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Intermediate Algebra for College Students

Allen R. Angel; Dennis C. Runde

Chapter 8

Quadratic Functions - all with Video Answers

Educators

Section 1

Solving Quadratic Equations by Completing the Square

00:19

Problem 1

Fill in the blanks with the appropriate word, phrase, or symbol $($ s) from the following list.
$
\begin{array}{lllllll}
\text { reciprocal } & \text { imaginary } & \text { quadratic } & \text { square } & \text { perfect } & \frac{2}{3} & \frac{3}{2} \\
25 & 10 & 100 & \text { one-half } & \text { complex } & \text { binomial }
\end{array}
$
A ______ equation is an equation of the form $a x^{2}+b x+c=0$, where $a, b$, and $c$ are real numbers and $a \neq 0$.

AG
Ankit Gupta
Numerade Educator
View

Problem 2

Fill in the blanks with the appropriate word, phrase, or symbol $($ s) from the following list.
$
\begin{array}{lllllll}
\text { reciprocal } & \text { imaginary } & \text { quadratic } & \text { square } & \text { perfect } & \frac{2}{3} & \frac{3}{2} \\
25 & 10 & 100 & \text { one-half } & \text { complex } & \text { binomial }
\end{array}
$
The square root of a negative number is an ______ number.

Nicole Hoffman
Nicole Hoffman
Numerade Educator
00:22

Problem 3

Fill in the blanks with the appropriate word, phrase, or symbol $($ s) from the following list.
$
\begin{array}{lllllll}
\text { reciprocal } & \text { imaginary } & \text { quadratic } & \text { square } & \text { perfect } & \frac{2}{3} & \frac{3}{2} \\
25 & 10 & 100 & \text { one-half } & \text { complex } & \text { binomial }
\end{array}
$
A number in the form $a+b i$ is a _______ number.

Julie Silva
Julie Silva
Numerade Educator
00:48

Problem 4

Fill in the blanks with the appropriate word, phrase, or symbol $($ s) from the following list.
$
\begin{array}{lllllll}
\text { reciprocal } & \text { imaginary } & \text { quadratic } & \text { square } & \text { perfect } & \frac{2}{3} & \frac{3}{2} \\
25 & 10 & 100 & \text { one-half } & \text { complex } & \text { binomial }
\end{array}
$
A perfect square trinomial is a trinomial that can be expressed as the square of a ___________.

James Kiss
James Kiss
Numerade Educator
01:29

Problem 5

Fill in the blanks with the appropriate word, phrase, or symbol $($ s) from the following list.
$
\begin{array}{lllllll}
\text { reciprocal } & \text { imaginary } & \text { quadratic } & \text { square } & \text { perfect } & \frac{2}{3} & \frac{3}{2} \\
25 & 10 & 100 & \text { one-half } & \text { complex } & \text { binomial }
\end{array}
$
To solve a quadratic equation by completing the square, we add a constant to both sides of the equation so the resulting trinomial is a __________ square trinomial.

Ernest Castorena
Ernest Castorena
Numerade Educator
00:20

Problem 6

Fill in the blanks with the appropriate word, phrase, or symbol $($ s) from the following list.
$
\begin{array}{lllllll}
\text { reciprocal } & \text { imaginary } & \text { quadratic } & \text { square } & \text { perfect } & \frac{2}{3} & \frac{3}{2} \\
25 & 10 & 100 & \text { one-half } & \text { complex } & \text { binomial }
\end{array}
$
Once one side of a quadratic equation is rewritten as a perfect square trinomial, the equation can be solved by using the __________ root property.

James Kiss
James Kiss
Numerade Educator
00:54

Problem 7

Fill in the blanks with the appropriate word, phrase, or symbol $($ s) from the following list.
$
\begin{array}{lllllll}
\text { reciprocal } & \text { imaginary } & \text { quadratic } & \text { square } & \text { perfect } & \frac{2}{3} & \frac{3}{2} \\
25 & 10 & 100 & \text { one-half } & \text { complex } & \text { binomial }
\end{array}
$
When a quadratic equation has a leading coefficient that is not 1 , you can multiply each term on both sides of the equation by the __________ of the leading coefficient.

