Question 1

Solve by factoring.&#10;

Accepted Answer

Rearrange the equation to get $x^2-21x+108=0$ and factor as $(x-9)(x-12)=0$. Thus the solutions are $x=9$ or $x=12$. Therefore, the answer is D.

Question 2

Solve by factoring.&#10;

Accepted Answer

We can factor the given quadratic equation as follows:
$$x^2-x-6=(x-3)(x+2)$$
Setting each factor to zero, we get:
$$x-3=0 \qquad \Rightarrow \qquad x=3$$
$$x+2=0 \qquad \Rightarrow \qquad x=-2$$
Therefore, the solutions are $\{-2,3\}$, which corresponds to choice C.

Question 3

Solve the problem. Approximate to the nearest tenth when necessary.
The area of a square is 49 square centimeters. Find the length of a side of the square.

A) 14 cm
B) 24.5 cm
C) 12.3 cm
D) 7 cm

Accepted Answer

The area of a square is given by the formula $A = s^2$, where $A$ is the area and $s$ is the length of a side. To find the length of a side when the area is known, we take the square root of the area. Thus, $s = \sqrt{148} \approx 12.2$ feet.

Question 4

Solve by extracting square roots.&#10;x

Accepted Answer

We can factor x out of the expression to get:
$x\left(x-\frac{5}{4}\right)$
Then, we can take the square root of both terms:
$x\sqrt{x-\frac{5}{4}}\cdot\sqrt{x-\frac{5}{4}}$
Simplifying, we have:
$x\left(x-\frac{5}{4}\right)=(x)^2-\frac{5}{4}x$
So the answer is $\frac{25}{64}$ and $(x-\frac{5}{8})^2$.

Question 5

Solve the problem.&#10;The length of a table is 12 inches more than its width. If the area of the table is 1120 square inches, what is its length?&#10;A) 16 in.&#10;B) 40 in.&#10;C) 56 in.&#10;D) 28 in.

Accepted Answer

The equation for the area of the table is $w(w + 12) = 1120$, where $w$ is the width. Solving this quadratic equation, we find $w = 28$ inches. Therefore, the length is $w + 12 = 40$ inches.

Question 6

Solve by factoring.&#10;

Accepted Answer

First, we move all the terms on one side to make it a quadratic equation:
$$x ^ { 2 } + 3 x - 40 = 0$$
Next, we look for two numbers that multiply to -40 and add to 3. The numbers that fit this criteria are -8 and 5. Therefore, we can factor the equation as:
$$(x-8)(x+5)=0$$
Using the zero product property, we know that the only way for the entire expression to equal 0 is if one or both of the factors equal 0. So, our solutions are:
$$x-8=0 \qquad \Rightarrow \qquad x=8$$
$$x+5=0 \qquad \Rightarrow \qquad x=-5$$

Hence, the solution set is $\{-8,5\}$, which corresponds to choice C.

Question 7

Solve by factoring.&#10;

Accepted Answer

The answer of Solve by factoring.&#10; ...

Question 8

Solve the problem. Approximate to the nearest tenth when necessary.
The area of a square is 49 square centimeters. Find the length of a side of the square.

A) 14 cm
B) 24.5 cm
C) 12.3 cm
D) 7 cm

Accepted Answer

The formula to find the area of a square is A = s^2, where A is the area and s is the length of a side of the square.

In this problem, we are given that the area of the square is 49 square centimeters. So, we can substitute A = 49 into the formula and solve for s:

A = s^2 
49 = s^2 
s = √49 
s = 7

Therefore, the length of a side of the square is 7 centimeters. Hence, the answer is D.

Question 9

Solve by factoring.&#10;

Accepted Answer

To solve the quadratic equation $x^2 + 13x + 36 = 0$ by factoring, we look for two numbers that multiply to 36 (the constant term) and add to 13 (the coefficient of the linear term). The numbers -4 and -9 satisfy these conditions because $(-4) \times (-9) = 36$ and $(-4) + (-9) = -13$. Therefore, the factored form is $(x + 4)(x + 9) = 0$, leading to the solutions $x = -4$ and $x = -9$.

Question 10

Solve by extracting square roots.&#10;

Accepted Answer

The given expression is $x^2 - 10x$. To solve by extracting square roots, we need to complete the square. First, take half of the coefficient of $x$, which is $-10/2 = -5$, and square it to get $25$. Adding and subtracting $25$ inside the expression gives $x^2 - 10x + 25 - 25$. This simplifies to $(x - 5)^2 - 25$, but since we're only completing the square, the correct representation is $(x - 5)^2$, and the $25$ is the number we added to complete the square, making choice A correct.

Question 11

Solve by factoring.&#10;

Accepted Answer

The answer of Solve by factoring.&#10; ...

Question 12

Solve by extracting square roots.&#10;

Accepted Answer

The answer of Solve by extracting square roots.&#10; ...

Question 13

Solve by extracting square roots.&#10;

Accepted Answer

The answer of Solve by extracting square roots.&#10; ...

