Question 1

Solve the equation for the indicated variable. $F = k \left( \frac { q _ { 1 } q _ { 2 } } { r ^ { 2 } } \right) ; \quad \text { for } r$

Accepted Answer

The answer of Solve the equation for the indicated variable....

Question 2

Find the solution set for the nonlinear inequality $\frac { 1 } { x - 3 } - \frac { 2 } { x - 2 } > 0$ .

Accepted Answer

A)  $( - \infty , - 3 ) \cup ( 2,4 )$ 
B)  $( - \infty , 2 ] \cup [ 3,4 ]$ 
C)  $( 2,3 )$ 
D)  $( - \infty , 2 )$ 
E)  $( - \infty , 2 ) \cup ( 3,4 )$ 
A)  $( - \infty , - 3 ) \cup ( 2,4 )$ 
B)  $( - \infty , 2 ] \cup [ 3,4 ]$ 
C)  $( 2,3 )$ 
D)  $( - \infty , 2 )$ 
E)  $( - \infty , 2 ) \cup ( 3,4 )$

Question 3

A cylindrical can has a volume of $36 \pi$ $\mathrm { cm } ^ { 3 }$ and a diameter of $3$ cm. What is its height?

Accepted Answer

Let @#LAT-DLM& be the height o

Question 4

Use scientific notation, laws of exponents, and a calculator to perform the indicated operations. State your answer correct to the number of significant digits indicated by the data. $\left( 4.01 \times 10 ^ { 16 } \right) \left( 8.11 \times 10 ^ { 10 } \right)$

Accepted Answer

The answer of Use scientific notation, laws of exponents, and...

Question 5

If $M ( 2,1 )$ is the midpoint of the line segment $A B$ , and if $A$ has coordinates $\left( - \frac { 1 } { 2 } , 6 \right)$ , find the coordinates of $B$ .

Accepted Answer

@#LAT-DLM& @#LAT-DLM& @#LAT-DLM& , @#LAT-DLM& @#LAT-DLM& @#LAT-DLM& .

Question 6

Factor the expression. $2 y ^ { 2 } x + x y + 5 y + 10 y ^ { 2 }$

Accepted Answer

A)  $x y ( 2 y - 1 ) ( x + 5 )$ 
B)  $y ^ { 2 } ( y + 1 ) ( 5 x + 5 )$ 
C)  $y ( 2 y + 1 ) ( x + 5 )$ 
D)  $y ( y + 2 ) ( 5 x + 1 )$ 
E)  $( y + 1 ) ^ { 2 } ( x + 5 )$ 
A)  $x y ( 2 y - 1 ) ( x + 5 )$ 
B)  $y ^ { 2 } ( y + 1 ) ( 5 x + 5 )$ 
C)  $y ( 2 y + 1 ) ( x + 5 )$ 
D)  $y ( y + 2 ) ( 5 x + 1 )$ 
E)  $( y + 1 ) ^ { 2 } ( x + 5 )$

Question 7

The owner of a tow truck wishes to change the mixture of antifreeze in his radiator. The radiator contains $15.5$ quarts of $35 \%$ antifreeze solution. How much would he need to drain and replace with pure antifreeze in order to get a $55 \%$ antifreeze solution?

Accepted Answer

Let @#LAT-DLM& be the amount of solution to drain.

Question 8

Use the properties of real numbers to write the expression without parentheses. $2 x \left( a - b - 2 c + \frac { d } { 2 } \right)$

Accepted Answer

A)  $x a - x b - 2 x c + x d$ 
B)  $2 x a - 2 x b - x c + 4 x d$ 
C)  $x a - 2 x b - 4 x c + x d$ 
D)  $2 x a - 2 x b - 4 x c + x d$ 
E)  $2 x a - x b - 2 x c + 2 x d$ 
A)  $x a - x b - 2 x c + x d$ 
B)  $2 x a - 2 x b - x c + 4 x d$ 
C)  $x a - 2 x b - 4 x c + x d$ 
D)  $2 x a - 2 x b - 4 x c + x d$ 
E)  $2 x a - x b - 2 x c + 2 x d$

