Question 1

A plane can fly 260 miles in the same time as it takes a car to go 100 miles. If the car travels 80 mph slower than the plane, find the speed of the plane.

Accepted Answer

The answer of A plane can fly 260 miles in...

Question 2

Divide using long division: $\frac { 9 x ^ { 3 } + 3 x ^ { 2 } + 6 x - 6 } { 3 x - 2 }$

Accepted Answer

A)  $3 x ^ { 2 } + 3 x + 4 + \frac { 2 } { 3 x - 2 }$ 
B)  $3 x ^ { 2 } + 3 x + 4 - \frac { 14 } { 3 x - 2 }$ 
C)  $3 x ^ { 2 } - x + 2 - \frac { 2 } { 3 x - 2 }$ 
D)  $3 x ^ { 2 } - x + 2 - \frac { 10 } { 3 x - 2 }$ 
A)  $3 x ^ { 2 } + 3 x + 4 + \frac { 2 } { 3 x - 2 }$ 
B)  $3 x ^ { 2 } + 3 x + 4 - \frac { 14 } { 3 x - 2 }$ 
C)  $3 x ^ { 2 } - x + 2 - \frac { 2 } { 3 x - 2 }$ 
D)  $3 x ^ { 2 } - x + 2 - \frac { 10 } { 3 x - 2 }$

Question 3

Perform the indicated operation. Simplify, if possible. $\frac { 6 x ^ { 2 } + 7 x - 10 } { 7 x ^ { 2 } + 8 x - 12 } \cdot \frac { 7 x ^ { 2 } + x - 6 } { 36 x ^ { 2 } - 25 }$

Accepted Answer

A)  $\frac { x + 1 } { 6 x + 5 }$ 
B)  $\frac { x - 1 } { 6 x - 5 }$ 
C)  $\frac { 2 x + 9 } { 290 }$ 
D)  $\frac { ( x + 2 ) ( 7 x + 6 ) } { ( x - 2 ) ( 6 x + 5 ) }$ 
A)  $\frac { x + 1 } { 6 x + 5 }$ 
B)  $\frac { x - 1 } { 6 x - 5 }$ 
C)  $\frac { 2 x + 9 } { 290 }$ 
D)  $\frac { ( x + 2 ) ( 7 x + 6 ) } { ( x - 2 ) ( 6 x + 5 ) }$

Question 4

Perform the operations and simplify the result when possible. $\frac { 6 x } { x + 1 } + \frac { 2 } { x + 1 } - \frac { 4 x } { x + 1 }$

Accepted Answer

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

Question 5

A boat can cruise at 35 mph in still water. What is its cruising speed upstream against a current of 5 mph?
 ______ mph

Accepted Answer

The answer of A boat can cruise at 35 mph...

Question 6

Multiply, then simplify if possible. $\frac { x ^ { 2 } - x } { x } \cdot \frac { 3 x - 9 } { 3 - 3 x }$

Accepted Answer

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

Question 7

Solve the proportion. $\frac { r - 2 } { 5 } = \frac { r } { 7 }$

Accepted Answer

The answer of Solve the proportion. \(\frac { r -...

Question 8

Solve the problem by writing a variation model. Under constant temperature, the volume occupied by a gas varies inversely to the pressure applied. If the gas occupies a volume of 18 cubic inches under a pressure of 5 pounds per square inch, find the volume when the gas is subjected to a pressure of 10 pounds per square inch. __________ in3

Accepted Answer

Question 9

Perform the division. $\left( 3 y - 12 + 15 y ^ { 2 } \right) \div ( 5 y - 4 )$

Accepted Answer

A)  $3 - y$ 
B)  $3 y + 3$ 
C)  $y + 3$ 
D)  $3 y - 3$ 
E)  $y - 3$ 
A)  $3 - y$ 
B)  $3 y + 3$ 
C)  $y + 3$ 
D)  $3 y - 3$ 
E)  $y - 3$

Question 10

Use the factor theorem and determine whether the first expression is a factor of P ( x ). $x - 4 ; P ( x ) = x ^ { 3 } - 4 x ^ { 2 } + 3 x - 10$

Accepted Answer

The answer of Use the factor theorem and determine whether...

