Question 1

Add, and then simplify, if possible. $\frac { 5 } { x + 2 } + \frac { 7 } { x - 4 }$

Accepted Answer

The answer of Add, and then simplify, if possible. \(\frac...

Question 2

Painter A can paint a house in 12 hours, Painter B can paint the same house in 8 hours, and Painter C can paint the house in 10 hours. How many hours will it take to paint the house if Painter A has to leave after working $1 \frac { 1 } { 2 }$ hours and Painter C arrives 4 hours after Painter A and Painter B start the job.

Accepted Answer

The answer of Painter A can paint a house in...

Question 3

Perform the operations and simplify the result when possible. $\frac { s + 7 } { s - 7 } - \frac { s - 7 } { s + 7 }$

Accepted Answer

The answer of Perform the operations and simplify the result...

Question 4

Use synthetic division to perform the division. $\frac { 11 x ^ { 2 } + 8 + 6 x ^ { 3 } } { x + 2 }$

Accepted Answer

A)  $6 x ^ { 2 } + x - 2 + \frac { 4 } { x + 2 }$ 
B)  $6 x ^ { 2 } + x - 2 - \frac { 4 } { x + 2 }$ 
C)  $6 x ^ { 2 } - x - 2 + \frac { 4 } { x + 2 }$ 
D)  $6 x ^ { 2 } - x + 2 - \frac { 4 } { x + 2 }$ 
E)  $6 x ^ { 2 } - x + 2 + \frac { 4 } { x + 2 }$ 
A)  $6 x ^ { 2 } + x - 2 + \frac { 4 } { x + 2 }$ 
B)  $6 x ^ { 2 } + x - 2 - \frac { 4 } { x + 2 }$ 
C)  $6 x ^ { 2 } - x - 2 + \frac { 4 } { x + 2 }$ 
D)  $6 x ^ { 2 } - x + 2 - \frac { 4 } { x + 2 }$ 
E)  $6 x ^ { 2 } - x + 2 + \frac { 4 } { x + 2 }$

Question 5

A woman can bicycle 27 miles in the same time as it takes her to walk 9 miles. She can ride 10 mph faster than she can walk. How fast can she walk?
 __________ mph

Accepted Answer

The answer of A woman can bicycle 27 miles in...

Question 6

The Washington Monument shown below casts a shadow of $166 \frac { 1 } { 2 }$ feet at the same time as a 6-foot-tall tourist casts a shadow of $1 \frac { 1 } { 2 }$ feet. Find the height of the monument.   __________ ft

Accepted Answer

The answer of The Washington Monument shown below casts a...

Question 7

Perform the operations and simplify the result when possible. $1 + x - \frac { x } { x - 7 }$

Accepted Answer

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

Question 8

Use synthetic division to perform the division. $\left( 4 x ^ { 3 } - 11 + 2 x ^ { 2 } \right) \div ( x + 1 )$

Accepted Answer

A)  $4 x ^ { 2 } - 2 x + 2 + \frac { 13 } { x + 1 }$ 
B)  $4 x ^ { 2 } + 2 x - 2 + \frac { 13 } { x + 1 }$ 
C)  $4 x ^ { 2 } - 2 x + 2 - \frac { 13 } { x + 2 }$ 
D)  $4 x ^ { 2 } - 2 x + 2 - \frac { 13 } { x - 1 }$ 
E)  $4 x ^ { 2 } - 2 x + 2 - \frac { 13 } { x + 1 }$ 
A)  $4 x ^ { 2 } - 2 x + 2 + \frac { 13 } { x + 1 }$ 
B)  $4 x ^ { 2 } + 2 x - 2 + \frac { 13 } { x + 1 }$ 
C)  $4 x ^ { 2 } - 2 x + 2 - \frac { 13 } { x + 2 }$ 
D)  $4 x ^ { 2 } - 2 x + 2 - \frac { 13 } { x - 1 }$ 
E)  $4 x ^ { 2 } - 2 x + 2 - \frac { 13 } { x + 1 }$

Question 9

Solve: $\frac { 5 } { x + 2 } + \frac { 15 } { x - 3 } = \frac { 5 x } { x ^ { 2 } - x - 6 }$

Accepted Answer

The answer of Solve: \(\frac { 5 } { x...

