Chapter 3 3 An accountant can complete a simple tax return in about

187)

For the straight line 2x+y– 3 = 0 find: (a) the slope; (b) the y–intercept; and

(c) sketch the graph.

187)

188)

An accountant can complete a simple tax return in about 1.5 hours and a complicated

return in about 4 hours. If she works 8 hours per day, find an equation that shows the

possible ways that both types of returns can be completed in a 5–day work week.

188)

189)

Graph the equation 5x +y+ 8 = 0.

189)

190)

In testing an experimental diet for beef cows, it was determined that the (average) live

weight w (in kilograms) of a cow was statistically a linear function of the number of days d

after the diet was started, where 0 d

300. The weight of a cow starting the diet was 125

kg and 100 days later it was 245 kg. Determine w as a linear function of d and find the

average weight of a cow when d= 200.

190)

191)

The slope of the line passing through the points (4, 9) and (6, k) is 5. Find k.

191)

192)

Determine whether the following lines are parallel, perpendicular or neither.

12x+ 4y= 16

24x+ 8y= 36

192)

193)

Solve the following system algebraically: 5x+ 2y= 36

8x– 3y= – 54

193)

42

194)

Solve the following system of equations algebraically. (If the system does not have a

solution, then say so or if it has more than one unique solution, then please describe the

solutions.)

4x+ 10y= 6

2

3x–5

3y= 1

194)

195)

The value of an antique figurine is expected to appreciate each year after it is purchased for

$550. If x is the number of years that have passed, the current value of the figurine can be

estimated by the function f(x) = 75x+ 550. Graph the function by finding and plotting two

points.

195)

196)

Determine whether the following lines are parallel, perpendicular or neither.

0.21x– 0.35y + 8 = 0

x+ 0.6y– 9 = 0

196)

197)

By sketching the graphs (using a graphing calculator or graphing paper) solve the system

of equations. 2x+ 3y= 26

3x– 2y= 13

197)

198)

The relationship between temperature on the Fahrenheit scale and the temperature on the

Celsius scale is C=5

9(F– 32). Find the slope and y–intercept of the equation.

198)

199)

Solve the following system of equations algebraically. (If the system does not have a

solution, then say so or if it has more than one unique solution, then please describe the

solutions.)

x+y+z= 2

x+ 2y+ 3z = 4

x+ 3y+ 5z= 7

199)

200)

Tickets to an opera at the Masonic Auditorium cost $14 for main floor seats and $10 for the

balcony seats. If $8600 must be collected to meet expenses, what is an equation for the

possible combinations of ticket sales to cover costs?

200)

201)

Solve the following questions algebraically: 2p+ 3q= 5

2p+ 6q = 10

201)

202)

A coordinate map of a zoo shows the outdoor aviary at (2, 4) and the snack bar at (2, 8).

What is an equation for the line between these two locations?

202)

203)

Solve the system: y=x– 4

x–y= 4

203)

204)

The shape of the main cable on a suspension bridge can be described by the function

y=1

500x2+1

250x+ 10, where y is the height of the cable (in feet) above the roadbed and x

is the horizontal distance (in feet) from the center of the bridge. A cross support passes by

the cable, and its position can be described by the function y= 0.2x+ 9.8. Where does the

cross–support intersect the cable? Use a graphing calculator to answer the question by

finding the point(s) of intersection of the two equations.

204)

205)

Solve the following system algebraically: 3x– 4y= 18

2x+ 5y= – 11

205)

206)

Suppose that a manufacturer will place 1000 units of a product on the market when the

price is $10 per unit, and 1400 units when the price is $12 per unit. Find the supply

equation for the product assuming the price p and quantity q are linearly related.

206)

207)

Two types of chickens, A and B, are raised in a chicken coop. Each day they receive 1.4

kilograms of corn and 2.4 kilograms of millet. Each chicken of type A requires 100 grams

of corn and 150 grams of millet. Each chicken of type B requires 60 grams of corn and 120

grams of millet. How many of each type of chicken will the corn and millet support so that

all of the food is consumed each day? Use a graphing calculator to solve the system by

finding the point of intersection of the two equations.

207)

208)

Solve the following system algebraically: 12x– 6y= 7

2x+ 9y=20x+ 3

208)

209)

Two species of fish, A and B, are raised in one pond at a fish farm where they are fed two

vitamin supplements. Each day they receive 100 grams of the first supplement and 200

grams of the second supplement. Each fish of species A requires 15 mg of the first

supplement and 30 mg of the second supplement. Each fish of species B requires 20 mg of

the first supplement and 40 mg of the second supplement. How many of each species of

fish will the pond support so that all of the supplements are consumed each day? Use a

graphing calculator to graph both of your equations at the same time. What do you notice

about the graphs?

209)

45

210)

The slope of a certain line is 4. If the x–value of a point on the line increases by 3 units, by

how many units does the y–value increase?

210)

211)

In testing an experimental diet for horses, it was determined that the (average) live weight

w (in kilograms) of a horse was statistically a linear function of the number of days d after

the diet was started where 0 d

300. The weight of a horse starting the diet was 170 kg

and 120 days later it was 362 kg. Determine w as a linear function of d and find the average

weight of a horse when d= 250.

211)

212)

The shape of a rope bridge stretched across a ravine can be described by the function

y= 0.003x2+ 0.006x+ 50, where y is the height of the bridge (in feet) above the bottom of

the ravine and x is the horizontal distance (in feet) from the center of the ravine. A hiker

traveling at night shines his flashlight across the ravine, and the path of the beam of light

can be described by the function y= 0.096x+ 49.4. Where does the beam of light intersect

the rope bridge? Use a graphing calculator to answer the question by finding the point(s) of

intersection of the two equations.

212)

213)

When the temperature T (in degrees Celsius) of a certain laboratory animal is reduced, its

heart rate r (in beats per minute) decreases. At a temperature of 37°C, the animal had a

heart rate of 200, and at a temperature of 32°C its heart rate was 140. If r is a linear function

of T for 26 T

38, (a) determine this function and (b) determine the heart rate at a

temperature of 30°C.

213)

214)

The shape of a paper streamer suspended above a dance floor can be described by the

function y=f(x) = 0.01x2+ 0.01x+ 7, where y is the height of the streamer (in feet) above

the floor and x is the horizontal distance (in feet) from the center of the room. Use a

graphing calculator to graph the function.

214)

215)

Find the equation of a line which is perpendicular to the line x= 0.521 and passes through

the point (0.1, –7).

215)

216)

Graph the equation 3x + 4y– 12 = 0.

216)

217)

Find the equation of a line having slope = 0.5 and x–intercept = 1.8.

217)

218)

A California homeowner with a 30–year fixed rate mortgage pays $170,000 after 5 years

and $266,000 after 9 years. Use a graphing calculator to graph the resulting equation and

determine how much the homeowner will have paid when the mortgage is paid off in 30

years.

218)

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