Question 1

Perform the indicated operation: $\frac { 3 + i } { 5 - 4 i }$

Accepted Answer

A)  $11 + 17 i$ 
B)  $3 + i$ 
C)  $\frac { 11 } { 41 } + \frac { 17 } { 41 } i$ 
D)  $\frac { 19 } { 41 } + \frac { 17 } { 41 } i$ 
A)  $11 + 17 i$ 
B)  $3 + i$ 
C)  $\frac { 11 } { 41 } + \frac { 17 } { 41 } i$ 
D)  $\frac { 19 } { 41 } + \frac { 17 } { 41 } i$

Question 2

A baseball diamond is a square, 90 feet on a side. If the third baseman fields a ground ball 80 feet directly behind third base, how far must he throw the ball to throw a runner out at first base?
 Find the exact answer. Then give an approximation to two decimal places. 
 
 Enter your answers without units. Separate the exact answer and approximation with a comma.

Accepted Answer

The answer of A baseball diamond is a square, 90...

Question 3

For right triangle ABC with the right angle at C, a = 9 cm and b = 40 cm. Find side c . c = ______ cm

Accepted Answer

The answer of For right triangle ABC with the right...

Question 4

Perform the indicated operation. Simplify, if possible. $( 4 \sqrt { 3 } - 1 ) ^ { 2 }$

Accepted Answer

A)  49 
B)  $49 - 8 \sqrt { 3 }$ 
C)  $49 - 4 \sqrt { 3 }$ 
D)  -72 
A)  49 
B)  $49 - 8 \sqrt { 3 }$ 
C)  $49 - 4 \sqrt { 3 }$ 
D)  -72

Question 5

A(n) __________ triangle has three sides of equal length and three 60 ∘ angles.

Accepted Answer

A(n) equilateral tri

Question 6

Evaluate the expression. $- 27 ^ { \frac { 1 } { 3 } }$

Accepted Answer

The answer of Evaluate the expression. \(- 27 ^ {...

Question 7

Simplify the expression. $\sqrt { 20 }$

Accepted Answer

A)  $5 \sqrt { 2 }$ 
B)  $2 \sqrt { 5 }$ 
C)  $4 \sqrt { 5 }$ 
D)  $2 \sqrt { 10 }$ 
E)  $25 \sqrt { 2 }$ 
A)  $5 \sqrt { 2 }$ 
B)  $2 \sqrt { 5 }$ 
C)  $4 \sqrt { 5 }$ 
D)  $2 \sqrt { 10 }$ 
E)  $25 \sqrt { 2 }$

Question 8

Perform the indicated operation. Simplify, if possible. $( 3 \sqrt { x + 3 } - 3 ) ^ { 2 }$

Accepted Answer

A)  $9 x + 36$ 
B)  $9 x + 36 - 18 \sqrt { x + 3 }$ 
C)  $9 x + 27$ 
D)  $9 x + 36 - 9 \sqrt { x + 3 }$ 
A)  $9 x + 36$ 
B)  $9 x + 36 - 18 \sqrt { x + 3 }$ 
C)  $9 x + 27$ 
D)  $9 x + 36 - 9 \sqrt { x + 3 }$

Question 9

Express the number in terms of i . $\sqrt { - \frac { 36 } { 25 } }$

Accepted Answer

A)  $- \frac { 6 } { 5 }$ 
B)  $- \frac { 6 } { 5 } \sqrt { i }$ 
C)  $- \frac { 36 } { 25 } i$ 
D)  $\frac { 6 } { 5 } i$ 
E)  $\frac { 5 } { 6 i }$ 
A)  $- \frac { 6 } { 5 }$ 
B)  $- \frac { 6 } { 5 } \sqrt { i }$ 
C)  $- \frac { 36 } { 25 } i$ 
D)  $\frac { 6 } { 5 } i$ 
E)  $\frac { 5 } { 6 i }$

Question 10

Find the missing lengths in the triangle. Give the answer to two decimal places.

Accepted Answer

A)  $x = 13.03 , y = 12.28$ 
B)  $x = 12.28 , y = 12.28$ 
C)  $x = 13.03 , y = 11.53$ 
D)  $x = 12.28 , y = 13.03$ 
E)  $x = 13.03 , y = 13.03$ 
A)  $x = 13.03 , y = 12.28$ 
B)  $x = 12.28 , y = 12.28$ 
C)  $x = 13.03 , y = 11.53$ 
D)  $x = 12.28 , y = 13.03$ 
E)  $x = 13.03 , y = 13.03$

Question 11

When solving equations containing radicals, try to __________ one radical expression on one side of the equation.