Teresa Liang
Teresa Liang
Numerade Educator
00:58

Problem 8

Fill in the blanks with the appropriate word, phrase, or symbol $($ s) from the following list.
$
\begin{array}{lllllll}
\text { reciprocal } & \text { imaginary } & \text { quadratic } & \text { square } & \text { perfect } & \frac{2}{3} & \frac{3}{2} \\
25 & 10 & 100 & \text { one-half } & \text { complex } & \text { binomial }
\end{array}
$
In a perfect square trinomial with a leading coefficient of 1 , the constant term is the square of __________ the coefficient of the first-degree term.

Amy Jiang
Amy Jiang
Numerade Educator
00:58

Problem 9

Fill in the blanks with the appropriate word, phrase, or symbol $($ s) from the following list.
$
\begin{array}{lllllll}
\text { reciprocal } & \text { imaginary } & \text { quadratic } & \text { square } & \text { perfect } & \frac{2}{3} & \frac{3}{2} \\
25 & 10 & 100 & \text { one-half } & \text { complex } & \text { binomial }
\end{array}
$
To solve the quadratic equation $x^{2}-10 x=24$ by completing the square, you would add _________ to both sides of the equation.

Cory Kuzinski
Cory Kuzinski
Numerade Educator
00:48

Problem 10

Fill in the blanks with the appropriate word, phrase, or symbol $($ s) from the following list.
$
\begin{array}{lllllll}
\text { reciprocal } & \text { imaginary } & \text { quadratic } & \text { square } & \text { perfect } & \frac{2}{3} & \frac{3}{2} \\
25 & 10 & 100 & \text { one-half } & \text { complex } & \text { binomial }
\end{array}
$
To obtain an equivalent equation with a leading coefficient of 1 , multiply both sides of the equation $\frac{2}{3} x^{2}+3 x-5=0$ by ________.

James Kiss
James Kiss
Numerade Educator
00:43

Problem 11

For Exercises 11-38, use the square root property to solve each equation. Write complex number solutions in the form a $\pm$ bi.
$$
x^{2}=64
$$

Jeffrey Morris
Jeffrey Morris
Numerade Educator
00:57

Problem 12

For Exercises 11-38, use the square root property to solve each equation. Write complex number solutions in the form a $\pm$ bi.
$$
y^{2}=121
$$

Amy Jiang
Amy Jiang
Numerade Educator
00:45

Problem 13

For Exercises 11-38, use the square root property to solve each equation. Write complex number solutions in the form a $\pm$ bi.
$$
x^{2}-25=0
$$

Edward Downes
Edward Downes
Numerade Educator
00:58

Problem 14

For Exercises 11-38, use the square root property to solve each equation. Write complex number solutions in the form a $\pm$ bi.
$$
x^{2}-49=0
$$

Amy Jiang
Amy Jiang
Numerade Educator
03:32

Problem 15

For Exercises 11-38, use the square root property to solve each equation. Write complex number solutions in the form a $\pm$ bi.
$$
x^{2}-24=0
$$

Julie Silva
Julie Silva
Numerade Educator
00:57

Problem 16

For Exercises 11-38, use the square root property to solve each equation. Write complex number solutions in the form a $\pm$ bi.
$$
p^{2}-45=0
$$

Amy Jiang
Amy Jiang
Numerade Educator
00:23

Problem 17

For Exercises 11-38, use the square root property to solve each equation. Write complex number solutions in the form a $\pm$ bi.
$$
p^{2}+81=0
$$

Edward Downes
Edward Downes
Numerade Educator
02:15

Problem 18

For Exercises 11-38, use the square root property to solve each equation. Write complex number solutions in the form a $\pm$ bi.
$$
q^{2}+144=0
$$

Joanna Quigley
Joanna Quigley
Numerade Educator
03:32

Problem 19

For Exercises 11-38, use the square root property to solve each equation. Write complex number solutions in the form a $\pm$ bi.
$$
x^{2}+24=0
$$

Julie Silva
Julie Silva
Numerade Educator
00:23

Problem 20

For Exercises 11-38, use the square root property to solve each equation. Write complex number solutions in the form a $\pm$ bi.
$$
r^{2}+48=0
$$

Edward Downes
Edward Downes
Numerade Educator
03:08

Problem 21

For Exercises 11-38, use the square root property to solve each equation. Write complex number solutions in the form a $\pm$ bi.
$$
y^{2}-5=22
$$

