 58

One number is 1 more than another number. The sum of their squares is 181. Find the numbers.

A)9, 10 or -10, -9
B)2, 3 or -3, -2
C)5, 6 or -6, -5
D)6, 7 or -7, -6
E)7, 8 or -8, -7

Question 59

The height, h, in feet, of a baseball above the ground t seconds after it is hit is given by $h = - 16 t ^ { 2 } + 80 t + 2.5.$ Use this equation to determine the number of seconds, to the nearest tenth of a second, from the time the ball is hit until the ball hits the ground.

A)4.7 s
B)4.8 s
C)4.9 s
D)5.0 s
E)5.1 s

Question 60

Two planes leave simultaneously from the same airport, one flying due east and the other due south. The eastbound plane is flying 50 miles per hour slower than the southbound plane. After 5 hours the planes are 2834 miles apart. Find the speed of the eastbound plane.

A)375 miles per hour
B)425 miles per hour
C)550 miles per hour
D)475 miles per hour
E)500 miles per hour

Question 61

Which of the following is not a solution to the inequality $- 5 \leq \frac { x + 6 } { 12 } \leq 5$ ?

A) $x = - 66$
B) $x = - 68$
C) $x = 51$
D) $x = 49$
E) $x = 6$

Question 62

Find all solutions of $| - 6 x - 3 | = 5$ .

A) $x = - \frac { 1 } { 3 } , \frac { 4 } { 3 }$
B) $x = - \frac { 4 } { 3 } , \frac { 1 } { 3 }$
C) $x = - \frac { 4 } { 3 }$
D) $x = - \frac { 9 } { 5 } , \frac { 11 } { 3 }$
E) $x = - \frac { 1 } { 3 }$

Question 63

A professional painter can paint a kitchen in 10 hours. His apprentice can paint the same kitchen in 14 hours. If they worked together, how long would it take for them to paint the kitchen?

A)12
B) $7 \frac { 23 } { 25 }$
C) $15 \frac { 21 } { 25 }$
D)4
E) $5 \frac { 5 } { 6 }$

Question 64

Which of the following is not a solution to the inequality $| 9 x + 6 | < 7$ ?

A) $x = 0$
B) $x = - \frac { 8 } { 9 }$
C) $x = - \frac { 4 } { 3 }$
D) $x = - \frac { 11 } { 18 }$
E) $x = - \frac { 13 } { 9 }$

Question 65

Use interval notation to express the solution set for the inequality below. $| 12 x + 3 | < 1$

A) $\left( - \infty , - \frac { 1 } { 6 } \right)$
B) $\left[ - \frac { 1 } { 3 } , \infty \right)$
C) $\left( - \frac { 1 } { 3 } , \infty \right)$
D) $\left( - \frac { 1 } { 3 } , - \frac { 1 } { 6 } \right)$
E) $\left( - \infty , - \frac { 1 } { 6 } \right]$

Question 66

Match the inequality $- 1 < x < 5$ with its graph.

A) $~~~~~~~~- 1~~~~~~~~~~5$
B) $~~~~~~~~- 1~~~~~~~~~~5$
C) $5$
D) $~~~~~~~~- 1~~~~~~~~~~5$
E) $~~~~~~~~- 1~~~~~~~~~~5$

Question 67

Use interval notation to express the solution set of the inequality below. $| 3 x - 6 | \geq 3$

A) $[ - 1,1 ]$
B) $[ - 3 , - 1 ]$
C) $[ 1,3 ]$
D) $( - \infty , - 3 ] \cup [ - 1 , \infty )$
E) $( - \infty , 1 ] \cup [ 3 , \infty )$

Question 68

Write an inequality that represents the interval $[ - 4,3 )$ .

A) $- 4 < x < 3$
B) $- 4 \leq x \leq 3$
C) $- 4 < x \leq 3$
D) $- 4 \leq x < 3$
E) $x \geq - 4$

Question 69

Solve the inequality below. $- 1 < \frac { 2 x - 3 } { 4 } < 7$

A) $\frac { 1 } { 2 } < x < \frac { 31 } { 2 }$
B) $- \frac { 3 } { 2 } < x < \frac { 29 } { 2 }$
C) $- \frac { 1 } { 2 } < x < \frac { 31 } { 2 }$
D) $- \frac { 1 } { 2 } < x < \frac { 33 } { 2 }$
E) $\frac { 1 } { 2 } < x < \frac { 33 } { 2 }$

Question 70

Match the inequality $| x | \leq 6$ with its graph.

