Question 1

Solve the equation. $\frac { 4 } { x - 7 } + \frac { 1 } { x + 7 } + \frac { 3 } { 2 \left( x ^ { 2 } - 49 \right) } = 0$

Accepted Answer

A)  $\frac { 9 } { 2 }$ 
B)  $- \frac { 2 } { 9 }$ 
C)  $- 4$ 
D)  $- 5$ 
E)  $- \frac { 9 } { 2 }$ 
A)  $\frac { 9 } { 2 }$ 
B)  $- \frac { 2 } { 9 }$ 
C)  $- 4$ 
D)  $- 5$ 
E)  $- \frac { 9 } { 2 }$

Question 2

Write the number in the statement in scientific notation. The distance to the edge of the observable universe is about $100,000,000,000,000,000,000,000,000$ m.

Accepted Answer

The answer of Write the number in the statement in...

Question 3

Perform the indicated operations. $\frac { \frac { 1 } { 12 } } { \frac { 1 } { 8 } - \frac { 1 } { 12 } }$

Accepted Answer

The answer of Perform the indicated operations. \(\frac { \frac...

Question 4

Find a perpendicular line that passes through the midpoint of $( 8 , - 12 )$ and $( 7,10 )$ .

Accepted Answer

A) 
 $4 y - 22 x + 59 = 0$ 
B) 
 $2 y - 4 x = 59$ 
C) 
 $44 y - 2 x + 59 = 0$ 
D) 
 $x - 22 y = 164$ 
E) 
 $22 x - y - 164 = 0$ 
A) 
 $4 y - 22 x + 59 = 0$ 
B) 
 $2 y - 4 x = 59$ 
C) 
 $44 y - 2 x + 59 = 0$ 
D) 
 $x - 22 y = 164$ 
E) 
 $22 x - y - 164 = 0$

Question 5

A running track has straight sides and semicircular ends. If the length of the track is $440$ yd and the two straight parts are each $110$ yd long, what is the radius of the semicircular part, to the nearest yard?

Accepted Answer

Let the radius of the semicirc

Question 6

Use properties of real numbers to write $- r ( s - 2 )$ without parentheses.

Accepted Answer

A)  $- 2 r + 2 s$ 
B)  $- r S + 2$ 
C)  $rs + 2 r$ 
D)  $- r s + 2 r$ 
E)  $- rs- 2 r$ 
A)  $- 2 r + 2 s$ 
B)  $- r S + 2$ 
C)  $rs + 2 r$ 
D)  $- r s + 2 r$ 
E)  $- rs- 2 r$

Question 7

Factor the expression. $\left( n ^ { 2 } + 1 \right) ^ { 2 } - 15 \left( n ^ { 2 } + 1 \right) + 50$

Accepted Answer

A)  $( n - 2 ) ( n - 3 ) ( n + 3 ) ( n + 2 )$ 
B)  $( n - 2 ) ^ { 2 } ( n + 3 ) ( n - 3 )$ 
C)  $( n + 1 ) ^ { 2 } ( n - 3 ) ( n + 3 )$ 
D)  $( n + 1 ) ( n - 1 ) ( n + 2 )$ 
E)  $( n + 2 ) ^ { 4 }$ 
A)  $( n - 2 ) ( n - 3 ) ( n + 3 ) ( n + 2 )$ 
B)  $( n - 2 ) ^ { 2 } ( n + 3 ) ( n - 3 )$ 
C)  $( n + 1 ) ^ { 2 } ( n - 3 ) ( n + 3 )$ 
D)  $( n + 1 ) ( n - 1 ) ( n + 2 )$ 
E)  $( n + 2 ) ^ { 4 }$

Question 8

A sealed warehouse measuring $12$ m wide, $18$ m long and 6 m high, is filled with pure oxygen. One cubic meter contains 1000 L, and 22.4 L of any gas contains $6.02 \times 10 ^ { 23 }$ molecules. How many molecules of oxygen are there in the room?

Accepted Answer

Volume @#LAT-DLM& ,

Question 9

Express the repeating decimal as a fraction. $0 . \overline { 8 }$

Accepted Answer

The answer of Express the repeating decimal as a fraction....

