Question 1

Solve the equation. $2 ( x - 1 ) - 7 = - 2 ( x + 2 ) - 9$

Accepted Answer

A)  $x = 4$ 
B)  $x = - 11$ 
C)  $x = - \frac { 67 } { 2 }$ 
D)  $x = - 3$ 
E)  $x = - 1$ 
A)  $x = 4$ 
B)  $x = - 11$ 
C)  $x = - \frac { 67 } { 2 }$ 
D)  $x = - 3$ 
E)  $x = - 1$

Question 2

Find all real solutions of the equation. $8 x ^ { 2 / 3 } - 250 = 6 + 4 x ^ { 2 / 3 }$

Accepted Answer

A)  $64$ 
B)  $\pm 64$ 
C)  $256$ 
D)  $\pm 512$ 
E)  No real solution 
A)  $64$ 
B)  $\pm 64$ 
C)  $256$ 
D)  $\pm 512$ 
E)  No real solution

Question 3

Factor the expression. $( x - 2 ) ^ { 7 / 2 } - ( x - 2 ) ^ { 3 / 2 }$

Accepted Answer

A)  $( x - 2 ) ^ { 2 } ( x - 1 ) ( x - 3 )$ 
B)  $( x - 2 ) ( x - 1 ) ( x + 3 )$ 
C)  $( x - 2 ) ^ { 3 / 2 } ( x + 1 ) ( x - 3 )$ 
D)  $( x - 2 ) ^ { 1 / 2 } ( x - 1 ) ( x - 3 )$ 
E)  $( x - 2 ) ^ { 3 / 2 } ( x - 1 ) ( x - 3 )$ 
A)  $( x - 2 ) ^ { 2 } ( x - 1 ) ( x - 3 )$ 
B)  $( x - 2 ) ( x - 1 ) ( x + 3 )$ 
C)  $( x - 2 ) ^ { 3 / 2 } ( x + 1 ) ( x - 3 )$ 
D)  $( x - 2 ) ^ { 1 / 2 } ( x - 1 ) ( x - 3 )$ 
E)  $( x - 2 ) ^ { 3 / 2 } ( x - 1 ) ( x - 3 )$

Question 4

Perform the indicated operations and simplify. $( 2 u - v ) ( 2 u + v )$

Accepted Answer

A)  $4 u ^ { 2 } - v ^ { 2 }$ 
B)  $8 u ^ { 2 } + 4 v ^ { 2 }$ 
C)  $16 u ^ { 2 } + 4 v ^ { 2 }$ 
D)  $16 u ^ { 2 } + 2 v ^ { 2 }$ 
E)  $16 u ^ { 2 } - 4 v ^ { 2 }$ 
A)  $4 u ^ { 2 } - v ^ { 2 }$ 
B)  $8 u ^ { 2 } + 4 v ^ { 2 }$ 
C)  $16 u ^ { 2 } + 4 v ^ { 2 }$ 
D)  $16 u ^ { 2 } + 2 v ^ { 2 }$ 
E)  $16 u ^ { 2 } - 4 v ^ { 2 }$

Question 5

Evaluate $- 2 ^ { 3 }$

Accepted Answer

A)  $- 16$ 
B)  $- 8$ 
C)  $- 4$ 
D)  $8$ 
E)  $16$ 
A)  $- 16$ 
B)  $- 8$ 
C)  $- 4$ 
D)  $8$ 
E)  $16$

Question 6

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

Accepted Answer

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

Question 7

Find the solution set for the nonlinear inequality $\frac { 2 x + 1 } { x - 4 } \leq 5$ .

Accepted Answer

A)  $( - \infty , - 4 ) \cup ( 7 , \infty )$ 
B)  $( - \infty , - 7 ) \cup [ 4 , \infty )$ 
C)  $( - \infty , 4 ) \cup [ 7 , \infty )$ 
D)  $( - \infty , 4 ]$ 
E)  $( - \infty , 7 )$ 
A)  $( - \infty , - 4 ) \cup ( 7 , \infty )$ 
B)  $( - \infty , - 7 ) \cup [ 4 , \infty )$ 
C)  $( - \infty , 4 ) \cup [ 7 , \infty )$ 
D)  $( - \infty , 4 ]$ 
E)  $( - \infty , 7 )$

Question 8

Write the statement in terms of inequalities. The distance from x to 3 is at most $6$ .

