Question 1

There are $63$ coins in Taylor's pockets, all quarters and dimes. The total value of his change is $ $9.60$ . Find the number of each type of coin.

Accepted Answer

If $x$ is the number of quarters, then there are $( 63 - x )$ dimes. The total value is
$0.25 x + 0.10 ( 63 - x ) = 9.60 \Leftrightarrow$ Thus, there are $x = 22$ quarters and $( 63 - 22 ) = 41$ dimes.

Question 2

Multiply the algebraic expressions using a Special Product Formula and simplify. $( 3 x + 4 y ) ^ { 2 }$

Accepted Answer

$( 3 x + 4 y ) ^ { 2 } = 9 x ^ { 2 } + 24 x y + 16 y ^ { 2 }$

Question 3

Multiply the algebraic expressions using the FOIL method and simplify. $( 4 x - 5 y ) ( 2 x - 4 y )$

Accepted Answer

$( 4 x - 5 y ) ( 2 x - 4 y ) = 8 x ^ { 2 } - 26 x y + 20 y ^ { 2 }$

Question 4

Simplify the expression and eliminate any negative exponents(s).
Assume that all letters denote positive numbers. $\sqrt [ 3 ] { r ^ { 2 } s } \sqrt [ 3 ] { 81 r ^ { 4 } s ^ { 2 } }$

Accepted Answer

The answer of Simplify the expression and eliminate any negative...

Question 5

Evaluate each expression.
(a) $\left( \frac { 5 } { 3 } \right) ^ { 0 } 3 ^ { - 1 }$
(b) $\frac { 3 ^ { - 3 } } { 5 ^ { 0 } }$
(c) $\left( \frac { 1 } { 3 } \right) ^ { - 2 }$

Accepted Answer

The answer of Evaluate each expression.
(a) \(\left( \frac { 5...

Question 6

Find the coordinates of the points shown in the figure.

Accepted Answer

A)  $( 1,2 )$ , $( 3,3 )$ 
B)  $( 1 , - 2 )$ , $( 3,3 )$ 
C)  $( - 1,2 )$ , $( 3 , - 3 )$ 
D)  $( 1 , - 2 )$ , $( 3 , - 3 )$ 
E)  $( 1 , - 2 )$ , $( - 3,3 )$ 
A)  $( 1,2 )$ , $( 3,3 )$ 
B)  $( 1 , - 2 )$ , $( 3,3 )$ 
C)  $( - 1,2 )$ , $( 3 , - 3 )$ 
D)  $( 1 , - 2 )$ , $( 3 , - 3 )$ 
E)  $( 1 , - 2 )$ , $( - 3,3 )$

Question 7

Solve the equation for x. $a x ^ { 2 } - ( 2 a - 1 ) x + ( a - 1 ) = 0 \quad ( a \neq 0 )$

Accepted Answer

The answer of Solve the equation for x. \(a x...

Question 8

The cost C of printing a magazine is jointly proportional to the number of

Accepted Answer

The cost C of printing a magazine is joi

Question 9

Simplify the expression. $\frac { \frac { x } { x - 1 } + \frac { 1 } { x + 1 } } { \frac { 5 } { x - 1 } - \frac { 2 } { x + 1 } }$

Accepted Answer

A)  $\frac { x ^ { 2 } + 2 x - 1 } { x - 1 }$ 
B)  $\frac { 3 x + 7 } { x ^ { 2 } + 2 x - 1 }$ 
C)  $\frac { 3 x + 7 } { x - 1 }$ 
D)  $\frac { x ^ { 2 } - 2 x + 1 } { x - 1 }$ 
E)  $\frac { x ^ { 2 } + 2 x - 1 } { 3 x + 7 }$ 
A)  $\frac { x ^ { 2 } + 2 x - 1 } { x - 1 }$ 
B)  $\frac { 3 x + 7 } { x ^ { 2 } + 2 x - 1 }$ 
C)  $\frac { 3 x + 7 } { x - 1 }$ 
D)  $\frac { x ^ { 2 } - 2 x + 1 } { x - 1 }$ 
E)  $\frac { x ^ { 2 } + 2 x - 1 } { 3 x + 7 }$

Question 10

Multiply the algebraic expressions using a Special Product Formula and simplify. $( 2 x - 5 y ) ^ { 2 } = 4 x ^ { 2 } - 20 x y + 25 y ^ { 2 }$

Accepted Answer

The answer of Multiply the algebraic expressions using a Special...

