PreCalculus Algebra and Trig

A tank contains 18 gallons of water when all of a sudden the water begins draining at a constant rate of 2 gallons per hour. Let tt represent the number of hours since the water began draining and let vv represent the volume of water in the tank. Write a formula that expresses v in terms of t. As tt increases from 3 to 5, vv varies from As t varies from 3 to 5, how much do t and v change by?

Write a formula that expresses v in terms of t. v = 18 - 2t 12 to 8 change it t = 2 change in v = -4

When running a 100 meter race Brendan reaches his maximum speed when he is 45 meters from the starting line and 6 seconds have elapsed since the start of the race. Brendan maintains this maximum (constant) speed for the rest of the race. If Brendan is 81 meters from the starting line 10 seconds after the start of the race: What is Brendan's max speed?

(D2-D1)/(T2-T1)= 81-45/10-6 https://www.chegg.com/homework-help/questions-and-answers/running-100-meter-race-alex-reaches-maximum-speed-45-meters-starting-line-6-seconds-elapse-q34830100

What is the range vs domain of f:

Set of all values that make sense to into f Domain: *INPUT, x* Range: *OUTPUT, y*

When working with functions, it is customary to graph the independent (input) variable on the horizontal axis. Therefore, a horizontal intercept is an input value that produces an output value of 0. In other words, it is a value of xx such that f(x)=0f(x)=0. If f(x)=2x+8f(x)=2x+8 with f(x)=yf(x)=y, what is the horizontal intercept? x=x=

y=mx+b=0 substitute 0 for x when solving for y. substitute 0 for y when solving for x

Consider a square whose size varies. Let s represent the side length of the square (in cm) and let PP represent the perimeter of the square (in cm). Write a formula that expresses PP in terms of s. Write a formula that expresses ss in terms of PP.

p = sX4 s = p/4

Which of the following are vertical intercepts for this relationship? Choose all that apply. -2 1.5 1 2 3 Which of the following are horizontal intercepts for this relationship? Choose all that apply. -2 1.5 1 2 3

vertical intercepts are the points where y axis crosses the x axis in values of y (where x and y values are the same)!!

A dog spots a cat 50 feet away and starts to chase it. At the same moment, the cat starts to run away from the dog. [Assume they are running in a straight line.] The dog is running at 12 feet per second and the cat is running at 10 feet per second. Let t represent the time elapsed (in seconds) since the chase began. Let d represent the distance between the cat and dog (in feet).

50 Feet away = Distance between cat and dog d = 50ft t = 12 ft per sec - 10 ft per sec = 2 ft per sec in terms of (means = (t)) d = t d = (distance between) 50 - 2t ft per second means multiply)

Total distance= 130 feet If Jo is 45 feet from her front door then: d= If Jo is 30 feet from her car then: d=

If Jo is 45 feet from her front door then: d= 45 If Jo is 30 feet from her car then: d=100

Consider the situation illustrated below. Jo walks 135 feet from the front door of her house to her car. Which of the following are quantities in this situation? Select all that apply. *Jo walking toward her car *The time that has elapsed since Jo left her front door *The distance from Jo's front door to her car *Jo's distance from her car *The color of Jo's house *Jo's distance from her house

The time that has elapsed since Jo left her front door The distance from Jo's front door to her car Jo's distance from her car Jo's distance from her house

Suppose xx and yy vary together such that y=4x+11y=4x+11. Suppose xx varies from x=2x=2 to x=12.5x=12.5.

https://www.chegg.com/homework-help/questions-and-answers/suppose-x-y-vary-together-y-4x-8--suppose-x-varies-x-2-x-75--interval-much-x-change-previe-q36757869

The volume of water in the tub changes from v=20v=20 to v=26v=26. Sarah wrote "Δv=20−26Δv=20-26". What is wrong with what Sarah wrote? Choose the best answer. Sarah represented a water volume of -6 gallons in the tub, which is impossible. Sarah should have written Δv=26−20Δv=26-20 to represent a positive value for the change in volume. Sarah should not have used the notation "ΔvΔv" Sarah represented a negative value for the change, which is never possible. Sarah represented a water volume of 6 gallons in the tub instead of a change in volume.

