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Algebra and Trigonometry

Judith A. Beecher, Judith A. Penna, Marvin L. Bittinger

Chapter 9

Systems of Equations and Matrices - all with Video Answers

Educators

AG

Section 1

Systems of Equations in Two Variables

01:05

Problem 1

Text Unavailable

Match the system of equations with one of the graphs ( $a$ ) - $(f),$ which follow.
A.(GRAPH CANNOT COPY)
B.(GRAPH CANNOT COPY)
C.(GRAPH CANNOT COPY)
D.(GRAPH CANNOT COPY)
E.(GRAPH CANNOT COPY)
F.(GRAPH CANNOT COPY)
$$\begin{aligned}
&x+y=-2\\
&y=x-8
\end{aligned}$$

AG
Ankit Gupta
Numerade Educator
00:41

Problem 2

Text Unavailable

Match the system of equations with one of the graphs ( $a$ ) - $(f),$ which follow.
A.(GRAPH CANNOT COPY)
B.(GRAPH CANNOT COPY)
C.(GRAPH CANNOT COPY)
D.(GRAPH CANNOT COPY)
E.(GRAPH CANNOT COPY)
F.(GRAPH CANNOT COPY)
$$\begin{aligned}
&x-y=-5\\
&x=-4 y
\end{aligned}$$

AG
Ankit Gupta
Numerade Educator
00:59

Problem 3

Text Unavailable

Match the system of equations with one of the graphs ( $a$ ) - $(f),$ which follow.
A.(GRAPH CANNOT COPY)
B.(GRAPH CANNOT COPY)
C.(GRAPH CANNOT COPY)
D.(GRAPH CANNOT COPY)
E.(GRAPH CANNOT COPY)
F.(GRAPH CANNOT COPY)
$$\begin{array}{r}
x-2 y=-1 \\
4 x-3 y=6
\end{array}$$

AG
Ankit Gupta
Numerade Educator
00:54

Problem 4

Text Unavailable

Match the system of equations with one of the graphs ( $a$ ) - $(f),$ which follow.
A.(GRAPH CANNOT COPY)
B.(GRAPH CANNOT COPY)
C.(GRAPH CANNOT COPY)
D.(GRAPH CANNOT COPY)
E.(GRAPH CANNOT COPY)
F.(GRAPH CANNOT COPY)
$$\begin{aligned}
2 x-y &=1 \\
x+2 y &=-7
\end{aligned}$$

AG
Ankit Gupta
Numerade Educator

Problem 5

Text Unavailable

Match the system of equations with one of the graphs ( $a$ ) - $(f),$ which follow.
A.(GRAPH CANNOT COPY)
B.(GRAPH CANNOT COPY)
C.(GRAPH CANNOT COPY)
D.(GRAPH CANNOT COPY)
E.(GRAPH CANNOT COPY)
F.(GRAPH CANNOT COPY)
$$\begin{array}{c}
2 x-3 y=-1 \\
-4 x+6 y=2
\end{array}$$

Check back soon!
00:56

Problem 6

Text Unavailable

Match the system of equations with one of the graphs ( $a$ ) - $(f),$ which follow.
A.(GRAPH CANNOT COPY)
B.(GRAPH CANNOT COPY)
C.(GRAPH CANNOT COPY)
D.(GRAPH CANNOT COPY)
E.(GRAPH CANNOT COPY)
F.(GRAPH CANNOT COPY)
$$\begin{aligned}
&4 x-2 y=5\\
&6 x-3 y=-10
\end{aligned}$$

