Deck 2: Equations and Inequalities

Question 1

Solve the equation. $4 x + 8 = 36$
a. $\quad x = 7$
b. $\quad x = 11$
c. $\quad x = 15$
d. $x = - 11$
e. $x = 1$

Answer 1

A

Question 2

Find the values of x and y. $x + 89 i = y - y i$
a. $\quad x = 89 , y = 89$
b. $\quad x = 89 , y = 178$
c. $x = - 89 , y = - 89$
d. $\quad x = 89 , y = - 89$
e. $\quad x = - 89 , y = 89$

Answer 2

C

Question 3

Solve the inequality. $2 x - 13 < - 7$
a. $\quad ( 3 , \infty )$
b. $[ 3 , \infty )$
c. $\quad ( - 3 , \infty )$
d. $\quad ( - \infty , 3 )$
e. $( - \infty , 3 ]$

Answer 3

D

Question 4

Solve the equation $x ^ { 2 } - 12 x - 45 = 0$ by completing the square.
a. $\quad x = - 3 , x = 6$
b. $\quad x = 3 , x = - 15$
c. $\quad x = 9 , x = 15$
d. $\quad x = - 3 , x = 15$
e. $\quad x = 6 , x = 3$

Question 5

Juan scored 10 points higher on his midterm and 26 points higher on his final than he did on his first exam.If his mean (average) score was 45, what was his score on the first exam? a. $\quad 32$
b. 40
c. 33
d. 31
e. 35

Question 6

x represents a real number.Find any restrictions on x. $$x + 2 = 5$$
a. $( 0 , \infty )$
b. $\quad 0$
c. $\quad \mathbf { x } \geq - 3$
d. $\quad ( - \infty , 2 )$
e. no restrictions

Question 7

Does the equation $6.269 x ^ { 2 } - 3.015 x + 3.445 = 0$ have any roots that are real numbers?
a. no
b. yes

Question 8

Solve the formula $$\frac { x ^ { 2 } } { g ^ { 2 } } + \frac { y ^ { 2 } } { e ^ { 2 } } = 1 ; y$$
for the indicated variable.
a.
$$y = e \sqrt { \left( 1 - \frac { x } { g } \right) \left( 1 + \frac { x } { g } \right) } , y = - e \sqrt { \left( 1 - \frac { x } { g } \right) \left( 1 + \frac { x } { g } \right) }$$
b.
$$y = \sqrt { e ( 1 - x g ) ( 1 + x g ) } , y = - \sqrt { e ( 1 - x g ) ( 1 + x g ) }$$
c.
$$y = \sqrt { e \left( 1 - \frac { x } { g } \right) ^ { 2 } } , y = - \sqrt { e \left( 1 - \frac { x } { g } \right) ^ { 2 } }$$
d.
$$y = e \sqrt { \left( \mathrm { a } - \frac { x } { g } \right) \left( \mathrm { a } + \frac { x } { g } \right) } , y = - e \sqrt { \left( \mathrm { a } - \frac { x } { g } \right) \left( \mathrm { a } + \frac { x } { g } \right) }$$
e. $y = \sqrt { e ( 2 - x g ) ( 1 + x g ) } , y = - \sqrt { e ( 2 - x g ) ( 1 + x g ) }$

Question 9

Simplify the expression. $i ^ { 14 }$
a. $- 6$
b. $- i$
c. $- 1$
$\mathrm { d } . \quad i$
e. 1

Question 10

Factor the expression over the set of complex numbers $9 a ^ { 2 } + 16$
a. $\quad ( - 3 a + 4 i ) ( - 3 a + 4 i )$
b. $\quad ( 3 a + 4 i ) ( 3 a - 4 i )$
c. $\quad ( 3 a + 4 ) ( 3 a - 4 )$
d. $\quad ( 3 + 4 i ) ( 3 - 4 i )$
e. $\quad ( 3 a + 4 i ) ( 3 a + 4 i )$

Question 11

Solve the inequality. $$\frac { 12 ( x - 8 ) } { 5 } \geq \frac { 6 ( x + 4 ) } { 4 }$$
a. $( - 28 , \infty )$
b. $( 28 , \infty )$
c. $[ - 28 , \infty )$
d. $[ 28 , \infty )$
e. none of the above