Question 10

Express the verbal model in symbols. C varies jointly as u , z, and y .

Accepted Answer

The answer of Express the verbal model in symbols. C...

Question 11

A __________ is the quotient of two numbers or two quantities with the same units.

Accepted Answer

The answer of A __________ is the quotient of two...

Question 12

Divide, then simplify if possible. $\frac { x ^ { 2 } - 9 } { 3 x + 9 } \div \frac { 3 - x } { x + 3 }$

Accepted Answer

The answer of Divide, then simplify if possible. \(\frac {...

Question 13

The equation $y = k x z$ defines __________ variation.

Accepted Answer

The answer of The equation $y = k x z$...

Question 14

Divide using long division: $\frac { 6 a ^ { 2 } - 7 a + 3 } { 2 a - 3 }$

Accepted Answer

A)  $3 a + 1$ 
B)  $3 a + 1 + \frac { 6 } { 2 a - 3 }$ 
C)  $3 a - 8 - \frac { 21 } { 2 a - 3 }$ 
D)  $3 a - 8 + \frac { 27 } { 2 a - 3 }$ 
A)  $3 a + 1$ 
B)  $3 a + 1 + \frac { 6 } { 2 a - 3 }$ 
C)  $3 a - 8 - \frac { 21 } { 2 a - 3 }$ 
D)  $3 a - 8 + \frac { 27 } { 2 a - 3 }$

Question 15

One crew can put up holiday decorations in the mall in 6 hours. A second crew can put up the decorations in 5 hours. How long will it take if both crews work together to decorate the mall?
 __________ hr

Accepted Answer

The answer of One crew can put up holiday decorations...

Question 16

Perform the operation and simplify the result if possible. $\frac { 2 x + 2 } { x - 5 } - \frac { x - 17 } { 5 - x }$

Accepted Answer

A)  $\frac { 17 x + 2 } { x - 5 }$ 
B)  $\frac { 2 x + 17 } { x - 5 }$ 
C)  $\frac { 2 x + 17 } { 5 - x }$ 
D)  3 
E)  2 
A)  $\frac { 17 x + 2 } { x - 5 }$ 
B)  $\frac { 2 x + 17 } { x - 5 }$ 
C)  $\frac { 2 x + 17 } { 5 - x }$ 
D)  3 
E)  2

Question 17

In a scale drawing, a 230-foot antenna tower is drawn $7 \frac { 1 } { 2 }$ inches high. The building next to it is drawn $2 \frac { 1 } { 4 }$ inches high. How tall is the actual building?
 __________ ft

Accepted Answer

The answer of In a scale drawing, a 230-foot antenna...

Question 18

The powers of x in $2 x ^ { 4 } + 3 x ^ { 3 } + 5 x ^ { 2 } - 6 x - 7$ are written in __________ order.

Accepted Answer

The answer of The powers of x in \(2 x...

Question 19

Solve: $P = \frac { R - C } { n }$ for R

Accepted Answer

A)  $R = P _ { n } - C$ 
B)  $R = C n - P$ 
C)  $R = P _ { n } + C$ 
D)  none of these 
A)  $R = P _ { n } - C$ 
B)  $R = C n - P$ 
C)  $R = P _ { n } + C$ 
D)  none of these

Question 20

Let $f ( x ) = \frac { x ^ { 3 } + 5 x ^ { 2 } - 20 } { x }$ . For what values of x is $f ( x ) = 4$ .

Accepted Answer

The answer of Let \(f ( x ) = \frac...