Question 9

Evaluate $( 32 ) ^ { - 0.2 }$

Accepted Answer

A)  $2$ 
B)  $\frac { 1 } { 2 }$ 
C)  $16$ 
D)  $\frac { 1 } { 4 }$ 
E)  $\frac { 1 } { 1024 }$ 
A)  $2$ 
B)  $\frac { 1 } { 2 }$ 
C)  $16$ 
D)  $\frac { 1 } { 4 }$ 
E)  $\frac { 1 } { 1024 }$

Question 10

Simplify the expression. $\frac { y ^ { 2 } - \frac { 1 } { 4 } } { 2 y ^ { 2 } + 4 y + \frac { 3 } { 2 } }$

Accepted Answer

A)  $\frac { 2 y - 1 } { 2 y + 3 }$ 
B)  $\frac { 3 } { 4 } \left( \frac { y - 1 } { 2 y + 3 } \right)$ 
C)  $\frac { 1 } { 2 } \left( \frac { 2 y + 3 } { 2 y - 1 } \right)$ 
D)  $\frac { 1 } { 2 } \left( \frac { 2 y - 1 } { 2 y + 3 } \right)$ 
E)  $2 \left( \frac { 2 y + 1 } { 2 y - 3 } \right)$ 
A)  $\frac { 2 y - 1 } { 2 y + 3 }$ 
B)  $\frac { 3 } { 4 } \left( \frac { y - 1 } { 2 y + 3 } \right)$ 
C)  $\frac { 1 } { 2 } \left( \frac { 2 y + 3 } { 2 y - 1 } \right)$ 
D)  $\frac { 1 } { 2 } \left( \frac { 2 y - 1 } { 2 y + 3 } \right)$ 
E)  $2 \left( \frac { 2 y + 1 } { 2 y - 3 } \right)$

Question 11

Find the approximate solutions of the equation $x ^ { 3 } - 9 x ^ { 2 } = 24 - 26 x$ by drawing a graph in the interval $[ 1,5 ]$ .

Accepted Answer

The answer of Find the approximate solutions of the equation...

Question 12

The stopping distance D of a car after the brakes have been applied varies directly as the square of the speed s. A certain car traveling at 50 mi/h can stop in 240 ft. What is the maximum speed it can be traveling if it needs to stop in 180 ft? Round your answer to one decimal place.

Accepted Answer

The answer of The stopping distance D of a car...

Question 13

Simplify the expression. $\frac { x ^ { 2 } + x - 2 } { x ^ { 2 } + 2 x - 3 }$

Accepted Answer

A)  $\frac { x + 1 } { x + 2 }$ 
B)  $\frac { x + 2 } { x + 3 }$ 
C)  $\frac { x - 3 } { x - 2 }$ 
D)  $\frac { x + 3 } { x + 2 }$ 
E)  $\frac { x - 2 } { x - 2 }$ 
A)  $\frac { x + 1 } { x + 2 }$ 
B)  $\frac { x + 2 } { x + 3 }$ 
C)  $\frac { x - 3 } { x - 2 }$ 
D)  $\frac { x + 3 } { x + 2 }$ 
E)  $\frac { x - 2 } { x - 2 }$

Question 14

Rationalize the numerator of the expression. $\sqrt { x - 1 } + \sqrt { x }$

Accepted Answer

The answer of Rationalize the numerator of the expression. \(\sqrt...

Question 15

Perform the subtraction and simplify. $\frac { 2 } { x + 3 } - \frac { 1 } { x ^ { 2 } + 5 x + 6 }$

Accepted Answer

The answer of Perform the subtraction and simplify. \(\frac {...