Question 12

A piece of tin, $y = 16$ inches on a side, is to have four equal squares cut from its corners, as in the illustration. If the edges are then to be folded up to make a box with a floor area of 16 square inches, find the depth of the box.

a. 11 in
b. 13 in
c. $\quad 6$ in
d. 12 in
e. 9 in

Question 13

A piece of sheet metal, 16 inches wide, is bent to form the gutter shown in the illustration.If the cross-sectional area is 32 square inches, find the depth of the gutter.
a. 5 in
b. 6 in
c. 7 in
d. 4 in

Question 14

Jake can wash a car in 40 minutes, while Harold can wash the same car in 50 minutes. How long will it take them to wash the car if they work together? a. $\quad 40$ minutes
b. $\frac { 9 } { 200 }$ minutes
c. 10 minutes
d. $\quad 30$ minutes
e. $\quad \frac { 200 } { 9 }$ minutes

Question 15

Solve the equation $$\frac { 9 } { x - 4 } = 1$$
a. $\quad x = 5$
b. $\quad x = 13$
c. $\quad x = 16$
d. $x = - 16$
e. $\quad x = - 13$

Question 16

A hose can fill a swimming pool in 18 hours.Another hose needs 3 more hours to fill the pool than the two hoses combined.How long would it take the second hose to fill the pool? a. 9 hours
b. 14 hours
c. 18 hours
d. 6 hours
e. 12 hours

Question 17

One morning, John drove 6 hours before stopping to eat.After lunch, he increased his speed by 10 mph. If he completed a 390-mile trip in 9 hours of driving time, how fast did he drive in the morning? a. $\quad 36 \mathrm { mph }$
b. $\quad 40 \mathrm { mph }$
c. $\quad 48 \mathrm { mph }$
d. $\quad 33 \mathrm { mph }$
e. $\quad 43 \mathrm { mph }$

Question 18

Simplify the expression. $i ^ { - 26 }$
a. $- i$
b. $- 3 i$
c. $- 1$
d. 1

Question 19

In electronics, the formula $V = I R$ is called Ohm's law. It gives the relationship in a circuit between the voltage $V$ (in volts), the current $I$ (in amperes), and the resistance $R$ (in ohms).
Find $\mathrm { V }$ when $I = 8 - 7 i$ amperes and $R = 2 + 8 i$ ohms.
a. $\quad V = i$ volts
b. $V = 72 + 78 i$ volts
c. $\quad V = 72$ volts
d. $V = 78$ volts
e. $\quad V = 72 + 50 i$ volts

Question 20

Do the operation and express the answer in a + bi form. $$\frac { 4 + i } { 8 - i \sqrt { 3 } }$$
a. $\quad \frac { 67 + \sqrt { 3 } } { 67 } - \frac { 8 + 4 \sqrt { 3 } } { 67 } i$
b. $\quad \frac { 32 + \sqrt { 3 } } { 67 } + \frac { 8 - 4 \sqrt { 3 } } { 1 } i$
c. $\quad \frac { 67 - \sqrt { 3 } } { 67 } - \frac { 8 - 4 \sqrt { 3 } } { 67 } i$
d. $\quad \frac { 32 - \sqrt { 3 } } { 67 } + \frac { 8 + 4 \sqrt { 3 } } { 67 } i$
e. $\quad \frac { 32 - \sqrt { 3 } } { 67 } - \frac { 8 - 4 \sqrt { 3 } } { 33 } i$

Question 21

Solve the equation $$\frac { 6 } { x - 4 } = 1$$
a. $\quad x = 10$
b. $\quad x = - 10$
c. $\quad x = 2$
d. $x = - 13$
e. $x = 13$

Question 22

Does the equation $6.356 x ^ { 2 } - 8.036 x + 1.688 = 0$ have any roots that are real numbers?
a. yes
b. no

Question 23

Find the values of x and y. $$x + 62 i = y - y i$$
a. $\quad x = 62 , y = 62$
b. $x = 62 , y = - 62$
c. $x = - 62 , y = - 62$
d. $x = 62 , y = 124$
e. $\quad x = - 62 , y = 62$