Accepted Answer

A)  $| x - 3 | \leq 6$ 
B)  $| x - 3 | \geq 6$ 
C)  $| x - 3 | < 6$ 
D)  $| x - 6 | \leq 3$ 
E)  $| x - 6 | \geq 3$ 
A)  $| x - 3 | \leq 6$ 
B)  $| x - 3 | \geq 6$ 
C)  $| x - 3 | < 6$ 
D)  $| x - 6 | \leq 3$ 
E)  $| x - 6 | \geq 3$

Question 9

Find an equation of the line with slope $- 1$ that passes through $( - 1,3 )$ .
(a) $2 x + 2 y - 1 = 0$
(b) $x - 2 y + 4 = 0$
(c) $x + y - 2 = 0$
(d) $x + y + 4 = 0$
(e) $3 x - y - 4 = 0$

Accepted Answer

To find the equation of a line with a gi

Question 10

Find all real solutions of the equation. $x ^ { 2 } - 6 x - 12 = 0$

Accepted Answer

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

Question 11

Rationalize the denominator. $\frac { 1 } { s ^ { 3 / 7 } }$

Accepted Answer

The answer of Rationalize the denominator. \(\frac { 1 }...

Question 12

Solve the equation. $4 x - 9 = 23$

Accepted Answer

A)  $- 8$ 
B)  $9$ 
C)  $- 6$ 
D)  $6$ 
E)  $8$ 
A)  $- 8$ 
B)  $9$ 
C)  $- 6$ 
D)  $6$ 
E)  $8$

Question 13

Find the approximate solutions of the equation $x ^ { 1/3 } - x ^ { 2 } = 0$ by drawing a graph in the interval $[ - 0.5,1.5 ]$ .

Accepted Answer

To find the approximate solutions of the

Question 14

Perform the subtraction and simplify. $\frac { 2 } { x + 3 } - \frac { 1 } { x ^ { 2 } + 8 x + 15 }$

Accepted Answer

The answer of Perform the subtraction and simplify. \(\frac {...

Question 15

The resistance of a wire varies directly as its length and inversely as the square of its diameter. A wire $50$ m long and $0.01$ m in diameter has a resistance of $25$ $\Omega$ . Write an equation to describe its resistance, and find the resistance of a wire made of the same material that is $20$ m long and has diameter $0.02$ m.

Accepted Answer

@#LAT-DLM& ; @#LAT-DLM& @#LAT-DLM& @#LAT-DLM& . Th

Question 16

Simplify $a b ^ { 3 } c ^ { 2 } \left( \frac { 2 a ^ { 2 } b } { c ^ { 4 } } \right) ^ { - 1 }$ and eliminate any negative exponents.

Accepted Answer

A) 
 $b ^ { 2 } c ^ { 6 }$ 
B) 
 $\frac { b ^ { 6 } c ^ { 2 } } { 2 a ^ { 2 } }$ 
C) 
 $\frac { 2 b ^ { 2 } c ^ { 6 } } { 3 a }$ 
D) 
 $\frac { b ^ { 2 } c ^ { 6 } } { 2 a }$ 
E) 
 $2 b ^ { 2 } c ^ { 6 }$ 
A) 
 $b ^ { 2 } c ^ { 6 }$ 
B) 
 $\frac { b ^ { 6 } c ^ { 2 } } { 2 a ^ { 2 } }$ 
C) 
 $\frac { 2 b ^ { 2 } c ^ { 6 } } { 3 a }$ 
D) 
 $\frac { b ^ { 2 } c ^ { 6 } } { 2 a }$ 
E) 
 $2 b ^ { 2 } c ^ { 6 }$

Question 17

Caitlin drove from Greensville to Bluesburg at a speed of 50 mi/h. On the way back, she drove at 75 mi/h. The total trip took $7 \frac { 1 } { 2 }$ h of driving time. Find the distance between these two cities.

Accepted Answer

The answer of Caitlin drove from Greensville to Bluesburg at...

Question 18

State whether the inequality is true or false. $- \sqrt { 2 } < - 1.41$

Accepted Answer

A) True 
 B)False

Question 19

Use properties of real numbers to write $3 ( 2 a + b )$ without parentheses.

Accepted Answer

A)  $6 a + 6 b$ 
B)  $3 + 2 a b$ 
C)  $6 a - b$ 
D)  $6 a + 3 b$ 
E)  $6 a - 3 b$ 
A)  $6 a + 6 b$ 
B)  $3 + 2 a b$ 
C)  $6 a - b$ 
D)  $6 a + 3 b$ 
E)  $6 a - 3 b$

Question 20

Find the solution set for the linear inequality $11 - 5 x < - 2$ .

