Algebra A Combined Function

Problem 3

Find the value of the following expressions when $x=2, y=-2,$ and $z=-5$.
$$
\frac{y^{3}}{y^{2}-1}
$$

Victor Salazar

Numerade Educator

Problem 4

Find the value of the following expressions when $x=2, y=-2,$ and $z=-5$.
$$
\frac{z}{z^{2}-5}
$$

Victor Salazar

Numerade Educator

00:52

Problem 5

Find the value of the following expressions when $x=2, y=-2,$ and $z=-5$.
$$
\frac{x^{2}+8 x+2}{x^{2}-x-6}
$$

Victor Salazar

Numerade Educator

00:43

Problem 6

Find the value of the following expressions when $x=2, y=-2,$ and $z=-5$.
$$
\frac{x+5}{x^{2}+4 x-8}
$$

Victor Salazar

Numerade Educator

The average cost per DVD, in dollars, for a company to produce $x$ DVDs on exercising is given by the formula $A=\frac{3 x+400}{x},$ where $A$ is the average cost per DVD and $x$ is the number of DVDs produced.
a. Find the cost for producing $1 \mathrm{DVD}$.
b. Find the average cost for producing 100 DVDs.
c. Does the cost per DVD decrease or increase when more DVDs are produced? Explain your answer.

Victor Salazar

Numerade Educator

02:45

Problem 8

For a certain model of fax machine, the manufacturing cost $C$ per machine is given by the equation
$$
C=\frac{250 x+10,000}{x}
$$
where $x$ is the number of fax machines manufactured and $\operatorname{cost} C$ is in dollars per machine.
a. Find the cost per fax machine when manufacturing 100 fax machines.
b. Find the cost per fax machine when manufacturing 1000 fax machines.
c. Does the cost per machine decrease or increase when more machines are manufactured? Explain why this is so.

Victor Salazar

Numerade Educator

02:45

Problem 9

Find any numbers for which each rational expression is undefined.
$$
\frac{7}{2 x}
$$

Victor Salazar

Numerade Educator

Problem 10

Find any numbers for which each rational expression is undefined.
$$
\frac{3}{5 x}
$$

Victor Salazar

Numerade Educator

Problem 11

Find any numbers for which each rational expression is undefined.
$$
\frac{x+3}{x+2}
$$

Victor Salazar

Numerade Educator

00:41

Problem 12

Find any numbers for which each rational expression is undefined.
$$
\frac{5 x+1}{x-9}
$$

Victor Salazar

Numerade Educator

Problem 13

Find any numbers for which each rational expression is undefined.
$$
\frac{x-4}{2 x-5}
$$

Victor Salazar

Numerade Educator

Problem 14

Find any numbers for which each rational expression is undefined.
$$
\frac{x+1}{5 x-2}
$$

Victor Salazar

Numerade Educator

00:56

Problem 15

Find any numbers for which each rational expression is undefined.
$$
\frac{9 x^{3}+4}{15 x^{2}+30 x}
$$

Victor Salazar

Numerade Educator

00:40

Problem 16

Find any numbers for which each rational expression is undefined.
$$
\frac{19 x^{3}+2}{x^{2}-x}
$$

Victor Salazar

Numerade Educator

00:51

Problem 17

Find any numbers for which each rational expression is undefined.
$$
\frac{x^{2}-5 x-2}{4}
$$

Victor Salazar

Numerade Educator

Problem 18

Find any numbers for which each rational expression is undefined.
$$
\frac{9 y^{5}+y^{3}}{9}
$$

Victor Salazar

Numerade Educator

Problem 19

Find any numbers for which each rational expression is undefined.
$$
\frac{3 x^{2}+9}{x^{2}-5 x-6}
$$

Victor Salazar

Numerade Educator

Problem 20

Find any numbers for which each rational expression is undefined.
$$
\frac{11 x^{2}+1}{x^{2}-5 x-14}
$$

Victor Salazar

Numerade Educator

Problem 21

Find any numbers for which each rational expression is undefined.
$$
\frac{x}{3 x^{2}+13 x+14}
$$