Question 24

Juan scored 4 points higher on his midterm and 2 points higher on his final than he did on his first exam.If his mean (average) score was 138, what was his score on the first exam? a. 134
b. 138
c. 136
d. 135
e. 143

Question 25

Solve the equation. $2 x + 6 = 22$
a. $x = 8$
b. $x = 18$
c. $x = 2$
d. $x = 14$
e. $x = - 14$

Question 26

One morning, John drove 6 hours before stopping to eat.After lunch, he increased his speed by 10 mph. If he completed a 390-mile trip in 9 hours of driving time, how fast did he drive in the morning? a. $\quad 33 \mathrm { mph }$
b. $\quad 36 \mathrm { mph }$
c. $\quad 48 \mathrm { mph }$
d. $\quad 43 \mathrm { mph }$
e. $\quad 40 \mathrm { mph }$

Question 27

Solve the formula $$\frac { x ^ { 2 } } { d ^ { 2 } } + \frac { y ^ { 2 } } { n ^ { 2 } } = 1 ; y$$
for the indicated variable.
a. $\quad y = \sqrt { n ( 2 - x d ) ( 1 + x d ) } , y = - \sqrt { n ( 2 - x d ) ( 1 + x d ) }$
b. $\quad y = \sqrt { n ( 1 - x d ) ( 1 + x d ) } , y = - \sqrt { n \left( 1 - x d ^ { d } \right) ( 1 + x d ) }$
c. $y = n \sqrt { \left( 1 - \frac { x } { d } \right) \left( 1 + \frac { x } { d } \right) } , y = - n \sqrt { \left( 1 - \frac { x } { d } \right) \left( 1 + \frac { x } { d } \right) }$
d. $y=\sqrt{n\left(1-\frac{x}{d}\right)^{2}}, y=-\sqrt{n\left(1-\frac{x}{d}\right)^{2}}$ e.

e. $y=n \sqrt{\left(\mathrm{a}-\frac{x}{d}\right)\left(\mathrm{a}+\frac{x}{d}\right)}, y=-n \sqrt{\left(\mathrm{a}-\frac{x}{d}\right)\left(\mathrm{a}+\frac{x}{d}\right)}$

Question 28

Express the relationship $4 < C < 18$ in terms of $F$ , if $F = \frac { 3 } { 2 } C + 17$ .
a. $\quad 24 < F < 45$
b. $\quad 22 < F < 43$
c. $\quad 21 < F < 42$
d. $\quad 27 < F < 40$
e. $\quad 23 < F < 44$

Question 29

x represents a real number.Find any restrictions on x. $x + 1 = 8$
a. no restrictions
b. $x \geq - 3$
c. 0
d. $\quad ( - \infty , 1 )$
e. $\quad ( 0 , \infty )$

Question 30

Solve the inequality.Express the solution set in interval notation. $$| 3 x - 2 | < 5$$
a. $\quad ( 3,7 )$
b. $$\left(-1, \frac{3}{7}\right)$$
c. $\left( - 1 , \frac { 7 } { 3 } \right)$
d. $\quad \left( 1 , \frac { 7 } { 3 } \right)$
e. $\left( - \infty , - \frac { 7 } { 3 } \right) \cup ( - 1 , \infty )$

Question 31

A piece of tin, y = 12 inches on a side, is to have four equal squares cut from its corners, as in the illustration.If the edges are then to be folded up to make a box with a floor area of 16 square inches,
Find the depth of the box.
a. 9 in
b. 4 in
c. 8 in
d. 7 in
e. 11 in

Question 32

Simplify the expression. $i ^ { 34 }$
a. 1
b. $\quad i$
c. $- i$
d. $- 6$
e. $- 1$

Question 33

Solve the inequality.Express the solution set in interval notation. $$5 < \left| \frac { x - 14 } { 3 } \right| < 8$$
a. $\quad ( - 38 , - 29 ) \cup ( 1,10 )$
b. $( - 10,1 ) \cup ( 29,38 )$
c. $( - 10 , - 1 ) \cup ( 29,38 )$
d. $( - 1,29 )$
e. none of the above

Question 34

Solve the inequality. $$\frac { 4 } { x } > 2$$
a. $\quad ( 0,2 ]$
b. $\quad ( 0,2 )$
c. $\quad [ 0,2 ]$
d. $\quad ( - \infty , 2 )$
e. $[ 0,2 )$