AG
Ankit Gupta
Numerade Educator
01:04

Problem 7

Text Unavailable

Solve graphically.
$$\begin{aligned}
x+y &=2 \\
3 x+y &=0
\end{aligned}$$

AG
Ankit Gupta
Numerade Educator
01:02

Problem 8

Text Unavailable

Solve graphically.
$$\begin{aligned}
x+y &=1 \\
3 x+y &=7
\end{aligned}$$

AG
Ankit Gupta
Numerade Educator
01:05

Problem 9

Text Unavailable

Solve graphically.
$$\begin{aligned}
&x+2 y=1\\
&x+4 y=3
\end{aligned}$$

AG
Ankit Gupta
Numerade Educator
01:06

Problem 10

Text Unavailable

Solve graphically.
$$\begin{array}{r}
3 x+4 y=5 \\
x-2 y=5
\end{array}$$

AG
Ankit Gupta
Numerade Educator
01:09

Problem 11

Text Unavailable

Solve graphically.
$$\begin{aligned}
&y+1=2 x\\
&y-1=2 x
\end{aligned}$$

AG
Ankit Gupta
Numerade Educator
02:00

Problem 12

Text Unavailable

Solve graphically.
$$\begin{aligned}
&2 x-y=1\\
&3 y=6 x-3
\end{aligned}$$

AG
Ankit Gupta
Numerade Educator
01:02

Problem 13

Text Unavailable

Solve graphically.
$$\begin{aligned}
&x-y=-6\\
&y=-2 x
\end{aligned}$$

AG
Ankit Gupta
Numerade Educator
01:00

Problem 14

Text Unavailable

Solve graphically.
$$\begin{aligned}
&2 x+y=5\\
&x=-3 y
\end{aligned}$$

AG
Ankit Gupta
Numerade Educator
01:51

Problem 15

Text Unavailable

Solve graphically.
$$\begin{aligned}
&2 y=x-1\\
&3 x=6 y+3
\end{aligned}$$

AG
Ankit Gupta
Numerade Educator
01:05

Problem 16

Text Unavailable

Solve graphically.
$$\begin{aligned}
&y=3 x+2\\
&3 x-y=-3
\end{aligned}$$

AG
Ankit Gupta
Numerade Educator
01:09

Problem 17

Text Unavailable

Solve using the substitution method.
$$\begin{array}{c}
x+y=9 \\
2 x-3 y=-2
\end{array}$$

AG
Ankit Gupta
Numerade Educator
01:41

Problem 18

Text Unavailable

Solve using the substitution method.
$$\begin{array}{r}
3 x-y=5 \\
x+y=\frac{1}{2}
\end{array}$$

AG
Ankit Gupta
Numerade Educator
01:05

Problem 19

Text Unavailable

Solve using the substitution method.
$$\begin{aligned}
&x-2 y=7\\
&x=y+4
\end{aligned}$$

AG
Ankit Gupta
Numerade Educator
01:00

Problem 20

Text Unavailable

Solve using the substitution method.
$$\begin{aligned}
&x+4 y=6\\
&x=-3 y+3
\end{aligned}$$

AG
Ankit Gupta
Numerade Educator
01:15

Problem 21

Text Unavailable

Solve using the substitution method.
$$\begin{aligned}
&y=2 x-6\\
&5 x-3 y=16
\end{aligned}$$

AG
Ankit Gupta
Numerade Educator
01:39

Problem 22

Text Unavailable

Solve using the substitution method.
$$\begin{aligned}
&3 x+5 y=2\\
&2 x-y=-3
\end{aligned}$$

AG
Ankit Gupta
Numerade Educator
00:53

Problem 23

Text Unavailable

Solve using the substitution method.
$$\begin{aligned}
&x+y=3\\
&y=4-x
\end{aligned}$$

AG
Ankit Gupta
Numerade Educator
00:56

Problem 24

Text Unavailable

Solve using the substitution method.
$$\begin{aligned}
&x-2 y=3\\
&2 x=4 y+6
\end{aligned}$$

AG
Ankit Gupta
Numerade Educator
01:21

Problem 25

Text Unavailable

Solve using the substitution method.
$$\begin{aligned}
&x-5 y=4\\
&y=7-2 x
\end{aligned}$$

AG
Ankit Gupta
Numerade Educator
01:13

Problem 26

Text Unavailable

Solve using the substitution method.
$$\begin{array}{c}
5 x+3 y=-1 \\
x+y=1
\end{array}$$