Question 10

Rationalize the denominator. $\sqrt { \frac { x } { 6 } }$

Accepted Answer

The answer of Rationalize the denominator. \(\sqrt { \frac {...

Question 11

Write an equation that expresses the statement that $T$ varies jointly as $s$ and the square of $r$ and inversely as the cube root of $c$ .

Accepted Answer

@#LAT-DLM& , where @#LAT-DLM&

Question 12

A certain board game requires a two-toned wood playing surface. The central portion is made of a rectangular piece of pine, measuring $4$ in by $12$ in. The outer border is made of redwood, and has equal width on all sides. The area of the redwood border must be one third the area of the central pine portion. What must the width of the redwood border be?

Accepted Answer

Let the width of the border be

Question 13

Find $A \cup B$ if $A = \{ x \mid x > \pi \}$ and $B = \{ x \mid - 1 < x < \pi \}$ .

Accepted Answer

A)  $\varnothing$ 
B)  $\{ x \mid x > - 1 \text { and } x \neq \pi \}$ 
C)  $\{ x \mid - 1  - \pi \}$ 
A)  $\varnothing$ 
B)  $\{ x \mid x > - 1 \text { and } x \neq \pi \}$ 
C)  $\{ x \mid - 1  - \pi \}$

Question 14

Alyson drove from Bluesville to Greensburg at a speed of 60 mi/h. On the way back, she drove at 45 mi/h. The total trip took $5 \frac { 3 } { 5 }$ h of driving time. Find the distance between these two cities.

Accepted Answer

The answer of Alyson drove from Bluesville to Greensburg at...

Question 15

Evaluate the expression. $4 ^ { - 3 }$

Accepted Answer

A)  $- \frac { 1 } { 256 }$ 
B)  $- \frac { 1 } { 64 }$ 
C)  $\frac { 1 } { 64 }$ 
D)  $\frac { 1 } { 256 }$ 
E)  $\frac { 1 } { 512 }$ 
A)  $- \frac { 1 } { 256 }$ 
B)  $- \frac { 1 } { 64 }$ 
C)  $\frac { 1 } { 64 }$ 
D)  $\frac { 1 } { 256 }$ 
E)  $\frac { 1 } { 512 }$

Question 16

Peter drove to the beach at $40$ mi $/$ h. Rock left the house at the same time but drove at $69$ mi $/$ h. When Rock arrived at the beach, Peter had another $30$ mi to drive. Approximately how far is it from their house to the beach?

Accepted Answer

Let @#LAT-DLM& be the distance

Question 17

Solve the equation. $\frac { x - 1 } { 4 x + 7 } = \frac { 1 } { 5 }$

Accepted Answer

A)  $x = - 7$ 
B)  $x = 10$ 
C)  $x = \frac { 19 } { 3 }$ 
D)  $x = 12$ 
E)  $x = - 21$ 
A)  $x = - 7$ 
B)  $x = 10$ 
C)  $x = \frac { 19 } { 3 }$ 
D)  $x = 12$ 
E)  $x = - 21$

Question 18

Solve the equation by completing the square. $x ^ { 2 } - 16 x = 17$

Accepted Answer

The answer of Solve the equation by completing the square....

Question 19

Factor the expression. $25 s ^ { 2 } - 4 r ^ { 2 }$

Accepted Answer

The answer of Factor the expression. \(25 s ^ {...

Question 20

Evaluate $\left( \frac { 1 } { 4 } \right) ^ { - 2 } \left( \frac { 1 } { 2 } \right) ^ { - 4 }$

Accepted Answer

A)  $\frac { 1 } { 64 }$ 
B)  $\frac { 1 } { 256 }$ 
C)  $64$ 
D)  $\frac { - 1 } { 4 }$ 
E)  $256$ 
A)  $\frac { 1 } { 64 }$ 
B)  $\frac { 1 } { 256 }$ 
C)  $64$ 
D)  $\frac { - 1 } { 4 }$ 
E)  $256$

Solve the equation. $\frac { 4 } { x - 7 } + \frac { 1 } { x + 7 } + \frac { 3 } { 2 \left( x ^ { 2 } - 49 \right) } = 0$

Write the number in the statement in scientific notation. The distance to the edge of the observable universe is about $100,000,000,000,000,000,000,000,000$ m.

