Question 1

Solve the equation. $$x ^ { 2 } \left( x ^ { 2 } + 3 \right) = 54$$

Accepted Answer

A)  $\{ \pm 6 i , \pm 3 \}$ 
B)  $\{ \pm 6 , \pm 3 \}$ 
C)  $\{ \pm 6 , \pm 3 i \}$ 
D)  $\{ \pm \sqrt { 6 } , \pm 3 i \}$ 
A)  $\{ \pm 6 i , \pm 3 \}$ 
B)  $\{ \pm 6 , \pm 3 \}$ 
C)  $\{ \pm 6 , \pm 3 i \}$ 
D)  $\{ \pm \sqrt { 6 } , \pm 3 i \}$

Question 2

Solve the equation by using the quadratic formula. $$0.01 x ^ { 2 } + 0.1 x + 0.24 = 0$$

Accepted Answer

A)  {-0.06, -0.04} 
B)  {-6, -4} 
C)  {0.06i, 0.04i} 
D)  {4i, 6i} 
A)  {-0.06, -0.04} 
B)  {-6, -4} 
C)  {0.06i, 0.04i} 
D)  {4i, 6i}

Question 3

Graph the function. $$f ( x ) = ( x - 4 ) ^ { 2 }$$

Accepted Answer

The answer of Graph the function. \[f ( x )...

Question 4

Determine the discriminant. Then use it to determine the number of x-intercepts that the function has. $$m ( x ) = - 3 x ^ { 2 } + 8 x - 9$$

Accepted Answer

A)  Discriminant: -44; no x-intercepts 
B)  Discriminant: -44; two x-intercepts 
C)  Discriminant: -172; no x-intercepts 
D)  Discriminant: -172; two x-intercepts 
A)  Discriminant: -44; no x-intercepts 
B)  Discriminant: -44; two x-intercepts 
C)  Discriminant: -172; no x-intercepts 
D)  Discriminant: -172; two x-intercepts

Question 5

A model rocket is launched from a raised platform at a speed of 112 feet per second. Its height in feet is given by $h ( t ) = - 16 t ^ { 2 } + 112 t + 20$ (t = seconds after launch) What is the maximum height reached by the rocket?

Accepted Answer

A)  216 feet 
B)  432 feet 
C)  108 feet 
D)  236 feet 
A)  216 feet 
B)  432 feet 
C)  108 feet 
D)  236 feet

Question 6

Solve the rational inequality. Write the answer in interval notation. $$\frac { x + 15 } { x } \geq 0$$

Accepted Answer

A)  $( - \infty , - 15 ]$ 
B)  $( - \infty , - 15 ] \cup ( 0 , \infty )$ 
C)  $( - \infty , \infty )$ 
D)  $( 0,15 ]$ 
A)  $( - \infty , - 15 ]$ 
B)  $( - \infty , - 15 ] \cup ( 0 , \infty )$ 
C)  $( - \infty , \infty )$ 
D)  $( 0,15 ]$

Question 7

A cable car carries tourists from street level down into a canyon, as shown in the figure below. The horizontal distance d between the two cable support towers is 450 feet, and the length of the cable between the towers is 3 times the vertical descent h (see figure). Find the vertical descent h into the canyon. Round to the nearest tenth of a foot.

Accepted Answer

The answer of A cable car carries tourists from street...

Question 8

The daily profit made by an automobile manufacturer is $P ( x ) = - 45 x ^ { 2 } + 2,250 x - 18,000$ where x is the number of cars produced per shift. How many cars must be produced per shift for the company to make a daily profit of $6000? Round any decimal part up to the next whole car.

Accepted Answer

About eith

Question 9

Graph the function. $$g ( x ) = \frac { 1 } { 5 } x ^ { 2 }$$

Accepted Answer

The answer of Graph the function. \[g ( x )...