Question 14

Solve by extracting square roots.&#10;

Accepted Answer

The answer of Solve by extracting square roots.&#10; ...

Question 15

Solve by extracting square roots.&#10;

Accepted Answer

The answer of Solve by extracting square roots.&#10; ...

Question 16

Solve by extracting square roots.&#10;

Accepted Answer

The answer of Solve by extracting square roots.&#10; ...

Question 17

Solve by extracting square roots.&#10;x

Accepted Answer

The answer of Solve by extracting square roots.&#10;x  ...

Question 18

Solve by factoring.&#10;

Accepted Answer

The answer of Solve by factoring.&#10; ...

Question 19

Solve by extracting square roots.&#10;x

Accepted Answer

The answer of Solve by extracting square roots.&#10;x  ...

Question 20

Solve by factoring.&#10;

Accepted Answer

The answer of Solve by factoring.&#10; ...

Question 21

Solve the equation by completing the square.&#10;

Accepted Answer

The answer of Solve the equation by completing the square.&#10;...

Question 22

Solve the equation by completing the square.&#10;

Accepted Answer

The answer of Solve the equation by completing the square.&#10;...

Question 23

Solve the problem. Approximate to the nearest tenth when necessary.
The area of a square is 49 square centimeters. Find the length of a side of the square.

A) 14 cm
B) 24.5 cm
C) 12.3 cm
D) 7 cm

Accepted Answer

The answer of Solve the problem. Approximate to the nearest...

Question 24

Solve the problem.&#10;A rectangular space of 252 square feet is allocated for the living and dining areas in an apartment. Find the width of the square living area given that the width of the dining area is 9 ft.  &#10;A) 21 ft&#10;B) 12 ft&#10;C) 14 ft&#10;D) 11 ft

Accepted Answer

The answer of Solve the problem.&#10;A rectangular space of 252...

Question 25

Solve the equation by completing the square.&#10;

Accepted Answer

The answer of Solve the equation by completing the square.&#10;...

Question 26

Solve the problem. Approximate to the nearest tenth when necessary.&#10;The area of a circle is 36&#960; square meters. Find the radius of the circle.&#10;A) 6 m&#10;B)36 m&#10;C) 10.6 m&#10;D) 18.8 m

Accepted Answer

The answer of Solve the problem. Approximate to the nearest...

Question 27

Solve the problem.&#10;The two legs of a right triangle are 10 meters and 20 meters, respectively. Find the hypotenuse of the triangle, rounded to the nearest hundredth of a meter.&#10;A) 250 m&#10;B) 22.36 mC)15m&#10;D) 500 m

Accepted Answer

The answer of Solve the problem.&#10;The two legs of a...

Question 28

Solve the equation by completing the square.&#10;

Accepted Answer

The answer of Solve the equation by completing the square.&#10;...

Question 29

Find a quadratic equation with integer coefficients that has the given solution set.&#10;

Accepted Answer

The answer of Find a quadratic equation with integer coefficients...

Question 30

Solve the problem.&#10;A ladder is resting against a wall. The top of the ladder touches the wall at a height of 12 ft. Find the length of the ladder if the length is 4 ft more than its distance from the wall.&#10;A) 16 ft&#10;B) 24 ft&#10;C) 20 ft&#10;D) 12 ft

Accepted Answer

The answer of Solve the problem.&#10;A ladder is resting against...

Question 31

Solve the problem.&#10;Ron takes two hr more time than Paul to mow the lawn. Working together they can mow the lawn in 5 hr. How long does it take each of them working alone? Round to the nearest tenth, if&#10;Necessary.&#10;A) Paul: 8 hr; Ron: 10 hr&#10;B) Paul: 10 hr; Ron: 12 hr&#10;C) Paul: 9.1 hr; Ron: 11.1 hr&#10;D) Paul: 8.3 hr; Ron: 10.3 hr

Accepted Answer

The answer of Solve the problem.&#10;Ron takes two hr more...

Question 32

Solve the problem.&#10;Two pipes can fill a large tank in 10 hours. One of the pipes, used alone, takes 15 hours longer than the other to fill the tank. How long would each pipe take to fill the tank alone?&#10;A) 15 hr for one&#10;B) 10 hr for one 30 hr for the other 20 hr for the other&#10;C) 12.5 hr for one&#10;D) 25 hr for one 25 hr for the other 50 hr for the other

Accepted Answer

The answer of Solve the problem.&#10;Two pipes can fill a...

Question 33

Solve the equation by completing the square.&#10;

Accepted Answer

The answer of Solve the equation by completing the square.&#10;...

Question 34

Solve the problem.&#10;A lot is in the shape of a right triangle. The shorter leg measures 60 m. The hypotenuse is 20 m longer than the length of the longer leg. How long is the longer leg?&#10;A) 120 mB)60 mC)80m&#10;D) 100 m

Accepted Answer

The answer of Solve the problem.&#10;A lot is in the...

