Question 1

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

Accepted Answer

The answer of Solve the equation. \(| x + 19...

Question 2

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

Accepted Answer

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

Question 3

Solve the equation by factoring. $$4 w = 3 - 4 w ^ { 2 }$$

Accepted Answer

A)  $w = - 3 / 2 , w = 2$ 
B)  $w = - 3 / 4 , w = 1 / 2$ 
C)  $w = 1 / 4 , w = - 1 / 2$ 
D)  $w = - 3 / 2 , w = 1 / 2$ 
E)  none of these 
A)  $w = - 3 / 2 , w = 2$ 
B)  $w = - 3 / 4 , w = 1 / 2$ 
C)  $w = 1 / 4 , w = - 1 / 2$ 
D)  $w = - 3 / 2 , w = 1 / 2$ 
E)  none of these

Question 4

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

Accepted Answer

The answer of A pasture is four times as long...

Question 5

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

Accepted Answer

The answer of What quantity of a 40% acid solution...

Question 6

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

Accepted Answer

The answer of Solve the equation. \(4 ( x +...

Question 7

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 ${ } ^ { 0 } C$ ?

Accepted Answer

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 
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 8

Find all real solutions of the equation. $$x ^ { 4 } = 16 x ^ { 2 }$$

Accepted Answer

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 
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 9

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

Accepted Answer

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

Question 10

Solve the equation. $\frac { 10 } { x - 12 } + \frac { 9 } { x + 12 } = \frac { 126 } { x ^ { 2 } - 144 }$

Accepted Answer

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

Question 11

Use the discriminant to determine the number of real solutions of the equation. $x ^ { 2 } - 5.66 x + 2.52 = 0$

Accepted Answer

The answer of Use the discriminant to determine the number...

Question 12

Josiah paints with watercolors on a sheet of paper 28 inches wide by 16 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 112 inches. How wide is the strip of the mat showing around the picture?

Accepted Answer

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

Question 13

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

Accepted Answer

The answer of Solve the inequality. Express the solution using...

Question 14

Find all real solutions of the equation. $\sqrt { 4 x + 25 } + 5 = x$

Accepted Answer

The answer of Find all real solutions of the equation....

Question 15

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

Accepted Answer

The answer of A car rental company offers two plans...

Question 16

Solve the equation by completing the square. $x ^ { 2 } - 5 x - 36 = 0$

Accepted Answer

A)  x = -9, x = -4 
B)  x = 9, x = -4 
C)  x = -9, x = -8 
D)  x = 9, x = 4 
E)  none of these 
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 17

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

Accepted Answer

The answer of Find all solutions of the equation and...

Question 18

Solve the equation by factoring. $$4 w = 3 - 4 w ^ { 2 }$$

Accepted Answer

A)  $w = - 3 / 2 , w = 2$ 
B)  $w = - 3 / 4 , w = 1 / 2$ 
C)  $w = 1 / 4 , w = - 1 / 2$ 
D)  $w = 3 / 2 , w = 1 / 2$ 
E)  none of these 
A)  $w = - 3 / 2 , w = 2$ 
B)  $w = - 3 / 4 , w = 1 / 2$ 
C)  $w = 1 / 4 , w = - 1 / 2$ 
D)  $w = 3 / 2 , w = 1 / 2$ 
E)  none of these

Question 19

Use the discriminant to determine the number of real solutions of the equation. $$x ^ { 2 } - 5.79 x + 2.37 = 0$$

Accepted Answer

A)  no real solutions 
B)  exactly one real solution 
C)  two real solutions 
D)  more than two real solutions 
E)  none of these 
A)  no real solutions 
B)  exactly one real solution 
C)  two real solutions 
D)  more than two real solutions 
E)  none of these

Question 20

Find all real solutions of the equation. $\sqrt { 5 x + 9 } + 3 = x$

Accepted Answer

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

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

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

Solve the equation by factoring. $4 w = 3 - 4 w ^ { 2 }$

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

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

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

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 ${ } ^ { 0 } C$ ?

Find all real solutions of the equation. $x ^ { 4 } = 16 x ^ { 2 }$

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

Solve the equation. $\frac { 10 } { x - 12 } + \frac { 9 } { x + 12 } = \frac { 126 } { x ^ { 2 } - 144 }$

Use the discriminant to determine the number of real solutions of the equation. $x ^ { 2 } - 5.66 x + 2.52 = 0$

Josiah paints with watercolors on a sheet of paper 28 inches wide by 16 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 112 inches. How wide is the strip of the mat showing around the picture?

