Deck 1: Equations and Graphs

Question 1

Solve the equation. $4 ( x + 6 ) + 7 = - 6 ( x + 11 ) + 67$

Answer 1

$-3$

Question 2

Evaluate the expression $\frac { 90 } { 9 - 3 i }$
and write the result in the form a + bi.

Answer 2

$9 + 3 i$

Question 3

Find all real solutions of the equation. $x ^ { 2 } - \sqrt { 53 } x + 1 = 0$

Answer 3

$x = ( \sqrt { 53 } - 7 ) / 2 , x = ( \sqrt { 53 } + 7 ) / 2$

Question 4

Evaluate the expression $i ^ { 33 }$ and write the result in the form a + bi.

Question 5

Evaluate the expression $( 5 + 10 i ) ( 7 - 9 i )$ and write the result in the form a + bi.

Question 6

Find all real solutions of the equation. $x ^ { 4 } = 4 x ^ { 2 }$

Question 7

An executive in an engineering firm earns a monthly salary plus a Christmas bonus of $8,900. If she earns a total of $96,500 per year, what is her monthly salary?

Question 8

Find all solutions of the equation and express them in the form a + bi. $x ^ { 2 } - 2 x + 10 = 0$

Question 9

Find all real solutions of the equation.

Question 10

Solve the equation.

Question 11

Use the discriminant to determine the number of real solutions of the equation.

Question 12

Catalina paints with watercolors on a sheet of paper a = 22 inches wide by b = 17 inches high. She then places this sheet on a mat so that a uniformly wide strip of the mat shows all around the picture. The perimeter of the mat is 102 inches. How wide is the strip of the mat showing around the picture?

Question 13

The average daily food consumption F of a herbivorous mammal with body weight x, where both F and x are measured in pounds, is given approximately by the equation
. Find the weight x of an elephant that consumes 400 lb of food per day.

Question 14

Solve the equation for $t$
$P = a + ar t$

Question 15

Determine whether the given values of the variables are solutions of the equation.
a)
b)

Question 16

Find all real solutions of the equation.

Question 17

Solve the equation by factoring. $x ^ { 2 } = - 5 ( x - 100 )$

Question 18

Solve the equation by completing the square. $x ^ { 2 } + 4 x - 9 / 4 = 0$

Question 19

What quantity of a 40% acid solution must be mixed with a 10% solution to produce 300 mL of a 30% solution?

Question 20

A pasture is four times as long as it is wide. Its area is $230,400 \mathrm { ft } ^ { 2 }$ How wide is the pasture?

Question 21

Determine whether the given value is a solution of the equation. $\frac { 1 } { x } - \frac { 1 } { x - 4 } = 1$ , $x = 2$

Question 22

A jeweler has three small solid spheres made of gold, of radius 1 mm, 2 mm, and 3 mm. He decides to melt these down and make just one sphere out of them. What will the radius of this larger sphere be? Round the answer to one decimal place.

Question 23

Solve the equation. $| x + 19 | = | 4 x + 7 |$

Question 24

The average daily food consumption F of a herbivorous mammal with body weight x, where both F and x are measured in pounds, is given approximately by the equation $F = 0.2 x ^ { 3 / 4 }$ . Find the weight x of an elephant that consumes 200 lb of food per day.

Question 25

A car rental company offers two plans for renting a car.
Plan A:$40 per day and $0.20 per mile.
Plan B: $60 per day with free unlimited mileage.
For what range of miles will plan B save you money?

Question 26

Solve the equation for $r$
$S = \frac { a } { 1 - \gamma }$

Question 27

Solve the inequality. Express the answer using interval notation.

Question 28

Solve the inequality. Express the solution using interval notation. $| 4 x + 2 | \geq 2$

Question 29

Solve the inequality. Express the solution using interval notation. $- 12 \leq 9 - 3 x \leq 18$

Question 30

Evaluate the expression $( 5 + 10 i ) ( 7 - 9 i )$
and write the result in the form a + bi.

Question 31

Solve the equation.

A) - 12
B) 12
C) 144
D) 6
E) 10

Question 32

Using calculus, it can be shown that if a ball is thrown upward with an initial velocity of 16 ft/s from the top of a building 256 ft high, then its height h above the ground t seconds later will be $h = 256 + 16 t - 16 t ^ { 2 }$
. During what time interval will the ball be at least 64 ft above the ground

Question 33

A pasture is four times as long as it is wide. Its area is
. How wide is the pasture?