Question 10

Solve the rational inequality. Write the answer in interval notation. $$\frac { t + 4 } { t - 5 } \leq - 2$$

Accepted Answer

A)  $( - \infty , 5 )$ 
B)  $[ - 4,5 )$ 
C)  $( - \infty , 2 ] \cup ( 5 , \infty )$ 
D)  $[ 2,5 )$ 
A)  $( - \infty , 5 )$ 
B)  $[ - 4,5 )$ 
C)  $( - \infty , 2 ] \cup ( 5 , \infty )$ 
D)  $[ 2,5 )$

Question 11

Solve the equation by using the square root property. $3 y ^ { 2 } = - 120$

Accepted Answer

A)  $\{ 2 \sqrt { 10 } \}$ 
B)  $\{ 2 i \sqrt { 10 } , - 2 i \sqrt { 10 } \}$ 
C)  $\{ 2 i \sqrt { 30 } , - 2 i \sqrt { 30 } \}$ 
D)  $\{ 2 \sqrt { 10 } , - 2 \sqrt { 10 } \}$ 
A)  $\{ 2 \sqrt { 10 } \}$ 
B)  $\{ 2 i \sqrt { 10 } , - 2 i \sqrt { 10 } \}$ 
C)  $\{ 2 i \sqrt { 30 } , - 2 i \sqrt { 30 } \}$ 
D)  $\{ 2 \sqrt { 10 } , - 2 \sqrt { 10 } \}$

Question 12

Solve the equation by using the quadratic formula. $$m ^ { 2 } = - 6 m + 7$$

Accepted Answer

A)  {-1} 
B)  {-1, 7} 
C)  {1} 
D)  {1, -7} 
A)  {-1} 
B)  {-1, 7} 
C)  {1} 
D)  {1, -7}

Question 13

Solve the inequality. $$- 8 y - 16 \geq y ^ { 2 }$$

Accepted Answer

A)  $( - \infty , \infty )$ 
B)  $\{ - 4 \}$ 
C)  $( - \infty , - 4 ) \cup ( - 4 , \infty )$ 
D) {  } 
A)  $( - \infty , \infty )$ 
B)  $\{ - 4 \}$ 
C)  $( - \infty , - 4 ) \cup ( - 4 , \infty )$ 
D) {  }

Question 14

Use the discriminant to determine the type and number of solutions: $$\frac { 2 } { 5 } x = - \frac { 4 } { 25 } - \frac { 1 } { 4 } x ^ { 2 }$$

Accepted Answer

A)  Two rational solutions 
B)  One rational solution 
C)  Two irrational solutions 
D)  Two imaginary solutions 
A)  Two rational solutions 
B)  One rational solution 
C)  Two irrational solutions 
D)  Two imaginary solutions

Question 15

Use the discriminant to determine the type and number of solutions. $$- 5 x ^ { 2 } + 5 x + 1 = 0$$

Accepted Answer

A)  Two rational solutions 
B)  Two irrational solutions 
C)  One rational solution 
D)  Two imaginary solutions 
A)  Two rational solutions 
B)  Two irrational solutions 
C)  One rational solution 
D)  Two imaginary solutions

Question 16

Graph the function. $$f ( x ) = - 2 ( x + 1 ) ^ { 2 } + 4$$

Accepted Answer

The answer of Graph the function. \[f ( x )...

Question 17

Solve for u. $$d = 9 \sqrt { u }$$

Accepted Answer

A)  $u = \frac { d } { 9 }$ 
B)  $u = \frac { d ^ { 2 } } { 9 }$ 
C)  $u = \frac { d } { 81 }$ 
D)  $u = \frac { d ^ { 2 } } { 81 }$ 
A)  $u = \frac { d } { 9 }$ 
B)  $u = \frac { d ^ { 2 } } { 9 }$ 
C)  $u = \frac { d } { 81 }$ 
D)  $u = \frac { d ^ { 2 } } { 81 }$

Question 18

Solve the quadratic equation by using any method. $$2 x ( x - 4 ) = - 19$$

Accepted Answer

The answer of Solve the quadratic equation by using any...

Question 19

Solve the rational inequality. Write the answer in interval notation. $$\frac { y ^ { 2 } - 6 y + 5 } { ( y + 2 ) ^ { 2 } } > 0$$

Accepted Answer

A)  $( - \infty , - 2 ) \cup ( - 2,1 ) \cup ( 5 , \infty )$ 
B)  $( - 2,1 ) \cup ( 5 , \infty )$ 
C)  $( - \infty , - 2 ) \cup ( 1,5 )$ 
D)  $( - 2,5 )$ 
A)  $( - \infty , - 2 ) \cup ( - 2,1 ) \cup ( 5 , \infty )$ 
B)  $( - 2,1 ) \cup ( 5 , \infty )$ 
C)  $( - \infty , - 2 ) \cup ( 1,5 )$ 
D)  $( - 2,5 )$

Question 20

The daily profit in dollars made by an automobile manufacturer is $P ( x ) = - 45 x ^ { 2 } + 2,250 x - 18,000$ where x is the number of cars produced per shift. How many cars must be produced per shift for the company to maximize its profit?