A) $~~~~~~~~- 6~~~~~~~~~~6$
B) $~~~~~~~~- 6~~~~~~~~~~6$
C) $~~~~~~~~- 6~~~~~~~~~~6$
D) $~~~~~~~~0~~~~~~~~~~6$
E) $~~~~~~~~-6~~~~~~~~~~6$

Question 71

Solve: $| - 5 + 9 x | - 12 < 12$

A) $x < \frac { 29 } { 9 }$
B) $- \frac { 29 } { 9 } < x < \frac { 19 } { 9 }$
C) $- \frac { 19 } { 9 } < x < \frac { 29 } { 9 }$
D) $- \frac { 5 } { 9 } < x < - \frac { 5 } { 9 }$
E)no solution

Question 72

The SMOG (Simplified Measure of Gobbledygook) readability formula estimates the reading grade level required by a person if he or she is to fully understand the written material assessed. The SMOG formula is defined as SMOG reading grade level $= \sqrt { w } + 3$ where w is the number of words that have three or more syllables that should appear in a sample of 30 sentences. A writer of children's books has decided to write a book that can be fully understood by children at the 5th-grade level. What is the maximum number of words with three or more syllables that should appear in any sample of 30 sentences of the book?

A)6
B)8
C)4
D)5
E)7

Question 73

The number of new privately-owned housing projects $H$ (in thousands) started from 2000 to 2005 can be modeled by $H = - 1993 + 204.9 t + \frac { 15,005 } { t },$ $10 \leq t \leq 15$ where $t$ represents the year, with $t = 10$ corresponding to 2000. Use the model to predict the year that about 1,700,000 new housing projects were started.

A)2003
B)2002
C)2001
D)2004
E)2000

Question 74

Find all solutions of $\left( x ^ { 2 } + 9 \right) ^ { 3 / 2 } = 125$ .

A) $x = \pm 4$
B) $x = \sqrt [ 3 ] { 9 }$
C) $x = - 4$
D) $x = 5$
E) $x = \pm \sqrt [ 3 ] { 9 }$

Question 75

A college charters a bus for $1404 to take a group of students to the Fiesta Bowl. When one more students join the trip, the cost per student decreases by $2.00. How many students were in the original group?

A)26
B)28
C)32
D)38
E)46

Question 76

Solve the rational equation below. $\frac { x } { x + 2 } = \frac { x + 7 } { x - 5 }$

A)19
B)-6
C)-8
D)-1
E)-16

Question 77

Match the inequality $| x | \geq 4$ with its graph.

A) $~~~~~~~~-4~~~~~~~~~~4$
B) $~~~~~~~~-4~~~~~~~~~~4$
C) $~~~~~~~~-4~~~~~~~~~~4$
D) $~~~~~~~~0~~~~~~~~~~4$
E) $~~~~~~~~-4~~~~~~~~~~4$

Question 78

Find the real solutions of the equation below involving absolute value. Check your solutions. $| x | = x ^ { 2 } + x - 35$

A) $\pm \sqrt { 35 }$
B) $- \sqrt { 35 } , 7$ .
C) $- \sqrt { 35 } , 7$
D) $\sqrt { 35 } , - 7$
E) $\sqrt { 35 } , 7$

Question 79

Find all solutions of $7 x + 57 = \frac { - 8 } { x }$ .

A) $x = - \frac { 8 } { 7 } , - 8$
B) $x = \frac { 7 } { 8 } , - 7$
C) $x = - \frac { 1 } { 7 } , - 8$
D) $x = - \frac { 7 } { 8 } , 8$
E) $x = - \frac { 1 } { 8 } , - 7$

Question 80

Solve the following absolute value equation for $r.$ $| 6 r - 18 | = 36$

A)-9
B)9
C)-9, 9
D)-3, -9
E)-3, 9