Jennifer White
Jennifer White
Numerade Educator
00:47

Problem 22

For Exercises 11-38, use the square root property to solve each equation. Write complex number solutions in the form a $\pm$ bi.
$$
z^{2}+8=40
$$

Nez Nikoo
Nez Nikoo
Numerade Educator
00:39

Problem 23

For Exercises 11-38, use the square root property to solve each equation. Write complex number solutions in the form a $\pm$ bi.
$$
a^{2}+7=2
$$

Amy Jiang
Amy Jiang
Numerade Educator
00:57

Problem 24

For Exercises 11-38, use the square root property to solve each equation. Write complex number solutions in the form a $\pm$ bi.
$$
b^{2}-5=-11
$$

Amy Jiang
Amy Jiang
Numerade Educator
00:35

Problem 25

For Exercises 11-38, use the square root property to solve each equation. Write complex number solutions in the form a $\pm$ bi.
$$
(p-4)^{2}=16
$$

Trinity Steen
Trinity Steen
Numerade Educator
00:57

Problem 26

For Exercises 11-38, use the square root property to solve each equation. Write complex number solutions in the form a $\pm$ bi.
$$
(x+3)^{2}=49
$$

Amy Jiang
Amy Jiang
Numerade Educator
00:57

Problem 27

For Exercises 11-38, use the square root property to solve each equation. Write complex number solutions in the form a $\pm$ bi.
$$
(x+3)^{2}+25=0
$$

Amy Jiang
Amy Jiang
Numerade Educator
00:35

Problem 28

For Exercises 11-38, use the square root property to solve each equation. Write complex number solutions in the form a $\pm$ bi.
$$
(y-4)^{2}+144=0
$$

AG
Ankit Gupta
Numerade Educator
00:57

Problem 29

For Exercises 11-38, use the square root property to solve each equation. Write complex number solutions in the form a $\pm$ bi.
$$
(a-2)^{2}+45=0
$$

Amy Jiang
Amy Jiang
Numerade Educator
00:57

Problem 31

For Exercises 11-38, use the square root property to solve each equation. Write complex number solutions in the form a $\pm$ bi.
$$
\left(b+\frac{1}{3}\right)^{2}=\frac{4}{9}
$$

Amy Jiang
Amy Jiang
Numerade Educator
00:57

Problem 32

For Exercises 11-38, use the square root property to solve each equation. Write complex number solutions in the form a $\pm$ bi.
$$
\left(b-\frac{1}{3}\right)^{2}=\frac{4}{9}
$$

Amy Jiang
Amy Jiang
Numerade Educator
00:57

Problem 33

For Exercises 11-38, use the square root property to solve each equation. Write complex number solutions in the form a $\pm$ bi.
$$
(2 a-5)^{2}=18
$$

Amy Jiang
Amy Jiang
Numerade Educator
00:57

Problem 34

For Exercises 11-38, use the square root property to solve each equation. Write complex number solutions in the form a $\pm$ bi.
$$
(4 y+1)^{2}=12
$$

Amy Jiang
Amy Jiang
Numerade Educator
00:23

Problem 35

For Exercises 11-38, use the square root property to solve each equation. Write complex number solutions in the form a $\pm$ bi.
$$
(5 x+9)^{2}+4=0
$$

Edward Downes
Edward Downes
Numerade Educator
00:57

Problem 36

For Exercises 11-38, use the square root property to solve each equation. Write complex number solutions in the form a $\pm$ bi.
$$
(7 r-3)^{2}+36=0
$$

Amy Jiang
Amy Jiang
Numerade Educator
03:08

Problem 37

For Exercises 11-38, use the square root property to solve each equation. Write complex number solutions in the form a $\pm$ bi.
$$
\left(2 y+\frac{1}{2}\right)^{2}=\frac{4}{25}
$$

Jennifer White
Jennifer White
Numerade Educator
00:57

Problem 38

For Exercises 11-38, use the square root property to solve each equation. Write complex number solutions in the form a $\pm$ bi.
$$
\left(3 x-\frac{1}{4}\right)^{2}=\frac{9}{25}
$$

Amy Jiang
Amy Jiang
Numerade Educator
01:43

Problem 39

Solve each equation by completing the square. Write complex number solutions in the form $a \pm b i$.
$$
x^{2}+4 x+3=0
$$

Julie Silva
Julie Silva
Numerade Educator
00:32

Problem 40

Solve each equation by completing the square. Write complex number solutions in the form $a \pm b i$.
$$
y^{2}+6 y+5=0
$$

