Question 1

The base of a triangle is 3 times its height. The area of the triangle is 92 square feet. If h represents the height of the triangle, write an equation that would find the height of the triangle.
A) $92 = h ( 3 h )$
B) $92 = \frac { 1 } { 2 } h ( 3 h )$
C) $92 = \frac { 1 } { 2 } \left( \frac { h } { 3 } \right) ( h )$
D) $92 = 2 h + 2 ( 3 h )$

Accepted Answer

The answer of The base of a triangle is 3...

Question 2

Solve: $25 x ^ { 2 } - 5 x - 12 = 0$
A) $x = - \frac { 4 } { 5 } , x = \frac { 3 } { 5 }$
B) $x = \frac { 5 } { 4 } , x = - \frac { 5 } { 3 }$
C) $x = - \frac { 5 } { 4 } , x = \frac { 5 } { 3 }$
D) $x = \frac { 4 } { 5 } , x = - \frac { 3 } { 5 }$

Accepted Answer

The answer of Solve: \(25 x ^ { 2 }...

Question 3

$5 x ^ { 2 } + 4 x - 3 = 0$ is written in _________ form.

Accepted Answer

The answer of \(5 x ^ { 2 } +...

Question 4

The length of a rectangular garden is three more than twice the width. The area is 90square feet. Find the width. w = ________ feet

Accepted Answer

The answer of The length of a rectangular garden is...

Question 5

The product of two positive consecutive even integers is 48. Find the integers. ( Hint: Let x= the smaller even integer and $x + 2 =$ the larger even integer.) Separate your answers with commas.

Accepted Answer

The answer of The product of two positive consecutive even...

Question 6

Find a polynomial equation of degree 3 with the solutions $- 1,6 \text {, and } 9$ . Leave answer in standard form with the smallest integer coefficients.

Accepted Answer

The answer of Find a polynomial equation of degree 3...

Question 7

Solve the equation. $68 a ^ { 2 } + 3 a - 5 = 0$ If there is more than one solution, separate your answers with commas.

Accepted Answer

The answer of Solve the equation. \(68 a ^ {...

Question 8

Solve the equation. $- z ^ { 4 } + 13 z ^ { 2 } - 36 = 0$, z = __________ If there is more than one solution, separate your answers with commas.

Accepted Answer

The answer of Solve the equation. \(- z ^ {...

Question 9

Solve the equation. $( m + 2 ) ( 7 m + 2 ) - 8 = 28 m$, m = __________ If there is more than one solution, separate your answers with commas.

Accepted Answer

The answer of Solve the equation. \(( m + 2...

Question 10

Solve the equation. $3 ( 4 b - 5 )$, b = __________ If there is more than one solution, separate your answers with commas.

Accepted Answer

The answer of Solve the equation. \(3 ( 4 b...

Question 11

Let $f ( x ) = x ^ { 3 } - 5 x ^ { 2 } + 4 x + 2$ For what value(s) of x is $f ( x ) = 2$ ?
 If there is more than one solution, separate your answers with commas.

Accepted Answer

The answer of Let \(f ( x ) = x...

Question 12

Solve the equation. $y ^ { 3 } - 49 y = 0$,  y = __________ If there is more than one solution, separate your answers with commas.

Accepted Answer

The answer of Solve the equation. \(y ^ { 3...

Question 13

Let $f ( x ) = x ^ { 2 } - 4 x + 4$ For what value(s) of x is $f ( x ) = 1$ ?
 If there is more than one solution, separate your answers with commas.

Accepted Answer

The answer of Let \(f ( x ) = x...

Question 14

Let $f ( x ) = ( x - 4 ) ( x + 4 )$ and $g ( x ) = 6 x$ . Find all values of x such that $f ( x ) = g ( x )$

Accepted Answer

The answer of Let \(f ( x ) = (...

Question 15

Solve the equation. $( x + 7 ) ^ { 2 } = - 2 ( x + 7 ) - 1$, x = __________ If there is more than one solution, separate your answers with commas.

Accepted Answer

The answer of Solve the equation. \(( x + 7...

Question 16

Solve the equation by first clearing it of fractions. $\frac { 5 } { 7 } a ^ { 2 } = \frac { 6 } { 7 } - a$, a = __________ If there is more than one solution, separate your answers with commas.

Accepted Answer

The answer of Solve the equation by first clearing it...

Question 17

Find a quadratic equation with solutions $\frac { 3 } { 5 } \text { and } - \frac { 5 } { 2 }$ . Leave the answer in standard form with the smallest integer coefficients.

Accepted Answer

The answer of Find a quadratic equation with solutions \(\frac...

Question 18

Explain what is incorrect about the following work. Then work the problem correctly. $w ^ { 2 } + 11 w + 12 = 0$

Accepted Answer

The answer of Explain what is incorrect about the following...