Sarah should have written Δv=26−20Δv=26-20 to represent a positive value for the change in volume.

In this context, what is the most reasonable interpretation for what the expression 18-4 represents? Choose the best response. * The volume of water in the tub after some change (14 gallons) * The current volume of water in the tub (18 gallons) * The change in the volume of water in the tub from 4 gallons to 18 gallons (14 gallons added to the tub) *The starting volume of water in the tub (4 gallons) *The initial volume of water in the tub (14 gallons)

The change in the volume of water in the tub from 4 gallons to 18 gallons (14 gallons added to the tub)

Where is the expression x^2−4x/x+2 undefined?

Undefined occurs when denominator is equal to zero x + 2 = 0 -2 -2

Suppose x and y are two variables that vary together such that the value of y is always 4 times as large as the value of x. Write a formula that expresses y in terms of x. Graph yy in terms of xx. (Hint: the graph will be a line. Determine two points that will be on the graph, and make sure your graph passes through those two points.) What does the graph of yy in terms of xx represent?

Write a formula that expresses y in terms of x. y=4x Graph: Plug in 2 values for X and plot on a graph All possible pairs of corresponding values of xx and yy.

Which of the following are varying quantities as Jo walks from the front door of her house to her car? -The height of Jo's front door -The number of seconds since Jo left her front door -Jo's distance from her front door -The distance from Jo's front door to her car -Jo's distance from her car

- (Not varying) The height of Jo's front door - (Varying) The number of seconds since Jo left her front door - (Varying) Jo's distance from her front door - (Fixed) The distance from Jo's front door to her car - (Varying) Jo's distance from her car

In the ball-launching context, which of the following represents the ball's height above the ground (in feet) 2 seconds after it was launched? g(t)=2 g*2 g(2) 2

g(2)

Marcos traveled for 2 hours and 17 minutes on Interstate 17 as he drove (without stopping) a distance of 155 miles from Phoenix to Flagstaff. Determine Marcos' average speed for the 155 mile trip. At what constant speed did Devon drive? After driving for 2.2 hours (2 hours and 12 mintues), Marcos' total distance traveled was 153 miles. At what constant speed (in miles per hour) will Marcos need to travel for the last 5 minutes of the trip so that he travels the 155 mile drive in 2 hours and 17 minutes?

Determine Marcos' average speed for the 155 mile trip Speed = distance/time 155/2 hours and 17 minutes 155 miles/2.283333 hours = 67.88 Speed = d/t 155 miles - 153 miles = 2 5 minutes = 5/60 = 1/12 hour 2 / 1/12 = 24

What is the vertical intercept in this situation and what does it represent? 25; the maximum distance Kristin can travel is 25 feet around the edge of the Ferris wheel 5; when Kristin has traveled 5 feet around the Ferris wheel she is 0 feet above the ground 25; Kristin's maximum height above the ground is 25 feet 15; when Kristin has traveled 0 feet around the Ferris wheel she is 15 feet above the ground 15; when Kristin has traveled 15 feet around the Ferris wheel she is 0 feet above the ground 5; when Kristin has traveled 0 feet around the Ferris wheel she is 5 feet above the ground Which of the following represent the vertical intercept? Select all that apply. f(5)f(5) 5 the value of dd such that f(d)=0f(d)=0 15 f(0)f(0) the value of dd such that f(d)=5

Domain: *INPUT, x* Range: *OUTPUT, y*

Kristin is on a Ferris wheel in a bucket at the 3-o'clock position and rides the Ferris wheel for one full rotation. The center of the Ferris wheel is 19 meters above the ground. If Kristin is 4.4 meters above the center of the Ferris wheel, what is her distance above the ground? If Kristin is −6 meters above the center of the Ferris wheel (she is 6 meters below the center of the Ferris wheel), what is her distance above the ground? Write a formula that expresses Kristin's distance above the ground (in meters), dd, in terms of Kristin's distance above the center of the Ferris wheel (in meters), x.