Erika Bustos
Erika Bustos
Numerade Educator
01:43

Problem 41

Solve each equation by completing the square. Write complex number solutions in the form $a \pm b i$.
$$
x^{2}-2 x-3=0
$$

Julie Silva
Julie Silva
Numerade Educator
00:22

Problem 42

Solve each equation by completing the square. Write complex number solutions in the form $a \pm b i$.
$$
y^{2}+4 y-21=0
$$

AG
Ankit Gupta
Numerade Educator
00:54

Problem 43

Solve each equation by completing the square. Write complex number solutions in the form $a \pm b i$.
$$
x^{2}+7 x+12=0
$$

AG
Ankit Gupta
Numerade Educator
04:09

Problem 44

Solve each equation by completing the square. Write complex number solutions in the form $a \pm b i$.
$$
x^{2}+9 x+18=0
$$

Kristen Marte
Kristen Marte
Numerade Educator
01:19

Problem 45

Solve each equation by completing the square. Write complex number solutions in the form $a \pm b i$.
$$
c^{2}-5 c+4=0
$$

AG
Ankit Gupta
Numerade Educator
00:39

Problem 46

Solve each equation by completing the square. Write complex number solutions in the form $a \pm b i$.
$$
d^{2}-11 d+18=0
$$

AG
Ankit Gupta
Numerade Educator
01:46

Problem 47

Solve each equation by completing the square. Write complex number solutions in the form $a \pm b i$.
$$
2 x^{2}+x-1=0
$$

Dharmendra Jain
Dharmendra Jain
Numerade Educator
00:28

Problem 48

Solve each equation by completing the square. Write complex number solutions in the form $a \pm b i$.
$$
3 c^{2}-4 c-4=0
$$

AG
Ankit Gupta
Numerade Educator
00:52

Problem 49

Solve each equation by completing the square. Write complex number solutions in the form $a \pm b i$.
$$
2 z^{2}-7 z-4=0
$$

AG
Ankit Gupta
Numerade Educator
04:09

Problem 50

Solve each equation by completing the square. Write complex number solutions in the form $a \pm b i$.
$$
4 a^{2}+9 a=9
$$

Kristen Marte
Kristen Marte
Numerade Educator
01:41

Problem 51

Solve each equation by completing the square. Write complex number solutions in the form $a \pm b i$.
$$
-x^{2}+6 x+7=0
$$

AG
Ankit Gupta
Numerade Educator
00:59

Problem 52

Solve each equation by completing the square. Write complex number solutions in the form $a \pm b i$.
$$
-z^{2}-4 z+12=0
$$

Victor Salazar
Victor Salazar
Numerade Educator
01:21

Problem 53

Solve each equation by completing the square. Write complex number solutions in the form $a \pm b i$.
$$
x^{2}+10 x=11
$$

Cory Kuzinski
Cory Kuzinski
Numerade Educator
01:41

Problem 54

Solve each equation by completing the square. Write complex number solutions in the form $a \pm b i$.
$$
-x^{2}=6 x-27
$$

AG
Ankit Gupta
Numerade Educator
01:41

Problem 55

Solve each equation by completing the square. Write complex number solutions in the form $a \pm b i$.
$$
b^{2}=3 b+28
$$

AG
Ankit Gupta
Numerade Educator
01:23

Problem 56

Solve each equation by completing the square. Write complex number solutions in the form $a \pm b i$.
$$
-x^{2}+40=-3 x
$$

AG
Ankit Gupta
Numerade Educator
01:19

Problem 57

Solve each equation by completing the square. Write complex number solutions in the form $a \pm b i$.
$$
x^{2}-4 x-10=0
$$

AG
Ankit Gupta
Numerade Educator
02:36

Problem 58

Solve each equation by completing the square. Write complex number solutions in the form $a \pm b i$.
$$
x^{2}-6 x+2=0
$$

Julie Silva
Julie Silva
Numerade Educator
00:55

Problem 59

Solve each equation by completing the square. Write complex number solutions in the form $a \pm b i$.
$$
m^{2}+6 m+1=0
$$

AG
Ankit Gupta
Numerade Educator
01:20

Problem 60

Solve each equation by completing the square. Write complex number solutions in the form $a \pm b i$.
$$
a^{2}+4 a-8=0
$$