Question 11

Use synthetic division to perform the division. $\left( 2 x ^ { 2 } - 13 x + 15 \right) \div ( x - 5 )$

Accepted Answer

A)  $2 x + 3$ 
B)  $2 x - 5$ 
C)  $2 x - 3$ 
D)  $2 x + 5$ 
E)  $2 x + 8$ 
A)  $2 x + 3$ 
B)  $2 x - 5$ 
C)  $2 x - 3$ 
D)  $2 x + 5$ 
E)  $2 x + 8$

Question 12

Subtract, and then simplify, if possible. $\frac { 10 } { a + 4 } - \frac { 14 } { a + 3 }$

Accepted Answer

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

Question 13

Perform the division. $\frac { 6 x ^ { 2 } - x ^ { 4 } } { - 9 x }$

Accepted Answer

The answer of Perform the division. \(\frac { 6 x...

Question 14

Perform the division. $\frac { 4 x ^ { 2 } - x ^ { 3 } } { - 14 x }$

Accepted Answer

A)  $\frac { 2 x } { 7 } + \frac { x ^ { 2 } } { 14 }$ 
B)  $- \frac { 2 x ^ { 2 } } { 7 } + \frac { x ^ { 2 } } { 14 }$ 
C)  $- \frac { 2 x } { 7 } + \frac { x ^ { 2 } } { 14 }$ 
D)  $- \frac { 2 x } { 7 } - \frac { x ^ { 2 } } { 14 }$ 
E)  $\frac { 2 x } { 7 } - \frac { x ^ { 2 } } { 14 }$ 
A)  $\frac { 2 x } { 7 } + \frac { x ^ { 2 } } { 14 }$ 
B)  $- \frac { 2 x ^ { 2 } } { 7 } + \frac { x ^ { 2 } } { 14 }$ 
C)  $- \frac { 2 x } { 7 } + \frac { x ^ { 2 } } { 14 }$ 
D)  $- \frac { 2 x } { 7 } - \frac { x ^ { 2 } } { 14 }$ 
E)  $\frac { 2 x } { 7 } - \frac { x ^ { 2 } } { 14 }$

Question 15

Express the verbal model in symbols. C varies directly as the square of p .

Accepted Answer

A)  $C = k \sqrt { p }$ 
B)  $C = k p ^ { 2 }$ 
C)  $C = k p$ 
D)  $C = \frac { k } { p ^ { 2 } }$ 
E)  $C = k + p ^ { 2 }$ 
A)  $C = k \sqrt { p }$ 
B)  $C = k p ^ { 2 }$ 
C)  $C = k p$ 
D)  $C = \frac { k } { p ^ { 2 } }$ 
E)  $C = k + p ^ { 2 }$

Question 16

Perform the indicated operation. Simplify, if possible. $\frac { x - 3 } { x - 4 } + \frac { x - 6 } { x + 1 }$

Accepted Answer

A)  $\frac { 2 x - 9 } { ( x - 4 ) ( x + 1 ) }$ 
B)  $\frac { 2 x - 9 } { 2 x - 3 }$ 
C)  $\frac { 2 x ^ { 2 } - 11 x - 19 } { ( x - 4 ) ( x + 1 ) }$ 
D)  $\frac { 2 x ^ { 2 } - 12 x + 21 } { ( x - 4 ) ( x + 1 ) }$ 
A)  $\frac { 2 x - 9 } { ( x - 4 ) ( x + 1 ) }$ 
B)  $\frac { 2 x - 9 } { 2 x - 3 }$ 
C)  $\frac { 2 x ^ { 2 } - 11 x - 19 } { ( x - 4 ) ( x + 1 ) }$ 
D)  $\frac { 2 x ^ { 2 } - 12 x + 21 } { ( x - 4 ) ( x + 1 ) }$

Question 17

If it takes a teacher 3 hours to fill out report cards, what part of the job does she accomplish in x hours?

Accepted Answer

The answer of If it takes a teacher 3 hours...

Question 18

Use synthetic division to perform the division. $\frac { 2 x ^ { 3 } - 12 - 29 x } { x - 4 }$

Accepted Answer

A)  $2 x ^ { 2 } - 8 x - 3$ 
B)  $2 x ^ { 2 } + 8 x + 3$ 
C)  $2 x ^ { 2 } + 8 x + 4$ 
D)  $2 x ^ { 2 } - 8 x + 3$ 
E)  $2 x ^ { 2 } + 8 x - 3$ 
A)  $2 x ^ { 2 } - 8 x - 3$ 
B)  $2 x ^ { 2 } + 8 x + 3$ 
C)  $2 x ^ { 2 } + 8 x + 4$ 
D)  $2 x ^ { 2 } - 8 x + 3$ 
E)  $2 x ^ { 2 } + 8 x - 3$

Question 19

Use the factor theorem and determine whether the first expression is a factor of P ( x ). $x + 1 ; P ( x ) = 4 x ^ { 2 } + 6 x + 2$ ( Hint : Write $x + 1$ as $x - ( - 1 )$ .)