Question 35

Jake can wash a car in 25 minutes, while Harold can wash the same car in 30 minutes. How long will it take them to wash the car if they work together? a. $\quad \frac { 150 } { 11 }$ minutes
b. 5 minutes
c. 20 minutes
d. $\frac { 11 } { 150 }$ minutes
e. 25 minutes

Question 36

Solve the inequality.Express the solution set in interval notation. $0 < | 4 x + 7 | < 11$
a. $\quad \left( - \frac { 7 } { 4 } , 1 \right)$
b. $\quad \left( - \infty , - \frac { 7 } { 4 } \right) \cup ( 1 , \infty )$
c. $\quad \left( - \frac { 9 } { 2 } , - \frac { 7 } { 4 } \right)$
d. $\quad ( - \infty , - 1 ) \cup \left( \frac { 7 } { 4 } , \infty \right)$
e. $\left( - \frac { 9 } { 2 } , - \frac { 7 } { 4 } \right) \cup \left( - \frac { 7 } { 4 } , 1 \right)$

Question 37

A hose can fill a swimming pool in 12 hours.Another hose needs 2 more hours to fill the pool than the two hoses combined.How long would it take the second hose to fill the pool? a. $\quad 4$ hours
b. 12 hours
c. 10 hours
d. 6 hours
e. 8 hours

Question 38

Simplify the expression. $i ^ { - 26 }$
a. $\quad i$
b. 1
c. $\quad - i$
d. $- 3 i$
e. - 1

Question 39

Solve the equation $x ^ { 2 } - 12 x - 45 = 0$ by completing the square.
a. $\quad x = 6 , x = 10$
b. $\quad x = 3 , x = - 15$
c. $\quad x = 9 , x = 15$
d. $\quad x = - 3 , x = 15$
e. $\quad x = - 3 , x = 6$

Question 40

A piece of sheet metal, 9 inches wide, is bent to form the gutter shown in the illustration.If the cross-sectional area is 10 square inches, find the depth of the gutter.
a. 2 in
b. 3 in
c. $\quad 5$ in
d. $\quad 4$ in

Question 41

Solve the inequality. Express the solution set in interval notation.
$$0 < | 4 x + 3 | < 7$$
a. $\quad \left( - \frac { 5 } { 2 } , - \frac { 3 } { 4 } \right)$
b. $\left( - \frac { 5 } { 2 } , - \frac { 3 } { 4 } \right) \cup \left( - \frac { 3 } { 4 } , 1 \right)$
c. $\left( - \frac { 3 } { 4 } , 1 \right)$
d. $\left( - \infty , - \frac { 3 } { 4 } \right) \cup ( 1 , \infty )$
e. $( - \infty , - 1 ) \cup \left( \frac { 3 } { 4 } , \infty \right)$

Question 42

A piece of tin, y = 17 inches on a side, is to have four equal squares cut from its corners, as in the illustration.If the edges are then to be folded up to make a box with a floor area of 81 square inches,
Find the depth of the box.

a. 4 in
b. 8 in
c. 11 in
d. 7 in
e. 9 in

Question 43

One morning, John drove 11 hours before stopping to eat.After lunch, he increased his speed by 10 mph.If he completed a 730-mile trip in 14 hours of driving time, how fast did he drive in the morning?

A)53 mph
B)43 mph
C)50 mph
D)46 mph
E)58 mph

Question 44

Solve the inequality. $$2 x - 13 < - 1$$
a. $\quad ( - \infty , 6 )$
b. $\quad ( - 6 , \infty )$
c. $\quad [ 6 , \infty )$
d. $\quad ( 6 , \infty )$
e. $\quad ( - \infty , 6 ]$

Question 45

Solve the inequality.Express the solution set in interval notation. $$8 < \left| \frac { x - 23 } { 3 } \right| < 10$$
a. $\quad ( - 7 , - 1 ) \cup ( 47,53 )$
b. $( - 53 , - 47 ) \cup ( 1,7 )$
c. $\quad ( - 1,47 )$
d. none of the above
e. $( - 7,1 ) \cup ( 47,53 )$