Accepted Answer

When solving equations containing radica

Question 12

Perform the operation. Write the answer in a+bi  form. $( 8 - 5 i ) - ( 4 + 2 i )$

Accepted Answer

A)  $7 - 11 i$ 
B)  $4 - 10 i$ 
C)  $7 - 8 i$ 
D)  $2 - 9 i$ 
E)  $4 - 7 i$ 
A)  $7 - 11 i$ 
B)  $4 - 10 i$ 
C)  $7 - 8 i$ 
D)  $2 - 9 i$ 
E)  $4 - 7 i$

Question 13

Solve: $\sqrt { 2 x + 9 } + 3 = x$

Accepted Answer

A)  $\{ 4,7 \}$ 
B)  $\{ 7,5 \}$ 
C)  no solution 
D)  $\{ 8 \}$ 
A)  $\{ 4,7 \}$ 
B)  $\{ 7,5 \}$ 
C)  no solution 
D)  $\{ 8 \}$

Question 14

Use the distance formula to define a triangle with vertices (-2,5) , (2,8) , and (6,5) .

Accepted Answer

A)  isosceles triangle 
B)  right triangle 
C)  equilateral triangle 
A)  isosceles triangle 
B)  right triangle 
C)  equilateral triangle

Question 15

Multiply. $\sqrt { - 2 } \sqrt { - 14 }$

Accepted Answer

A)  $7 \sqrt { 2 } i$ 
B)  $2 \sqrt { 7 } i$ 
C)  $- 2 \sqrt { 7 }$ 
D)  $- 2 \sqrt { 7 i }$ 
E)  $- 7 \sqrt { 2 }$ 
A)  $7 \sqrt { 2 } i$ 
B)  $2 \sqrt { 7 } i$ 
C)  $- 2 \sqrt { 7 }$ 
D)  $- 2 \sqrt { 7 i }$ 
E)  $- 7 \sqrt { 2 }$

Question 16

Find the missing lengths in the triangle. Give the answer to two decimal places. 
  
x= __________ y= __________

Accepted Answer

The answer of Find the missing lengths in the triangle....

Question 17

Square the quantity and simplify the result, if possible. $( 3 \sqrt { 2 r } - 5 ) ^ { 2 }$

Accepted Answer

A)  $18 r + 30 \sqrt { 2 r } + 25$ 
B)  $- 18 r + 30 \sqrt { 2 r } - 25$ 
C)  $18 r - 30 \sqrt { 2 r } + 25$ 
D)  $- 18 r + 30 \sqrt { 2 r } + 25$ 
E)  $18 r - 30 \sqrt { 2 r } - 25$ 
A)  $18 r + 30 \sqrt { 2 r } + 25$ 
B)  $- 18 r + 30 \sqrt { 2 r } - 25$ 
C)  $18 r - 30 \sqrt { 2 r } + 25$ 
D)  $- 18 r + 30 \sqrt { 2 r } + 25$ 
E)  $18 r - 30 \sqrt { 2 r } - 25$

Question 18

A __________ number is any number that can be written in the form $a + b i$ , where a and b are real numbers and $i = \sqrt { - 1 }$ .

Accepted Answer

A)  fractional 
B)  positive 
C)  rational 
D)  complex 
E)  real 
A)  fractional 
B)  positive 
C)  rational 
D)  complex 
E)  real

Question 19

Solve the equation for the specified variable. $u = \sqrt { 2 g w } \text { for } w$

Accepted Answer

A)  $w = \sqrt { 2 g u }$ 
B)  $w = \frac { u } { \sqrt { 2 g } }$ 
C)  $w = \frac { 2 g } { u ^ { 2 } }$ 
D)  $w = \frac { u } { 2 g }$ 
E)  $w = \frac { u ^ { 2 } } { 2 g }$ 
A)  $w = \sqrt { 2 g u }$ 
B)  $w = \frac { u } { \sqrt { 2 g } }$ 
C)  $w = \frac { 2 g } { u ^ { 2 } }$ 
D)  $w = \frac { u } { 2 g }$ 
E)  $w = \frac { u ^ { 2 } } { 2 g }$

Question 20

Simplify the expression. $\sqrt [ 3 ] { 32 }$

Accepted Answer

The answer of Simplify the expression. \(\sqrt [ 3 ]...

Perform the indicated operation: $\frac { 3 + i } { 5 - 4 i }$

For right triangle ABC with the right angle at C, a = 9 cm and b = 40 cm. Find side c . c = ______ cm

Perform the indicated operation. Simplify, if possible. $( 4 \sqrt { 3 } - 1 ) ^ { 2 }$

A(n) __________ triangle has three sides of equal length and three 60 ^∘ angles.

Evaluate the expression. $- 27 ^ { \frac { 1 } { 3 } }$

Simplify the expression. $\sqrt { 20 }$

Perform the indicated operation. Simplify, if possible. $( 3 \sqrt { x + 3 } - 3 ) ^ { 2 }$

Express the number in terms of i . $\sqrt { - \frac { 36 } { 25 } }$

Find the missing lengths in the triangle. Give the answer to two decimal places.

When solving equations containing radicals, try to __________ one radical expression on one side of the equation.