Question 19

Solve the equation. $x ^ { 3 } - 6 x ^ { 2 } = 16 x$, x = __________ If there is more than one solution, separate your answers with commas.

Accepted Answer

The answer of Solve the equation. \(x ^ { 3...

Quiz 5: Exponents, Polynomials, and Polynomial Functions

The base of a triangle is 3 times its height. The area of the triangle is 92 square feet. If h represents the height of the triangle, write an equation that would find the height of the triangle.

Solve: $25 x ^ { 2 } - 5 x - 12 = 0$

$5 x ^ { 2 } + 4 x - 3 = 0$ is written in _________ form.

The length of a rectangular garden is three more than twice the width. The area is 90square feet. Find the width. w = ________ feet

The product of two positive consecutive even integers is 48. Find the integers. ( Hint: Let x= the smaller even integer and $x + 2 =$ the larger even integer.) Separate your answers with commas.

Find a polynomial equation of degree 3 with the solutions $- 1,6 \text {, and } 9$ . Leave answer in standard form with the smallest integer coefficients.

Solve the equation. $68 a ^ { 2 } + 3 a - 5 = 0$ If there is more than one solution, separate your answers with commas.

Solve the equation. $- z ^ { 4 } + 13 z ^ { 2 } - 36 = 0$ , z = __________ If there is more than one solution, separate your answers with commas.

Solve the equation. $( m + 2 ) ( 7 m + 2 ) - 8 = 28 m$ , m = __________ If there is more than one solution, separate your answers with commas.

Solve the equation. $3 ( 4 b - 5 )$ , b = __________ If there is more than one solution, separate your answers with commas.

Let $f ( x ) = x ^ { 3 } - 5 x ^ { 2 } + 4 x + 2$ For what value(s) of x is $f ( x ) = 2$ ? If there is more than one solution, separate your answers with commas.

Solve the equation. $y ^ { 3 } - 49 y = 0$ , y = __________ If there is more than one solution, separate your answers with commas.

Let $f ( x ) = x ^ { 2 } - 4 x + 4$ For what value(s) of x is $f ( x ) = 1$ ? If there is more than one solution, separate your answers with commas.

Let $f ( x ) = ( x - 4 ) ( x + 4 )$ and $g ( x ) = 6 x$ . Find all values of x such that $f ( x ) = g ( x )$

Solve the equation. $( x + 7 ) ^ { 2 } = - 2 ( x + 7 ) - 1$ , x = __________ If there is more than one solution, separate your answers with commas.

Solve the equation by first clearing it of fractions. $\frac { 5 } { 7 } a ^ { 2 } = \frac { 6 } { 7 } - a$ , a = __________ If there is more than one solution, separate your answers with commas.

Find a quadratic equation with solutions $\frac { 3 } { 5 } \text { and } - \frac { 5 } { 2 }$ . Leave the answer in standard form with the smallest integer coefficients.

Explain what is incorrect about the following work. Then work the problem correctly. $w ^ { 2 } + 11 w + 12 = 0$

Solve the equation. $x ^ { 3 } - 6 x ^ { 2 } = 16 x$ , x = __________ If there is more than one solution, separate your answers with commas.

Quiz 5: Exponents, Polynomials, and Polynomial Functions

The base of a triangle is 3 times its height. The area of the triangle is 92 square feet. If h represents the height of the triangle, write an equation that would find the height of the triangle.

Solve: 25x2−5x−12=025 x ^ { 2 } - 5 x - 12 = 025x2−5x−12=0

5x2+4x−3=05 x ^ { 2 } + 4 x - 3 = 05x2+4x−3=0 is written in _________ form.

The length of a rectangular garden is three more than twice the width. The area is 90square feet. Find the width. w = ________ feet

The product of two positive consecutive even integers is 48. Find the integers. ( Hint: Let x= the smaller even integer and x+2=x + 2 =x+2= the larger even integer.) Separate your answers with commas.

Find a polynomial equation of degree 3 with the solutions −1,6, and 9- 1,6 \text {, and } 9−1,6, and 9 . Leave answer in standard form with the smallest integer coefficients.

Solve the equation. 68a2+3a−5=068 a ^ { 2 } + 3 a - 5 = 068a2+3a−5=0 If there is more than one solution, separate your answers with commas.

Solve the equation. −z4+13z2−36=0- z ^ { 4 } + 13 z ^ { 2 } - 36 = 0−z4+13z2−36=0 , z = __________ If there is more than one solution, separate your answers with commas.

Solve the equation. (m+2)(7m+2)−8=28m( m + 2 ) ( 7 m + 2 ) - 8 = 28 m(m+2)(7m+2)−8=28m , m = __________ If there is more than one solution, separate your answers with commas.