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

Find all real solutions of the equation. $\sqrt { 4 x + 25 } + 5 = x$

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

Solve the equation by completing the square. $x ^ { 2 } - 5 x - 36 = 0$

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

Solve the equation by factoring. $4 w = 3 - 4 w ^ { 2 }$

Use the discriminant to determine the number of real solutions of the equation. $x ^ { 2 } - 5.79 x + 2.37 = 0$

Find all real solutions of the equation. $\sqrt { 5 x + 9 } + 3 = x$

Functions

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Trigonometric Functions: Right Triangle Approach

Trigonometric Functions: Unit Circle Approach

Conic Sections

Polar Coordinates and Parametric Equations

Vectors in Two and Three Dimensions

Systems of Equations and Inequalities

Matrices and Determinants

Conic Sections

Sequences and Series

Counting and Probability

Filters

Exam 1: Equations and Graphs

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

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

Solve the equation by factoring. 4w=3−4w24 w = 3 - 4 w ^ { 2 }4w=3−4w2

A pasture is four times as long as it is wide. Its area is 230,400ft2230,400 \mathrm { ft } ^ { 2 }230,400ft2 . How long is the pasture?

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

Solve the equation. 4(x+6)+7=−6(x+11)+674 ( x + 6 ) + 7 = - 6 ( x + 11 ) + 674(x+6)+7=−6(x+11)+67

Find all real solutions of the equation. x4=16x2x ^ { 4 } = 16 x ^ { 2 }x4=16x2

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

Solve the equation. 10x−12+9x+12=126x2−144\frac { 10 } { x - 12 } + \frac { 9 } { x + 12 } = \frac { 126 } { x ^ { 2 } - 144 }x−1210​+x+129​=x2−144126​

Use the discriminant to determine the number of real solutions of the equation. x2−5.66x+2.52=0x ^ { 2 } - 5.66 x + 2.52 = 0x2−5.66x+2.52=0

Josiah paints with watercolors on a sheet of paper 28 inches wide by 16 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 112 inches. How wide is the strip of the mat showing around the picture?

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

Find all real solutions of the equation. 4x+25+5=x\sqrt { 4 x + 25 } + 5 = x4x+25​+5=x

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

Solve the equation by completing the square. x2−5x−36=0x ^ { 2 } - 5 x - 36 = 0x2−5x−36=0

Find all solutions of the equation and express them in the form a + bi. x2−2x+10=0x ^ { 2 } - 2 x + 10 = 0x2−2x+10=0

Solve the equation by factoring. 4w=3−4w24 w = 3 - 4 w ^ { 2 }4w=3−4w2

Use the discriminant to determine the number of real solutions of the equation. x2−5.79x+2.37=0x ^ { 2 } - 5.79 x + 2.37 = 0x2−5.79x+2.37=0

Find all real solutions of the equation. 5x+9+3=x\sqrt { 5 x + 9 } + 3 = x5x+9​+3=x

Functions

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Trigonometric Functions: Right Triangle Approach

Trigonometric Functions: Unit Circle Approach

Conic Sections

Polar Coordinates and Parametric Equations

Vectors in Two and Three Dimensions

Systems of Equations and Inequalities

Matrices and Determinants

Conic Sections

Sequences and Series

Counting and Probability

Filters

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

Solve the equation by factoring. $4 w = 3 - 4 w ^ { 2 }$

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

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

Find all real solutions of the equation. $x ^ { 4 } = 16 x ^ { 2 }$

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

Solve the equation. $\frac { 10 } { x - 12 } + \frac { 9 } { x + 12 } = \frac { 126 } { x ^ { 2 } - 144 }$

Use the discriminant to determine the number of real solutions of the equation. $x ^ { 2 } - 5.66 x + 2.52 = 0$

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

Find all real solutions of the equation. $\sqrt { 4 x + 25 } + 5 = x$

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

Solve the equation by completing the square. $x ^ { 2 } - 5 x - 36 = 0$

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

Solve the equation by factoring. $4 w = 3 - 4 w ^ { 2 }$

Use the discriminant to determine the number of real solutions of the equation. $x ^ { 2 } - 5.79 x + 2.37 = 0$

Find all real solutions of the equation. $\sqrt { 5 x + 9 } + 3 = x$