Perform the operation. Write the answer in a+bi form. $( 8 - 5 i ) - ( 4 + 2 i )$

Solve: $\sqrt { 2 x + 9 } + 3 = x$

Use the distance formula to define a triangle with vertices (-2,5) , (2,8) , and (6,5) .

Multiply. $\sqrt { - 2 } \sqrt { - 14 }$

Find the missing lengths in the triangle. Give the answer to two decimal places. x= y=

Square the quantity and simplify the result, if possible. $( 3 \sqrt { 2 r } - 5 ) ^ { 2 }$

A __________ number is any number that can be written in the form $a + b i$ , where a and b are real numbers and $i = \sqrt { - 1 }$ .

Solve the equation for the specified variable. $u = \sqrt { 2 g w } \text { for } w$

Simplify the expression. $\sqrt [ 3 ] { 32 }$

A Review of Basic Algebra

Graphs, Equations of Lines, and Functions

Systems of Equations

Inequalities

Exponents, Polynomials, and Polynomial Functions

Rational Expression and Equations

Quadratic Equations, Functions, and Inequalities

Exponential and Logarithmic Functions

Conic Sections; More Graphing

Miscellaneous Topics

Filters

Exam 7: Radical Expressions and Equations

Perform the indicated operation: 3+i5−4i\frac { 3 + i } { 5 - 4 i }5−4i3+i​

For right triangle ABC with the right angle at C, a = 9 cm and b = 40 cm. Find side c . c = ______ cm

Perform the indicated operation. Simplify, if possible. (43−1)2( 4 \sqrt { 3 } - 1 ) ^ { 2 }(43​−1)2

A(n) __________ triangle has three sides of equal length and three 60 ∘ angles.

Evaluate the expression. −2713- 27 ^ { \frac { 1 } { 3 } }−2731​

Simplify the expression. 20\sqrt { 20 }20​

Perform the indicated operation. Simplify, if possible. (3x+3−3)2( 3 \sqrt { x + 3 } - 3 ) ^ { 2 }(3x+3​−3)2

Express the number in terms of i . −3625\sqrt { - \frac { 36 } { 25 } }−2536​​

Find the missing lengths in the triangle. Give the answer to two decimal places.

When solving equations containing radicals, try to __________ one radical expression on one side of the equation.

Perform the operation. Write the answer in a+bi form. (8−5i)−(4+2i)( 8 - 5 i ) - ( 4 + 2 i )(8−5i)−(4+2i)

Solve: 2x+9+3=x\sqrt { 2 x + 9 } + 3 = x2x+9​+3=x

Use the distance formula to define a triangle with vertices (-2,5) , (2,8) , and (6,5) .

Multiply. −2−14\sqrt { - 2 } \sqrt { - 14 }−2​−14​

Find the missing lengths in the triangle. Give the answer to two decimal places. x= __________ y= __________

Square the quantity and simplify the result, if possible. (32r−5)2( 3 \sqrt { 2 r } - 5 ) ^ { 2 }(32r​−5)2

A __________ number is any number that can be written in the form a+bia + b ia+bi , where a and b are real numbers and i=−1i = \sqrt { - 1 }i=−1​ .

Solve the equation for the specified variable. u=2gw for wu = \sqrt { 2 g w } \text { for } wu=2gw​ for w

Simplify the expression. 323\sqrt [ 3 ] { 32 }332​

A Review of Basic Algebra

Graphs, Equations of Lines, and Functions

Systems of Equations

Inequalities

Exponents, Polynomials, and Polynomial Functions

Rational Expression and Equations

Quadratic Equations, Functions, and Inequalities

Exponential and Logarithmic Functions

Conic Sections; More Graphing

Miscellaneous Topics

Filters

Perform the indicated operation: $\frac { 3 + i } { 5 - 4 i }$

Perform the indicated operation. Simplify, if possible. $( 4 \sqrt { 3 } - 1 ) ^ { 2 }$

A(n) __________ triangle has three sides of equal length and three 60 ^∘ angles.

Evaluate the expression. $- 27 ^ { \frac { 1 } { 3 } }$

Simplify the expression. $\sqrt { 20 }$

Perform the indicated operation. Simplify, if possible. $( 3 \sqrt { x + 3 } - 3 ) ^ { 2 }$

Express the number in terms of i . $\sqrt { - \frac { 36 } { 25 } }$

Perform the operation. Write the answer in a+bi form. $( 8 - 5 i ) - ( 4 + 2 i )$

Solve: $\sqrt { 2 x + 9 } + 3 = x$

Multiply. $\sqrt { - 2 } \sqrt { - 14 }$

Find the missing lengths in the triangle. Give the answer to two decimal places. x= y=

Square the quantity and simplify the result, if possible. $( 3 \sqrt { 2 r } - 5 ) ^ { 2 }$

A __________ number is any number that can be written in the form $a + b i$ , where a and b are real numbers and $i = \sqrt { - 1 }$ .

Solve the equation for the specified variable. $u = \sqrt { 2 g w } \text { for } w$

Simplify the expression. $\sqrt [ 3 ] { 32 }$