Perform the indicated operations. $\frac { \frac { 1 } { 12 } } { \frac { 1 } { 8 } - \frac { 1 } { 12 } }$

Find a perpendicular line that passes through the midpoint of $( 8 , - 12 )$ and $( 7,10 )$ .

A running track has straight sides and semicircular ends. If the length of the track is $440$ yd and the two straight parts are each $110$ yd long, what is the radius of the semicircular part, to the nearest yard?

Use properties of real numbers to write $- r ( s - 2 )$ without parentheses.

Factor the expression. $\left( n ^ { 2 } + 1 \right) ^ { 2 } - 15 \left( n ^ { 2 } + 1 \right) + 50$

A sealed warehouse measuring $12$ m wide, $18$ m long and 6 m high, is filled with pure oxygen. One cubic meter contains 1000 L, and 22.4 L of any gas contains $6.02 \times 10 ^ { 23 }$ molecules. How many molecules of oxygen are there in the room?

Express the repeating decimal as a fraction. $0 . \overline { 8 }$

Rationalize the denominator. $\sqrt { \frac { x } { 6 } }$

Write an equation that expresses the statement that $T$ varies jointly as $s$ and the square of $r$ and inversely as the cube root of $c$ .

Find $A \cup B$ if $A = \{ x \mid x > \pi \}$ and $B = \{ x \mid - 1 < x < \pi \}$ .

Alyson drove from Bluesville to Greensburg at a speed of 60 mi/h. On the way back, she drove at 45 mi/h. The total trip took $5 \frac { 3 } { 5 }$ h of driving time. Find the distance between these two cities.

Evaluate the expression. $4 ^ { - 3 }$

Peter drove to the beach at $40$ mi $/$ h. Rock left the house at the same time but drove at $69$ mi $/$ h. When Rock arrived at the beach, Peter had another $30$ mi to drive. Approximately how far is it from their house to the beach?

Solve the equation. $\frac { x - 1 } { 4 x + 7 } = \frac { 1 } { 5 }$

Solve the equation by completing the square. $x ^ { 2 } - 16 x = 17$

Factor the expression. $25 s ^ { 2 } - 4 r ^ { 2 }$

Evaluate $\left( \frac { 1 } { 4 } \right) ^ { - 2 } \left( \frac { 1 } { 2 } \right) ^ { - 4 }$

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. 4x−7+1x+7+32(x2−49)=0\frac { 4 } { x - 7 } + \frac { 1 } { x + 7 } + \frac { 3 } { 2 \left( x ^ { 2 } - 49 \right) } = 0x−74​+x+71​+2(x2−49)3​=0

Write the number in the statement in scientific notation. The distance to the edge of the observable universe is about 100,000,000,000,000,000,000,000,000100,000,000,000,000,000,000,000,000100,000,000,000,000,000,000,000,000 m.

Perform the indicated operations. 11218−112\frac { \frac { 1 } { 12 } } { \frac { 1 } { 8 } - \frac { 1 } { 12 } }81​−121​121​​

Find a perpendicular line that passes through the midpoint of (8,−12)( 8 , - 12 )(8,−12) and (7,10)( 7,10 )(7,10) .

A running track has straight sides and semicircular ends. If the length of the track is 440440440 yd and the two straight parts are each 110110110 yd long, what is the radius of the semicircular part, to the nearest yard?

Use properties of real numbers to write −r(s−2)- r ( s - 2 )−r(s−2) without parentheses.

Factor the expression. (n2+1)2−15(n2+1)+50\left( n ^ { 2 } + 1 \right) ^ { 2 } - 15 \left( n ^ { 2 } + 1 \right) + 50(n2+1)2−15(n2+1)+50

A sealed warehouse measuring 121212 m wide, 181818 m long and 6 m high, is filled with pure oxygen. One cubic meter contains 1000 L, and 22.4 L of any gas contains 6.02×10236.02 \times 10 ^ { 23 }6.02×1023 molecules. How many molecules of oxygen are there in the room?

