Question 1

What is the first step in solving the following formula for $t$ ? $\mathrm{zt}^{2}=\mathrm{kl}-3$

Accepted Answer

Solve for

Question 2

Choose the one alternative that best completes the statement or answers the question.
Use the quadratic formula to solve the equation. (All solutions are real numbers.)
-$\mathrm{x}^{2}=9-4 \mathrm{x}$

Accepted Answer

A)  $\{2+\sqrt{13}\}$ 
B)  $\{-2+2 \sqrt{13},-2-2 \sqrt{13}\}$ 
C)  $\{-1+\sqrt{13},-1-\sqrt{13}\}$ 
D)  $\{-2+\sqrt{13},-2-\sqrt{13}\}$ 
A)  $\{2+\sqrt{13}\}$ 
B)  $\{-2+2 \sqrt{13},-2-2 \sqrt{13}\}$ 
C)  $\{-1+\sqrt{13},-1-\sqrt{13}\}$ 
D)  $\{-2+\sqrt{13},-2-\sqrt{13}\}$

Question 3

Choose the one alternative that best completes the statement or answers the question.
Use the quadratic formula to solve the equation. (All solutions are real numbers.)
-$\frac{3}{4} s^{2}+\frac{1}{2} s+\frac{1}{12}=0$

Accepted Answer

A)  $\left\{\frac{-1+\sqrt{2}}{3}, \frac{-1-\sqrt{2}}{3}\right\}$ 
B)  $\left\{-\frac{1}{3}\right\}$ 
C)  $\left\{\frac{1}{3}\right\}$ 
D)  $\left\{\frac{1}{3},-\frac{1}{3}\right\}$ 
A)  $\left\{\frac{-1+\sqrt{2}}{3}, \frac{-1-\sqrt{2}}{3}\right\}$ 
B)  $\left\{-\frac{1}{3}\right\}$ 
C)  $\left\{\frac{1}{3}\right\}$ 
D)  $\left\{\frac{1}{3},-\frac{1}{3}\right\}$

Question 4

$\frac{16}{\mathrm{~b}+2}=1+\frac{2}{\mathrm{~b}-4}$

Accepted Answer

A)  $\{6,10\}$ 
B)  $\varnothing$ 
C)  $\{-12\}$ 
D)  $\{-2,4\}$ 
A)  $\{6,10\}$ 
B)  $\varnothing$ 
C)  $\{-12\}$ 
D)  $\{-2,4\}$

Question 5

Solve the inequality, and graph the solution set.
-$\mathrm{v}^{2}-13 \mathrm{v}+42 \geq 0$

Accepted Answer

A)  $[7, \infty)$
  
B)  $(-\infty, 6]$
  
C)  $[6,7]$
  
D)  $(-\infty, 6] \cup[7, \infty)$
  
A)  $[7, \infty)$
  
B)  $(-\infty, 6]$
  
C)  $[6,7]$
  
D)  $(-\infty, 6] \cup[7, \infty)$

Question 6

Choose the equation that matches the graph.
-

Accepted Answer

A)  $f(x)=3 x^{2}+2 x-5$ 
B)  $f(x)=3 x^{2}-2 x-5$ 
C)  $x=3 y^{2}-2 y-5$ 
D)  $x=3 y^{2}-2 y+5$ 
A)  $f(x)=3 x^{2}+2 x-5$ 
B)  $f(x)=3 x^{2}-2 x-5$ 
C)  $x=3 y^{2}-2 y-5$ 
D)  $x=3 y^{2}-2 y+5$

Question 7

Use the discriminant to determine if the equation can be solved by factoring. If the equation can be solved by factoring, then factor it.
-$b^{2}-2 b-24=0$

Accepted Answer

A)  $(b-4)(b+6)=0$ 
B)  Cannot be solved by factoring 
C)  $(b+2)(b+4)=0$ 
D)  $(b+4)(b-6)=0$ 
A)  $(b-4)(b+6)=0$ 
B)  Cannot be solved by factoring 
C)  $(b+2)(b+4)=0$ 
D)  $(b+4)(b-6)=0$

Question 8

Solve the problem. Round your answer to the nearest tenth, when appropriate.
-A rock falls from a tower that is $78.4 \mathrm{~m}$ high. As it is falling, its height is given by the formula $\mathrm{h}=78.4-4.9 \mathrm{t}^{2}$. How many seconds will it take for the rock to hit the ground $(\mathrm{h}=0)$ ?