Question 11

Find the sum, difference, or product. $2 ( 2 - 5 t ) - t ^ { 2 } ( t - 2 ) + \left( t ^ { 4 } - 1 \right)$

Accepted Answer

The answer of Find the sum, difference, or product. \(2...

Question 12

Find an equation of the line with slope $2 / 5$ and $y$ - intercept 1.

Accepted Answer

A) 
 $2 x - 5 y + 5 = 0$ 
B) 
 $x - 5 y + 5 = 0$ 
C) 
 $2 x + 5 y + 5 = 0$ 
D) 
 $x - 5 y - 5 = 0$ 
E) 
 $2 x - 5 y = 0$ 
A) 
 $2 x - 5 y + 5 = 0$ 
B) 
 $x - 5 y + 5 = 0$ 
C) 
 $2 x + 5 y + 5 = 0$ 
D) 
 $x - 5 y - 5 = 0$ 
E) 
 $2 x - 5 y = 0$

Question 13

Perform the indicated operations and simplify. $\left( 1 - x ^ { 2 / 3 } \right) \left( 2 + x ^ { 1 / 3 } \right)$

Accepted Answer

A)  $2 + \sqrt [ 3 ] { x } - 2 ( \sqrt [ 3 ] { x } ) ^ { 3 } + x$ 
B)  $1 + \sqrt [ 3 ] { x } - ( \sqrt [ 3 ] { x } ) ^ { 2 } - x$ 
C)  $2 + \sqrt [ 3 ] { x } - \sqrt [ 3 ] { x } - x ^ { 2 }$ 
D)  $2 + \sqrt [ 3 ] { x } - 2 ( \sqrt [ 3 ] { x } ) ^ { 2 } - x$ 
E)  $2 + \sqrt [ 3 ] { x } + 2 ( \sqrt [ 3 ] { x } ) ^ { 2 }$ 
A)  $2 + \sqrt [ 3 ] { x } - 2 ( \sqrt [ 3 ] { x } ) ^ { 3 } + x$ 
B)  $1 + \sqrt [ 3 ] { x } - ( \sqrt [ 3 ] { x } ) ^ { 2 } - x$ 
C)  $2 + \sqrt [ 3 ] { x } - \sqrt [ 3 ] { x } - x ^ { 2 }$ 
D)  $2 + \sqrt [ 3 ] { x } - 2 ( \sqrt [ 3 ] { x } ) ^ { 2 } - x$ 
E)  $2 + \sqrt [ 3 ] { x } + 2 ( \sqrt [ 3 ] { x } ) ^ { 2 }$

Question 14

Simplify the expression. $\frac { 2 y } { y ^ { 2 } - 1 } + \frac { 1 } { ( y - 1 ) }$

Accepted Answer

A)  $\frac { 3 y + 1 } { ( y - 1 ) ^ { 2 } }$ 
B)  $3 \frac { y + 1 } { ( 3 y - 1 ) ( 3 y + 1 ) }$ 
C)  $\frac { 3 y + 1 } { ( y - 1 ) ( y + 1 ) }$ 
D)  $\frac { y + 1 } { ( y - 1 ) ( y + 1 ) }$ 
E)  $\frac { ( 3 y + 1 ) ( y + 1 ) } { ( y - 1 ) }$ 
A)  $\frac { 3 y + 1 } { ( y - 1 ) ^ { 2 } }$ 
B)  $3 \frac { y + 1 } { ( 3 y - 1 ) ( 3 y + 1 ) }$ 
C)  $\frac { 3 y + 1 } { ( y - 1 ) ( y + 1 ) }$ 
D)  $\frac { y + 1 } { ( y - 1 ) ( y + 1 ) }$ 
E)  $\frac { ( 3 y + 1 ) ( y + 1 ) } { ( y - 1 ) }$

Question 15

Simplify the expression. Assume the letters denote any real numbers. $\sqrt { 36 a ^ { 6 } b ^ { 6 } }$

Accepted Answer

The answer of Simplify the expression. Assume the letters denote...

Question 16

Determine an appropriate viewing rectangle for the equation $y = 2 x ^ { 3 } + x - 3$ and use it to draw the graph.