AG
Ankit Gupta
Numerade Educator
01:34

Problem 27

Text Unavailable

Solve using the substitution method.
$$\begin{array}{r}
x+2 y=2 \\
4 x+4 y=5
\end{array}$$

AG
Ankit Gupta
Numerade Educator
01:30

Problem 28

Text Unavailable

Solve using the substitution method.
$$\begin{aligned}
&2 x-y=2\\
&4 x+y=3
\end{aligned}$$

AG
Ankit Gupta
Numerade Educator
01:31

Problem 29

Text Unavailable

Solve using the substitution method.
$$\begin{aligned}
&3 x-y=5\\
&3 y=9 x-15
\end{aligned}$$

AG
Ankit Gupta
Numerade Educator
00:57

Problem 30

Text Unavailable

Solve using the substitution method.
$$\begin{aligned}
&2 x-y=7\\
&y=2 x-5
\end{aligned}$$

AG
Ankit Gupta
Numerade Educator
01:38

Problem 31

Text Unavailable

Solve using the elimination method. Also determine
whether each system is consistent or inconsistent and whether the equations are dependent or independent.
\begin{aligned}
&x+2 y=7\\
&x-2 y=-5
\end{aligned}

AG
Ankit Gupta
Numerade Educator
01:24

Problem 32

Text Unavailable

Solve using the elimination method. Also determine whether each system is consistent or inconsistent and whether the equations are dependent or independent.
\begin{array}{r}
3 x+4 y=-2 \\
-3 x-5 y=1
\end{array}

AG
Ankit Gupta
Numerade Educator
02:01

Problem 33

Text Unavailable

Solve using the elimination method. Also determine whether each system is consistent or inconsistent and whether the equations are dependent or independent.
\begin{array}{c}
x-3 y=2 \\
6 x+5 y=-34
\end{array}

AG
Ankit Gupta
Numerade Educator
01:30

Problem 34

Text Unavailable

Solve using the elimination method. Also determine whether each system is consistent or inconsistent and whether the equations are dependent or independent.
\begin{array}{r}
x+3 y=0 \\
20 x-15 y=75
\end{array}

AG
Ankit Gupta
Numerade Educator
01:03

Problem 35

Text Unavailable

Solve using the elimination method. Also determine whether each system is consistent or inconsistent and whether the equations are dependent or independent.
$$\begin{aligned}
&3 x-12 y=6\\
&2 x-8 y=4
\end{aligned}$$

AG
Ankit Gupta
Numerade Educator
01:23

Problem 36

Text Unavailable

Solve using the elimination method. Also determine whether each system is consistent or inconsistent and whether the equations are dependent or independent.
$$\begin{aligned}
&2 x+6 y=7\\
&3 x+9 y=10
\end{aligned}$$

AG
Ankit Gupta
Numerade Educator
01:06

Problem 37

Text Unavailable

Solve using the elimination method. Also determine whether each system is consistent or inconsistent and whether the equations are dependent or independent.
$$\begin{aligned}
&4 x-2 y=3\\
&2 x-y=4
\end{aligned}$$

AG
Ankit Gupta
Numerade Educator
01:33

Problem 38

Text Unavailable

Solve using the elimination method. Also determine whether each system is consistent or inconsistent and whether the equations are dependent or independent.
$$\begin{aligned}
&6 x+9 y=12\\
&4 x+6 y=8
\end{aligned}$$

AG
Ankit Gupta
Numerade Educator
01:45

Problem 39

Text Unavailable

Solve using the elimination method. Also determine whether each system is consistent or inconsistent and whether the equations are dependent or independent.
$$\begin{aligned}
&2 x=5-3 y\\
&4 x=11-7 y
\end{aligned}$$

AG
Ankit Gupta
Numerade Educator
01:23

Problem 40

Text Unavailable

Solve using the elimination method. Also determine whether each system is consistent or inconsistent and whether the equations are dependent or independent.
$$\begin{aligned}
&7(x-y)=14\\
&2 x=y+5
\end{aligned}$$

AG
Ankit Gupta
Numerade Educator
02:00

Problem 41

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Solve using the elimination method. Also determine whether each system is consistent or inconsistent and whether the equations are dependent or independent.
$0.3 x-0.2 y=-0.9$
$0.2 x-0.3 y=-0.6$
(Hint: since each coefficient has one decimal place, first multiply each equation by 10 to clear the decimals.)