Accepted Answer

A)  $8.9 \mathrm{sec}$ 
B)  $1254.4 \mathrm{sec}$ 
C)  $8.6 \mathrm{sec}$ 
D)  $4 \mathrm{sec}$ 
A)  $8.9 \mathrm{sec}$ 
B)  $1254.4 \mathrm{sec}$ 
C)  $8.6 \mathrm{sec}$ 
D)  $4 \mathrm{sec}$

Question 9

Solve for $x$. Assume that $a$ and $b$ represent positive real numbers.
-$x^{2}-b=0$

Accepted Answer

A)  $\{b,-b\}$ 
B)  $\{\sqrt{b}, \sqrt{-b}\}$ 
C)  $\{b\}$ 
D)  $\{\sqrt{b},-\sqrt{b}\}$ 
A)  $\{b,-b\}$ 
B)  $\{\sqrt{b}, \sqrt{-b}\}$ 
C)  $\{b\}$ 
D)  $\{\sqrt{b},-\sqrt{b}\}$

Question 10

Solve the equation by completing the square.
-$21 \mathrm{~d}^{2}+34 \mathrm{~d}+8=0$

Accepted Answer

A)  $\left\{\frac{2}{7}, \frac{4}{3}\right\}$ 
B)  $\left\{-\frac{2}{7},-\frac{4}{3}\right\}$ 
C)  $\left\{\frac{7}{2}, \frac{3}{4}\right\}$ 
D)  $\left\{-\frac{7}{2},-\frac{4}{3}\right\}$ 
A)  $\left\{\frac{2}{7}, \frac{4}{3}\right\}$ 
B)  $\left\{-\frac{2}{7},-\frac{4}{3}\right\}$ 
C)  $\left\{\frac{7}{2}, \frac{3}{4}\right\}$ 
D)  $\left\{-\frac{7}{2},-\frac{4}{3}\right\}$

Question 11

Use the square root property to solve the equation.
-$x^{2}=100$

Accepted Answer

A)  $\{10\}$ 
B)  $\{50\}$ 
C)  $\{10,-10\}$ 
D)  $\{11,-11\}$ 
A)  $\{10\}$ 
B)  $\{50\}$ 
C)  $\{10,-10\}$ 
D)  $\{11,-11\}$

Question 12

Find the nonreal complex solutions of the equation.
-$\mathrm{x}^{2}+4 \mathrm{x}+20=0$

Accepted Answer

A)  $\{2,-6\}$ 
B)  $\{-2+2 \sqrt{5} i,-2-2 \sqrt{5} i\}$ 
C)  $\{-2+4 \mathrm{i},-2-4 \mathrm{i}\}$ 
D)  $\{2+4 \mathrm{i}, 2-4 \mathrm{i}\}$ 
A)  $\{2,-6\}$ 
B)  $\{-2+2 \sqrt{5} i,-2-2 \sqrt{5} i\}$ 
C)  $\{-2+4 \mathrm{i},-2-4 \mathrm{i}\}$ 
D)  $\{2+4 \mathrm{i}, 2-4 \mathrm{i}\}$

Question 13

$x=\frac{1}{7} y^{2}+8 y-1$

Accepted Answer

A)  To the right; wider 
B)  To the right; narrower 
C)  To the left; narrower 
D)  To the left; wider 
A)  To the right; wider 
B)  To the right; narrower 
C)  To the left; narrower 
D)  To the left; wider

Question 14

Solve the equation.
-$(2 m-4)^{2}-4(2 m-4)-5=0$

Accepted Answer

A)  $\left\{-\frac{5}{4}, \frac{1}{2}\right\}$ 
B)  $\left\{\frac{3}{2}, \frac{9}{2}\right\}$ 
C)  $\left\{\frac{3}{2},-\frac{9}{2}\right\}$ 
D)  $\left\{\frac{5}{2},-\frac{1}{2}\right\}$ 
A)  $\left\{-\frac{5}{4}, \frac{1}{2}\right\}$ 
B)  $\left\{\frac{3}{2}, \frac{9}{2}\right\}$ 
C)  $\left\{\frac{3}{2},-\frac{9}{2}\right\}$ 
D)  $\left\{\frac{5}{2},-\frac{1}{2}\right\}$

Question 15

An uncovered box is to be made from a rectangular piece of tin by cutting 2 -in. squares out of the corners and folding up the sides. The volume of the box will be $100 \mathrm{in.}^{3}$. Find the dimensions of the rectangular piece of tin. Round to the nearest tenth, if necessary.