Accepted Answer

The answer of Use the factor theorem and determine whether...

Question 20

Solve the proportion. $\frac { 2 } { c } = \frac { c - 4 } { 6 }$

Accepted Answer

A)  $c = 6 , c = - 2$ 
B)  $c = 2 , c = - 3$ 
C)  c=-3 
D)  c=-2 
E)  no solution 
A)  $c = 6 , c = - 2$ 
B)  $c = 2 , c = - 3$ 
C)  c=-3 
D)  c=-2 
E)  no solution

A plane can fly 260 miles in the same time as it takes a car to go 100 miles. If the car travels 80 mph slower than the plane, find the speed of the plane.

Divide using long division: $\frac { 9 x ^ { 3 } + 3 x ^ { 2 } + 6 x - 6 } { 3 x - 2 }$

Perform the indicated operation. Simplify, if possible. $\frac { 6 x ^ { 2 } + 7 x - 10 } { 7 x ^ { 2 } + 8 x - 12 } \cdot \frac { 7 x ^ { 2 } + x - 6 } { 36 x ^ { 2 } - 25 }$

Perform the operations and simplify the result when possible. $\frac { 6 x } { x + 1 } + \frac { 2 } { x + 1 } - \frac { 4 x } { x + 1 }$

A boat can cruise at 35 mph in still water. What is its cruising speed upstream against a current of 5 mph? ______ mph

Multiply, then simplify if possible. $\frac { x ^ { 2 } - x } { x } \cdot \frac { 3 x - 9 } { 3 - 3 x }$

Solve the proportion. $\frac { r - 2 } { 5 } = \frac { r } { 7 }$

Perform the division. $\left( 3 y - 12 + 15 y ^ { 2 } \right) \div ( 5 y - 4 )$

Use the factor theorem and determine whether the first expression is a factor of P ( x ). $x - 4 ; P ( x ) = x ^ { 3 } - 4 x ^ { 2 } + 3 x - 10$

Use synthetic division to perform the division. $\left( 2 x ^ { 2 } - 13 x + 15 \right) \div ( x - 5 )$

Subtract, and then simplify, if possible. $\frac { 10 } { a + 4 } - \frac { 14 } { a + 3 }$

Perform the division. $\frac { 6 x ^ { 2 } - x ^ { 4 } } { - 9 x }$

Perform the division. $\frac { 4 x ^ { 2 } - x ^ { 3 } } { - 14 x }$

Express the verbal model in symbols. C varies directly as the square of p .

Perform the indicated operation. Simplify, if possible. $\frac { x - 3 } { x - 4 } + \frac { x - 6 } { x + 1 }$

If it takes a teacher 3 hours to fill out report cards, what part of the job does she accomplish in x hours?

Use synthetic division to perform the division. $\frac { 2 x ^ { 3 } - 12 - 29 x } { x - 4 }$

Use the factor theorem and determine whether the first expression is a factor of P ( x ). $x + 1 ; P ( x ) = 4 x ^ { 2 } + 6 x + 2$ ( Hint : Write $x + 1$ as $x - ( - 1 )$ .)

Solve the proportion. $\frac { 2 } { c } = \frac { c - 4 } { 6 }$

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

A plane can fly 260 miles in the same time as it takes a car to go 100 miles. If the car travels 80 mph slower than the plane, find the speed of the plane.

Divide using long division: 9x3+3x2+6x−63x−2\frac { 9 x ^ { 3 } + 3 x ^ { 2 } + 6 x - 6 } { 3 x - 2 }3x−29x3+3x2+6x−6​

Perform the indicated operation. Simplify, if possible. 6x2+7x−107x2+8x−12⋅7x2+x−636x2−25\frac { 6 x ^ { 2 } + 7 x - 10 } { 7 x ^ { 2 } + 8 x - 12 } \cdot \frac { 7 x ^ { 2 } + x - 6 } { 36 x ^ { 2 } - 25 }7x2+8x−126x2+7x−10​⋅36x2−257x2+x−6​

Perform the operations and simplify the result when possible. 6xx+1+2x+1−4xx+1\frac { 6 x } { x + 1 } + \frac { 2 } { x + 1 } - \frac { 4 x } { x + 1 }x+16x​+x+12​−x+14x​

A boat can cruise at 35 mph in still water. What is its cruising speed upstream against a current of 5 mph? ______ mph

Multiply, then simplify if possible. x2−xx⋅3x−93−3x\frac { x ^ { 2 } - x } { x } \cdot \frac { 3 x - 9 } { 3 - 3 x }xx2−x​⋅3−3x3x−9​