Victor Salazar

Numerade Educator

00:49

Problem 22

Find any numbers for which each rational expression is undefined.
$$
\frac{x}{2 x^{2}+15 x+27}
$$

Victor Salazar

Numerade Educator

00:37

Problem 23

Simplify each expression.
$$
\frac{x+7}{7+x}
$$

Victor Salazar

Numerade Educator

00:32

Problem 24

Simplify each expression.
$$
\frac{y+9}{9+y}
$$

Victor Salazar

Numerade Educator

00:37

Problem 25

Simplify each expression.
$$
\frac{x-7}{7-x}
$$

Victor Salazar

Numerade Educator

00:33

Problem 26

Simplify each expression.
$$
\frac{y-9}{9-y}
$$

Victor Salazar

Numerade Educator

00:35

Problem 27

Simplify each expression.
$$
\frac{2}{8 x+16}
$$

Victor Salazar

Numerade Educator

Problem 28

Simplify each expression.
$$
\frac{3}{9 x+6}
$$

Victor Salazar

Numerade Educator

00:33

Problem 29

Simplify each expression.
$$
\frac{x-2}{x^{2}-4}
$$

Victor Salazar

Numerade Educator

Problem 30

Simplify each expression.
$$
\frac{x+5}{x^{2}-25}
$$

Victor Salazar

Numerade Educator

00:54

Problem 31

Simplify each expression.
$$
\frac{2 x-10}{3 x-30}
$$

Victor Salazar

Numerade Educator

00:55

Problem 32

Simplify each expression.
$$
\frac{3 x-9}{4 x-16}
$$

Victor Salazar

Numerade Educator

Problem 33

Simplify each expression.
$$
\frac{-5 a-5 b}{a+b}
$$

Victor Salazar

Numerade Educator

00:34

Problem 34

Simplify each expression.
$$
\frac{-4 x-4 y}{x+y}
$$

Victor Salazar

Numerade Educator

00:45

Problem 35

Simplify each expression.
$$
\frac{7 x+35}{x^{2}+5 x}
$$

Victor Salazar

Numerade Educator

00:31

Problem 36

Simplify each expression.
$$
\frac{9 x+99}{x^{2}+11 x}
$$

Victor Salazar

Numerade Educator

00:37

Problem 37

Simplify each expression.
$$
\frac{x+5}{x^{2}-4 x-45}
$$

Victor Salazar

Numerade Educator

Problem 38

Simplify each expression.
$$
\frac{x-3}{x^{2}-6 x+9}
$$

Victor Salazar

Numerade Educator

00:45

Problem 39

Simplify each expression.
$$
\frac{5 x^{2}+11 x+2}{x+2}
$$

Victor Salazar

Numerade Educator

00:51

Problem 40

Simplify each expression.
$$
\frac{12 x^{2}+4 x-1}{2 x+1}
$$

Victor Salazar

Numerade Educator

Problem 41

Simplify each expression.
$$
\frac{x^{3}+7 x^{2}}{x^{2}+5 x-14}
$$

Victor Salazar

Numerade Educator

00:47

Problem 42

Simplify each expression.
$$
\frac{x^{4}-10 x^{3}}{x^{2}-17 x+70}
$$

Victor Salazar

Numerade Educator

Problem 43

Simplify each expression.
$$
\frac{14 x^{2}-21 x}{2 x-3}
$$

Victor Salazar

Numerade Educator

00:29

Problem 44

Simplify each expression.
$$
\frac{4 x^{2}+24 x}{x+6}
$$

Victor Salazar

Numerade Educator

00:44

Problem 45

Simplify each expression.
$$
\frac{x^{2}+7 x+10}{x^{2}-3 x-10}
$$

Victor Salazar

Numerade Educator

01:15

Problem 46

Simplify each expression.
$$
\frac{2 x^{2}+7 x-4}{x^{2}+3 x-4}
$$

Victor Salazar

Numerade Educator

00:54

Problem 47

Simplify each expression.
$$
\frac{3 x^{2}+7 x+2}{3 x^{2}+13 x+4}
$$

Victor Salazar

Numerade Educator

01:20

Problem 48

Simplify each expression.
$$
\frac{4 x^{2}-4 x+1}{2 x^{2}+9 x-5}