AG
Ankit Gupta
Numerade Educator
01:59

Problem 42

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Solve using the elimination method. Also determine whether each system is consistent or inconsistent and whether the equations are dependent or independent.
$0.2 x-0.3 y=0.3$
$0.4 x+0.6 y=-0.2$
(Hint: since each coefficient has one decimal place, first multiply each equation by 10 to clear the decimals.)

AG
Ankit Gupta
Numerade Educator

Problem 43

Text Unavailable

Solve using the elimination method. Also determine whether each system is consistent or inconsistent and whether the equations are dependent or independent.
$\frac{1}{5} x+\frac{1}{2} y=6$
$\frac{3}{5} x-\frac{1}{2} y=2$
(Hint: First multiply by the least common denominator to clear fractions.)

Check back soon!
03:20

Problem 44

Text Unavailable

Solve using the elimination method. Also determine whether each system is consistent or inconsistent and whether the equations are dependent or independent.
$\frac{2}{3} x+\frac{3}{5} y=-17$
$\frac{1}{2} x-\frac{1}{3} y=-1$
(Hint: First multiply by the least common denominator to clear fractions.)

AG
Ankit Gupta
Numerade Educator
00:39

Problem 45

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Determine whether the statement is true or false.
If the graph of a system of equations is a pair of parallel lines, the system of equations is inconsistent.

AG
Ankit Gupta
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00:27

Problem 46

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Determine whether the statement is true or false.
If we obtain the equation $0=0$ when using the elimination method to solve a system of equations, the system has no solution.

AG
Ankit Gupta
Numerade Educator
01:01

Problem 47

Text Unavailable

Determine whether the statement is true or false.
If a system of two linear equations in two variables is consistent, it has exactly one solution.

AG
Ankit Gupta
Numerade Educator
00:59

Problem 48

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Determine whether the statement is true or false.
If a system of two linear equations in two variables is dependent, it has infinitely many solutions.

AG
Ankit Gupta
Numerade Educator
01:17

Problem 49

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Determine whether the statement is true or false.
It is possible for a system of two linear equations in two variables to be consistent and dependent.

AG
Ankit Gupta
Numerade Educator
00:44

Problem 50

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Determine whether the statement is true or false.
It is possible for a system of two linear equations in two variables to be inconsistent and dependent.

AG
Ankit Gupta
Numerade Educator
01:27

Problem 51

Text Unavailable

Determine whether the statement is true or false.
The Better Business Bureau received the most complaints from consumers about cell-phone providers and cable/satellite TV providers in 2009 . These two industries accounted for a total of $70,093$ complaints, with cable/satellite TV providers receiving 4861 fewer complaints than cell-phone providers (Source: Better Business Bureau). How many complaints did each industry receive?

AG
Ankit Gupta
Numerade Educator
View

Problem 52

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It is projected that in 2018 , the average total of medical bills for an obese adult will be $\$ 2460$ higher than the average for an adult with a healthy weight. Together, the average amount of medical bills for an obese adult and an adult with a healthy weight are projected to total $\$ 14,170 .$ (Source: Kenneth Thorpe, Emory University) Find the projected average amount of medical bills for an obese adult and for an adult with a healthy weight.

AG
Ankit Gupta
Numerade Educator
01:33

Problem 53

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Surgery. It is estimated that in $2030,$ there will be a total of 4.072 million knee replacement and hip replacement surgeries, with knee replacements outnumbering hip replacements by 2.928 million (Source: Indianapolis Star research) Find the estimated number of each type of joint replacement.