Question 16

Perform the indicated operation. $\frac { 1 } { 4 } + \frac { 1 } { 12 }$

Accepted Answer

A)  $\frac { 1 } { 16 }$ 
B)  $\frac { 1 } { 48 }$ 
C)  $\frac { 1 } { 4 }$ 
D)  $\frac { 1 } { 3 }$ 
E)  $3$ 
A)  $\frac { 1 } { 16 }$ 
B)  $\frac { 1 } { 48 }$ 
C)  $\frac { 1 } { 4 }$ 
D)  $\frac { 1 } { 3 }$ 
E)  $3$

Question 17

Find the set $A \cup B$ if $A = \left\{ - 3 , - 2,0 , \frac { 1 } { 3 } , \frac { 2 } { 3 } , 6,9 \right\}$ and $B = \left\{ 0 , \frac { 1 } { 3 } , \frac { 2 } { 3 } \right\}$

Accepted Answer

A)  $\left( 0 , - 2 , - 3,6,9 , \frac { 1 } { 3 } , \frac { 2 } { 3 } \right)$ 
B)  $\left( 0 , - 2,3,6,9 , \frac { - 1 } { 3 } , \frac { 2 } { 3 } \right)$ 
C)  $\left\{ 0,2 , - 3,6,9 , \frac { 1 } { 3 } , \frac { - 2 } { 3 } \right\}$ 
D)  $\{ 0 , - 2 , - 3,6 , - 9 \}$ 
E)  $\left\{ 0 , - 2 , - 3,6,9 , \frac { 2 } { 3 } \right)$ 
A)  $\left( 0 , - 2 , - 3,6,9 , \frac { 1 } { 3 } , \frac { 2 } { 3 } \right)$ 
B)  $\left( 0 , - 2,3,6,9 , \frac { - 1 } { 3 } , \frac { 2 } { 3 } \right)$ 
C)  $\left\{ 0,2 , - 3,6,9 , \frac { 1 } { 3 } , \frac { - 2 } { 3 } \right\}$ 
D)  $\{ 0 , - 2 , - 3,6 , - 9 \}$ 
E)  $\left\{ 0 , - 2 , - 3,6,9 , \frac { 2 } { 3 } \right)$

Question 18

Find all real solutions of the equation. $| 5 x | = 9$

Accepted Answer

A)  $x = \frac { 9 } { 5 }$ ,
$x = - \frac { 9 } { 5 }$ 
B)  $x = \frac { 9 } { 5 }$ 
C)  $x = - \frac { 4 } { 5 }$ ,
$x = \frac { 4 } { 5 }$ 
D)  $x = 5$ ,
$x = 9$ 
E)  no solution 
A)  $x = \frac { 9 } { 5 }$ ,
$x = - \frac { 9 } { 5 }$ 
B)  $x = \frac { 9 } { 5 }$ 
C)  $x = - \frac { 4 } { 5 }$ ,
$x = \frac { 4 } { 5 }$ 
D)  $x = 5$ ,
$x = 9$ 
E)  no solution

Question 19

Carolyn and Brian work in an accounting office. If they work together they can complete a corporate tax return in $2.5$ hours. Working alone it would take Brian $35$ minutes longer than Carolyn to complete the return. How long does it take each person working alone to finish the job? If a third person is used to help complete the task, and works with the same efficiency as Brian, what is the total time it would take to complete the return if all three work together?

Accepted Answer

Let @#LAT-DLM& be the time it takes Carolyn to wor

Question 20

The resistance $R$ of a wire varies directly as its length $L$ and inversely as the square of twice its radius.
(a) Write an equation that expresses this direct variation.
(b) Find the constant of proportionality if a wire $2.4$ m long and
$0.004$ m in diameter has a resistance of
$150$ ohms.
(b), find the diameter of a wire that has a resistance of $90$ ohms and is
$1.2$ m long.
(c) Using the constant of proportionality from part

Accepted Answer

(a)
@#LAT-DLM&
(b) @#LAT-DLM&,

Solve the equation for the indicated variable. $F = k \left( \frac { q _ { 1 } q _ { 2 } } { r ^ { 2 } } \right) ; \quad \text { for } r$

Find the solution set for the nonlinear inequality $\frac { 1 } { x - 3 } - \frac { 2 } { x - 2 } > 0$ .

A cylindrical can has a volume of $36 \pi$ $\mathrm { cm } ^ { 3 }$ and a diameter of $3$ cm. What is its height?