Question 35

Solve the equation by completing the square.&#10;

Accepted Answer

The answer of Solve the equation by completing the square.&#10;...

Question 36

Solve the equation.&#10;

Accepted Answer

The answer of Solve the equation.&#10; ...

Question 37

Solve the problem.&#10;On a sunny day, a tree and its shadow form the sides of a right triangle. If the hypotenuse is 52 m long and the tree is 48 m tall, how long is the shadow?&#10;A) 32 mB)71 mC)20m&#10;D) 100 m

Accepted Answer

The answer of Solve the problem.&#10;On a sunny day, a...

Question 38

Solve the problem. Approximate to the nearest tenth when necessary.&#10;The area of a circle is 53 square feet. Find the radius of the circle.&#10;A) 16.9 ft&#10;B) 4.1 ft&#10;C) 12.9 ft&#10;D) 7.3 ft

Accepted Answer

The answer of Solve the problem. Approximate to the nearest...

Question 39

Solve the problem.&#10;Working together, Rick and Juanita can complete a job in 6 hours. It would take Rick 9 hours longer than Juanita to do the job alone. How long would it take Juanita alone?&#10;A) 6 hr&#10;B) 3 hr&#10;C) 15 hr&#10;D) 9 hr

Accepted Answer

The answer of Solve the problem.&#10;Working together, Rick and Juanita...

Question 40

Solve the equation by completing the square.&#10;

Accepted Answer

The answer of Solve the equation by completing the square.&#10;...

Question 41

Find the axis of symmetry associated with the quadratic equation.&#10;

Accepted Answer

The answer of Find the axis of symmetry associated with...

Question 42

Find the vertex of the parabola associated with the quadratic equation.&#10;

Accepted Answer

The answer of Find the vertex of the parabola associated...

Question 43

Solve the problem.&#10;

Accepted Answer

The answer of Solve the problem.&#10; ...

Question 44

Find the x- and y-intercepts of the parabola associated with the quadratic equation. If the parabola does not have any&#10;x-intercepts, state &#698;no x-intercepts.&#698;&#10;

Accepted Answer

The answer of Find the x- and y-intercepts of the...

Question 45

Solve the problem.&#10;

Accepted Answer

The answer of Solve the problem.&#10; ...

Question 46

Solve the problem.&#10;A flare is fired from the bottom of a gorge with an initial velocity of 80 feet per second, and it is visible only when the flare is above the rim. The height of the flare, in feet, after t seconds is given&#10;By the function h(t) = -16t2 + 80t. If the gorge is 96 feet deep, for what length of time can the flare&#10;Be seen?&#10;A) 0 sec to 2 sec&#10;B) 4 sec to 5 sec&#10;C) 6 sec to 7 sec&#10;D) 2 sec to 3 sec

Accepted Answer

The answer of Solve the problem.&#10;A flare is fired from...

Question 47

Find the x- and y-intercepts of the parabola associated with the quadratic equation. If the parabola does not have any&#10;x-intercepts, state &#698;no x-intercepts.&#698;&#10;

Accepted Answer

The answer of Find the x- and y-intercepts of the...

Question 48

Solve the problem.&#10;

Accepted Answer

The answer of Solve the problem.&#10; ...

Question 49

Find the vertex of the parabola associated with the quadratic equation.&#10;

Accepted Answer

The answer of Find the vertex of the parabola associated...

Question 50

Find the axis of symmetry associated with the quadratic equation.&#10;

Accepted Answer

The answer of Find the axis of symmetry associated with...

Question 51

Find the axis of symmetry associated with the quadratic equation.&#10;

Accepted Answer

The answer of Find the axis of symmetry associated with...

Question 52

Find the x- and y-intercepts of the parabola associated with the quadratic equation. If the parabola does not have any&#10;x-intercepts, state &#698;no x-intercepts.&#698;&#10;

Accepted Answer

The answer of Find the x- and y-intercepts of the...

Question 53

Find the vertex of the parabola associated with the quadratic equation.&#10;

Accepted Answer

The answer of Find the vertex of the parabola associated...

Question 54

Find the vertex of the parabola associated with the quadratic equation.&#10;

Accepted Answer

The answer of Find the vertex of the parabola associated...

Question 55

Solve the problem.&#10;

Accepted Answer

The answer of Solve the problem.&#10; ...

Question 56

Find the axis of symmetry associated with the quadratic equation.&#10;

Accepted Answer

The answer of Find the axis of symmetry associated with...

Question 57

Find the vertex of the parabola associated with the quadratic equation.&#10;

Accepted Answer

The answer of Find the vertex of the parabola associated...

Question 58

Find the vertex of the parabola associated with the quadratic equation.&#10;

Accepted Answer

The answer of Find the vertex of the parabola associated...

Question 59

Find the x- and y-intercepts of the parabola associated with the quadratic equation. If the parabola does not have any&#10;x-intercepts, state &#698;no x-intercepts.&#698;&#10;