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Ankit Gupta
Numerade Educator
01:15

Problem 54

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The two most common names for streets in the United States are Second Street and Main
Street, with $15,684$ streets bearing one of these names. There are 260 more streets named Second Street than Main Street. (Source: 2006 Tele Atlas digital map data) How many streets bear each name?

AG
Ankit Gupta
Numerade Educator
01:41

Problem 55

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Injuries. Skiers and snowboarders suffer about $288,400$ injuries each winter, with skiing accounting for about 400 more injuries than snowboarding (Source: U.S. Consumer Product Safety Commission). How many injuries occur in each winter sport?
(IMAGE CANNOT COPY)

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Ankit Gupta
Numerade Educator
01:29

Problem 56

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Together, a $20-\mathrm{fl}$ oz Coca-Cola and a $20-\mathrm{fl}$ oz Pepsi contain 34 tsp of added sugar. The Coca-Cola contains 1 tsp less of added sugar than the Pepsi. (Source: Nutrition Action HealthLetter, January/February, 2010 ) Find the amount of added sugar in each type of soft drink.
(IMAGE CANNOT COPY)

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Ankit Gupta
Numerade Educator
02:45

Problem 57

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A mail-order lacrosse equipment business shipped 120 packages one day. Customers are charged $\$ 3.50$ for each standard-delivery package and $\$ 7.50$ for each express-delivery package. Total shipping charges for the day were $\$ 596 .$ How many of each kind of package were shipped?

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Ankit Gupta
Numerade Educator
02:14

Problem 58

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One evening 1500 concert tickets were sold for the Fairmont Summer Jazz Festival. Tickets cost $\$ 25$ for a covered pavilion seat and $\$ 15$ for a lawn seat. Total receipts were $\$ 28,500 .$ How many of each type of ticket were sold?

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Ankit Gupta
Numerade Educator
02:20

Problem 59

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Bernadette inherited $\$ 15,000$ and invested it in two municipal bonds, which pay $4 \%$ and $5 \%$ simple interest. The annual interest is $\$ 690 .$ Find the amount invested at each rate.

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Ankit Gupta
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02:19

Problem 60

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Tee Shirt Sales. Mack's Tee Shirt Shack sold 36 shirts one day. All short-sleeved tee shirts cost $\$ 12$ each and all long-sleeved tee shirts cost $\$ 18$ each. Total receipts for the day were $\$ 522 .$ How many of each kind of shirt were sold?

AG
Ankit Gupta
Numerade Educator
01:21

Problem 61

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The owner of The Daily Grind coffee shop mixes French roast coffee worth $\$ 9.00$ per pound with Kenyan coffee worth $\$ 7.50$ per pound in order to get 10 lb of a mixture worth $\$ 8.40$ per pound. How much of each type of coffee was used?

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Ankit Gupta
Numerade Educator
01:09

Problem 62

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Commissions. Jackson Manufacturing offers its sales representatives a choice between being paid a commission of $8 \%$ of sales or being paid a monthly salary of $\$ 1500$ plus a commission of $1 \%$ of sales. For what monthly sales do the two plans pay the same amount?

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Ankit Gupta
Numerade Educator
01:38

Problem 63

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Nutrition. A one-cup serving of spaghetti with meatballs contains 260 Cal (calories) and 32 g of carbohydrates. A one-cup serving of chopped iceberg lettuce contains $5 \mathrm{Cal}$ and $1 \mathrm{g}$ of carbohydrates. (Source: Home and Garden Bulletin No. 72,
U.S. Government Printing Office, Washington, D.C. 20402 ) How many servings of each would be required to obtain $400 \mathrm{Cal}$ and $50 \mathrm{g}$ of carbohydrates?

AG
Ankit Gupta
Numerade Educator
01:11

Problem 64

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Nutrition. One serving of tomato soup contains $100 \mathrm{Cal}$ and $18 \mathrm{g}$ of carbohydrates. One slice of whole wheat bread contains 70 Cal and
13 g of carbohydrates. (Source: Home and Garden Bulletin No. 72, U.S. Government Printing Office, Washington, D.C. 20402 ) How many servings of each would be required to obtain $230 \mathrm{Cal}$ and $42 \mathrm{g}$ of carbohydrates?

