Resources

Resources

Solve polynomial equations

Solve the system of equations by using the substitution method.

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-4x+7y=20

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Y= 3x+15

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X=

Y=

875+w \geq 903w

w

w^2 + 25 = 0

Write your answer in simplified, rationalized form.

w =

w =

f

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f^2 - 18f + 81 = 0

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Write each solution as an integer, proper fraction, or improper fraction in simplest form. If there are multiple solutions, separate them with commas.

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f =

u

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9u^2 - 30u + 25 = 0

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Write each solution as an integer, proper fraction, or improper fraction in simplest form. If there are multiple solutions, separate them with commas.

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u = \_\_\_

q

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q^2 + 22q + 121 = 0

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Write each solution as an integer, proper fraction, or improper fraction in simplest form. If there are multiple solutions, separate them with commas.

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q =

j

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16j^2 - 25 = 0

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Write each solution as an integer, proper fraction, or improper fraction in simplest form. If there are multiple solutions, separate them with commas.

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j =

s

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4s^2 - 35s - 9 = 0

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Write each solution as an integer, proper fraction, or improper fraction in simplest form. If there are multiple solutions, separate them with commas.

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s =

p

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-32p^2 - 8 = 0

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Write your answer in simplified, rationalized form.

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p =

p =

u

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7u^2 + 13u - 2 = 0

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Write each solution as an integer, proper fraction, or improper fraction in simplest form. If there are multiple solutions, separate them with commas.

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u = \_\_

z

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z^2 - 10z + 21 = 0

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Write each solution as an integer, proper fraction, or improper fraction in simplest form. If there are multiple solutions, separate them with commas.

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z = \_\_

g

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g^2 - 10g + 21 = 0

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Write each solution as an integer, proper fraction, or improper fraction in simplest form. If there are multiple solutions, separate them with commas.

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g = \_\_

q

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q^2 - 14q + 13 = 0

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Write each solution as an integer, proper fraction, or improper fraction in simplest form. If there are multiple solutions, separate them with commas.

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d

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Reduce any fractions to lowest terms. Don't round your answer, and don't use mixed fractions.

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-38 d-57 \geq-19 d+76

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\square

Find the solution to the system of equations.

y= -5x + 6

y= 3x - 2

We want to solve the following equation.

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\sqrt[3]{x}=|x-2|-1

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One of the solutions is

x \approx 0.3

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Find the other solution.

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Hint: Use a graphing calculator.

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Round your answer to the nearest tenth.

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x \approx

We want to solve the following equation.

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2^{x}=2+3 x

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One of the solutions is

x \approx 3.7

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Find the other solution.

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Hint: Use a graphing calculator.

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Round your answer to the nearest tenth.

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x \approx

Ernesto solves the equation below by first squaring both sides of the equation.

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\sqrt{\frac{1}{2} w+8}=-2

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What extraneous solution does Ernesto obtain?

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w=

Consider the equation

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-3 \cdot e^{5 w}=-88 \text {. }

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Solve the equation for

w

. Express the solution as a logarithm in basee.

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w=

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Approximate the value of

w

. Round your answer to the nearest thousandth.

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w \approx

x^{3}+7 x^{2}-36

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The polynomial has zeros at

-6

2

. If the remaining zero is

z

, then what is the value of

-z

Find the solutions of the quadratic equation

2 x^{2}-8 x-9=0

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1

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2 \pm \frac{\sqrt{34}}{2} i

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-2 \pm \frac{\sqrt{34}}{2} i

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2 \pm \frac{\sqrt{34}}{2}

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1 \pm \frac{\sqrt{34}}{4}

x

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5 x-29>-34 \quad

\quad 2 x+31<29

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1

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x<-1

x>-1

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x<-1

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x>-1

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(D) There are no solutions

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(E) All values of

x

V=\frac{1}{3} \pi r^{2} h

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The formula gives the volume

V

of a right circular cone with radius

r

h

. What is the volume, in cubic inches, of a right circular cone with a radius of

12

inches and a height of

2

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1

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96 \pi

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72 \pi

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24 \pi

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8 \pi

V=\frac{1}{3} \pi r^{2} h

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The formula gives the volume

V

of a right circular cone with radius

r

h

. What is the volume, in cubic meters, of a right circular cone with a radius of

4

meters and a height of

3

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1

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16 \pi

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36 \pi

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48 \pi

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144 \pi

V=\frac{4}{3} \pi r^{3}

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The formula gives the volume

V

of a sphere with radius

r

. What is the volume, in cubic inches, of a sphere with a radius of

6

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1

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864 \pi

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288 \pi

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216 \pi

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48 \pi

0.75 C+1.25 A \leq 7

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Horace works as a professional hair stylist. The given inequality shows the amount of time, in hours, Horace spends on giving haircuts each day, where

C

represents the number of child haircuts and

A

represents the number of adult haircuts. If Horace gave

5

child haircuts today, what is the most number of adult haircuts he can give with the remaining time?

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1

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(A) Horace can give at most

1

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(B) Horace can give at most

2

adult haircuts.

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(C) Horace can give at most

3

adult haircuts.

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(D) Horace can give at most

5

adult haircuts.

7 y^{2}=50 x-150

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y=\frac{3-x}{2}

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\left(x_{1}, y_{1}\right)

\left(x_{2}, y_{2}\right)

are distinct solutions to the system of equations shown, what is the product of the

y_{1}

y_{2}

g

is given in three equivalent forms.

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Which form most quickly reveals the zeros (or roots) of the function?

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1

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g(x)=-2(x+1)(x+7)

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g(x)=-2 x^{2}-16 x-14

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g(x)=-2(x+4)^{2}+18

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Write one of the zeros.

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x=

The equation of a circle is

(x+3)^{2}+(y-4)^{2}=49

. What are the center and radius of the circle?

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1

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(A) The center is

(3,4)

and the radius is

7

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(B) The center is

(-3,4)

and the radius is

7

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(C) The center is

(-3,-4)

and the radius is

7

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(D) The center is

(-3,4)

and the radius is

49

g

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8g^2 - 18g - 5 = 0

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Write each solution as an integer, proper fraction, or improper fraction in simplest form. If there are multiple solutions, separate them with commas.

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g =

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