Question 34

Solve the equation.3(x + 11) + 1 = - 3(x + 5) + 7

A) 3
B) - 7
C) 10
D) 7
E) - 18

Question 35

What quantity of a 50% acid solution must be mixed with a 20% solution to produce 300 mL of a 40% solution?

A) 100 mL
B) 180 mL
C) 120 mL
D) 240 mL
E) 200 mL

Question 36

Al paints with watercolors on a sheet of paper 22 inches wide by 17 inches high. He then places this sheet on a mat so that a uniformly wide strip of the mat shows all around the picture. The perimeter of the mat is 102 inches. How wide is the strip of the mat showing around the picture?

Question 37

Determine which of the given choices is a solution of the equation.

A) 1
B) - 1
C) 0
D) 2
E) none of these

Question 38

The average daily food consumption F of a herbivorous mammal with body weight x, where both F and x are measured in pounds, is given approximately by the equation . Find the weight x of an elephant that consumes 400 lb of food per day.

Question 39

Find all solutions of the equation $x ^ { 2 } - 2 x + 5 = 0$
and express them in the form a + bi.

Question 40

Solve the equation for $h$ . $A = 2 \pi r h + 2 \pi r ^ { 2 }$

A) $h = \frac { A - r ^ { 2 } } { r }$

B) $h = \frac { A - \pi r ^ { 2 } } { \pi r }$

C) $h = \frac { A - 2 \pi r } { 2 \pi }$

D) $h = A - r$

E) none of these

Question 41

Caitlin paints with watercolors on a sheet of paper 28 inches wide by 16 inches high. She then places this sheet on a mat so that a uniformly wide strip of the mat shows all around the picture. The perimeter of the mat is 112 inches. How wide is the strip of the mat showing around the picture?

A) 8 inches
B) 4 inches
C) 6 inches
D) 2 inches
E) 3 inches

Question 42

Solve the equation.

Question 43

Solve the equation by factoring. $6 w ^ { 2 } = 11 w - 3$

A) $w = 3 / 2 , w = 3 / 5$
B) $w = 1 / 5 , w = 1 / 3$
C) $w = 3 / 11 , w = 3 / 2$
D) $w = 3 / 2 , w = 1 / 3$
E) none of these

Question 44

Solve the inequality. $\left| \frac { x + 5 } { 2 } \right| \geq 5$

A) $[ - 15,5 ]$
B) $[ 15 , \infty )$
C) $( - \infty , - 15 ] \cup [ 5 , \infty )$
D) $( - \infty , - 15 ) \cup ( 5 , \infty )$
E) $Ø$

Question 45

Solve the equation by completing the square.

A) x = -9, x = -4
B) x = 9, x = -4
C) x = -9, x = -8
D) x = 9, x = 4
E) none of these

Question 46

Solve the equation. $| x + 11 | = | 2 x + 5 |$

A) $x = 8$ and $x = - 18 / 5$
B) $x = 3$ and $x = - 13 / 4$
C) $x = 6$ and $x = - 16 / 3$
D) $x = \pm 6$
E) $x = 6$

Question 47

Find all real solutions of the equation.

A) x = 0, x = 20
B) x = 5, x = 20
C) x = 0, x = -25
D) x = 20, x = 80
E) none of these

Question 48

Grain is falling from a chute onto the ground, forming a conical pile whose diameter is always three times its height. How high is the pile (to the nearest hundredth of a foot) when it contains of grain?

Question 49

Solve the inequality. $$| 7 x - 2 | < 4$$

A) $\left[ - \frac { 2 } { 7 } , \frac { 6 } { 7 } \right]$

B) $\left( - \frac { 2 } { 7 } , \frac { 6 } { 7 } \right)$

C) $\left( - \infty , - \frac { 2 } { 7 } \right)$

D) $\left( - \infty , - \frac { 2 } { 7 } \right) \cup \left( \frac { 6 } { 7 } , \infty \right)$

E) $\varnothing$

Question 50

Find all solutions of the equation and express them in the form a + bi

A) x = 3 + 2i, x = 3 - 2i
B) x = 1 + 3i, x = 1 - 3i
C) x = 1, x = - 1
D) x = 4 + 12i, x = 4 - 12i
E) no solutions

Question 51

In the vicinity of a bonfire the temperature T in ${ } ^ { 0 } C$ at a distance of x meters from the center of the fire was given by $T = \frac { 800,000 } { x ^ { 2 } + 400 }$ At what range of distances from the fire's center was the temperature less than 400 ${ } ^ { 0 } C$ ?