Add, and then simplify, if possible. $\frac { 5 } { x + 2 } + \frac { 7 } { x - 4 }$

Perform the operations and simplify the result when possible. $\frac { s + 7 } { s - 7 } - \frac { s - 7 } { s + 7 }$

Use synthetic division to perform the division. $\frac { 11 x ^ { 2 } + 8 + 6 x ^ { 3 } } { x + 2 }$

A woman can bicycle 27 miles in the same time as it takes her to walk 9 miles. She can ride 10 mph faster than she can walk. How fast can she walk? __________ mph

Perform the operations and simplify the result when possible. $1 + x - \frac { x } { x - 7 }$

Use synthetic division to perform the division. $\left( 4 x ^ { 3 } - 11 + 2 x ^ { 2 } \right) \div ( x + 1 )$

Solve: $\frac { 5 } { x + 2 } + \frac { 15 } { x - 3 } = \frac { 5 x } { x ^ { 2 } - x - 6 }$

Express the verbal model in symbols. C varies jointly as u , z, and y .

A __________ is the quotient of two numbers or two quantities with the same units.

Divide, then simplify if possible. $\frac { x ^ { 2 } - 9 } { 3 x + 9 } \div \frac { 3 - x } { x + 3 }$

The equation $y = k x z$ defines __________ variation.

Divide using long division: $\frac { 6 a ^ { 2 } - 7 a + 3 } { 2 a - 3 }$

One crew can put up holiday decorations in the mall in 6 hours. A second crew can put up the decorations in 5 hours. How long will it take if both crews work together to decorate the mall? __________ hr

Perform the operation and simplify the result if possible. $\frac { 2 x + 2 } { x - 5 } - \frac { x - 17 } { 5 - x }$

In a scale drawing, a 230-foot antenna tower is drawn $7 \frac { 1 } { 2 }$ inches high. The building next to it is drawn $2 \frac { 1 } { 4 }$ inches high. How tall is the actual building? __________ ft

The powers of x in $2 x ^ { 4 } + 3 x ^ { 3 } + 5 x ^ { 2 } - 6 x - 7$ are written in __________ order.

Solve: $P = \frac { R - C } { n }$ for R

Let $f ( x ) = \frac { x ^ { 3 } + 5 x ^ { 2 } - 20 } { x }$ . For what values of x is $f ( x ) = 4$ .

A Review of Basic Algebra

Graphs, Equations of Lines, and Functions

Systems of Equations

Inequalities

Exponents, Polynomials, and Polynomial Functions

Radical Expressions and Equations

Quadratic Equations, Functions, and Inequalities

Exponential and Logarithmic Functions

Conic Sections; More Graphing

Miscellaneous Topics

Filters

Exam 6: Rational Expression and Equations

Add, and then simplify, if possible. 5x+2+7x−4\frac { 5 } { x + 2 } + \frac { 7 } { x - 4 }x+25​+x−47​

Perform the operations and simplify the result when possible. s+7s−7−s−7s+7\frac { s + 7 } { s - 7 } - \frac { s - 7 } { s + 7 }s−7s+7​−s+7s−7​

Use synthetic division to perform the division. 11x2+8+6x3x+2\frac { 11 x ^ { 2 } + 8 + 6 x ^ { 3 } } { x + 2 }x+211x2+8+6x3​

A woman can bicycle 27 miles in the same time as it takes her to walk 9 miles. She can ride 10 mph faster than she can walk. How fast can she walk? __________ mph

The Washington Monument shown below casts a shadow of 16612166 \frac { 1 } { 2 }16621​ feet at the same time as a 6-foot-tall tourist casts a shadow of 1121 \frac { 1 } { 2 }121​ feet. Find the height of the monument. __________ ft

Perform the operations and simplify the result when possible. 1+x−xx−71 + x - \frac { x } { x - 7 }1+x−x−7x​

Use synthetic division to perform the division. (4x3−11+2x2)÷(x+1)\left( 4 x ^ { 3 } - 11 + 2 x ^ { 2 } \right) \div ( x + 1 )(4x3−11+2x2)÷(x+1)

Solve: 5x+2+15x−3=5xx2−x−6\frac { 5 } { x + 2 } + \frac { 15 } { x - 3 } = \frac { 5 x } { x ^ { 2 } - x - 6 }x+25​+x−315​=x2−x−65x​

Express the verbal model in symbols. C varies jointly as u , z, and y .

