Question

A car enters an interstate highway 15 miles north of a city. The car travels north at an average speed of 62.5 mph. Which equation models the car's distance d from the city after traveling for h hours?
A) 62.5 = 15h + d
B) 15 = h + 62.5
C) d = 62.5h + 15
D) d = 15h + 62.5

Answer 1

@jalyssa_ar00

Answer 2

well you know that 62.5 is the rate at which the distance is changing every hour. and you're trying to find d so it's going to be be d equals. something

Answer 3

15 is your initial condition, since when the car started it was already 15 away

Answer 4

that's never going to change so it wouldn't make sense for it to give it a variable.

Answer 5

since h can be anything you'll just leave it as h

Answer 6

So.. the correct answer would be D ?

Answer 7

no, because 15 is your starting point and that never changes regardless of h

Answer 8

Okay so C would be correct?

Answer 9

yes

Answer 10

Thanks so much. Could you help me with a few more?

Answer 11

sure, if i can.

Answer 12

An empty 5-gal water jug weighs 0.75 lb. With 3 c of water inside, the jug weighs 2.25 lb. Which equation models the jug's weight y when it contains x cups of water?
A) y = 2x + 0.75
B) y = 0.5x + 0.75
C) y = -x + 3
D) y = -0.167x + 2.25

Answer 13

well we know that 0.75 is our constant. since the jug by itself always weighs that much.

Answer 14

lets set up an equation using the givens.
\[2.25 = w(3) + 0.75\]

Answer 15

i used w to signify the rate at which it changes depending on the number of cups.

Answer 16

alright so when you solve for w what do you get?

Answer 17

0.75 times 3 equals 2.25 but I'm not sure if that's what you were asking

Answer 18

Okay so do you understand how i got that equation?

Answer 19

Yes. Would the answer be B ?

Answer 20

yes.

Answer 21

Thank you so much. :)

Answer 22

No problem, I'm glad to help.

Answer 23

Could you help me with a few more?

Answer 24

sure.

Answer 25

A concession stand vendor counts the money in the register. After 2 h, it has $82.75. After 6 h, it has $360.75. How much money will be in the register at the end of an 8-hour shift?
A) $480.00
B) $489.25
C) $499.75
D) $500.00

Answer 26

okay so what we're going to have to do here is use some subsitution.

Answer 27

the equation to model this will be:
y = mx + b
y is amount
m is rate per hour
x is hour
b is how much you started with

Answer 28

I messed up. I put A & It was incorrect.

Answer 29

so using what we're given you get two equations:
82.75 = m(2) + b and 360.75 = m(6) + b

Answer 30

we can't solve for 2 variables at once so we'll solve for one in terms of the other.
So we'll start by converting the first one in terms of b

Answer 31

Could we skip this one & go to the next one?

Answer 32

sure.

Answer 33

The cost of producing 4 metal units is $204.80. The cost of producing 8 units is $209.60. What is the cost to produce 12 units?
A) $212.80
B) $214.00
C) $214.40
D) $216.80

Answer 34

I think it would be B but I'm not sure...

Answer 35

this is similar, since we don't know the initial cost.
so with the y = mx + b:

we get 204.80 = 4m + b and 209.60 = 8m + b

Answer 36

let's but the first one in terms of b since that's easier. so subtract 4m from both sides:
204.80 - 4m = b

Answer 37

the 4m on the right side is gone since 4m - 4m is 0
now that we have this equation for b we can plug it into the second equation for b

Answer 38

so now we get 209.60 = 8m + (204.80 - 4m)

Answer 39

since the m's have the same variable we subtract them and get
209.60 = 204.80 + 4m

Answer 40

subtract 204.80 from both sides gets you:
209.60 - 204.80 = 204.80 - 204.80 + 4m
4.80 = 4m

Answer 41

divide by 4 and m is 1.20

Answer 42

now we know m = 1.20 so we'll plug it into the other equation
204.80 - 4m = b
204.80 - (4 * 1.20) = b

Answer 43

204.80 - 4.80 = b
b = 200

Answer 44

so now you have your equation that you can plug a value into:
y = 1.20x + 200

Answer 45

so for 12 units you get y = 1.20(12) + 200

Answer 46

which becomes y = 14.40 + 200

Answer 47

So the correct answer would be $214.40 ?

Answer 48

Yup, you've got it.

Answer 49

Thank you for explaining that to me :)

Answer 50

No problem.

Answer 51

Could you help with 1 more?

Answer 52

sure

Answer 53

Look at the scatter plot. Which of these equations is the best representation of the trend line?
A) y = 4x + 2
B) y = 1/4x + 2
C) y = -1/4x + 2
D) y = 1/4x - 2

Answer 54

Do you have a picture of the scatter plot?

Answer 55

It wont let me get the photo of it.

Answer 56

But the scatter plot shows the line going through 4 dots with 3 dots above the line & 2 below the line.

Answer 57

are there number values on it?

Answer 58

It's just a basic y coordinate, x coordinate graph with the numbers on the left side.

Answer 59

something like this

Answer 60

?

Answer 61

No, one sec..