Question 1

Simplify the complex fraction.

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 2

Perform the operation and simplify the result when possible.

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 3

Assume that all variables represent positive numbers. Assume that   varies jointly with   and   . If   when   and   , find   when   and   .

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 4

Perform the operation and simplify the result when possible.

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 5

Use similar triangles to help solve the problem. A tree casts a shadow of 24 feet at the same time as a 5-foot tall man casts a shadow of 4 feet. Find the height of the tree.

Accepted Answer

A)  h = 27 ft 
B)  h = 42 ft 
C)  h = 30 ft 
D)  h = 35 ft 
E)  h = 22 ft 
A)  h = 27 ft 
B)  h = 42 ft 
C)  h = 30 ft 
D)  h = 35 ft 
E)  h = 22 ft

Question 6

Determine the domain of the given function.

Accepted Answer

A)    
B)    
C)    
D)    
A)    
B)    
C)    
D)

Question 7

Perform the division. Write the answer without using negative exponents.

Accepted Answer

A)    
B)    
C)    
D)    
A)    
B)    
C)    
D)

Question 8

Solve the equation and check the solution.

Accepted Answer

A)  - 16 
B)  - 8 
C)  16 
D)  8 
E)  no solution 
A)  - 16 
B)  - 8 
C)  16 
D)  8 
E)  no solution

Question 9

A recipe for spaghetti sauce requires 6 bottles of ketchup to make 8 gallons of sauce. How many bottles of ketchup are needed to make 56 gallons of sauce?

Accepted Answer

The answer of A recipe for spaghetti sauce requires 6...

Question 10

Solve the equation and check the solution.

Accepted Answer

A)  - 105 
B)  105 
C)  210 
D)  - 210 
E)  no solution 
A)  - 105 
B)  105 
C)  210 
D)  - 210 
E)  no solution

Question 11

Perform the operation. Simplify the answer, if possible.

Accepted Answer

The answer of Perform the operation. Simplify the answer, if...

Question 12

Perform the division:   by   .

Accepted Answer

The answer of Perform the division:   by ...

Question 13

Simplify this rational expression. Assume the denominator never equals zero.

Accepted Answer

A)  1 
B)  2 a - 8 x 
C)  8 x - 2 a 
D)  -1 
E)  Does not simplify further. 
A)  1 
B)  2 a - 8 x 
C)  8 x - 2 a 
D)  -1 
E)  Does not simplify further.

Question 14

Let P ( x ) = 4 x  3 - 3 x  2 + 2 x - 5. Evaluate P ( x ) by substituting the given value of x into the polynomial and simplifying. Then evaluate the polynomial by using the remainder theorem and synthetic division. P (-4)

Accepted Answer

A)  P (-4) = -327 
B)  P (-4) = -317 
C)  P (-4) = -322 
D)  P (-4) = -347 
A)  P (-4) = -327 
B)  P (-4) = -317 
C)  P (-4) = -322 
D)  P (-4) = -347

Question 15

Add the rational expressions. Be sure to express your answer in simplest form.

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 16

Solve the proportion for the variable.   z = __________

Accepted Answer

The answer of Solve the proportion for the variable. ...

Question 17

Use similar triangles to help solve the problem. An airplane ascends 160 feet as it flies a horizontal distance of 1,000 feet. How much altitude will it gain as it flies a horizontal distance of 1 mile? ( Hint: 5,280 feet = 1 mile.) Round your answer to the nearest integer.

Accepted Answer

A)  x = 870 ft 
B)  x = 813 ft 
C)  x = 845 ft 
D)  x = 885 ft 
E)  x = 833 ft 
A)  x = 870 ft 
B)  x = 813 ft 
C)  x = 845 ft 
D)  x = 885 ft 
E)  x = 833 ft

Question 18

Perform the division:   by   .

Accepted Answer

A)    
B)    
C)    
D)    
A)    
B)    
C)    
D)

Question 19

The focal length f of a lens is given by the formula   where d1 is the distance from the object to the lens and d2 is the distance from the lens to the image. Solve the formula for f .

Accepted Answer

The answer of The focal length f of a lens...

Question 20

Simplify:

Accepted Answer

A)    
B)    
C)    
D)    
A)    
B)    
C)    
D)

Simplify the complex fraction. $Simplify the complex fraction.$

Perform the operation and simplify the result when possible.