Amy Jiang
Amy Jiang
Numerade Educator
01:43

Problem 61

Solve each equation by completing the square. Write complex number solutions in the form $a \pm b i$.
$$
p^{2}-4 p+13=0
$$

Julie Silva
Julie Silva
Numerade Educator
02:34

Problem 62

Solve each equation by completing the square. Write complex number solutions in the form $a \pm b i$.
$$
q^{2}-6 q+13=0
$$

Julie Silva
Julie Silva
Numerade Educator
02:03

Problem 63

Solve each equation by completing the square. Write complex number solutions in the form $a \pm b i$.
$$
n^{2}-n=3
$$

AG
Ankit Gupta
Numerade Educator
01:27

Problem 64

Solve each equation by completing the square. Write complex number solutions in the form $a \pm b i$.
$$
p^{2}-p=5
$$

AG
Ankit Gupta
Numerade Educator
01:42

Problem 65

Solve each equation by completing the square. Write complex number solutions in the form $a \pm b i$.
$$
x^{2}+3 x+6=0
$$

Cullen Miller
Cullen Miller
Numerade Educator
00:52

Problem 66

Solve each equation by completing the square. Write complex number solutions in the form $a \pm b i$.
$$
z^{2}-5 z+7=0
$$

AG
Ankit Gupta
Numerade Educator
04:09

Problem 67

Solve each equation by completing the square. Write complex number solutions in the form $a \pm b i$.
$$
9 x^{2}-9 x=0
$$

Kristen Marte
Kristen Marte
Numerade Educator
00:22

Problem 68

Solve each equation by completing the square. Write complex number solutions in the form $a \pm b i$.
$$
4 y^{2}+12 y=0
$$

AG
Ankit Gupta
Numerade Educator
00:54

Problem 69

Solve each equation by completing the square. Write complex number solutions in the form $a \pm b i$.
$$
a^{2}-4 a+7=0
$$

AG
Ankit Gupta
Numerade Educator
01:41

Problem 70

Solve each equation by completing the square. Write complex number solutions in the form $a \pm b i$.
$$
b^{2}-2 b+6=0
$$

AG
Ankit Gupta
Numerade Educator
00:36

Problem 71

Solve each equation by completing the square. Write complex number solutions in the form $a \pm b i$.
$$
36 c^{2}-36 c+25=0
$$

AG
Ankit Gupta
Numerade Educator
00:26

Problem 72

Solve each equation by completing the square. Write complex number solutions in the form $a \pm b i$.
$$
100 d^{2}-300 d+229=0
$$

AG
Ankit Gupta
Numerade Educator
01:43

Problem 73

Solve each equation by completing the square. Write complex number solutions in the form $a \pm b i$.
$$
-\frac{1}{2} p^{2}-p+\frac{3}{2}=0
$$

Julie Silva
Julie Silva
Numerade Educator
01:19

Problem 74

Solve each equation by completing the square. Write complex number solutions in the form $a \pm b i$.
$$
-\frac{1}{5} q^{2}+\frac{4}{5} q+1=0
$$

AG
Ankit Gupta
Numerade Educator
01:20

Problem 75

Solve each equation by completing the square. Write complex number solutions in the form $a \pm b i$.
$$
2 x^{2}=8 x+64
$$

Amy Jiang
Amy Jiang
Numerade Educator
01:03

Problem 76

Solve each equation by completing the square. Write complex number solutions in the form $a \pm b i$.
$$
2 x^{2}+6 x=20
$$

AG
Ankit Gupta
Numerade Educator
00:28

Problem 77

Solve each equation by completing the square. Write complex number solutions in the form $a \pm b i$.
$$
\frac{3}{4} w^{2}+\frac{1}{2} w-\frac{1}{4}=0
$$

AG
Ankit Gupta
Numerade Educator
00:28

Problem 78

Solve each equation by completing the square. Write complex number solutions in the form $a \pm b i$.
$$
\frac{3}{4} c^{2}-2 c+1=0
$$

AG
Ankit Gupta
Numerade Educator
01:42

Problem 79

Solve each equation by completing the square. Write complex number solutions in the form $a \pm b i$.
$$
-\frac{3}{2} x^{2}+6 x+\frac{3}{2}=0
$$