$$

Victor Salazar

Numerade Educator

Problem 49

Simplify each expression.
$$
\frac{2 x^{2}-8}{4 x-8}
$$

Victor Salazar

Numerade Educator

01:02

Problem 50

Simplify each expression.
$$
\frac{5 x^{2}-500}{35 x+350}
$$

Victor Salazar

Numerade Educator

00:41

Problem 51

Simplify each expression.
$$
\frac{4-x^{2}}{x-2}
$$

Victor Salazar

Numerade Educator

Problem 52

Simplify each expression.
$$
\frac{49-y^{2}}{y-7}
$$

Victor Salazar

Numerade Educator

Problem 53

Simplify each expression.
$$
\frac{x^{2}-1}{x^{2}-2 x+1}
$$

Victor Salazar

Numerade Educator

00:44

Problem 54

Simplify each expression.
$$
\frac{x^{2}-16}{x^{2}-8 x+16}
$$

Victor Salazar

Numerade Educator

Problem 55

Simplify each expression. Each exercise contains a four-term polynomial that should be factored by grouping.
$$
\frac{x^{2}+x y+2 x+2 y}{x+2}
$$

Victor Salazar

Numerade Educator

00:49

Problem 56

Simplify each expression. Each exercise contains a four-term polynomial that should be factored by grouping.
$$
\frac{a b+a c+b^{2}+b c}{b+c}
$$

Victor Salazar

Numerade Educator

Problem 57

Simplify each expression. Each exercise contains a four-term polynomial that should be factored by grouping.
$$
\frac{5 x+15-x y-3 y}{2 x+6}
$$

Victor Salazar

Numerade Educator

01:03

Problem 58

Simplify each expression. Each exercise contains a four-term polynomial that should be factored by grouping.
$$
\frac{x y-6 x+2 y-12}{y^{2}-6 y}
$$

Victor Salazar

Numerade Educator

01:16

Problem 59

Simplify each expression. Each exercise contains a four-term polynomial that should be factored by grouping.
$$
\frac{2 x y+5 x-2 y-5}{3 x y+4 x-3 y-4}
$$

Victor Salazar

Numerade Educator

01:13

Problem 60

Simplify each expression. Each exercise contains a four-term polynomial that should be factored by grouping.
$$
\frac{2 x y+2 x-3 y-3}{2 x y+4 x-3 y-6}
$$

Victor Salazar

Numerade Educator

01:25

Problem 61

Then list four equivalent forms for each rational expression.
$$
-\frac{x-10}{x+8}
$$

Victor Salazar

Numerade Educator

Problem 62

Then list four equivalent forms for each rational expression.
$$
-\frac{x+11}{x-4}
$$

Victor Salazar

Numerade Educator

Problem 63

Then list four equivalent forms for each rational expression.
$$
-\frac{5 y-3}{y-12}
$$

Victor Salazar

Numerade Educator

00:57

Problem 64

Then list four equivalent forms for each rational expression.
$$
-\frac{8 y-1}{y-15}
$$

Victor Salazar

Numerade Educator

00:47

Problem 65

Simplify each expression. Then determine whether the given answer is correct.
$$
\frac{9-x^{2}}{x-3} ; \text { Answer: }-3-x
$$

Victor Salazar

Numerade Educator

00:50

Problem 66

Simplify each expression. Then determine whether the given answer is correct.
$$
\frac{100-x^{2}}{x-10} ; \text { Answer: }-10-x
$$

Victor Salazar

Numerade Educator

00:58

Problem 67

Simplify each expression. Then determine whether the given answer is correct.
$$
\frac{7-34 x-5 x^{2}}{25 x^{2}-1} ; \text { Answer: } \frac{x+7}{-5 x-1}
$$