Solve the proportion. r−25=r7\frac { r - 2 } { 5 } = \frac { r } { 7 }5r−2​=7r​

Perform the division. (3y−12+15y2)÷(5y−4)\left( 3 y - 12 + 15 y ^ { 2 } \right) \div ( 5 y - 4 )(3y−12+15y2)÷(5y−4)

Use the factor theorem and determine whether the first expression is a factor of P ( x ). x−4;P(x)=x3−4x2+3x−10x - 4 ; P ( x ) = x ^ { 3 } - 4 x ^ { 2 } + 3 x - 10x−4;P(x)=x3−4x2+3x−10

Use synthetic division to perform the division. (2x2−13x+15)÷(x−5)\left( 2 x ^ { 2 } - 13 x + 15 \right) \div ( x - 5 )(2x2−13x+15)÷(x−5)

Subtract, and then simplify, if possible. 10a+4−14a+3\frac { 10 } { a + 4 } - \frac { 14 } { a + 3 }a+410​−a+314​

Perform the division. 6x2−x4−9x\frac { 6 x ^ { 2 } - x ^ { 4 } } { - 9 x }−9x6x2−x4​

Perform the division. 4x2−x3−14x\frac { 4 x ^ { 2 } - x ^ { 3 } } { - 14 x }−14x4x2−x3​

Express the verbal model in symbols. C varies directly as the square of p .

Perform the indicated operation. Simplify, if possible. x−3x−4+x−6x+1\frac { x - 3 } { x - 4 } + \frac { x - 6 } { x + 1 }x−4x−3​+x+1x−6​

If it takes a teacher 3 hours to fill out report cards, what part of the job does she accomplish in x hours?

Use synthetic division to perform the division. 2x3−12−29xx−4\frac { 2 x ^ { 3 } - 12 - 29 x } { x - 4 }x−42x3−12−29x​

Use the factor theorem and determine whether the first expression is a factor of P ( x ). x+1;P(x)=4x2+6x+2x + 1 ; P ( x ) = 4 x ^ { 2 } + 6 x + 2x+1;P(x)=4x2+6x+2 ( Hint : Write x+1x + 1x+1 as x−(−1)x - ( - 1 )x−(−1) .)

Solve the proportion. 2c=c−46\frac { 2 } { c } = \frac { c - 4 } { 6 }c2​=6c−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

Divide using long division: $\frac { 9 x ^ { 3 } + 3 x ^ { 2 } + 6 x - 6 } { 3 x - 2 }$

Perform the indicated operation. Simplify, if possible. $\frac { 6 x ^ { 2 } + 7 x - 10 } { 7 x ^ { 2 } + 8 x - 12 } \cdot \frac { 7 x ^ { 2 } + x - 6 } { 36 x ^ { 2 } - 25 }$

Perform the operations and simplify the result when possible. $\frac { 6 x } { x + 1 } + \frac { 2 } { x + 1 } - \frac { 4 x } { x + 1 }$

Multiply, then simplify if possible. $\frac { x ^ { 2 } - x } { x } \cdot \frac { 3 x - 9 } { 3 - 3 x }$

Solve the proportion. $\frac { r - 2 } { 5 } = \frac { r } { 7 }$

Perform the division. $\left( 3 y - 12 + 15 y ^ { 2 } \right) \div ( 5 y - 4 )$

Use the factor theorem and determine whether the first expression is a factor of P ( x ). $x - 4 ; P ( x ) = x ^ { 3 } - 4 x ^ { 2 } + 3 x - 10$

Use synthetic division to perform the division. $\left( 2 x ^ { 2 } - 13 x + 15 \right) \div ( x - 5 )$

Subtract, and then simplify, if possible. $\frac { 10 } { a + 4 } - \frac { 14 } { a + 3 }$

Perform the division. $\frac { 6 x ^ { 2 } - x ^ { 4 } } { - 9 x }$

Perform the division. $\frac { 4 x ^ { 2 } - x ^ { 3 } } { - 14 x }$

Perform the indicated operation. Simplify, if possible. $\frac { x - 3 } { x - 4 } + \frac { x - 6 } { x + 1 }$

Use synthetic division to perform the division. $\frac { 2 x ^ { 3 } - 12 - 29 x } { x - 4 }$

Use the factor theorem and determine whether the first expression is a factor of P ( x ). $x + 1 ; P ( x ) = 4 x ^ { 2 } + 6 x + 2$ ( Hint : Write $x + 1$ as $x - ( - 1 )$ .)

Solve the proportion. $\frac { 2 } { c } = \frac { c - 4 } { 6 }$