Assume that all variables represent positive numbers. Assume that varies jointly with and . If when and , find when and .

Perform the operation and simplify the result when possible.

Use similar triangles to help solve the problem. A tree casts a shadow of 24 feet at the same time as a 5-foot tall man casts a shadow of 4 feet. Find the height of the tree.

Determine the domain of the given function.

Perform the division. Write the answer without using negative exponents.

Solve the equation and check the solution.

A recipe for spaghetti sauce requires 6 bottles of ketchup to make 8 gallons of sauce. How many bottles of ketchup are needed to make 56 gallons of sauce?

Solve the equation and check the solution.

Perform the operation. Simplify the answer, if possible.

Perform the division: by .

Simplify this rational expression. Assume the denominator never equals zero.

Let P ( x ) = 4 x ³- 3 x ²+ 2 x - 5. Evaluate P ( x ) by substituting the given value of x into the polynomial and simplifying. Then evaluate the polynomial by using the remainder theorem and synthetic division. P (-4)

Add the rational expressions. Be sure to express your answer in simplest form.

Solve the proportion for the variable. z = __________

Use similar triangles to help solve the problem. An airplane ascends 160 feet as it flies a horizontal distance of 1,000 feet. How much altitude will it gain as it flies a horizontal distance of 1 mile? ( Hint: 5,280 feet = 1 mile.) Round your answer to the nearest integer.

Perform the division: by .

The focal length f of a lens is given by the formula where d1 is the distance from the object to the lens and d2 is the distance from the lens to the image. Solve the formula for f .

Simplify:

A Review of Basic Algebra

Graphs, Equations of Lines, and Functions

Systems of Linear Equations

Inequalities

Polynomials, Polynomial Functions, and Equations

Radical Expressions and Equations

Quadratic Equations and Functions; Inequalities; and Algebra, Composition, and Inverses of Functions

Exponential and Logarithmic Functions

Conic Sections and More Graphing

Miscellaneous Topics

Filters

Exam 6: Rational Expressions

Simplify the complex fraction.

Perform the operation and simplify the result when possible.

Assume that all variables represent positive numbers. Assume that varies jointly with and . If when and , find when and .

Perform the operation and simplify the result when possible.

Use similar triangles to help solve the problem. A tree casts a shadow of 24 feet at the same time as a 5-foot tall man casts a shadow of 4 feet. Find the height of the tree.

Determine the domain of the given function.

Perform the division. Write the answer without using negative exponents.

Solve the equation and check the solution.

A recipe for spaghetti sauce requires 6 bottles of ketchup to make 8 gallons of sauce. How many bottles of ketchup are needed to make 56 gallons of sauce?

Solve the equation and check the solution.

Perform the operation. Simplify the answer, if possible.

Perform the division: by .

Simplify this rational expression. Assume the denominator never equals zero.

Let P ( x ) = 4 x 3 - 3 x 2 + 2 x - 5. Evaluate P ( x ) by substituting the given value of x into the polynomial and simplifying. Then evaluate the polynomial by using the remainder theorem and synthetic division. P (-4)

Add the rational expressions. Be sure to express your answer in simplest form.

Solve the proportion for the variable. z = __________

Use similar triangles to help solve the problem. An airplane ascends 160 feet as it flies a horizontal distance of 1,000 feet. How much altitude will it gain as it flies a horizontal distance of 1 mile? ( Hint: 5,280 feet = 1 mile.) Round your answer to the nearest integer.

Perform the division: by .

The focal length f of a lens is given by the formula where d1 is the distance from the object to the lens and d2 is the distance from the lens to the image. Solve the formula for f .

Simplify:

A Review of Basic Algebra

Graphs, Equations of Lines, and Functions

Systems of Linear Equations

Inequalities

Polynomials, Polynomial Functions, and Equations

Radical Expressions and Equations

Quadratic Equations and Functions; Inequalities; and Algebra, Composition, and Inverses of Functions

Exponential and Logarithmic Functions

Conic Sections and More Graphing

Miscellaneous Topics

Filters

Simplify the complex fraction. $Simplify the complex fraction.$

Let P ( x ) = 4 x ³- 3 x ²+ 2 x - 5. Evaluate P ( x ) by substituting the given value of x into the polynomial and simplifying. Then evaluate the polynomial by using the remainder theorem and synthetic division. P (-4)