Use scientific notation, laws of exponents, and a calculator to perform the indicated operations. State your answer correct to the number of significant digits indicated by the data. $\left( 4.01 \times 10 ^ { 16 } \right) \left( 8.11 \times 10 ^ { 10 } \right)$

If $M ( 2,1 )$ is the midpoint of the line segment $A B$ , and if $A$ has coordinates $\left( - \frac { 1 } { 2 } , 6 \right)$ , find the coordinates of $B$ .

Factor the expression. $2 y ^ { 2 } x + x y + 5 y + 10 y ^ { 2 }$

The owner of a tow truck wishes to change the mixture of antifreeze in his radiator. The radiator contains $15.5$ quarts of $35 \%$ antifreeze solution. How much would he need to drain and replace with pure antifreeze in order to get a $55 \%$ antifreeze solution?

Use the properties of real numbers to write the expression without parentheses. $2 x \left( a - b - 2 c + \frac { d } { 2 } \right)$

Evaluate $( 32 ) ^ { - 0.2 }$

Simplify the expression. $\frac { y ^ { 2 } - \frac { 1 } { 4 } } { 2 y ^ { 2 } + 4 y + \frac { 3 } { 2 } }$

Find the approximate solutions of the equation $x ^ { 3 } - 9 x ^ { 2 } = 24 - 26 x$ by drawing a graph in the interval $[ 1,5 ]$ .

The stopping distance D of a car after the brakes have been applied varies directly as the square of the speed s. A certain car traveling at 50 mi/h can stop in 240 ft. What is the maximum speed it can be traveling if it needs to stop in 180 ft? Round your answer to one decimal place.

Simplify the expression. $\frac { x ^ { 2 } + x - 2 } { x ^ { 2 } + 2 x - 3 }$

Rationalize the numerator of the expression. $\sqrt { x - 1 } + \sqrt { x }$

Perform the subtraction and simplify. $\frac { 2 } { x + 3 } - \frac { 1 } { x ^ { 2 } + 5 x + 6 }$

Perform the indicated operation. $\frac { 1 } { 4 } + \frac { 1 } { 12 }$

Find the set $A \cup B$ if $A = \left\{ - 3 , - 2,0 , \frac { 1 } { 3 } , \frac { 2 } { 3 } , 6,9 \right\}$ and $B = \left\{ 0 , \frac { 1 } { 3 } , \frac { 2 } { 3 } \right\}$

Find all real solutions of the equation. $| 5 x | = 9$

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 for the indicated variable. F=k(q1q2r2); for rF = k \left( \frac { q _ { 1 } q _ { 2 } } { r ^ { 2 } } \right) ; \quad \text { for } rF=k(r2q1​q2​​); for r

Find the solution set for the nonlinear inequality 1x−3−2x−2>0\frac { 1 } { x - 3 } - \frac { 2 } { x - 2 } > 0x−31​−x−22​>0 .

A cylindrical can has a volume of 36π36 \pi36π cm3\mathrm { cm } ^ { 3 }cm3 and a diameter of 333 cm. What is its height?

If M(2,1)M ( 2,1 )M(2,1) is the midpoint of the line segment ABA BAB , and if AAA has coordinates (−12,6)\left( - \frac { 1 } { 2 } , 6 \right)(−21​,6) , find the coordinates of BBB .

Factor the expression. 2y2x+xy+5y+10y22 y ^ { 2 } x + x y + 5 y + 10 y ^ { 2 }2y2x+xy+5y+10y2

The owner of a tow truck wishes to change the mixture of antifreeze in his radiator. The radiator contains 15.515.515.5 quarts of 35%35 \%35% antifreeze solution. How much would he need to drain and replace with pure antifreeze in order to get a 55%55 \%55% antifreeze solution?

Use the properties of real numbers to write the expression without parentheses. 2x(a−b−2c+d2)2 x \left( a - b - 2 c + \frac { d } { 2 } \right)2x(a−b−2c+2d​)

Evaluate (32)−0.2( 32 ) ^ { - 0.2 }(32)−0.2

Simplify the expression. y2−142y2+4y+32\frac { y ^ { 2 } - \frac { 1 } { 4 } } { 2 y ^ { 2 } + 4 y + \frac { 3 } { 2 } }2y2+4y+23​y2−41​​

Find the approximate solutions of the equation x3−9x2=24−26xx ^ { 3 } - 9 x ^ { 2 } = 24 - 26 xx3−9x2=24−26x by drawing a graph in the interval [1,5][ 1,5 ][1,5] .