Accepted Answer

A)  5 in. by 9 in. 
B)  Cannot be determined without additional information 
C)  5 in. by 10 in. 
D)  4 in. by 9 in. 
A)  5 in. by 9 in. 
B)  Cannot be determined without additional information 
C)  5 in. by 10 in. 
D)  4 in. by 9 in.

Question 16

Use the square root property to solve the equation.
-$(7 \mathrm{t}-3)^{2}=7$

Accepted Answer

A)  $\left\{\frac{\sqrt{3}}{7} i,-\frac{\sqrt{3}}{7}\right\}$ 
B)  $\left\{\frac{3+\sqrt{7}}{7}, \frac{3-\sqrt{7}}{7}\right\}$ 
C)  $\left\{\frac{3-\sqrt{7}}{7},-\frac{3-\sqrt{7}}{7}\right\}$ 
D)  $\{3+\sqrt{7}, 3-\sqrt{7}\}$ 
A)  $\left\{\frac{\sqrt{3}}{7} i,-\frac{\sqrt{3}}{7}\right\}$ 
B)  $\left\{\frac{3+\sqrt{7}}{7}, \frac{3-\sqrt{7}}{7}\right\}$ 
C)  $\left\{\frac{3-\sqrt{7}}{7},-\frac{3-\sqrt{7}}{7}\right\}$ 
D)  $\{3+\sqrt{7}, 3-\sqrt{7}\}$

Question 17

$f(x)=\frac{1}{6} x^{2}-7 x-4$

Accepted Answer

A)  Up; wider 
B)  Down; narrower 
C)  Down; wider 
D)  Up; narrower 
A)  Up; wider 
B)  Down; narrower 
C)  Down; wider 
D)  Up; narrower

Question 18

The solution set of the inequality $x^{2}+9 x+20 \geq 0$ is $(-\infty,-5] \cup[-4, \infty)$. Without doing any work, give the solution to $x^{2}+9 x+20<0$.

Accepted Answer

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

Question 19

Find the value of $k$ so that the equation will have exactly one rational solution.
-$k x^{2}+30 x+9=0$

Accepted Answer

A)  5 
B)  3 
C)  9 
D)  25 
A)  5 
B)  3 
C)  9 
D)  25

Question 20

The equation $s=-16 t^{2}+63 t+400$ gives the position $s$ in feet above the ground, where $t$ is the number of seconds elapsed after a ball is projected upward from a building. Determine the height of the building, if possible. Explain your reasoning.

Accepted Answer

The height of the bu

What is the first step in solving the following formula for $t$ ? $\mathrm{zt}^{2}=\mathrm{kl}-3$

Choose the one alternative that best completes the statement or answers the question. Use the quadratic formula to solve the equation. (All solutions are real numbers.) - $\mathrm{x}^{2}=9-4 \mathrm{x}$

Choose the one alternative that best completes the statement or answers the question. Use the quadratic formula to solve the equation. (All solutions are real numbers.) - $\frac{3}{4} s^{2}+\frac{1}{2} s+\frac{1}{12}=0$

$\frac{16}{\mathrm{~b}+2}=1+\frac{2}{\mathrm{~b}-4}$

Solve the inequality, and graph the solution set. - $\mathrm{v}^{2}-13 \mathrm{v}+42 \geq 0$ $Solve the inequality, and graph the solution set. - \mathrm{v}^{2}-13 \mathrm{v}+42 \geq 0$

Choose the equation that matches the graph. -

Use the discriminant to determine if the equation can be solved by factoring. If the equation can be solved by factoring, then factor it. - $b^{2}-2 b-24=0$

Solve for $x$ . Assume that $a$ and $b$ represent positive real numbers. - $x^{2}-b=0$