Accepted Answer

To determine an appropriate viewing rect

Question 17

Simplify the expression. $\frac { 2 x } { x - 3 } - \frac { 2 } { x + 1 }$

Accepted Answer

A)  $\frac { x ^ { 2 } + 2 x + 6 } { ( x - 2 ) ( x + 3 ) }$ 
B)  $\frac { 2 x ^ { 2 } + 6 } { ( x - 3 ) ( x + 1 ) }$ 
C)  $\frac { 2 x ^ { 2 } + 6 } { ( x - 3 ) ( x + 1 ) }$. 
D)  $\frac { x ^ { 2 } + 3 } { ( x - 2 ) ( x + 3 ) }$ 
E)  $\frac { x ^ { 2 } + 1 } { ( x + 2 ) ( x - 3 ) }$ 
A)  $\frac { x ^ { 2 } + 2 x + 6 } { ( x - 2 ) ( x + 3 ) }$ 
B)  $\frac { 2 x ^ { 2 } + 6 } { ( x - 3 ) ( x + 1 ) }$ 
C)  $\frac { 2 x ^ { 2 } + 6 } { ( x - 3 ) ( x + 1 ) }$. 
D)  $\frac { x ^ { 2 } + 3 } { ( x - 2 ) ( x + 3 ) }$ 
E)  $\frac { x ^ { 2 } + 1 } { ( x + 2 ) ( x - 3 ) }$

Question 18

Perform the indicated operations and simplify. $( t + 3 ) ( 2 t - 1 ) - 3 ( t + 2 )$

Accepted Answer

A)  $2 t ^ { 2 } + 6 t + 4$ 
B)  $2 t ^ { 2 } + 2 t - 9$ 
C)  $2 t ^ { 2 } - 2 t - 10$ 
D)  $2 t ^ { 2 } - 3 t - 5$ 
E)  $2 t ^ { 2 } + 5 t + 4$ 
A)  $2 t ^ { 2 } + 6 t + 4$ 
B)  $2 t ^ { 2 } + 2 t - 9$ 
C)  $2 t ^ { 2 } - 2 t - 10$ 
D)  $2 t ^ { 2 } - 3 t - 5$ 
E)  $2 t ^ { 2 } + 5 t + 4$

Question 19

Find three consecutive integers whose sum is 57.

Accepted Answer

Let @#LAT-DLM& be th

Question 20

Factor the expression. $y ^ { 2 } + x y - 2 x ^ { 2 }$

Accepted Answer

A)  $- ( 2 x + x y ) ( y - 2 x )$ 
B)  $- ( 2 x + y ) ( x - y )$ 
C)  $( 2 x - y ) ( x - y )$ 
D)  $( 2 x + y ) ( x + y )$ 
E)  $- ( 2 x + y ) ( x - 2 y )$ 
A)  $- ( 2 x + x y ) ( y - 2 x )$ 
B)  $- ( 2 x + y ) ( x - y )$ 
C)  $( 2 x - y ) ( x - y )$ 
D)  $( 2 x + y ) ( x + y )$ 
E)  $- ( 2 x + y ) ( x - 2 y )$

There are $63$ coins in Taylor's pockets, all quarters and dimes. The total value of his change is $ $9.60$ . Find the number of each type of coin.

Multiply the algebraic expressions using a Special Product Formula and simplify. $( 3 x + 4 y ) ^ { 2 }$

Multiply the algebraic expressions using the FOIL method and simplify. $( 4 x - 5 y ) ( 2 x - 4 y )$

Simplify the expression and eliminate any negative exponents(s). Assume that all letters denote positive numbers. $\sqrt [ 3 ] { r ^ { 2 } s } \sqrt [ 3 ] { 81 r ^ { 4 } s ^ { 2 } }$

Evaluate each expression. (a) $\left( \frac { 5 } { 3 } \right) ^ { 0 } 3 ^ { - 1 }$ (b) $\frac { 3 ^ { - 3 } } { 5 ^ { 0 } }$ (c) $\left( \frac { 1 } { 3 } \right) ^ { - 2 }$

Find the coordinates of the points shown in the figure.