Cullen Miller
Cullen Miller
Numerade Educator
02:39

Problem 80

Solve each equation by completing the square. Write complex number solutions in the form $a \pm b i$.
$$
-\frac{2}{3} x^{2}+4 x-\frac{14}{3}=0
$$

Julie Silva
Julie Silva
Numerade Educator
00:25

Problem 81

Solve each equation by completing the square. Write complex number solutions in the form $a \pm b i$.
$$
2 x^{2}-x=-5
$$

AG
Ankit Gupta
Numerade Educator
00:46

Problem 82

Solve each equation by completing the square. Write complex number solutions in the form $a \pm b i$.
$$
5 y^{2}-3 y=-2
$$

AG
Ankit Gupta
Numerade Educator
01:02

Problem 83

Solve each equation by completing the square. Write complex number solutions in the form $a \pm b i$.
$$
\frac{5}{6} z^{2}+\frac{15}{2} z+\frac{5}{3}=0
$$

Erika Bustos
Erika Bustos
Numerade Educator
00:46

Problem 84

Solve each equation by completing the square. Write complex number solutions in the form $a \pm b i$.
$$
\frac{5}{2} x^{2}+\frac{3}{2} x-\frac{5}{4}=0
$$

AG
Ankit Gupta
Numerade Educator
01:00

Problem 85

In Exercises $85-88$, the area, $A$, of each rectangle is given. a) Write an equation for the area. b) Solve the equation for $x$.

Mrinal Rana
Mrinal Rana
Numerade Educator
01:00

Problem 86

In Exercises $85-88$, the area, $A$, of each rectangle is given. a) Write an equation for the area. b) Solve the equation for $x$.

Mrinal Rana
Mrinal Rana
Numerade Educator
01:00

Problem 87

In Exercises $85-88$, the area, $A$, of each rectangle is given. a) Write an equation for the area. b) Solve the equation for $x$.

Mrinal Rana
Mrinal Rana
Numerade Educator
01:00

Problem 88

In Exercises $85-88$, the area, $A$, of each rectangle is given. a) Write an equation for the area. b) Solve the equation for $x$.

Mrinal Rana
Mrinal Rana
Numerade Educator
01:35

Problem 89

A formula for approximating the stopping distance, $d$, in feet, for a specific car on snow is $d=\frac{1}{6} x^{2}$, where $x$ is the speed of the car, in miles per hour, before the brakes are applied. If the car's stopping distance was 24 feet, what was the car's speed before the brakes were applied?

Victor Salazar
Victor Salazar
Numerade Educator
02:28

Problem 90

A formula for approximating the stopping distance, $d$, in feet, for a specific car on dry pavement is $d=\frac{1}{10} x^{2}$, where $x$ is the speed of the car, in miles per hour, before the brakes are applied. If the car's stopping distance was 90 feet, what was the car's speed before the brakes were applied?

Gladys Fowler
Gladys Fowler
Numerade Educator
01:36

Problem 91

The product of two consecutive positive odd integers is 35 . Determine the two odd integers.

Avi Zellman
Avi Zellman
Numerade Educator
03:16

Problem 92

The product of two consecutive positive even integers is 48 . Determine the two even integers.

Anna Jones
Anna Jones
Numerade Educator
01:00

Problem 93

Donna has marked off an area in her yard where she will plant tomato plants. Determine the dimensions of the rectangular area if the length is 2 feet greater than twice the width and the area is 60 square feet.

Mrinal Rana
Mrinal Rana
Numerade Educator
01:36

Problem 94

Gary is designing a rectangular area in his yard for a butterfly garden. Determine the dimensions of the garden if the length is 8 feet greater than twice the width and the area is 120 square feet.

Juhi Singh
Juhi Singh
Numerade Educator
01:00

Problem 95

Bill is designing a square patio whose diagonal is 6 feet longer than the length of a side. Determine the length of one side.

Teresa Fuston
Teresa Fuston
Numerade Educator
02:12

Problem 96

The Lakeside Hotel is planning to build a shallow wading pool for children. If the pool is to be square and the diagonal of the square is 7 feet longer than a side, determine the length of one side of the pool.

Khushbu Rani
Khushbu Rani
Numerade Educator
02:16

Problem 97

When a triangle is inscribed in a semicircle where a diameter of the circle is a side of the triangle, the triangle formed is always a right triangle. If an isosceles triangle (two equal sides) is inscribed in a semicircle of radius 10 inches, determine the length of the other two sides of the triangle.