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Ankit Gupta
Numerade Educator
01:11

Problem 65

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Motion. A Leisure Time Cruises riverboat travels $46 \mathrm{km}$ downstream in $2 \mathrm{hr}$. It travels $51 \mathrm{km}$ upstream in 3 hr. Find the speed of the boat and the speed of the stream.

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Ankit Gupta
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01:14

Problem 66

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Motion. A DC10 airplane travels $3000 \mathrm{km}$ with a tailwind in 3 hr. It travels $3000 \mathrm{km}$ with a headwind in 4 hr. Find the speed of the plane and the speed of the wind.

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Ankit Gupta
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01:14

Problem 67

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Motion. Two private airplanes travel toward each other from cities that are $780 \mathrm{km}$ apart at speeds of $190 \mathrm{km} / \mathrm{h}$ and $200 \mathrm{km} / \mathrm{h} .$ They left at the same time. In how many hours will they meet?

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Ankit Gupta
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01:07

Problem 68

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Motion. Christopher's boat travels $45 \mathrm{mi}$ downstream in 3 hr. The return trip upstream takes 5 hr. Find the speed of the boat in still water and the speed of the current.

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Ankit Gupta
Numerade Educator
01:45

Problem 69

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Supply and Demand. The supply and demand for a video-game system are related to price by the equations
$$\begin{aligned}
&y=70+2 x\\
&y=175-5 x
\end{aligned}$$
respectively, where $y$ is the price, in dollars, and $x$ is the number of units, in thousands. Find the equilibrium point for this product.

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Ankit Gupta
Numerade Educator
01:33

Problem 70

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Supply and Demand. The supply and demand for a particular model of treadmill are related to price by the equations$$\begin{aligned}
&y=240+40 x\\
&y=500-25 x
\end{aligned}$$
respectively, where $y$ is the price, in dollars, and $x$ is the number of units, in thousands. Find the equilibrium point for this product.
(IMAGE CANNOT COPY)

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Ankit Gupta
Numerade Educator
01:06

Problem 71

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The point at which a company's costs equal its revenues is the break-even point, C represents the production cost, in dollars, of x units of a product and $R$ represents the revenue, in dollars, from the sale of $x$ units. Find the number of units that must be produced and sold in order to break even. That is, find
the value of $x$ for which $C=R$
$$\begin{aligned}
&C=14 x+350\\
&R=16.5 x
\end{aligned}$$

AG
Ankit Gupta
Numerade Educator
00:59

Problem 72

Text Unavailable

The point at which a company's costs equal its revenues is the break-even point, C represents the production cost, in dollars, of x units of a product and $R$ represents the revenue, in dollars, from the sale of $x$ units. Find the number of units that must be produced and sold in order to break even. That is, find
the value of $x$ for which $C=R$
$$\begin{aligned}
&C=8.5 x+75\\
&R=10 x
\end{aligned}$$

AG
Ankit Gupta
Numerade Educator
01:11

Problem 73

Text Unavailable

The point at which a company's costs equal its revenues is the break-even point, C represents the production cost, in dollars, of x units of a product and $R$ represents the revenue, in dollars, from the sale of $x$ units. Find the number of units that must be produced and sold in order to break even. That is, find
the value of $x$ for which $C=R$
$$\begin{aligned}
&C=15 x+12,000\\
&R=18 x-6000
\end{aligned}$$

AG
Ankit Gupta
Numerade Educator
00:50

Problem 74

Text Unavailable

The point at which a company's costs equal its revenues is the break-even point, C represents the production cost, in dollars, of x units of a product and $R$ represents the revenue, in dollars, from the sale of $x$ units. Find the number of units that must be produced and sold in order to break even. That is, find
the value of $x$ for which $C=R$
$$\begin{aligned}
&C=3 x+400\\
&R=7 x-600
\end{aligned}$$