Question 46

x represents a real number.Find any restrictions on x. $x + 8 = 3$
a. $\quad ( 0 , \infty )$
b. 0
c. $\quad \mathrm { x } \geq - 3$
d. $( - \infty , 8 )$
e. no restrictions

Question 47

Jake can wash a car in 45 minutes, while Harold can wash the same car in 50 minutes. How long will it take them to wash the car if they work together? a. $\frac { 19 } { 450 }$ minutes
b. $\frac { 450 } { 19 }$ minutes
c. $\quad 40$ minutes
d. 45 minutes
e. 5 minutes

Question 48

Solve the formula $$\frac { x ^ { 2 } } { a ^ { 2 } } + \frac { y ^ { 2 } } { f ^ { 2 } } = 1 ; y$$
for the indicated variable.

Question 49

Factor the expression over the set of complex numbers $4 a ^ { 2 } + 9$
a. $\quad ( 2 + 3 i ) ( 2 - 3 i )$
b. $\quad ( 2 a + 3 ) ( 2 a - 3 )$
c. $\quad ( - 2 a + 3 i ) ( - 2 a + 3 i )$
d. $\quad ( 2 a + 3 i ) ( 2 a - 3 i )$
e. $\quad ( 2 a + 3 i ) ( 2 a + 3 i )$

Question 50

Juan scored 5 points higher on his midterm and 37 points higher on his final than he did on his first exam.If his mean (average) score was 81, what was his score on the first exam? a. 65
b. 74
c. 69
d. $\quad 67$
e. 66

Question 51

Solve the equation. $$4 x + 2 = 22$$
a. $\quad x = 10$
b. $x = 6$
c. $x = - 1$
d. $x = - 6$
e. $x = 5$

Question 52

Solve the inequality. $$\frac { 4 } { x } > 2$$
a. $( 0,2 ]$
b. $\quad ( - \infty , 2 )$
c. $[ 0,2 ]$
d. $\quad ( 0,2 )$
e. $\quad [ 0,2 )$

Question 53

Does the equation $3.788 x ^ { 2 } - 1.254 x + 8.805 = 0$ have any roots that are real numbers?
a. no
b. yes

Question 54

In electronics, the formula V = IR is called Ohm's law.It gives the relationship in a circuit between the voltage V (in volts), the current I (in amperes), and the resistance R (in ohms). Find $\mathrm { V }$ when $I = 5 - 2 i$ amperes and $R = 6 + 9 i \mathrm { ohms }$ .
a. $\quad V = 57$ volts
b. $\quad V = 48 + 57 i$ volts
c. $\quad V = 48 + 33 i$ volts
d. $\quad V = 48$ volts
e. $\quad V = i$ volts

Question 55

Solve the inequality. $\frac { 18 ( x - 8 ) } { 5 } \geq \frac { 9 ( x + 4 ) } { 4 }$
a. none of the above
b. $\quad ( 28 , \infty )$
c. $[ - 28 , \infty )$
d. $\quad ( - 28 , \infty )$
e. $[ 28 , \infty )$

Question 56

Express the relationship $6 < C < 16$ in terms of $F$ , if $F = \frac { 9 } { 2 } C + 17$ .
a. $\quad 42 < F < 87$
b. $\quad 45 < F < 90$
c. $\quad 44 < F < 89$
d. $\quad 43 < F < 88$
e. $\quad 48 < F < 85$

Question 57

Solve the equation $$\frac { 10 } { x - 5 } = 1$$
a. $\quad x = 18$
b. $\quad x = 5$
c. $\quad x = - 15$
d. $\quad x = - 18$
e. $x = 15$

Question 58

Do the operation and express the answer in a + bi form. $$\frac { 3 + i } { 5 - i \sqrt { 7 } }$$
a.
$$\frac { 15 + \sqrt { 7 } } { 32 } + \frac { 5 - 3 \sqrt { 7 } } { 1 } i$$
b. $\quad \frac { 32 + \sqrt { 7 } } { 32 } - \frac { 5 + 3 \sqrt { 7 } } { 32 } i$
c. $\quad \frac { 15 - \sqrt { 7 } } { 32 } + \frac { 5 + 3 \sqrt { 7 } } { 32 } i$
d. $\quad \frac { 32 - \sqrt { 7 } } { 32 } - \frac { 5 - 3 \sqrt { 7 } } { 32 } i$
e. $\quad \frac { 15 - \sqrt { 7 } } { 32 } - \frac { 5 - 3 \sqrt { 7 } } { 16 } i$