Solve the equation by completing the square. - $21 \mathrm{~d}^{2}+34 \mathrm{~d}+8=0$

Use the square root property to solve the equation. - $x^{2}=100$

Find the nonreal complex solutions of the equation. - $\mathrm{x}^{2}+4 \mathrm{x}+20=0$

$x=\frac{1}{7} y^{2}+8 y-1$

Solve the equation. - $(2 m-4)^{2}-4(2 m-4)-5=0$

An uncovered box is to be made from a rectangular piece of tin by cutting 2 -in. squares out of the corners and folding up the sides. The volume of the box will be $100 \mathrm{in.}^{3}$ . Find the dimensions of the rectangular piece of tin. Round to the nearest tenth, if necessary.

Use the square root property to solve the equation. - $(7 \mathrm{t}-3)^{2}=7$

$f(x)=\frac{1}{6} x^{2}-7 x-4$

The solution set of the inequality $x^{2}+9 x+20 \geq 0$ is $(-\infty,-5] \cup[-4, \infty)$ . Without doing any work, give the solution to $x^{2}+9 x+20<0$ .

Find the value of $k$ so that the equation will have exactly one rational solution. - $k x^{2}+30 x+9=0$

The equation $s=-16 t^{2}+63 t+400$ gives the position $s$ in feet above the ground, where $t$ is the number of seconds elapsed after a ball is projected upward from a building. Determine the height of the building, if possible. Explain your reasoning.

Review of the Real Number System

Linear Equations, Inequalities, and Applications

Linear Equations, Graphs, and Functions

Systems of Linear Equations

Exponents, Polynomials, and Polynomial Functions

Factoring

Rational Expressions and Functions

Roots, Radicals, and Root Functions

Inverse, Exponential, and Logarithmic Functions

Nonlinear Functions, Conic Sections, and Nonlinear Systems

Further Topics in Algebra

Appendices

Filters

Exam 9: Quadratic Equations, Inequalities, and Functions

What is the first step in solving the following formula for ttt ? zt2=kl−3\mathrm{zt}^{2}=\mathrm{kl}-3zt2=kl−3

Choose the one alternative that best completes the statement or answers the question. Use the quadratic formula to solve the equation. (All solutions are real numbers.) - x2=9−4x\mathrm{x}^{2}=9-4 \mathrm{x}x2=9−4x

Choose the one alternative that best completes the statement or answers the question. Use the quadratic formula to solve the equation. (All solutions are real numbers.) - 34s2+12s+112=0\frac{3}{4} s^{2}+\frac{1}{2} s+\frac{1}{12}=043​s2+21​s+121​=0

16 b+2=1+2 b−4\frac{16}{\mathrm{~b}+2}=1+\frac{2}{\mathrm{~b}-4} b+216​=1+ b−42​

Solve the inequality, and graph the solution set. - v2−13v+42≥0\mathrm{v}^{2}-13 \mathrm{v}+42 \geq 0v2−13v+42≥0

Choose the equation that matches the graph. -

Use the discriminant to determine if the equation can be solved by factoring. If the equation can be solved by factoring, then factor it. - b2−2b−24=0b^{2}-2 b-24=0b2−2b−24=0

Solve for xxx . Assume that aaa and bbb represent positive real numbers. - x2−b=0x^{2}-b=0x2−b=0

Solve the equation by completing the square. - 21 d2+34 d+8=021 \mathrm{~d}^{2}+34 \mathrm{~d}+8=021 d2+34 d+8=0

Use the square root property to solve the equation. - x2=100x^{2}=100x2=100

Find the nonreal complex solutions of the equation. - x2+4x+20=0\mathrm{x}^{2}+4 \mathrm{x}+20=0x2+4x+20=0

x=17y2+8y−1x=\frac{1}{7} y^{2}+8 y-1x=71​y2+8y−1

Solve the equation. - (2m−4)2−4(2m−4)−5=0(2 m-4)^{2}-4(2 m-4)-5=0(2m−4)2−4(2m−4)−5=0

An uncovered box is to be made from a rectangular piece of tin by cutting 2 -in. squares out of the corners and folding up the sides. The volume of the box will be 100in.3100 \mathrm{in.}^{3}100in.3 . Find the dimensions of the rectangular piece of tin. Round to the nearest tenth, if necessary.