A) $x \leq 20 \mathrm {~m}$
B) $x \leq 40 \mathrm {~m}$
C) $x \geq 1 \mathrm {~m}$
D) $x \geq 40 \mathrm {~m}$
E) none of these

Question 52

Evaluate the expression (4 + 7i)(11 - 4i) and write the result in the form a + bi.

Question 53

Evaluate the expression and write the result in the form a + bi

A) 4 + 5i
B) 4 - 5i
C) - 5 - 4i
D) 5 + 4i
E) none of these

Question 54

Solve the inequality. $- 4 \leq 2 - 3 x \leq 14$

A) $( 4,2 )$
B) $[ - 4,2 ]$
C) $[ - 2,4 )$
D) $[ - 4,2 )$
E) $[ - 2,4 ]$

Question 55

Solve the nonlinear inequality. $x ^ { 2 } + 3 x > 4$

A) $( - \infty , - 4 ) \cup ( 1 , \infty )$


B) $( - \infty , - 4 ) \cup ( 2 , \infty )$


C) $( - \infty , - 5 ) \cup ( 1 , \infty )$ ;


D) $( - \infty , - 2 ) \cup ( 1 , \infty )$


E) $( - \infty , - 1 ) \cup ( 4 , \infty )$

Question 56

Find all real solutions of the equation.

A) x = 0, x = 4, x = -4
B) x = 0
C) x = 0, x = 16, x = -16
D) x = 0, x = 16
E) none of these

Question 57

Evaluate the expression and write the result in the form a + bi.

Question 58

Find all real solutions of the equation.

A) 0
B) 0, 11
C) 11
D) 1, 0
E) -11

Question 59

Caitlin paints with watercolors on a sheet of paper 28 inches wide by 16 inches high. She then places this sheet on a mat so that a uniformly wide strip of the mat shows all around the picture. The perimeter of the mat is 112 inches. How wide is the strip of the mat showing around the picture?

A) 8 inches
B) 4 inches
C) 6 inches
D) 2 inches
E) 3 inches

Question 60

Evaluate the expression and write the result in the form

A) -1
B) 1
C) i
D) -i
E) none of these

Question 61

Solve the nonlinear inequality.

Question 62

Solve the inequality. $- 4 \leq 2 - 3 x \leq 14$

A) ( -4, 2 )
B) [ -4, 2 ]
C) [ -2, 4 )
D) [ -4, 2 )
E) [ -2, 4 ]

Question 63

Find all real solutions of the equation. $x ^ { 2 } - \sqrt { 29 } x + 1 = 0$

A) $x = 12 , x = - 17 / 2$

B) $x = \sqrt { 29 } / 2 , x = \sqrt { 17 } / 2$

C) $x = \sqrt { 19 } / 2 , x = - \sqrt { 17 } / 2$

D) $x = \frac { \sqrt { 29 } - 5 } { 2 } , x = \frac { \sqrt { 29 } + 5 } { 2 }$

E) none of these

Question 64

Use the discriminant to determine the number of real solutions of the equation.

Question 65

Find all solutions of the equation and express them in the form a + bi.

Question 66

Using calculus, it can be shown that if a ball is thrown upward with an initial velocity of 16 ft/s from the top of a building 256 ft high, then its height h above the ground t seconds later will be During what time interval will the ball be at least 64 ft above the ground?

Question 67

Find all real solutions of the equation.

Question 68

Find all real solutions of the equation.

Question 69

The average daily food consumption F of a herbivorous mammal with body weight x, where both F and x are measured in pounds, is given approximately by the equation . Find the weight x of an elephant that consumes 400 lb of food per day.

Question 70

Solve the inequality.

Question 71

Solve the equation.

Question 72

Solve the equation by completing the square.

Question 73

A jeweler has three small solid spheres made of gold, of radius 1 mm, 2 mm, and 3 mm. He decides to melt these down and make just one sphere out of them. What will the radius of this larger sphere be? Round the answer to one decimal place

A)
B)
C)
D)
E) none of these

Question 74

Solve the equation by factoring.

Question 75

Evaluate the expression (4 + 7i)(11 - 4i) and write the result in the form a + bi

A) 72 + 61i
B) 44 + 77i
C) 61 + 72i
D) -61 - 72i
E) none of these

Question 76

Solve the inequality.

Question 77

Evaluate the expression and write the result in the form a + bi.

Question 78

Solve the equation.

Question 79

Find all real solutions of the equation.

Question 80

Solve the equation.