If Kristin is 4.4 meters above the center of the Ferris wheel, what is her distance above the ground? 19+4.4 If Kristin is −6 meters above the center of the Ferris wheel (she is 6 meters below the center of the Ferris wheel), what is her distance above the ground? 19-6 Write a formula that expresses Kristin's distance above the ground (in meters), d, in terms of Kristin's distance above the center of the Ferris wheel (in meters), x. d = 19 + x

Which of the following best describes a variable to represent Jo's distance from her front door as she walks toward her car? Let d represent an unknown distance that Jo is from her front door. Let d represent Jo's distance (in feet) from her front door. Let d represent Jo's distance walked. Let d represent Jo's distance from her front door.

Let d represent Jo's distance (in feet) from her front door. (Variables need to be specific and contain units of measure)

Water begins flowing into a large tank that already has 11 gallons of water in it. Which of the following statements defines a variable to represent the amount of water added to the tank? Let u represent the number of gallons of water in the tank Let u represent the number of gallons Let u represent the volume of water in the tank Write an expression (in terms of uu) to represent the total number of gallons of water in the tank.

Let u represent the number of gallons of water in the tank *Gallons become the variable because the amount is no longer constant when water is added* Expression: 11 + u

An empty 36 gallon tank begins filling with water. Which of the following statements defines a variable to represent the amount of water in the tank? Let v represent the number of gallons of water in the tank Let v represent the number of gallons Let v represent the volume of water in the tank Write an expression (in terms of v) to represent the number of gallons of water needed to *fill the tank.*

Let v represent the number of gallons of water in the tank 36 - v *Filling* signifies a total minus an added amount needed to fill the space.

The perimeter of a rectangle is the distance around the edge of the rectangle. Suppose the width of a rectangle is constantly 2 inches, but the length of the rectangle can vary. This is shown in the diagram below. Is the perimeter of the rectangle proportional to the length of the rectangle?

No, because the perimeter of the rectangle (in inches) is not always the same number of times as large as the length of the rectangle (in inches).

Suppose y is proportional to xx. The graph of y in terms of x is shown below. Write a formula that expresses y in terms of x. (Hint: y is how many times as large as x?) Write a formula that expresses x in terms of y.

Write a formula that expresses y in terms of xx. (Hint: y is how many times as large as x?) y=3x Write a formula that expresses x in terms of y. x = y/3

Josh and Vanessa are 210 feet apart when they start walking toward one another. They are walking at the same speed, so whenever Josh travels some number of feet, Vanessa travels the same number of feet. Let x represent the number of feet Josh has traveled since he started walking toward Vanessa. Write an expression in terms of x that represents the number of feet Josh has walked toward Vanessa since they started walking. Write an expression in terms of x that represents the number of feet Vanessa has walked toward Josh since they started walking. Write an expression in terms of x that represents the total number of feet Josh and Vanessa have walked toward one another since they started walking. Write an expression in terms of x that represents the distance (in feet) between Josh and Vanessa. Write an expression in terms of x that represents the total number of feet Josh and Vanessa have walked toward one another since they started walking. Write an expression in terms of x that represents the distance (in feet) between Josh and Vanessa.

Write an expression in terms of x that represents the number of feet Josh has walked toward Vanessa since they started walking. x Write an expression in terms of x that represents the number of feet Vanessa has walked toward Josh since they started walking. x Write an expression in terms of x that represents the total number of feet Josh and Vanessa have walked toward one another since they started walking. 2x Write an expression in terms of x that represents the distance (in feet) between Josh and Vanessa. 210-2x

Jeff and Alice are 210 feet apart when they start walking toward one another. Alice walks twice as fast as Jeff so whenever Jeff travels x feet, Alice travels 2x feet. Let x represent the number of feet Jeff has traveled since he started walking toward Alice. Write an expression in terms of x to represent the total number of feet Jeff and Alice have walked toward one another.