Accepted Answer

A)  20 
B)  25 
C)  35 
D)  30 
A)  20 
B)  25 
C)  35 
D)  30

Solve the equation. $x ^ { 2 } \left( x ^ { 2 } + 3 \right) = 54$

Solve the equation by using the quadratic formula. $0.01 x ^ { 2 } + 0.1 x + 0.24 = 0$

Graph the function. $f ( x ) = ( x - 4 ) ^ { 2 }$

Determine the discriminant. Then use it to determine the number of x-intercepts that the function has. $m ( x ) = - 3 x ^ { 2 } + 8 x - 9$

A model rocket is launched from a raised platform at a speed of 112 feet per second. Its height in feet is given by $h ( t ) = - 16 t ^ { 2 } + 112 t + 20$ (t = seconds after launch) What is the maximum height reached by the rocket?

Solve the rational inequality. Write the answer in interval notation. $\frac { x + 15 } { x } \geq 0$

The daily profit made by an automobile manufacturer is $P ( x ) = - 45 x ^ { 2 } + 2,250 x - 18,000$ where x is the number of cars produced per shift. How many cars must be produced per shift for the company to make a daily profit of $6000? Round any decimal part up to the next whole car.

Graph the function. $g ( x ) = \frac { 1 } { 5 } x ^ { 2 }$

Solve the rational inequality. Write the answer in interval notation. $\frac { t + 4 } { t - 5 } \leq - 2$

Solve the equation by using the square root property. $3 y ^ { 2 } = - 120$

Solve the equation by using the quadratic formula. $m ^ { 2 } = - 6 m + 7$

Solve the inequality. $- 8 y - 16 \geq y ^ { 2 }$

Use the discriminant to determine the type and number of solutions: $\frac { 2 } { 5 } x = - \frac { 4 } { 25 } - \frac { 1 } { 4 } x ^ { 2 }$

Use the discriminant to determine the type and number of solutions. $- 5 x ^ { 2 } + 5 x + 1 = 0$

Graph the function. $f ( x ) = - 2 ( x + 1 ) ^ { 2 } + 4$

Solve for u. $d = 9 \sqrt { u }$

Solve the quadratic equation by using any method. $2 x ( x - 4 ) = - 19$

Solve the rational inequality. Write the answer in interval notation. $\frac { y ^ { 2 } - 6 y + 5 } { ( y + 2 ) ^ { 2 } } > 0$

The daily profit in dollars made by an automobile manufacturer is $P ( x ) = - 45 x ^ { 2 } + 2,250 x - 18,000$ where x is the number of cars produced per shift. How many cars must be produced per shift for the company to maximize its profit?

Linear Equations and Inequalities in One Variable

Linear Equations in Two Variables and Functions

Systems of Linear Equations and Inequalities

Polynomials

Rational Expressions and Rational Equations

Radicals and Complex Numbers

Exponential and Logarithmic Functions and Applications

Conic Sections

Binomial Expansions, Sequences, and Series

Online: Transformations, Piecewise-Defined Functions, and Probability

Filters

Exam 7: Quadratic Equations, Functions and Inequalities

Solve the equation. x2(x2+3)=54x ^ { 2 } \left( x ^ { 2 } + 3 \right) = 54x2(x2+3)=54

Solve the equation by using the quadratic formula. 0.01x2+0.1x+0.24=00.01 x ^ { 2 } + 0.1 x + 0.24 = 00.01x2+0.1x+0.24=0

Graph the function. f(x)=(x−4)2f ( x ) = ( x - 4 ) ^ { 2 }f(x)=(x−4)2

Determine the discriminant. Then use it to determine the number of x-intercepts that the function has. m(x)=−3x2+8x−9m ( x ) = - 3 x ^ { 2 } + 8 x - 9m(x)=−3x2+8x−9

A model rocket is launched from a raised platform at a speed of 112 feet per second. Its height in feet is given by h(t)=−16t2+112t+20h ( t ) = - 16 t ^ { 2 } + 112 t + 20h(t)=−16t2+112t+20 (t = seconds after launch) What is the maximum height reached by the rocket?

