The gas tank of a certain car contains 16 gal when the driver of the car begins a trip. For each mile driven by the driver, the amount of gas in the tank decreases by 0.032 gal. Write a linear function for the number of gallons of gas in the tank in terms of the number of miles driven. What is the domain for the linear function in part (a)? The domain is the maximum amount miles that can be driven before the tank is empty. Use your function to find the number of gallons in the tank after driving 150 miles?

Q: Suppose that the height (in centimeters) of a candle is a linear function of the amount of time (in…

A: let  x=h,y=t x1=22,x2=20.3 y1=10,y2=27

Q: A landscaping company charges $43 per cubic yard of mulch plus a delivery charge of $27. Find a…

A:

Q: An Uber driver charges $8 to pick up a passenger and 35 cents per mile for any trip. Write a linear…

A: Given Data : Charges to pick a passenger is $8                      Charges for per mile is 35 cents…

Q: n 1980, the minimum wage was $3.10 per hour, and in 1997 it was $5.15 per hour. Find a linear…

A: In 1980, the minimum wage was $3.10 per hour, and in 1997 it was $5.15 per hour. Find a linear…

Q: Suppose that the height (in centimeters) of a candle is a linear function of the amount of time (in…

A: After 12 hours of burning, the height of candle is 27.8 cm. After 27 hours of burning, the height is…

Q: Suppose that the height (in centimeters) of a candle is a linear function of the amount of time (in…

A: Explained below

Q: An account executive receives a base salary plus a commission. On $20,000 in monthly sales, an…

A:

Q: The total cost, y, for Leah and x friends to go to an amusement park can be modeled by a linear…

A:

Q: landscaping

A: We will find a linear equation.

Q: A landscaping company charges $47 per cubic yard of mulch plus a delivery charge of $26. Find a…

A: For 1 cubic yard of mulch, the cost is $73. Therefore total cost for x cubic yards of mulch is given…

Q: Write a formula for a linear function f whose graph satisfies the condition slope -2/3 and y…

A: Given that the slope(m) of the linear function is -2/3 and the y-intercept is (0, 1/5) which means…

Q: sketch a graph of the linear function f(t)= 2t - 5

A: See the details solution in below

Q: A new work truck sells for $68,000 and depreciates at $ -6,500 per year. Write a linear function of…

A: To find the value of truck after 5 years of purchase

Q: A manufacturer of economy cars has determined that 54,000 cars per month can be sold at a price of…

A:

Q: 6. Use the table to write a linear function that relates y to x. -1 2 y 3 -3 Sub

A:

Q: supply

A: Please refer to the image below

Q: Determine the intercepts of the graph of the linear function f (x) = 2x + 5.

A: given the linear function: fx=2x+5

Q: Use the graph to write a linear function that relates y to r. y 4 1 -3-2-1 1 2 3 x 2 y =

A: By observing the given graph we find this.

Q: A concert hall has a maximum capacity of 4050. When the ticket price is $31.00 the average…

A: We have to find the function that models the per concent revenue in terms of the attendance x.

Q: Is the function y = -4x + 2 linear or nonlinear? a Linear Nonlinear

A: To determine :- If y = -4x + 2 is linear or non-linear.

Q: Suppose that Internet domain names are sold at a price of $P per month for $2 ≤ P ≤ $100. The number…

A: Consider that the number of customers are linear functions of price that is, C=aP+b. Given when…

Q: For a basic subscription, a cable television provider charges an activation fee of $60, plus $125…

A: Given: Activation fee = $60 Charges per month = $125

Q: The manager of a furniture factory finds that it costs $2600 to manufacture 70 chairs in one day and…

A:

Q: The monthly cost (in dollars) of a long-distance phone plan is a linear function of the total…

A: from the question for a linear function, our co-ordinates will be (37,18.68) and (71,21.74) slope of…

Q: The number of people afflicted with the common cold C in the winter months steadily decreased by 212…

A:

Q: Suppose that the selling price p of an item for the quantity x sold is given by the function p=-1/5…