Victor Salazar

Numerade Educator

01:21

Problem 68

Simplify each expression. Then determine whether the given answer is correct.
$$
\frac{2-15 x-8 x^{2}}{64 x^{2}-1} ; \text { Answer: } \frac{x+2}{-8 x-1}
$$

Victor Salazar

Numerade Educator

00:40

Problem 69

Perform each indicated operation.
$$
\frac{1}{3} \cdot \frac{9}{11}
$$

Victor Salazar

Numerade Educator

00:39

Problem 70

Perform each indicated operation.
$$
\frac{5}{27} \cdot \frac{2}{5}
$$

Victor Salazar

Numerade Educator

00:34

Problem 71

Perform each indicated operation.
$$
\frac{1}{3} \div \frac{1}{4}
$$

Victor Salazar

Numerade Educator

00:40

Problem 72

Perform each indicated operation.
$$
\frac{7}{8} \div \frac{1}{2}
$$

Victor Salazar

Numerade Educator

Problem 73

Perform each indicated operation.
$$
\frac{13}{20} \div \frac{2}{9}
$$

Victor Salazar

Numerade Educator

Problem 74

Perform each indicated operation.
$$
\frac{8}{15} \div \frac{5}{8}
$$

Victor Salazar

Numerade Educator

Problem 75

Which of the following are incorrect and why?
$$
\frac{5 a-15}{5} \text { simplifies to } a-3
$$

Victor Salazar

Numerade Educator

Problem 76

Which of the following are incorrect and why?
$$
\frac{7 m-9}{7} \text { simplifies to } m-9
$$

Victor Salazar

Numerade Educator

00:45

Problem 77

Which of the following are incorrect and why?
$$
\frac{1+2}{1+3} \text { simplifies to } \frac{2}{3}
$$

Victor Salazar

Numerade Educator

Problem 78

Which of the following are incorrect and why?
$$
\frac{46}{54} \text { simplifies to } \frac{6}{5}
$$

Victor Salazar

Numerade Educator

01:03

Problem 79

Explain how to write a fraction in lowest terms

Victor Salazar

Numerade Educator

01:05

Problem 80

Explain how to write a rational expression in lowest terms.

Victor Salazar

Numerade Educator

00:50

Problem 81

Explain why the denominator of a fraction or a rational expression must not equal 0 .

Victor Salazar

Numerade Educator

00:47

Problem 82

Does $\frac{(x-3)(x+3)}{x-3}$ have the same value as $x+3$ for all real numbers? Explain why or why not.

Victor Salazar

Numerade Educator

00:55

Problem 83

The dose of medicine prescribed for a child depends on the child's age $A$ in years and the adult dose $D$ for the medication. Young's Rule is a formula used by pediatricians that gives a child's dose $C$ as
$$
C=\frac{D A}{A+12}
$$
Suppose that an 8-year-old child needs medication, and the normal adult dose is $1000 \mathrm{mg}$. What size dose should the child receive?

Heather Zimmers

Numerade Educator

01:14

Problem 84

Calculating body-mass index is a way to gauge whether a person should lose weight. Doctors recommend that body-mass index values fall between 19 and $25 .$ The formula for body-mass index $B$ is
$$
B=\frac{705 w}{h^{2}}
$$
where $w$ is weight in pounds and $h$ is height in inches. Should a 148 -pound person who is 5 feet 6 inches tall lose weight?

Victor Salazar

Numerade Educator

00:55

Problem 85

Anthropologists and forensic scientists use a measure called the cephalic index to help classify skulls. The cephalic index of a skull with width $W$ and length $L$ from front to back is given by the formula
$$
C=\frac{100 W}{L}
$$
A long skull has an index value less than $75,$ a medium skull has an index value between 75 and $85,$ and a broad skull has an index value over $85 .$ Find the cephalic index of a skull that is 5 inches wide and 6.4 inches long. Classify the skull.

Heather Zimmers

Numerade Educator