Solve the rational inequality. Write the answer in interval notation. x+15x≥0\frac { x + 15 } { x } \geq 0xx+15​≥0

Graph the function. g(x)=15x2g ( x ) = \frac { 1 } { 5 } x ^ { 2 }g(x)=51​x2

Solve the rational inequality. Write the answer in interval notation. t+4t−5≤−2\frac { t + 4 } { t - 5 } \leq - 2t−5t+4​≤−2

Solve the equation by using the square root property. 3y2=−1203 y ^ { 2 } = - 1203y2=−120

Solve the equation by using the quadratic formula. m2=−6m+7m ^ { 2 } = - 6 m + 7m2=−6m+7

Solve the inequality. −8y−16≥y2- 8 y - 16 \geq y ^ { 2 }−8y−16≥y2

Use the discriminant to determine the type and number of solutions: 25x=−425−14x2\frac { 2 } { 5 } x = - \frac { 4 } { 25 } - \frac { 1 } { 4 } x ^ { 2 }52​x=−254​−41​x2

Use the discriminant to determine the type and number of solutions. −5x2+5x+1=0- 5 x ^ { 2 } + 5 x + 1 = 0−5x2+5x+1=0

Graph the function. f(x)=−2(x+1)2+4f ( x ) = - 2 ( x + 1 ) ^ { 2 } + 4f(x)=−2(x+1)2+4

Solve for u. d=9ud = 9 \sqrt { u }d=9u​

Solve the quadratic equation by using any method. 2x(x−4)=−192 x ( x - 4 ) = - 192x(x−4)=−19

Solve the rational inequality. Write the answer in interval notation. y2−6y+5(y+2)2>0\frac { y ^ { 2 } - 6 y + 5 } { ( y + 2 ) ^ { 2 } } > 0(y+2)2y2−6y+5​>0

The daily profit in dollars made by an automobile manufacturer is P(x)=−45x2+2,250x−18,000P ( x ) = - 45 x ^ { 2 } + 2,250 x - 18,000P(x)=−45x2+2,250x−18,000 where x is the number of cars produced per shift. How many cars must be produced per shift for the company to maximize its profit?

Linear Equations and Inequalities in One Variable

Linear Equations in Two Variables and Functions

Systems of Linear Equations and Inequalities

Polynomials

Rational Expressions and Rational Equations

Radicals and Complex Numbers

Exponential and Logarithmic Functions and Applications

Conic Sections

Binomial Expansions, Sequences, and Series

Online: Transformations, Piecewise-Defined Functions, and Probability

Filters

Solve the equation. $x ^ { 2 } \left( x ^ { 2 } + 3 \right) = 54$

Solve the equation by using the quadratic formula. $0.01 x ^ { 2 } + 0.1 x + 0.24 = 0$

Graph the function. $f ( x ) = ( x - 4 ) ^ { 2 }$

Determine the discriminant. Then use it to determine the number of x-intercepts that the function has. $m ( x ) = - 3 x ^ { 2 } + 8 x - 9$

A model rocket is launched from a raised platform at a speed of 112 feet per second. Its height in feet is given by $h ( t ) = - 16 t ^ { 2 } + 112 t + 20$ (t = seconds after launch) What is the maximum height reached by the rocket?

Solve the rational inequality. Write the answer in interval notation. $\frac { x + 15 } { x } \geq 0$

Graph the function. $g ( x ) = \frac { 1 } { 5 } x ^ { 2 }$

Solve the rational inequality. Write the answer in interval notation. $\frac { t + 4 } { t - 5 } \leq - 2$

Solve the equation by using the square root property. $3 y ^ { 2 } = - 120$

Solve the equation by using the quadratic formula. $m ^ { 2 } = - 6 m + 7$

Solve the inequality. $- 8 y - 16 \geq y ^ { 2 }$

Use the discriminant to determine the type and number of solutions: $\frac { 2 } { 5 } x = - \frac { 4 } { 25 } - \frac { 1 } { 4 } x ^ { 2 }$

Use the discriminant to determine the type and number of solutions. $- 5 x ^ { 2 } + 5 x + 1 = 0$

Graph the function. $f ( x ) = - 2 ( x + 1 ) ^ { 2 } + 4$

Solve for u. $d = 9 \sqrt { u }$

Solve the quadratic equation by using any method. $2 x ( x - 4 ) = - 19$

Solve the rational inequality. Write the answer in interval notation. $\frac { y ^ { 2 } - 6 y + 5 } { ( y + 2 ) ^ { 2 } } > 0$

The daily profit in dollars made by an automobile manufacturer is $P ( x ) = - 45 x ^ { 2 } + 2,250 x - 18,000$ where x is the number of cars produced per shift. How many cars must be produced per shift for the company to maximize its profit?