Solve the equation. 3(4b−5)3 ( 4 b - 5 )3(4b−5) , b = __________ If there is more than one solution, separate your answers with commas.

Let f(x)=x3−5x2+4x+2f ( x ) = x ^ { 3 } - 5 x ^ { 2 } + 4 x + 2f(x)=x3−5x2+4x+2 For what value(s) of x is f(x)=2f ( x ) = 2f(x)=2 ? If there is more than one solution, separate your answers with commas.

Solve the equation. y3−49y=0y ^ { 3 } - 49 y = 0y3−49y=0 , y = __________ If there is more than one solution, separate your answers with commas.

Let f(x)=x2−4x+4f ( x ) = x ^ { 2 } - 4 x + 4f(x)=x2−4x+4 For what value(s) of x is f(x)=1f ( x ) = 1f(x)=1 ? If there is more than one solution, separate your answers with commas.

Let f(x)=(x−4)(x+4)f ( x ) = ( x - 4 ) ( x + 4 )f(x)=(x−4)(x+4) and g(x)=6xg ( x ) = 6 xg(x)=6x . Find all values of x such that f(x)=g(x)f ( x ) = g ( x )f(x)=g(x)

Solve the equation. (x+7)2=−2(x+7)−1( x + 7 ) ^ { 2 } = - 2 ( x + 7 ) - 1(x+7)2=−2(x+7)−1 , x = __________ If there is more than one solution, separate your answers with commas.

Solve the equation by first clearing it of fractions. 57a2=67−a\frac { 5 } { 7 } a ^ { 2 } = \frac { 6 } { 7 } - a75​a2=76​−a , a = __________ If there is more than one solution, separate your answers with commas.

Find a quadratic equation with solutions 35 and −52\frac { 3 } { 5 } \text { and } - \frac { 5 } { 2 }53​ and −25​ . Leave the answer in standard form with the smallest integer coefficients.

Explain what is incorrect about the following work. Then work the problem correctly. w2+11w+12=0w ^ { 2 } + 11 w + 12 = 0w2+11w+12=0

Solve the equation. x3−6x2=16xx ^ { 3 } - 6 x ^ { 2 } = 16 xx3−6x2=16x , x = __________ If there is more than one solution, separate your answers with commas.

Solve: $25 x ^ { 2 } - 5 x - 12 = 0$

$5 x ^ { 2 } + 4 x - 3 = 0$ is written in _________ form.

The product of two positive consecutive even integers is 48. Find the integers. ( Hint: Let x= the smaller even integer and $x + 2 =$ the larger even integer.) Separate your answers with commas.

Find a polynomial equation of degree 3 with the solutions $- 1,6 \text {, and } 9$ . Leave answer in standard form with the smallest integer coefficients.

Solve the equation. $68 a ^ { 2 } + 3 a - 5 = 0$ If there is more than one solution, separate your answers with commas.

Solve the equation. $- z ^ { 4 } + 13 z ^ { 2 } - 36 = 0$ , z = __________ If there is more than one solution, separate your answers with commas.

Solve the equation. $( m + 2 ) ( 7 m + 2 ) - 8 = 28 m$ , m = __________ If there is more than one solution, separate your answers with commas.

Solve the equation. $3 ( 4 b - 5 )$ , b = __________ If there is more than one solution, separate your answers with commas.

Let $f ( x ) = x ^ { 3 } - 5 x ^ { 2 } + 4 x + 2$ For what value(s) of x is $f ( x ) = 2$ ? If there is more than one solution, separate your answers with commas.

Solve the equation. $y ^ { 3 } - 49 y = 0$ , y = __________ If there is more than one solution, separate your answers with commas.

Let $f ( x ) = x ^ { 2 } - 4 x + 4$ For what value(s) of x is $f ( x ) = 1$ ? If there is more than one solution, separate your answers with commas.

Let $f ( x ) = ( x - 4 ) ( x + 4 )$ and $g ( x ) = 6 x$ . Find all values of x such that $f ( x ) = g ( x )$

Solve the equation. $( x + 7 ) ^ { 2 } = - 2 ( x + 7 ) - 1$ , x = __________ If there is more than one solution, separate your answers with commas.

Solve the equation by first clearing it of fractions. $\frac { 5 } { 7 } a ^ { 2 } = \frac { 6 } { 7 } - a$ , a = __________ If there is more than one solution, separate your answers with commas.

Find a quadratic equation with solutions $\frac { 3 } { 5 } \text { and } - \frac { 5 } { 2 }$ . Leave the answer in standard form with the smallest integer coefficients.

Explain what is incorrect about the following work. Then work the problem correctly. $w ^ { 2 } + 11 w + 12 = 0$

Solve the equation. $x ^ { 3 } - 6 x ^ { 2 } = 16 x$ , x = __________ If there is more than one solution, separate your answers with commas.