Solve the equation for x. $a x ^ { 2 } - ( 2 a - 1 ) x + ( a - 1 ) = 0 \quad ( a \neq 0 )$

The cost C of printing a magazine is jointly proportional to the number of

Simplify the expression. $\frac { \frac { x } { x - 1 } + \frac { 1 } { x + 1 } } { \frac { 5 } { x - 1 } - \frac { 2 } { x + 1 } }$

Multiply the algebraic expressions using a Special Product Formula and simplify. $( 2 x - 5 y ) ^ { 2 } = 4 x ^ { 2 } - 20 x y + 25 y ^ { 2 }$

Find the sum, difference, or product. $2 ( 2 - 5 t ) - t ^ { 2 } ( t - 2 ) + \left( t ^ { 4 } - 1 \right)$

Find an equation of the line with slope $2 / 5$ and $y$ - intercept 1.

Perform the indicated operations and simplify. $\left( 1 - x ^ { 2 / 3 } \right) \left( 2 + x ^ { 1 / 3 } \right)$

Simplify the expression. $\frac { 2 y } { y ^ { 2 } - 1 } + \frac { 1 } { ( y - 1 ) }$

Simplify the expression. Assume the letters denote any real numbers. $\sqrt { 36 a ^ { 6 } b ^ { 6 } }$

Determine an appropriate viewing rectangle for the equation $y = 2 x ^ { 3 } + x - 3$ and use it to draw the graph.

Simplify the expression. $\frac { 2 x } { x - 3 } - \frac { 2 } { x + 1 }$

Perform the indicated operations and simplify. $( t + 3 ) ( 2 t - 1 ) - 3 ( t + 2 )$

Find three consecutive integers whose sum is 57.

Factor the expression. $y ^ { 2 } + x y - 2 x ^ { 2 }$

Functions

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Trigonometric Functions: Unit Circle Approach

Trigonometric Functions: Right Triangle Approach

Analytic Trigonometry

Polar Coordinates and Parametric Equations

Vectors in Two and Three Dimensions

Systems of Equations and Inequalities

Conic Sections

Sequences and Series

Limits: a Preview of Calculus

Filters

Exam 1: Fundamentals

There are 636363 coins in Taylor's pockets, all quarters and dimes. The total value of his change is $ 9.609.609.60 . Find the number of each type of coin.

Multiply the algebraic expressions using a Special Product Formula and simplify. (3x+4y)2( 3 x + 4 y ) ^ { 2 }(3x+4y)2

Multiply the algebraic expressions using the FOIL method and simplify. (4x−5y)(2x−4y)( 4 x - 5 y ) ( 2 x - 4 y )(4x−5y)(2x−4y)

Simplify the expression and eliminate any negative exponents(s). Assume that all letters denote positive numbers. r2s381r4s23\sqrt [ 3 ] { r ^ { 2 } s } \sqrt [ 3 ] { 81 r ^ { 4 } s ^ { 2 } }3r2s​381r4s2​

Evaluate each expression. (a) (53)03−1\left( \frac { 5 } { 3 } \right) ^ { 0 } 3 ^ { - 1 }(35​)03−1 (b) 3−350\frac { 3 ^ { - 3 } } { 5 ^ { 0 } }503−3​ (c) (13)−2\left( \frac { 1 } { 3 } \right) ^ { - 2 }(31​)−2

Find the coordinates of the points shown in the figure.

Solve the equation for x. ax2−(2a−1)x+(a−1)=0(a≠0)a x ^ { 2 } - ( 2 a - 1 ) x + ( a - 1 ) = 0 \quad ( a \neq 0 )ax2−(2a−1)x+(a−1)=0(a=0)

The cost C of printing a magazine is jointly proportional to the number of

Simplify the expression. xx−1+1x+15x−1−2x+1\frac { \frac { x } { x - 1 } + \frac { 1 } { x + 1 } } { \frac { 5 } { x - 1 } - \frac { 2 } { x + 1 } }x−15​−x+12​x−1x​+x+11​​

Multiply the algebraic expressions using a Special Product Formula and simplify. (2x−5y)2=4x2−20xy+25y2( 2 x - 5 y ) ^ { 2 } = 4 x ^ { 2 } - 20 x y + 25 y ^ { 2 }(2x−5y)2=4x2−20xy+25y2

Find the sum, difference, or product. 2(2−5t)−t2(t−2)+(t4−1)2 ( 2 - 5 t ) - t ^ { 2 } ( t - 2 ) + \left( t ^ { 4 } - 1 \right)2(2−5t)−t2(t−2)+(t4−1)

Find an equation of the line with slope 2/52 / 52/5 and yyy - intercept 1.

