Question 1

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

Accepted Answer

The answer of Find all solutions of the equation \(x...

Question 2

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

Accepted Answer

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 
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 3

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?

Accepted Answer

A)  $2 \leq t \leq 5 \mathrm { sec }$ 
B)  $3 \leq t \leq 4 \mathrm { sec }$ 
C)  $0 \leq t \leq 4 \mathrm { sec }$ 
D)  $t \geq 4 \mathrm { sec }$ 
E)  $t \geq 5 \mathrm { sec }$ 
A)  $2 \leq t \leq 5 \mathrm { sec }$ 
B)  $3 \leq t \leq 4 \mathrm { sec }$ 
C)  $0 \leq t \leq 4 \mathrm { sec }$ 
D)  $t \geq 4 \mathrm { sec }$ 
E)  $t \geq 5 \mathrm { sec }$

Question 4

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.

Accepted Answer

The answer of The average daily food consumption F of...

Question 5

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

Accepted Answer

A)  $x = 9 / 2 , x = 2$ 
B)  $x = - 3 / 2 , x = 1 / 2$ 
C)  $x = - 3 / 2 , x = 2$ 
D)  $x = - 9 / 2 , x = 1 / 2$ 
E)  none of these 
A)  $x = 9 / 2 , x = 2$ 
B)  $x = - 3 / 2 , x = 1 / 2$ 
C)  $x = - 3 / 2 , x = 2$ 
D)  $x = - 9 / 2 , x = 1 / 2$ 
E)  none of these

Question 6

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 7

Determine whether the given values of the variables are solutions of the equation. $2 - 5 x = 8 + x$ 
a) $x = 0$ 
b) $x = - 1$

Accepted Answer

The answer of Determine whether the given values of the...

Question 8

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 $F = 0.4 x ^ { 3 / 4 }$ . Find the weight x of an elephant that consumes 400 lb of food per day.

Accepted Answer

A)  15,000 lb 
B)  $20,000 \mathrm { lb }$ 
C)  $10,0001 \mathrm {~b}$ 
D)  5,000 $1 \mathrm {~b}$ 
E)  none of these 
A)  15,000 lb 
B)  $20,000 \mathrm { lb }$ 
C)  $10,0001 \mathrm {~b}$ 
D)  5,000 $1 \mathrm {~b}$ 
E)  none of these

Question 9

Evaluate the expression $\frac { 41 } { 4 - 5 i }$ and write the result in the form a + bi.

Accepted Answer

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

Question 10

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?

Accepted Answer

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

Question 11

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

Accepted Answer

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

Question 12

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.

Accepted Answer

The answer of The average daily food consumption F of...

Question 13

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 14

Solve the inequality. $3 - x \geq 3 x + 15$

Accepted Answer

The answer of Solve the inequality. \(3 - x \geq...

Question 15

Solve the inequality. Express the solution using interval notation. $$- 4 \leq 2 - 3 x \leq 14$$

Accepted Answer

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

Question 16

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

Accepted Answer

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

Question 17

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...

Question 18

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

Accepted Answer

The answer of Evaluate the expression \(( 5 + 10...

Question 19

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

Accepted Answer

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

Question 20

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

Accepted Answer

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

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

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

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.

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

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?

Determine whether the given values of the variables are solutions of the equation. $2 - 5 x = 8 + x$ a) $x = 0$ b) $x = - 1$

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 $F = 0.4 x ^ { 3 / 4 }$ . Find the weight x of an elephant that consumes 400 lb of food per day.

Evaluate the expression $\frac { 41 } { 4 - 5 i }$ and write the result in the form a + bi.

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

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.

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

Solve the inequality. $3 - x \geq 3 x + 15$

Solve the inequality. Express the solution using interval notation. $- 4 \leq 2 - 3 x \leq 14$

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

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

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

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

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

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 solutions of the equation x2−2x+5=0x ^ { 2 } - 2 x + 5 = 0x2−2x+5=0 and express them in the form a + bi.

Solve the equation for hhh . A=2πrh+2πr2A = 2 \pi r h + 2 \pi r ^ { 2 }A=2πrh+2πr2

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=0.2x3/4F = 0.2 x ^ { 3 / 4 }F=0.2x3/4 . Find the weight x of an elephant that consumes 200 lb of food per day.

Solve the equation by completing the square. x2+4x−94=0x ^ { 2 } + 4 x - \frac { 9 } { 4 } = 0x2+4x−49​=0

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?

Determine whether the given values of the variables are solutions of the equation. 2−5x=8+x2 - 5 x = 8 + x2−5x=8+x a) x=0x = 0x=0 b) x=−1x = - 1x=−1

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=0.4x3/4F = 0.4 x ^ { 3 / 4 }F=0.4x3/4 . Find the weight x of an elephant that consumes 400 lb of food per day.

Evaluate the expression 414−5i\frac { 41 } { 4 - 5 i }4−5i41​ and write the result in the form a + bi.

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

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=0.2x3/4F = 0.2 x ^ { 3 / 4 }F=0.2x3/4 . Find the weight x of an elephant that consumes 200 lb of food per day.

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

Solve the inequality. 3−x≥3x+153 - x \geq 3 x + 153−x≥3x+15

Solve the inequality. Express the solution using interval notation. −4≤2−3x≤14- 4 \leq 2 - 3 x \leq 14−4≤2−3x≤14

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

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

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

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

Find all real solutions of the equation. x2−53x+1=0x ^ { 2 } - \sqrt { 53 } x + 1 = 0x2−53​x+1=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 solutions of the equation $x ^ { 2 } - 2 x + 5 = 0$ and express them in the form a + bi.

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

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.

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

Determine whether the given values of the variables are solutions of the equation. $2 - 5 x = 8 + x$ a) $x = 0$ b) $x = - 1$

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 $F = 0.4 x ^ { 3 / 4 }$ . Find the weight x of an elephant that consumes 400 lb of food per day.

Evaluate the expression $\frac { 41 } { 4 - 5 i }$ and write the result in the form a + bi.

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

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.

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

Solve the inequality. $3 - x \geq 3 x + 15$

Solve the inequality. Express the solution using interval notation. $- 4 \leq 2 - 3 x \leq 14$

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

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

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

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

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