Question 1

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 2

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 3

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

Accepted Answer

The answer of Determine whether the given value is a...

Question 4

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 5

Determine which of the given choices is a solution of the equation. $$2 - 5 x = 8 + x$$

Accepted Answer

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

Question 6

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

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Question 7

Use the discriminant to determine the number of real solutions of the equation.x2 - 5.66x + 2.52 = 0

Accepted Answer

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

Question 8

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 $1200 \mathrm { ft } ^ { 3 }$ of grain?

Accepted Answer

A)  $6.99 \mathrm { ft }$ 
B)  $7.88 \mathrm { ft }$ 
C)  $6.28 \mathrm { ft }$ 
D)  $7.5 \mathrm { ft }$ 
E)  none of these 
A)  $6.99 \mathrm { ft }$ 
B)  $7.88 \mathrm { ft }$ 
C)  $6.28 \mathrm { ft }$ 
D)  $7.5 \mathrm { ft }$ 
E)  none of these

Question 9

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?

Accepted Answer

The answer of Catalina paints with watercolors on a sheet...

Question 10

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?

Accepted Answer

The answer of Al paints with watercolors on a sheet...

Question 11

Solve the equation. $5 x - 3 = 6 x + 4$

Accepted Answer

The answer of Solve the equation. \(5 x - 3...

Question 12

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 13

Determine which of the given choices is a solution of the equation. $2 - 5 x = 8 + x$

Accepted Answer

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

Question 14

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

The answer of Using calculus, it can be shown that...

Question 15

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

Accepted Answer

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 
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 16

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)  $- 11$

Question 17

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

Accepted Answer

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

Question 18

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 19

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

Accepted Answer

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

Question 20

Solve the equation. $$\frac { 7 } { x - 8 } + \frac { 7 } { x + 8 } = \frac { 154 } { x ^ { 2 } - 64 }$$

Accepted Answer

The answer of Solve the equation. \[\frac { 7 }...

Evaluate the expression $( 5 + 10 i ) ( 7 - 9 i )$ 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?

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

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

Determine which of the given choices is a solution of the equation. $2 - 5 x = 8 + x$

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 ${ } ^ { 0 } C$ ?

Use the discriminant to determine the number of real solutions of the equation.x2 - 5.66x + 2.52 = 0

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 $1200 \mathrm { ft } ^ { 3 }$ of grain?

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?

Solve the equation. $5 x - 3 = 6 x + 4$

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

Determine which of the given choices is a solution of the equation. $2 - 5 x = 8 + x$

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

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

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

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

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

Solve the equation. $\frac { 7 } { x - 8 } + \frac { 7 } { x + 8 } = \frac { 154 } { x ^ { 2 } - 64 }$

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

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.

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?

Determine whether the given value is a solution of the equation. 1x−1x−4=1\frac { 1 } { x } - \frac { 1 } { x - 4 } = 1x1​−x−41​=1 , x=2x = 2x=2

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​

Determine which of the given choices is a solution of the equation. 2−5x=8+x2 - 5 x = 8 + x2−5x=8+x

Use the discriminant to determine the number of real solutions of the equation.x2 - 5.66x + 2.52 = 0

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 1200ft31200 \mathrm { ft } ^ { 3 }1200ft3 of grain?

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?

Solve the equation. 5x−3=6x+45 x - 3 = 6 x + 45x−3=6x+4

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

Determine which of the given choices is a solution of the equation. 2−5x=8+x2 - 5 x = 8 + x2−5x=8+x

Solve the equation by factoring. 6w2=11w−36 w ^ { 2 } = 11 w - 36w2=11w−3

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

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

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

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

Solve the equation. 7x−8+7x+8=154x2−64\frac { 7 } { x - 8 } + \frac { 7 } { x + 8 } = \frac { 154 } { x ^ { 2 } - 64 }x−87​+x+87​=x2−64154​

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

Evaluate the expression $( 5 + 10 i ) ( 7 - 9 i )$ 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?

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

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

Determine which of the given choices is a solution of the equation. $2 - 5 x = 8 + x$

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 $1200 \mathrm { ft } ^ { 3 }$ of grain?

Solve the equation. $5 x - 3 = 6 x + 4$

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

Determine which of the given choices is a solution of the equation. $2 - 5 x = 8 + x$

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

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

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

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

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

Solve the equation. $\frac { 7 } { x - 8 } + \frac { 7 } { x + 8 } = \frac { 154 } { x ^ { 2 } - 64 }$