A: Revenue, R(x) = Price x Quantity Hence, R(x) = [-(1/5)x + 50]x = 50x - (1/5)x2

Q: A manufacturer of economy cars has determined that 51,000 cars per month can be sold at a price of…

A: Given,  A manufacturer of economy cars has determined that 51,000 cars per month can be sold at a…

Q: Suppose the weight of a 2-year-old is 28 pounds. When the child is 5, he weighs 58 pounds. Determine…

A:

Q: Wyatt has a baby daughter. When she was first born, she was 20 inches long, and she grows 1 inch…

A: topic - linear function

Q: What is the significance of the point where the graph of a linear function and its inverse intersect

A: Let f be a function such that  f(x) =y Then f-1(y)=x The point of intersection of the graphs of f…

Q: Write a linear function that relates y to x . y 3 2 1. 2 3 4 5 x

A: we know that a straight line given by formula y-b=m(x-a) where m is slope of line

Q: A farmer finds there is a linear relationship between the number of bean stalks, n, she plants and…

A: Let x be the number of stalks she plants and y be the amount of beans, each plant yields. Consider…

Q: Suppose that the height (in centimeters) of a candle is a linear function of the amount of time (in…

A: Given query is to find the height of candle after 14 hours.

Q: A company paid $130,000 for a new 18-wheeler. When itis 11 years old it will be wor th $9,000. Using…

A: So it's a equation making after reading the statement so I'm providing hand written solution.

Q: Jason has a baby daughter. When she was first born, she was 19 inches long, and she grows 3/4 of an…

A: Her height when she was born = 19 inches. She grows = 3/4 inches per month. Her height grows in a…

Q: A sporting goods company sold 830 soccer balls in 2014. Since then, they have sold 10 fewer soccer…

A: Number of soccer balls sold in 2014 = 830 Each year decrease in sale = 10 Numbee of ball decrease…

Q: 11. Construct a linear function that represents the table of values shown.

A:

Q: A mobile plan charges a base monthly rate of $10 for the first 500 minutes of air time plus a charge…

A:

Q: A house purchased for $250,000 in 2010 increases in value by $10,500 each year. a. Express the value…

A: Explained below

Q: Tom is driving to Seattle. Suppose that the distance to his destination (in miles) is a linear…

A: Given: Tom has 54 miles to his destination after 49 minutes of driving, and he has 33.2 miles to his…

Q: A company paid $150,000 for a new 18-wheeler. When it is 9 years old it will be worth $60,000. Using…

A: The straight line depreciation means the value of truck decresing with the same amount every yearAt…

Q: A manufacturer of economy cars has determined that 52,000 cars per month can be sold at a price of…

A: Let x and y represents the price per car and number of cars per month, respectively. From the given,…

Q: A taxi company charges $5.00 for the first quarter mile and $0.60 for each additional quarter mile.…

A: To find the linear function F for the total fare , if x is the number of miles  So, we can say ,…

Q: A manufacturer of economy cars has determined that 54,000 cars per month can be sold at a price of…

A: The linear relationship between independent variable x and dependent variable y is give as :…

Q: A manufacturer of economy cars has determined that 50,000 cars per month can be sold at a price of…

A: Solution: A linear function that predicts the number of cars that will be sold at a price of x…

Q: What is linear property of the mathematical function?

A:

Q: The monthly cost (in dollars) of a long distance phone plan is a linear function of the total…

A: The monthly cost is the sum of the fixed cost and variable cost. The variable cost can be written as…

Q: 3. The manager of a furniture factory finds that it costs $2200 to produce 100 chairs in one day and…

A: It is given that the costs of 100 chairs is $2200 and for 300 chairs is $4800 in one day. Let C(x)…

Q: A new work truck sells for $64,000 and depreciates at $ -6,500 per year. Write a linear function of…

A:

Q: Suppose that the height (in centimeters) of a candle is a linear function of the amount of time (in…

A: Here the height of the candle and the time are in a linear relationship. So first, we have to…

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.