The stopping distance D of a car after the brakes have been applied varies directly as the square of the speed s. A certain car traveling at 50 mi/h can stop in 240 ft. What is the maximum speed it can be traveling if it needs to stop in 180 ft? Round your answer to one decimal place.

Simplify the expression. x2+x−2x2+2x−3\frac { x ^ { 2 } + x - 2 } { x ^ { 2 } + 2 x - 3 }x2+2x−3x2+x−2​

Rationalize the numerator of the expression. x−1+x\sqrt { x - 1 } + \sqrt { x }x−1​+x​

Perform the subtraction and simplify. 2x+3−1x2+5x+6\frac { 2 } { x + 3 } - \frac { 1 } { x ^ { 2 } + 5 x + 6 }x+32​−x2+5x+61​

Perform the indicated operation. 14+112\frac { 1 } { 4 } + \frac { 1 } { 12 }41​+121​

Find the set A∪BA \cup BA∪B if A={−3,−2,0,13,23,6,9}A = \left\{ - 3 , - 2,0 , \frac { 1 } { 3 } , \frac { 2 } { 3 } , 6,9 \right\}A={−3,−2,0,31​,32​,6,9} and B={0,13,23}B = \left\{ 0 , \frac { 1 } { 3 } , \frac { 2 } { 3 } \right\}B={0,31​,32​}

Find all real solutions of the equation. ∣5x∣=9| 5 x | = 9∣5x∣=9

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 for the indicated variable. $F = k \left( \frac { q _ { 1 } q _ { 2 } } { r ^ { 2 } } \right) ; \quad \text { for } r$

Find the solution set for the nonlinear inequality $\frac { 1 } { x - 3 } - \frac { 2 } { x - 2 } > 0$ .

A cylindrical can has a volume of $36 \pi$ $\mathrm { cm } ^ { 3 }$ and a diameter of $3$ cm. What is its height?

If $M ( 2,1 )$ is the midpoint of the line segment $A B$ , and if $A$ has coordinates $\left( - \frac { 1 } { 2 } , 6 \right)$ , find the coordinates of $B$ .

Factor the expression. $2 y ^ { 2 } x + x y + 5 y + 10 y ^ { 2 }$

The owner of a tow truck wishes to change the mixture of antifreeze in his radiator. The radiator contains $15.5$ quarts of $35 \%$ antifreeze solution. How much would he need to drain and replace with pure antifreeze in order to get a $55 \%$ antifreeze solution?

Use the properties of real numbers to write the expression without parentheses. $2 x \left( a - b - 2 c + \frac { d } { 2 } \right)$

Evaluate $( 32 ) ^ { - 0.2 }$

Simplify the expression. $\frac { y ^ { 2 } - \frac { 1 } { 4 } } { 2 y ^ { 2 } + 4 y + \frac { 3 } { 2 } }$

Find the approximate solutions of the equation $x ^ { 3 } - 9 x ^ { 2 } = 24 - 26 x$ by drawing a graph in the interval $[ 1,5 ]$ .

Simplify the expression. $\frac { x ^ { 2 } + x - 2 } { x ^ { 2 } + 2 x - 3 }$

Rationalize the numerator of the expression. $\sqrt { x - 1 } + \sqrt { x }$

Perform the subtraction and simplify. $\frac { 2 } { x + 3 } - \frac { 1 } { x ^ { 2 } + 5 x + 6 }$

Perform the indicated operation. $\frac { 1 } { 4 } + \frac { 1 } { 12 }$

Find the set $A \cup B$ if $A = \left\{ - 3 , - 2,0 , \frac { 1 } { 3 } , \frac { 2 } { 3 } , 6,9 \right\}$ and $B = \left\{ 0 , \frac { 1 } { 3 } , \frac { 2 } { 3 } \right\}$

Find all real solutions of the equation. $| 5 x | = 9$