Question 59

Solve the equation $x ^ { 2 } - 8 x - 65 = 0$ by completing the square.
a. $\quad x = 4 , x = 9$
b. $\quad x = - 5 , x = 13$
c. $\quad x = 9 , x = 13$
d. $\quad x = - 5 , x = 4$
e. $x = 5 , x = - 13$

Question 60

Solve the inequality.Express the solution set in interval notation. $| 3 x - 4 | < 7$
a. $\quad \left( - 1 , \frac { 11 } { 3 } \right)$
b. $\left( - 1 , \frac { 3 } { 11 } \right)$
c. $\quad \left( 1 , \frac { 11 } { 3 } \right)$
d. $( 3,11 )$
e. $\left( - \infty , - \frac { 11 } { 3 } \right) \cup ( - 1 , \infty )$

Question 61

A college student earns $35 per day delivering advertising brochures door-to-door, plus 25 cents for each person he interviews.How many people did he interview on a day when he earned $46? a. 44
b. 43
c. 45
d. 49
e. 46

Question 62

Solve the formula for $r$ .
$$\frac { 1 } { r } = \frac { 1 } { m } + \frac { 1 } { j }$$
a. $\quad r = m + j$
b. $\quad r = \frac { m j } { m + j }$
c. $\quad r = \frac { m + j } { m j }$
d. $\quad r = m - j$
e. $\quad r = \frac { m j } { m - j }$

Question 63

Find the values of x and y. $$x + 8 i = y - y i$$
a. $\quad x = 8 , y = - 8$
b. $x = - 8 , y = - 8$
c. $\quad x = - 8 , y = 8$
d. $x = 8 , y = 16$
e. $x = 8 , y = 8$

Question 64

Solve the equation. $$\frac { 3 x - 3 } { x + 3 } + \frac { 3 x - 6 } { x - 3 } = \frac { 3 - 6 x } { 3 - x }$$
a. $\quad x = 7$
b. $\quad x = 14$
c. $\quad x = 0$
d. $\quad x = - 6$
e. $\quad x = - 3$

Question 65

A piece of sheet metal, 21 inches wide, is bent to form the gutter shown in the illustration. If the cross-sectional area is 54 square inches, find the depth of the gutter.


a. $\quad 9$ in
b. 6 in
c. $\quad 7$ in
d. 8 in

Question 66

Express the relationship $10 < C < 20$ in terms of $F$ , if $F = \frac { 5 } { 2 } C + 11$ .
a. $\quad 37 < F < 62$
b. $\quad 34 < F < 59$
c. $\quad 36 < F < 61$
d. $\quad 40 < F < 57$
e. $\quad 35 < F < 60$

Question 67

Solve the inequality.Express the solution set in interval notation. $| 5 x - 2 | < 7$
a. $\quad \left( 1 , \frac { 9 } { 5 } \right)$
b. $\left( - 1 , \frac { 5 } { 9 } \right)$
c. $( 5,9 )$
d. $\left( - 1 , \frac { 9 } { 5 } \right)$
e. $\left( - \infty , - \frac { 9 } { 5 } \right) \cup ( - 1 , \infty )$

Question 68

Solve the inequality. $\frac { 10 ( x - 8 ) } { 5 } \geq \frac { 5 ( x + 4 ) } { 4 }$
a. $\quad ( - 28 , \infty )$
b. $[ 28 , \infty )$
c. $\quad ( 28 , \infty )$
d. $[ - 28 , \infty )$
e. none of the above

Question 69

Factor the expression over the set of complex numbers $$25 a ^ { 2 } + 16$$
a. $\quad ( 5 a + 4 i ) ( 5 a - 4 i )$
b. $\quad ( 5 + 4 i ) ( 5 - 4 i )$
c. $\quad ( - 5 a + 4 i ) ( - 5 a + 4 i )$
d. $\quad ( 5 a + 4 i ) ( 5 a + 4 i )$
e. $\quad ( 5 a + 4 ) ( 5 a - 4 )$