Accepted Answer

A)  $\left( \frac { 18 } { 5 } , \infty \right)$ 
B)  $\left( \frac { 13 } { 5 } , \infty \right)$ 
C)  $\left( - \infty , - \frac { 5 } { 13 } \right)$ 
D)  $\left( - \infty , \frac { 13 } { 5 } \right)$ 
E)  No solution 
A)  $\left( \frac { 18 } { 5 } , \infty \right)$ 
B)  $\left( \frac { 13 } { 5 } , \infty \right)$ 
C)  $\left( - \infty , - \frac { 5 } { 13 } \right)$ 
D)  $\left( - \infty , \frac { 13 } { 5 } \right)$ 
E)  No solution

Solve the equation. $2 ( x - 1 ) - 7 = - 2 ( x + 2 ) - 9$

Find all real solutions of the equation. $8 x ^ { 2 / 3 } - 250 = 6 + 4 x ^ { 2 / 3 }$

Factor the expression. $( x - 2 ) ^ { 7 / 2 } - ( x - 2 ) ^ { 3 / 2 }$

Perform the indicated operations and simplify. $( 2 u - v ) ( 2 u + v )$

Evaluate $- 2 ^ { 3 }$

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

Find the solution set for the nonlinear inequality $\frac { 2 x + 1 } { x - 4 } \leq 5$ .

Write the statement in terms of inequalities. The distance from x to 3 is at most $6$ .

Find an equation of the line with slope $- 1$ that passes through $( - 1,3 )$ . (a) $2 x + 2 y - 1 = 0$ (b) $x - 2 y + 4 = 0$ (c) $x + y - 2 = 0$ (d) $x + y + 4 = 0$ (e) $3 x - y - 4 = 0$

Find all real solutions of the equation. $x ^ { 2 } - 6 x - 12 = 0$

Rationalize the denominator. $\frac { 1 } { s ^ { 3 / 7 } }$

Solve the equation. $4 x - 9 = 23$

Find the approximate solutions of the equation $x ^ { 1/3 } - x ^ { 2 } = 0$ by drawing a graph in the interval $[ - 0.5,1.5 ]$ .

Perform the subtraction and simplify. $\frac { 2 } { x + 3 } - \frac { 1 } { x ^ { 2 } + 8 x + 15 }$

Simplify $a b ^ { 3 } c ^ { 2 } \left( \frac { 2 a ^ { 2 } b } { c ^ { 4 } } \right) ^ { - 1 }$ and eliminate any negative exponents.

Caitlin drove from Greensville to Bluesburg at a speed of 50 mi/h. On the way back, she drove at 75 mi/h. The total trip took $7 \frac { 1 } { 2 }$ h of driving time. Find the distance between these two cities.

State whether the inequality is true or false. $- \sqrt { 2 } < - 1.41$

Use properties of real numbers to write $3 ( 2 a + b )$ without parentheses.

Find the solution set for the linear inequality $11 - 5 x < - 2$ .

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

Solve the equation. 2(x−1)−7=−2(x+2)−92 ( x - 1 ) - 7 = - 2 ( x + 2 ) - 92(x−1)−7=−2(x+2)−9

Find all real solutions of the equation. 8x2/3−250=6+4x2/38 x ^ { 2 / 3 } - 250 = 6 + 4 x ^ { 2 / 3 }8x2/3−250=6+4x2/3

Factor the expression. (x−2)7/2−(x−2)3/2( x - 2 ) ^ { 7 / 2 } - ( x - 2 ) ^ { 3 / 2 }(x−2)7/2−(x−2)3/2

Perform the indicated operations and simplify. (2u−v)(2u+v)( 2 u - v ) ( 2 u + v )(2u−v)(2u+v)

Evaluate −23- 2 ^ { 3 }−23

Simplify the expression. −x2+1x3−x−1\frac { - x ^ { 2 } + 1 } { x ^ { 3 } - x - 1 }x3−x−1−x2+1​

Find the solution set for the nonlinear inequality 2x+1x−4≤5\frac { 2 x + 1 } { x - 4 } \leq 5x−42x+1​≤5 .

Write the statement in terms of inequalities. The distance from x to 3 is at most 666 .