Write an expression in terms of x to represent the total number of feet Jeff and Alice have walked toward one another. 2x (Alice) + x (Jeff) Write an expression in terms of x to represent the distance (in feet) between Jeff and Alice. 210= 2x + x Let dd represent the distance (in feet) between Jeff and Alice. Write a formula that expresses d in terms of x. d= 210-(2x+x)

Kristin is on a Ferris wheel in a bucket at the 3-o'clock position and rides the Ferris wheel for one full rotation. The top of the Ferris wheel is 34 meters above the ground. Write a formula that expresses Kristin's vertical distance (in meters) from the top of the Ferris wheel, dd, in terms of Kristin's height above the ground (in meters), xx.

d=34-x Expresses distance means d = *Remember to locate the variable and the constant* Total height is constant Kristen's height is X because it varies

A 21-inch candle has a wick on each end. The wicks on each end of the candle are lit at the same time. Let x represent the burned length for one end of the candle (in inches). Assume both ends of the candle are burning at the same rate. Express the candle's total burned length (in inches) in terms of the burned length of one end of the candle, xx. Express the remaining length of the candle (in inches) in terms of the burned length of one end of the candle, xx.

each signifies *2* variables moving at the same rate Express the candle's total burned length (in inches) in terms of the burned length of one end of the candle, x. *The length burned on one side is equal to the length burned on the other side. Therefore, any length burned X 2 determines the total burned length* *x2* *The length burned on one side is equal to the length burned on the other side. Therefore, any length burned X 2 determines the total burned length. The 2 X the burned length on side side - the total length = remaining length* *21-2x*

Suppose x and y are related by a constant rate of change and ΔyΔx=2ΔyΔx=2, and y=4y=4 when x=3x=3. Write a formula that expresses y in terms of x.

https://www.chegg.com/homework-help/questions-and-answers/ay-ar-suppose-x-y-related-constant-rate-change-2-y-3-z-2--write-formula-expresses-y-terms--q31078160

A bathtub contains 45 gallons of water and the total weight of the tub and water is approximately 710.775 pounds. You pull the plug and the water begins to drain. Let v represent the number of gallons of water that has drained from the tub since the plug was pulled. Note that water weights 8.345 pounds per gallon.

https://www.chegg.com/homework-help/questions-and-answers/bathtub-contains-45-gallons-water-total-weight-tub-water-approximately-724775-pounds-pull--q43944601

Suppose the value of y and the value of x vary together at a constant rate of change (so that Δy=0.75⋅ΔxΔy=0.75⋅Δx), and y=2.5y=2.5 when x=2x=2. We are given that y=2.5y=2.5 when x=2x=2. Plot a point on the graph to represent these values.

https://www.chegg.com/homework-help/questions-and-answers/suppose-y-varies-constant-rate-change-075-respect-z-y-075--z-y-25-z-2--given-y-25-x-2-plot-q31120415

A car is driving away from a crosswalk. The formula d=t2+2td=t2+2t expresses the car's distance from the crosswalk in feet, dd, in terms of the number of seconds, tt, since the car started moving.

s = d/t https://www.chegg.com/homework-help/questions-and-answers/car-driving-away-crosswalk-formula-d-3t-expresses-car-s-distance-crosswalk-feet-d-terms-nu-q32192708

In the tub filling context, compare the meanings of "v=7v=7" and "Δv=7Δv=7". Choose the best answer. they both represent the fact that 7 gallons of water are in the tub v=7v=7 represents "7 gallons of water in the tub" and Δv=7Δv=7 represents "a change of 7 gallons of water from when v=7v=7" v=7v=7 represents "7 gallons of water in the tub" and Δv=7Δv=7 represents "a change of 7 gallons of water from some beginning volume" they both represent the fact that 7 gallons of water were added to the tub from any beginning volume

v=7v=7 represents "7 gallons of water in the tub" and Δv=7Δv=7 represents "a change of 7 gallons of water from some beginning volume"

Which of the following statements are true? Select all that apply. The perimeter is always 12 inches longer than the length of one of the sides. The perimeter is four times as long as the length of one side. The perimeter can be found by multiplying the length and width of the square (in inches). The perimeter increases when the length of one side increases. Write an expression (in terms of xx) that represents the square's perimeter (in inches).

x (*) 4

x in terms of y = y in terms of x =

x = y y=x