Question 70

Simplify the expression. $i ^ { - 34 }$
a. $\quad i$
b. 1
c. $- i$
d. $- 3 i$
e. $- 1$

Question 71

Solve the inequality. $2 x - 15 < - 7$
a. $\quad ( - 4 , \infty )$
b. $\quad ( - \infty , 4 ]$
c. $\quad ( - \infty , 4 )$
d. $( 4 , \infty )$
e. $\quad [ 4 , \infty )$

Question 72

Do the operation and express the answer in $a + b i$ form.
$$\frac { 4 + i } { 4 - i \sqrt { 3 } }$$
a. $\quad \frac { 16 - \sqrt { 3 } } { 19 } + \frac { 4 + 4 \sqrt { 3 } } { 19 } i$
b. $\quad \frac { 16 + \sqrt { 3 } } { 19 } + \frac { 4 - 4 \sqrt { 3 } } { 1 } i$
c. $\quad \frac { 19 + \sqrt { 3 } } { 19 } - \frac { 4 + 4 \sqrt { 3 } } { 19 } i$
d. $\quad \frac { 16 - \sqrt { 3 } } { 19 } - \frac { 4 - 4 \sqrt { 3 } } { 17 } i$
e. $$\frac { 19 - \sqrt { 3 } } { 19 } - \frac { 4 - 4 \sqrt { 3 } } { 19 } i$$

Question 73

A hose can fill a swimming pool in 8 hours.Another hose needs 4 more hours to fill the pool than the two hoses combined.How long would it take the second hose to fill the pool? a. 16 hours
b. 14 hours
c. 12 hours
d. 4 hours
e. 8 hours

Question 74

Simplify the expression. $i ^ { 38 }$
a. $\quad i$
b. $- i$
c. $- 1$
d. $- 6$
e. 1

Question 75

In electronics, the formula $V = I R$ is called Ohm's law. It gives the relationship in a circuit between the voltage $V$ (in volts), the current $I$ (in amperes), and the resistance $R$ (in ohms).
Find $\mathrm { V }$ when $I = 8 - 3 i$ amperes and $R = 6 + 8 i$ ohms.
a. $\quad V = 82$ volts
b. $\quad V = 72$ volts
c. $\quad V = i$ volts
d. $\quad V = 72 + 82 i$ volts
e. $\quad V = 72 + 46 i$ volts

Question 76

Solve the inequality.Express the solution set in interval notation. $3 < \left| \frac { x - 11 } { 4 } \right| < 6$
a. $\quad ( - 35 , - 23 ) \cup ( 1,13 )$
b. $\quad ( - 13 , - 1 ) \cup ( 23,35 )$
c. none of the above
d. $( - 13,1 ) \cup ( 23,35 )$
e. $( - 1,23 )$

Question 77

Solve the equation $$\frac { x } { 5 } + 1 = 7$$
a. 35
b. $x = 23$
c. $\quad x = 40$
d. $x = 28$
e. $x = 30$

Question 78

Solve the inequality. $$\frac { 8 } { x } > 2$$
a. $( 0,4 )$
b. $[ 0,4 )$
c. $\quad ( 0,4 ]$
d. $( - \infty , 4 )$
e. $[ 0,4 ]$

Question 79

Solve the inequality.Express the solution set in interval notation. $$0 < | 8 x + 3 | < 11$$
a. $\quad \left( - \frac { 7 } { 4 } , - \frac { 3 } { 8 } \right) \cup \left( - \frac { 3 } { 8 } , 1 \right)$
b. $\quad \left( - \frac { 3 } { 8 } , 1 \right)$
c. $\quad \left( - \frac { 7 } { 4 } , - \frac { 3 } { 8 } \right)$
d. $\quad ( - \infty , - 1 ) \cup \left( \frac { 3 } { 8 } , \infty \right)$
e. $\left( - \infty , - \frac { 3 } { 8 } \right) \cup ( 1 , \infty )$

Question 80

Solve the formula for $n$ . $p = 4 n$
a. $n = 4 p$
b. $n = 4$
c. $\quad n = \frac { p } { 4 }$
d. $\quad n = p$
e. $n = \frac { 4 } { p }$