Question 1

Find all real solutions of the equation. $\frac { 1 } { x - 4 } - \frac { 25 } { x ^ { 2 } } = 0$

Accepted Answer

A)  x = 0, x = 20 
B)  x = 5, x = 20 
C)  x = 0, x = -25 
D)  x = 20, x = 80 
E)  none of these 
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 2

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

Accepted Answer

The answer of Evaluate the expression \(i ^ { 33...

Question 3

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

Accepted Answer

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

Question 4

Joshua 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 5

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

Accepted Answer

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 
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 6

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

Accepted Answer

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

Question 7

Evaluate the expression $i ^ { 43 }$ and write the result in the form $a + b i$

Accepted Answer

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

Question 8

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?

Accepted Answer

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

Question 9

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

Accepted Answer

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)  $\varnothing$ 
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 10

Solve the equation. $$| 5 - 4 x | + 8 = 16$$

Accepted Answer

A)  $x = - 0.75$ 
B)  $x = \pm 0.75$ 
C)  $x = 2.25$ and $x = 6.25$ 
D)  $x = - 0.75$ and $x = 3.25$ 
E)  $x = 1.25$ and $x = 5.25$ 
A)  $x = - 0.75$ 
B)  $x = \pm 0.75$ 
C)  $x = 2.25$ and $x = 6.25$ 
D)  $x = - 0.75$ and $x = 3.25$ 
E)  $x = 1.25$ and $x = 5.25$

Question 11

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 12

Find all real solutions of the equation. $\frac { 1 } { x - 7 } - \frac { 64 } { x ^ { 2 } } = 0$

Accepted Answer

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

Find all real solutions of the equation. $\frac { 1 } { x - 4 } - \frac { 25 } { x ^ { 2 } } = 0$

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

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

Joshua 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?

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

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

Evaluate the expression $i ^ { 43 }$ and write the result in the form $a + b i$

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?

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

Solve the equation. $| 5 - 4 x | + 8 = 16$

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

Find all real solutions of the equation. $\frac { 1 } { x - 7 } - \frac { 64 } { x ^ { 2 } } = 0$

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

Find all real solutions of the equation. 1x−4−25x2=0\frac { 1 } { x - 4 } - \frac { 25 } { x ^ { 2 } } = 0x−41​−x225​=0

Evaluate the expression i33i ^ { 33 }i33 and write the result in the form a + bi.

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

Joshua 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?

Find all real solutions of the equation. x2−29x+1=0x ^ { 2 } - \sqrt { 29 } x + 1 = 0x2−29​x+1=0

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

Evaluate the expression i43i ^ { 43 }i43 and write the result in the form a+bia + b ia+bi

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?

Solve the inequality. ∣7x−2∣<4| 7 x - 2 | < 4∣7x−2∣<4

Solve the equation. ∣5−4x∣+8=16| 5 - 4 x | + 8 = 16∣5−4x∣+8=16

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

Find all real solutions of the equation. 1x−7−64x2=0\frac { 1 } { x - 7 } - \frac { 64 } { x ^ { 2 } } = 0x−71​−x264​=0

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

Find all real solutions of the equation. $\frac { 1 } { x - 4 } - \frac { 25 } { x ^ { 2 } } = 0$

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

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

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

Evaluate the expression $i ^ { 43 }$ and write the result in the form $a + b i$

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

Solve the equation. $| 5 - 4 x | + 8 = 16$

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

Find all real solutions of the equation. $\frac { 1 } { x - 7 } - \frac { 64 } { x ^ { 2 } } = 0$