Express the repeating decimal as a fraction. 0.8‾0 . \overline { 8 }0.8

Rationalize the denominator. x6\sqrt { \frac { x } { 6 } }6x​​

Write an equation that expresses the statement that TTT varies jointly as sss and the square of rrr and inversely as the cube root of ccc .

Find A∪BA \cup BA∪B if A={x∣x>π}A = \{ x \mid x > \pi \}A={x∣x>π} and B={x∣−1<x<π}B = \{ x \mid - 1 < x < \pi \}B={x∣−1<x<π} .

Alyson drove from Bluesville to Greensburg at a speed of 60 mi/h. On the way back, she drove at 45 mi/h. The total trip took 5355 \frac { 3 } { 5 }553​ h of driving time. Find the distance between these two cities.

Evaluate the expression. 4−34 ^ { - 3 }4−3

Peter drove to the beach at 404040 mi /// h. Rock left the house at the same time but drove at 696969 mi /// h. When Rock arrived at the beach, Peter had another 303030 mi to drive. Approximately how far is it from their house to the beach?

Solve the equation. x−14x+7=15\frac { x - 1 } { 4 x + 7 } = \frac { 1 } { 5 }4x+7x−1​=51​

Solve the equation by completing the square. x2−16x=17x ^ { 2 } - 16 x = 17x2−16x=17

Factor the expression. 25s2−4r225 s ^ { 2 } - 4 r ^ { 2 }25s2−4r2

Evaluate (14)−2(12)−4\left( \frac { 1 } { 4 } \right) ^ { - 2 } \left( \frac { 1 } { 2 } \right) ^ { - 4 }(41​)−2(21​)−4

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. $\frac { 4 } { x - 7 } + \frac { 1 } { x + 7 } + \frac { 3 } { 2 \left( x ^ { 2 } - 49 \right) } = 0$

Write the number in the statement in scientific notation. The distance to the edge of the observable universe is about $100,000,000,000,000,000,000,000,000$ m.

Perform the indicated operations. $\frac { \frac { 1 } { 12 } } { \frac { 1 } { 8 } - \frac { 1 } { 12 } }$

Find a perpendicular line that passes through the midpoint of $( 8 , - 12 )$ and $( 7,10 )$ .

A running track has straight sides and semicircular ends. If the length of the track is $440$ yd and the two straight parts are each $110$ yd long, what is the radius of the semicircular part, to the nearest yard?

Use properties of real numbers to write $- r ( s - 2 )$ without parentheses.

Factor the expression. $\left( n ^ { 2 } + 1 \right) ^ { 2 } - 15 \left( n ^ { 2 } + 1 \right) + 50$

A sealed warehouse measuring $12$ m wide, $18$ m long and 6 m high, is filled with pure oxygen. One cubic meter contains 1000 L, and 22.4 L of any gas contains $6.02 \times 10 ^ { 23 }$ molecules. How many molecules of oxygen are there in the room?

Express the repeating decimal as a fraction. $0 . \overline { 8 }$

Rationalize the denominator. $\sqrt { \frac { x } { 6 } }$

Write an equation that expresses the statement that $T$ varies jointly as $s$ and the square of $r$ and inversely as the cube root of $c$ .

Find $A \cup B$ if $A = \{ x \mid x > \pi \}$ and $B = \{ x \mid - 1 < x < \pi \}$ .

Alyson drove from Bluesville to Greensburg at a speed of 60 mi/h. On the way back, she drove at 45 mi/h. The total trip took $5 \frac { 3 } { 5 }$ h of driving time. Find the distance between these two cities.

Evaluate the expression. $4 ^ { - 3 }$

Peter drove to the beach at $40$ mi $/$ h. Rock left the house at the same time but drove at $69$ mi $/$ h. When Rock arrived at the beach, Peter had another $30$ mi to drive. Approximately how far is it from their house to the beach?

Solve the equation. $\frac { x - 1 } { 4 x + 7 } = \frac { 1 } { 5 }$

Solve the equation by completing the square. $x ^ { 2 } - 16 x = 17$

Factor the expression. $25 s ^ { 2 } - 4 r ^ { 2 }$

Evaluate $\left( \frac { 1 } { 4 } \right) ^ { - 2 } \left( \frac { 1 } { 2 } \right) ^ { - 4 }$