Jay Patel
Jay Patel
Numerade Educator
04:38

Problem 98

Refer to Exercise 97. Suppose a triangle is inscribed in a semicircle whose diameter is 12 meters. If one side of the inscribed triangle is 6 meters, determine the third side.

Ahmad Reda
Ahmad Reda
Numerade Educator
00:30

Problem 99

The area of a circle is $24 \pi$ square feet. Use the formula $A=\pi r^{2}$ to determine the radius of the circle.

Amy Jiang
Amy Jiang
Numerade Educator
01:27

Problem 100

The area of a circle is $16.4 \pi$ square meters. Determine the radius of the circle.
Use the formula $A=p\left(1+\frac{r}{n}\right)^{n t}$ to answer Exercises 101-104.

Heather Zimmers
Heather Zimmers
Numerade Educator
05:11

Problem 101

Use the formula $A=p\left(1+\frac{r}{n}\right)^{n}$ to answer Exercises 101-104.
Frank initially invested $\$ 500$ in a savings account where interest is compounded annually. If after 2 years the amount in the account is $\$ 540.80$, determine the annual interest rate.

Supratim Roy
Supratim Roy
Numerade Educator
01:07

Problem 102

Margret initially invested $\$ 1500$ in a savings account where interest is compounded annually. If after 3 years the amount in the account is $\$ 1687.30$, determine the annual interest rate.

Charles Carter
Charles Carter
Numerade Educator
02:46

Problem 103

Steve initially invested $\$ 1200$ in a savings account where interest is compounded semiannually. If after 3 years the amount in the account is $\$ 1432.86$, determine the annual interest rate.

Yujie Wang
Yujie Wang
College of San Mateo
03:53

Problem 104

Angela initially invested $\$ 1500$ in a savings account where interest is compounded semiannually. If after 4 years the amount in the account is $\$ 2052.85$, determine the annual interest rate.

AG
Ankit Gupta
Numerade Educator
01:38

Problem 105

The surface area, $S$, and volume, $V$, of a right circular cylinder of radius, $r$, and height, $h$, are given by the formulas
a) Determine the surface area of the cylinder if its height is 10 inches and its volume is 160 cubic inches.
b) Determine the radius if the height is 10 inches and the volume is 160 cubic inches.
c) Determine the radius if the height is 10 inches and the surface area is 160 square inches.

Melissa Stefan
Melissa Stefan
Numerade Educator
03:23

Problem 106

On the following grid, the points $\left(x_{1}, y_{1}\right),\left(x_{2}, y_{2}\right)$, and $\left(x_{1}, y_{2}\right)$ are plotted.
a) Explain why $\left(x_{1}, y_{2}\right)$ is placed where it is and not somewhere else on the graph.
b) Express the length of the orange dashed line in terms of $y_{2}$ and $y_{1}$. Explain how you determined your answer.
c) Express the length of the green dashed line in terms of $x_{2}$ and $x_{1}$.
d) Using the Pythagorean Theorem and the right triangle $A B C$, derive a formula for the distance, $d$, between points $\left(x_{1}, y_{1}\right)$ and $\left(x_{2}, y_{2}\right) .^{*}$ Explain how you determined the formula.
e) Use the formula you determined in part d) to determine the distance of the line segment between the points $(1,4)$ and $(3,7)$.

Jacquelyn Trost
Jacquelyn Trost
Numerade Educator
00:48

Problem 107

Solve $-4(2 z-6)=-3(z-4)+z$

Jake Zanazzi
Jake Zanazzi
Numerade Educator
05:16

Problem 108

Thea invested $\$ 10,000$ for 1 year, part at $7 \%$ and part at $6 \frac{1}{4} \%$. If she earned a total interest of $\$ 656.50$, how much was invested at each rate?

Nidhi Garg
Nidhi Garg
Numerade Educator
01:22

Problem 109

Solve $|x+3|=|2 x-7|$.

AG
Ankit Gupta
Numerade Educator
00:52

Problem 110

Determine the slope of the line through $(-2,5)$ and $(0,5)$.

Geno Ellis
Geno Ellis
Numerade Educator
00:44

Problem 111

Multiply $(x-2)\left(4 x^{2}+9 x-3\right)$.

Cory Kuzinski
Cory Kuzinski
Numerade Educator