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[link] shows the input,
and output,
for a linear function
a. Fill in the missing values of the table. b. Write the linear function
round to 3 decimal places.
|
–10 |
5.5 |
67.5 |
b |
|
30 |
–26 |
a |
–44 |
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[link] shows the input,
and output,
for a linear function
a. Fill in the missing values of the table. b. Write the linear function
|
0.5 |
0.8 |
12 |
b |
|
400 |
700 |
a |
1,000,000 |
a.
;
b.
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Graph the linear function
on a domain of
for the function whose slope is
and
y -intercept is
. Label the points for the input values of
and
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Graph the linear function
on a domain of
for the function whose slope is 75 and
y -intercept is
. Label the points for the input values of
and
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Graph the linear function
where
on the same set of axes on a domain of
for the following values of
and
-
-
-
-
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Extensions
Real-world applications
At noon, a barista notices that she has $20 in her tip jar. If she makes an average of $0.50 from each customer, how much will she have in her tip jar if she serves
more customers during her shift?
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A gym membership with two personal training sessions costs $125, while gym membership with five personal training sessions costs $260. What is cost per session?
$45 per training session.
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A clothing business finds there is a linear relationship between the number of shirts,
it can sell and the price,
it can charge per shirt. In particular, historical data shows that 1,000 shirts can be sold at a price of
, while 3,000 shirts can be sold at a price of $22. Find a linear equation in the form
that gives the price
they can charge for
shirts.
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A phone company charges for service according to the formula:
where
is the number of minutes talked, and
is the monthly charge, in dollars. Find and interpret the rate of change and initial value.
The rate of change is 0.1. For every additional minute talked, the monthly charge increases by $0.1 or 10 cents. The initial value is 24. When there are no minutes talked, initially the charge is $24.
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A farmer finds there is a linear relationship between the number of bean stalks,
she plants and the yield,
each plant produces. When she plants 30 stalks, each plant yields 30 oz of beans. When she plants 34 stalks, each plant produces 28 oz of beans. Find a linear relationships in the form
that gives the yield when
stalks are planted.
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A city’s population in the year 1960 was 287,500. In 1989 the population was 275,900. Compute the rate of growth of the population and make a statement about the population rate of change in people per year.
The slope is
This means for every year between 1960 and 1989, the population dropped by 400 per year in the city.
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A town’s population has been growing linearly. In 2003, the population was 45,000, and the population has been growing by 1,700 people each year. Write an equation,
for the population
years after 2003.
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Suppose that average annual income (in dollars) for the years 1990 through 1999 is given by the linear function:
where
is the number of years after 1990. Which of the following interprets the slope in the context of the problem?
- As of 1990, average annual income was $23,286.
- In the ten-year period from 1990–1999, average annual income increased by a total of $1,054.
- Each year in the decade of the 1990s, average annual income increased by $1,054.
- Average annual income rose to a level of $23,286 by the end of 1999.
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When temperature is 0 degrees Celsius, the Fahrenheit temperature is 32. When the Celsius temperature is 100, the corresponding Fahrenheit temperature is 212. Express the Fahrenheit temperature as a linear function of
the Celsius temperature,
- Find the rate of change of Fahrenheit temperature for each unit change temperature of Celsius.
- Find and interpret
- Find and interpret
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Questions & Answers
If auger is pair are the roots of equation x2+5x-3=0
Wayne and Dennis like to ride the bike path from Riverside Park to the beach. Dennis’s speed is seven miles per hour faster than Wayne’s speed, so it takes Wayne 2 hours to ride to the beach while it takes Dennis 1.5 hours for the ride. Find the speed of both bikers.
from theory: distance [miles] = speed [mph] × time [hours]
info #1
speed_Dennis × 1.5 = speed_Wayne × 2
=> speed_Wayne = 0.75 × speed_Dennis (i)
info #2
speed_Dennis = speed_Wayne + 7 [mph] (ii)
use (i) in (ii) => [...]
speed_Dennis = 28 mph
speed_Wayne = 21 mph
George
Let W be Wayne's speed in miles per hour and D be Dennis's speed in miles per hour. We know that W + 7 = D and W * 2 = D * 1.5.
Substituting the first equation into the second:
W * 2 = (W + 7) * 1.5
W * 2 = W * 1.5 + 7 * 1.5
0.5 * W = 7 * 1.5
W = 7 * 3 or 21
W is 21
D = W + 7
D = 21 + 7
D = 28
Salma
Devon is 32 32 years older than his son, Milan. The sum of both their ages is 54 54. Using the variables d d and m m to represent the ages of Devon and Milan, respectively, write a system of equations to describe this situation. Enter the equations below, separated by a comma.
find product (-6m+6) ( 3m²+4m-3)
what is the solution
bill
how did you arrive at this answer?
bill
i really want to learn
Amira
I only got 42 the rest i don't know how to solve it. Please i need help from anyone to help me improve my solving mathematics please
Amira
Hw did u arrive to this answer.
Aphelele
-6m(3mA²+4m-3)+6(3mA²+4m-3)
=-18m²A²-24m²+18m+18mA²+24m-18
Rearrange like items
-18m²A²-24m²+42m+18A²-18
Salma
complete the table of valuesfor each given equatio then graph.
1.x+2y=3
given that (7x-5):(2+4x)=8:7find the value of x
Nandala
please why isn't that the 0is in ten thousand place
please why is it that the 0is in the place of ten thousand
Grace
Send the example to me here and let me see
Stephen
A meditation garden is in the shape of a right triangle, with one leg 7 feet. The length of the hypotenuse is one more than the length of one of the other legs. Find the lengths of the hypotenuse and the other leg
state in which quadrant or on which axis each of the following angles given measure. in standard position would lie 89°
I am eliacin, I need your help in maths
Rood
hmm can we speak here?
Amoon
however, may I ask you some questions about Algarba?
Amoon
what the last part of the problem mean?
Roger
The Jones family took a 15 mile canoe ride down the Indian River in three hours. After lunch, the return trip back up the river took five hours. Find the rate, in mph, of the canoe in still water and the rate of the current.
Shakir works at a computer store. His weekly pay will be either a fixed amount, $925, or $500 plus 12% of his total sales. How much should his total sales be for his variable pay option to exceed the fixed amount of $925.
I'm guessing, but it's somewhere around $4335.00 I think
Lewis
12% of sales will need to exceed 925 - 500, or 425 to exceed fixed amount option. What amount of sales does that equal? 425 ÷ (12÷100) = 3541.67. So the answer is sales greater than 3541.67.
Check:
Sales = 3542
Commission 12%=425.04
Pay = 500 + 425.04 = 925.04.
925.04 > 925.00
Munster
difference between rational and irrational numbers
When traveling to Great Britain, Bethany exchanged $602 US dollars into £515 British pounds. How many pounds did she receive for each US dollar?
how to reduced echelon form
Jazmine trained for 3 hours on Saturday. She ran 8 miles and then biked 24 miles. Her biking speed is 4 mph faster than her running speed. What is her running speed?
d=r×t
the equation would be 8/r+24/r+4=3
worked out
Sheirtina
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Source:
OpenStax, Precalculus. OpenStax CNX. Jan 19, 2016 Download for free at https://legacy.cnx.org/content/col11667/1.6
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