A __________ is the quotient of two numbers or two quantities with the same units.

Divide, then simplify if possible. x2−93x+9÷3−xx+3\frac { x ^ { 2 } - 9 } { 3 x + 9 } \div \frac { 3 - x } { x + 3 }3x+9x2−9​÷x+33−x​

The equation y=kxzy = k x zy=kxz defines __________ variation.

Divide using long division: 6a2−7a+32a−3\frac { 6 a ^ { 2 } - 7 a + 3 } { 2 a - 3 }2a−36a2−7a+3​

One crew can put up holiday decorations in the mall in 6 hours. A second crew can put up the decorations in 5 hours. How long will it take if both crews work together to decorate the mall? __________ hr

Perform the operation and simplify the result if possible. 2x+2x−5−x−175−x\frac { 2 x + 2 } { x - 5 } - \frac { x - 17 } { 5 - x }x−52x+2​−5−xx−17​

In a scale drawing, a 230-foot antenna tower is drawn 7127 \frac { 1 } { 2 }721​ inches high. The building next to it is drawn 2142 \frac { 1 } { 4 }241​ inches high. How tall is the actual building? __________ ft

The powers of x in 2x4+3x3+5x2−6x−72 x ^ { 4 } + 3 x ^ { 3 } + 5 x ^ { 2 } - 6 x - 72x4+3x3+5x2−6x−7 are written in __________ order.

Solve: P=R−CnP = \frac { R - C } { n }P=nR−C​ for R

Let f(x)=x3+5x2−20xf ( x ) = \frac { x ^ { 3 } + 5 x ^ { 2 } - 20 } { x }f(x)=xx3+5x2−20​ . For what values of x is f(x)=4f ( x ) = 4f(x)=4 .

A Review of Basic Algebra

Graphs, Equations of Lines, and Functions

Systems of Equations

Inequalities

Exponents, Polynomials, and Polynomial Functions

Radical Expressions and Equations

Quadratic Equations, Functions, and Inequalities

Exponential and Logarithmic Functions

Conic Sections; More Graphing

Miscellaneous Topics

Filters

Add, and then simplify, if possible. $\frac { 5 } { x + 2 } + \frac { 7 } { x - 4 }$

Perform the operations and simplify the result when possible. $\frac { s + 7 } { s - 7 } - \frac { s - 7 } { s + 7 }$

Use synthetic division to perform the division. $\frac { 11 x ^ { 2 } + 8 + 6 x ^ { 3 } } { x + 2 }$

Perform the operations and simplify the result when possible. $1 + x - \frac { x } { x - 7 }$

Use synthetic division to perform the division. $\left( 4 x ^ { 3 } - 11 + 2 x ^ { 2 } \right) \div ( x + 1 )$

Solve: $\frac { 5 } { x + 2 } + \frac { 15 } { x - 3 } = \frac { 5 x } { x ^ { 2 } - x - 6 }$

Divide, then simplify if possible. $\frac { x ^ { 2 } - 9 } { 3 x + 9 } \div \frac { 3 - x } { x + 3 }$

The equation $y = k x z$ defines __________ variation.

Divide using long division: $\frac { 6 a ^ { 2 } - 7 a + 3 } { 2 a - 3 }$

Perform the operation and simplify the result if possible. $\frac { 2 x + 2 } { x - 5 } - \frac { x - 17 } { 5 - x }$

In a scale drawing, a 230-foot antenna tower is drawn $7 \frac { 1 } { 2 }$ inches high. The building next to it is drawn $2 \frac { 1 } { 4 }$ inches high. How tall is the actual building? __________ ft

The powers of x in $2 x ^ { 4 } + 3 x ^ { 3 } + 5 x ^ { 2 } - 6 x - 7$ are written in __________ order.

Solve: $P = \frac { R - C } { n }$ for R

Let $f ( x ) = \frac { x ^ { 3 } + 5 x ^ { 2 } - 20 } { x }$ . For what values of x is $f ( x ) = 4$ .