AG
Ankit Gupta
Numerade Educator
02:00

Problem 75

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Decline in Air Travel. The number of people flying to, from, and within the United States in 2009 was at its lowest level since 2004 . In 2009 , the number of air travelers totaled 769.6 million, a decrease of $8.2 \%$ from 2004 (Source: Bureau of Transportation Statistics, Department of Transportation). Find the number of air travelers in 2004

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Ankit Gupta
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01:25

Problem 76

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Internet Retail Sales. Online retail sales totaled $\$ 133.6$ billion in $2008 .$ This was about three times the total in 2002 . (Source: U.S. Census Bureau) Find the online sales total in 2002 .

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Ankit Gupta
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01:36

Problem 77

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Consider the function
$$f(x)=x^{2}-4 x+3$$
What are the inputs if the output is $15 ?$

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Ankit Gupta
Numerade Educator
01:03

Problem 78

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Consider the function
$$f(x)=x^{2}-4 x+3$$
Given an output of $8,$ find the corresponding inputs.

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Ankit Gupta
Numerade Educator
00:49

Problem 79

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Consider the function
$$f(x)=x^{2}-4 x+3$$
What is the output if the input is $-2 ?$

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Ankit Gupta
Numerade Educator
01:03

Problem 80

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Consider the function
$$f(x)=x^{2}-4 x+3$$
Find the zeros of the function.

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Ankit Gupta
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02:03

Problem 81

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Nancy jogs and walks to campus each day. She averages $4 \mathrm{km} / \mathrm{h}$ walking and $8 \mathrm{km} / \mathrm{h}$ jogging. The distance from home to the campus is $6 \mathrm{km}$ and she makes the trip in 1 hr. How far does she jog on each trip?

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Ankit Gupta
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01:52

Problem 82

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Shirts.com advertises a limited-time sale, offering 1 turtleneck for $\$ 15$ and 2 turtlenecks for $\$ 25 .$ A total of 1250 turtlenecks are sold and $\$ 16,750$ is taken in. How many customers ordered
2 turtlenecks?

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Ankit Gupta
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04:10

Problem 83

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A train leaves Union Station for Central Station, $216 \mathrm{km}$ away, at $9 \mathrm{A} . \mathrm{M}$. One hour later, a train leaves Central Station for Union Station. They meet at noon. If the second train had started at 9 A.M. and the first train at 10: 30 A.M., they would still have met at noon. Find the speed of each train.

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Ankit Gupta
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02:03

Problem 84

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An automobile radiator contains $16 \mathrm{L}$ of antifreeze and water. This mixture is $30 \%$ antifreeze. How much of this mixture should be drained and replaced with pure antifreeze so that the final mixture will be $50 \%$ antifreeze?

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Ankit Gupta
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01:43

Problem 85

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Two solutions of the equation $A x+B y=1$ are $(3,-1)$ and $(-4,-2) .$ Find $A$ and $B$

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Ankit Gupta
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01:15

Problem 86

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You are in line at a ticket window. There are 2 more people ahead of you in line than there are behind you. In the entire line, there are three times as many people as there are behind you. How many people are ahead of you?

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Ankit Gupta
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01:46

Problem 87

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The Honda Civic Hybrid vehicle, powered by gasoline-electric technology, gets 49 miles per gallon (mpg) in city driving and 51 mpg in highway driving (Source: Honda.com). The car is driven $447 \mathrm{mi}$ on 9 gal of gasoline. How many miles were driven in the city and how many were driven on the highway?

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Ankit Gupta
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02:34

Problem 88

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Heather is standing on a railroad bridge, as shown in the figure below. A train is approaching from the direction shown by the yellow arrow. If Heather runs at a speed of 10 mph toward the train, she will reach point $P$ on the bridge at the same moment that the train does. If she runs to point $Q$ at the other end of the bridge at a speed of $10 \mathrm{mph}$, she will reach point $Q$ also at the same moment that the train does. How fast, in miles per hour, is the train traveling?
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AG
Ankit Gupta
Numerade Educator