Perform the indicated operations and simplify. (1−x2/3)(2+x1/3)\left( 1 - x ^ { 2 / 3 } \right) \left( 2 + x ^ { 1 / 3 } \right)(1−x2/3)(2+x1/3)

Simplify the expression. 2yy2−1+1(y−1)\frac { 2 y } { y ^ { 2 } - 1 } + \frac { 1 } { ( y - 1 ) }y2−12y​+(y−1)1​

Simplify the expression. Assume the letters denote any real numbers. 36a6b6\sqrt { 36 a ^ { 6 } b ^ { 6 } }36a6b6​

Determine an appropriate viewing rectangle for the equation y=2x3+x−3y = 2 x ^ { 3 } + x - 3y=2x3+x−3 and use it to draw the graph.

Simplify the expression. 2xx−3−2x+1\frac { 2 x } { x - 3 } - \frac { 2 } { x + 1 }x−32x​−x+12​

Perform the indicated operations and simplify. (t+3)(2t−1)−3(t+2)( t + 3 ) ( 2 t - 1 ) - 3 ( t + 2 )(t+3)(2t−1)−3(t+2)

Find three consecutive integers whose sum is 57.

Factor the expression. y2+xy−2x2y ^ { 2 } + x y - 2 x ^ { 2 }y2+xy−2x2

Functions

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Trigonometric Functions: Unit Circle Approach

Trigonometric Functions: Right Triangle Approach

Analytic Trigonometry

Polar Coordinates and Parametric Equations

Vectors in Two and Three Dimensions

Systems of Equations and Inequalities

Conic Sections

Sequences and Series

Limits: a Preview of Calculus

Filters

There are $63$ coins in Taylor's pockets, all quarters and dimes. The total value of his change is $ $9.60$ . Find the number of each type of coin.

Multiply the algebraic expressions using a Special Product Formula and simplify. $( 3 x + 4 y ) ^ { 2 }$

Multiply the algebraic expressions using the FOIL method and simplify. $( 4 x - 5 y ) ( 2 x - 4 y )$

Simplify the expression and eliminate any negative exponents(s). Assume that all letters denote positive numbers. $\sqrt [ 3 ] { r ^ { 2 } s } \sqrt [ 3 ] { 81 r ^ { 4 } s ^ { 2 } }$

Evaluate each expression. (a) $\left( \frac { 5 } { 3 } \right) ^ { 0 } 3 ^ { - 1 }$ (b) $\frac { 3 ^ { - 3 } } { 5 ^ { 0 } }$ (c) $\left( \frac { 1 } { 3 } \right) ^ { - 2 }$

Solve the equation for x. $a x ^ { 2 } - ( 2 a - 1 ) x + ( a - 1 ) = 0 \quad ( a \neq 0 )$

Simplify the expression. $\frac { \frac { x } { x - 1 } + \frac { 1 } { x + 1 } } { \frac { 5 } { x - 1 } - \frac { 2 } { x + 1 } }$

Multiply the algebraic expressions using a Special Product Formula and simplify. $( 2 x - 5 y ) ^ { 2 } = 4 x ^ { 2 } - 20 x y + 25 y ^ { 2 }$

Find the sum, difference, or product. $2 ( 2 - 5 t ) - t ^ { 2 } ( t - 2 ) + \left( t ^ { 4 } - 1 \right)$

Find an equation of the line with slope $2 / 5$ and $y$ - intercept 1.

Perform the indicated operations and simplify. $\left( 1 - x ^ { 2 / 3 } \right) \left( 2 + x ^ { 1 / 3 } \right)$

Simplify the expression. $\frac { 2 y } { y ^ { 2 } - 1 } + \frac { 1 } { ( y - 1 ) }$

Simplify the expression. Assume the letters denote any real numbers. $\sqrt { 36 a ^ { 6 } b ^ { 6 } }$

Determine an appropriate viewing rectangle for the equation $y = 2 x ^ { 3 } + x - 3$ and use it to draw the graph.

Simplify the expression. $\frac { 2 x } { x - 3 } - \frac { 2 } { x + 1 }$

Perform the indicated operations and simplify. $( t + 3 ) ( 2 t - 1 ) - 3 ( t + 2 )$

Factor the expression. $y ^ { 2 } + x y - 2 x ^ { 2 }$