Find an equation of the line with slope −1- 1−1 that passes through (−1,3)( - 1,3 )(−1,3) . (a) 2x+2y−1=02 x + 2 y - 1 = 02x+2y−1=0 (b) x−2y+4=0x - 2 y + 4 = 0x−2y+4=0 (c) x+y−2=0x + y - 2 = 0x+y−2=0 (d) x+y+4=0x + y + 4 = 0x+y+4=0 (e) 3x−y−4=03 x - y - 4 = 03x−y−4=0

Find all real solutions of the equation. x2−6x−12=0x ^ { 2 } - 6 x - 12 = 0x2−6x−12=0

Rationalize the denominator. 1s3/7\frac { 1 } { s ^ { 3 / 7 } }s3/71​

Solve the equation. 4x−9=234 x - 9 = 234x−9=23

Find the approximate solutions of the equation x1/3−x2=0x ^ { 1/3 } - x ^ { 2 } = 0x1/3−x2=0 by drawing a graph in the interval [−0.5,1.5][ - 0.5,1.5 ][−0.5,1.5] .

Perform the subtraction and simplify. 2x+3−1x2+8x+15\frac { 2 } { x + 3 } - \frac { 1 } { x ^ { 2 } + 8 x + 15 }x+32​−x2+8x+151​

Simplify ab3c2(2a2bc4)−1a b ^ { 3 } c ^ { 2 } \left( \frac { 2 a ^ { 2 } b } { c ^ { 4 } } \right) ^ { - 1 }ab3c2(c42a2b​)−1 and eliminate any negative exponents.

Caitlin drove from Greensville to Bluesburg at a speed of 50 mi/h. On the way back, she drove at 75 mi/h. The total trip took 7127 \frac { 1 } { 2 }721​ h of driving time. Find the distance between these two cities.

State whether the inequality is true or false. −2<−1.41- \sqrt { 2 } < - 1.41−2​<−1.41

Use properties of real numbers to write 3(2a+b)3 ( 2 a + b )3(2a+b) without parentheses.

Find the solution set for the linear inequality 11−5x<−211 - 5 x < - 211−5x<−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

Solve the equation. $2 ( x - 1 ) - 7 = - 2 ( x + 2 ) - 9$

Find all real solutions of the equation. $8 x ^ { 2 / 3 } - 250 = 6 + 4 x ^ { 2 / 3 }$

Factor the expression. $( x - 2 ) ^ { 7 / 2 } - ( x - 2 ) ^ { 3 / 2 }$

Perform the indicated operations and simplify. $( 2 u - v ) ( 2 u + v )$

Evaluate $- 2 ^ { 3 }$

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

Find the solution set for the nonlinear inequality $\frac { 2 x + 1 } { x - 4 } \leq 5$ .

Write the statement in terms of inequalities. The distance from x to 3 is at most $6$ .

Find an equation of the line with slope $- 1$ that passes through $( - 1,3 )$ . (a) $2 x + 2 y - 1 = 0$ (b) $x - 2 y + 4 = 0$ (c) $x + y - 2 = 0$ (d) $x + y + 4 = 0$ (e) $3 x - y - 4 = 0$

Find all real solutions of the equation. $x ^ { 2 } - 6 x - 12 = 0$

Rationalize the denominator. $\frac { 1 } { s ^ { 3 / 7 } }$

Solve the equation. $4 x - 9 = 23$

Find the approximate solutions of the equation $x ^ { 1/3 } - x ^ { 2 } = 0$ by drawing a graph in the interval $[ - 0.5,1.5 ]$ .

Perform the subtraction and simplify. $\frac { 2 } { x + 3 } - \frac { 1 } { x ^ { 2 } + 8 x + 15 }$

Simplify $a b ^ { 3 } c ^ { 2 } \left( \frac { 2 a ^ { 2 } b } { c ^ { 4 } } \right) ^ { - 1 }$ and eliminate any negative exponents.

Caitlin drove from Greensville to Bluesburg at a speed of 50 mi/h. On the way back, she drove at 75 mi/h. The total trip took $7 \frac { 1 } { 2 }$ h of driving time. Find the distance between these two cities.

State whether the inequality is true or false. $- \sqrt { 2 } < - 1.41$

Use properties of real numbers to write $3 ( 2 a + b )$ without parentheses.

Find the solution set for the linear inequality $11 - 5 x < - 2$ .