Use the square root property to solve the equation. - (7t−3)2=7(7 \mathrm{t}-3)^{2}=7(7t−3)2=7

f(x)=16x2−7x−4f(x)=\frac{1}{6} x^{2}-7 x-4f(x)=61​x2−7x−4

The solution set of the inequality x2+9x+20≥0x^{2}+9 x+20 \geq 0x2+9x+20≥0 is (−∞,−5]∪[−4,∞)(-\infty,-5] \cup[-4, \infty)(−∞,−5]∪[−4,∞) . Without doing any work, give the solution to x2+9x+20<0x^{2}+9 x+20<0x2+9x+20<0 .

Find the value of kkk so that the equation will have exactly one rational solution. - kx2+30x+9=0k x^{2}+30 x+9=0kx2+30x+9=0

The equation s=−16t2+63t+400s=-16 t^{2}+63 t+400s=−16t2+63t+400 gives the position sss in feet above the ground, where ttt is the number of seconds elapsed after a ball is projected upward from a building. Determine the height of the building, if possible. Explain your reasoning.

Review of the Real Number System

Linear Equations, Inequalities, and Applications

Linear Equations, Graphs, and Functions

Systems of Linear Equations

Exponents, Polynomials, and Polynomial Functions

Factoring

Rational Expressions and Functions

Roots, Radicals, and Root Functions

Inverse, Exponential, and Logarithmic Functions

Nonlinear Functions, Conic Sections, and Nonlinear Systems

Further Topics in Algebra

Appendices

Filters

What is the first step in solving the following formula for $t$ ? $\mathrm{zt}^{2}=\mathrm{kl}-3$

Choose the one alternative that best completes the statement or answers the question. Use the quadratic formula to solve the equation. (All solutions are real numbers.) - $\mathrm{x}^{2}=9-4 \mathrm{x}$

Choose the one alternative that best completes the statement or answers the question. Use the quadratic formula to solve the equation. (All solutions are real numbers.) - $\frac{3}{4} s^{2}+\frac{1}{2} s+\frac{1}{12}=0$

$\frac{16}{\mathrm{~b}+2}=1+\frac{2}{\mathrm{~b}-4}$

Solve the inequality, and graph the solution set. - $\mathrm{v}^{2}-13 \mathrm{v}+42 \geq 0$ $Solve the inequality, and graph the solution set. - \mathrm{v}^{2}-13 \mathrm{v}+42 \geq 0$

Use the discriminant to determine if the equation can be solved by factoring. If the equation can be solved by factoring, then factor it. - $b^{2}-2 b-24=0$

Solve for $x$ . Assume that $a$ and $b$ represent positive real numbers. - $x^{2}-b=0$

Solve the equation by completing the square. - $21 \mathrm{~d}^{2}+34 \mathrm{~d}+8=0$

Use the square root property to solve the equation. - $x^{2}=100$

Find the nonreal complex solutions of the equation. - $\mathrm{x}^{2}+4 \mathrm{x}+20=0$

$x=\frac{1}{7} y^{2}+8 y-1$

Solve the equation. - $(2 m-4)^{2}-4(2 m-4)-5=0$

An uncovered box is to be made from a rectangular piece of tin by cutting 2 -in. squares out of the corners and folding up the sides. The volume of the box will be $100 \mathrm{in.}^{3}$ . Find the dimensions of the rectangular piece of tin. Round to the nearest tenth, if necessary.

Use the square root property to solve the equation. - $(7 \mathrm{t}-3)^{2}=7$

$f(x)=\frac{1}{6} x^{2}-7 x-4$

The solution set of the inequality $x^{2}+9 x+20 \geq 0$ is $(-\infty,-5] \cup[-4, \infty)$ . Without doing any work, give the solution to $x^{2}+9 x+20<0$ .

Find the value of $k$ so that the equation will have exactly one rational solution. - $k x^{2}+30 x+9=0$

The equation $s=-16 t^{2}+63 t+400$ gives the position $s$ in feet above the ground, where $t$ is the number of seconds elapsed after a ball is projected upward from a building. Determine the height of the building, if possible. Explain your reasoning.