A car passes through a tollbooth at 8:00 A.M. and begins traveling east at an average speed of the same tollbooth an hour later and begins traveling east at an average speed of 60 miles per hour. a. Write an equation for each car that relates the number of hours x since 8:00 A.M. to the distance in miles y the car has traveled. Explain what the slope of each equation represents. b. Graph the system of equations on the coordinate plane. c. If neither car stops, at what time will the second car catch up to the first car? Explain how you determine your answer.
Answers
The distance traveled by both cars is an illustration of a linear function.
The equations of both cars are [tex]\mathbf{y=60x - 540}[/tex] and [tex]\mathbf{y=45x - 360}[/tex]Both cars meet at 12:00pmCar A
Speed = 45 miles per hour
So, the coordinates of car A are:
[tex]\mathbf{(x,y) = (8,0) (9, 45) (10, 90) ....}[/tex]
Car B
Speed = 60 miles per hour
So, the coordinates of car B are:
[tex]\mathbf{(x,y) = (9, 0) (10, 60) (11, 120) ....}[/tex]
(a) The equation of both cars
Car A
This is calculated as:
[tex]\mathbf{y = mx+ b}[/tex]
Where m represents slope/speed.
So, m = 45
This gives
[tex]\mathbf{y = 45x + b}[/tex]
y = 0, when x = 8.
So, we have:
[tex]\mathbf{0= 45\times 8 + b}[/tex]
[tex]\mathbf{0= 360 + b}[/tex]
Solve for b
[tex]\mathbf{b=- 360}[/tex]
So, the equation of car A is:
[tex]\mathbf{y=45x - 360}[/tex]
Car B
This is calculated as:
[tex]\mathbf{y = mx+ b}[/tex]
Where m represents slope/speed.
So, m = 60
This gives
[tex]\mathbf{y = 60x + b}[/tex]
y = 0, when x = 9.
So, we have:
[tex]\mathbf{0= 60\times 9 + b}[/tex]
[tex]\mathbf{0= 540 + b}[/tex]
Solve for b
[tex]\mathbf{b=- 540}[/tex]
So, the equation of car B is:
[tex]\mathbf{y=60x - 540}[/tex]
(b) The graphs
See attachment
(c) The time which both cars meet
We have:
[tex]\mathbf{y=60x - 540}[/tex] and [tex]\mathbf{y=45x - 360}[/tex]
Equate both
[tex]\mathbf{60x - 540=45x - 360}[/tex]
Collect like terms
[tex]\mathbf{60x - 45x = 540- 360}[/tex]
[tex]\mathbf{15x = 180}[/tex]
Divide both sides by 15
[tex]\mathbf{x = 12}[/tex]
This means that both cars meet at 12:00pm
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Related Questions
(-5+2)•(-1/2)
I don’t know how to do this problem. Would anyone be able to assist? Thanks!
Answers
Answer:
3/2 or 1 1/2 or 1.5
Step-by-step explanation:
first do the equations in each parentheses:
(-5+2) = -3
(-1/2) = -1/2
then multiply both sides:
-3 • -1/2 (which is the same as -3 • -1 over 2)
= 3/2 or 1 1/2 or 1.5
What is the slope of the graph shown below?
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-7 -6 -5 -4 -3 -2 -1 4.1 2 3 4 5 6 7
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-5
-6
Answers
Answer:
slope is 1
Step-by-step explanation:
slope is rise over run
It costs $7 each way to travel to work each weekday by train. What is the weekly expense each way?
Answers
Answer:
it could either be 35 or 70
Step-by-step explanation:
A rope is 255 centimeters long you need the rope to be 1.5 meters long. How many centimeters should you cut off
Answers
Answer:
105cm
Step-by-step explanation:
first convert 1.5 metres to cm;
1m = 100cm
1.5 =?
1.5×100= 150cm
we then subtract:
255-150=105cm
Jafari decided to stock up on sweets for his birthday party, so he bought 105 sweets in January. The second month he bought twice that number of sweets. In March he bought thrice the number of sweets that he bought in February. If the sweets are to be shared equally among 45 guests, how many will each guest receive?
Answers
Answer: Each guest will receive 21 pieces.
In the equation 80 divided by 10=8 the number 80 is the
Answers
solve pls brainliest
Answers
a) -7
b)
-7
7
c) 7
7
These are the answers
Answer:
a. 7
b. -7 then 7
c. 7 for both
Step-by-step explanation:
1.6x – 2.88 = 3.4x
X=?????
Answers
1.6x-3.4x-2.88=0
-1.8x-2.88=0
-1.8x=2.88
x= -1.6
Answer:
x = -1.6
Step-by-step explanation:
Solve for x:
Combine like terms. Here we combine 1.6x and 3.4x, obtaining 1.8x on the right side of the equation and -2.88 on the left side:
-2.88 = 1.8x
Solve for x by dividing both sides by 1.8:
x = -2.88/1.8, or x = -1.6
Please help me on my exam qts please!
26) It costs a flat fee of $20 to rent a chainsaw, plus $4 per day for each day rented. Let'x' represent the number
of days rented, and 'y' represents the charge to the person renting the chainsaw. Write an equation for this
situation in y = mx + b form and then find out what the cost is if Bill rents the chainsaw for ten days.
Answers
Answer:
you should of not said exam you will prob get banned now
Step-by-step explanation:
One year of membership at a rec center includes a fixed monthly cost and a one-time membership fee. The following table contains some of the ordered pairs for this linear relationship between the number of months enrolled and the total cost paid for the membership.
Which graph correctly represents this linear relationship?
PLS ANSWERR AND EXPLAIN HOW YOU GOT THE ANSWE PLSSS YOULL BE MARKED AS BRAINLIST.just plss helpp
Answers
Answer:
Graf 2 is correct
Step-by-step explanation:
The correct graph that represents the linear relationship is Graph B with a positive slope.
The table shows a linear relationship between the number of months enrolled and the total cost paid for the membership.
To determine which graph represents this relationship, we need to check if the cost increases or decreases as the number of months enrolled increases. If the cost increases, it means the graph should have a positive slope. If the cost decreases, it means the graph should have a negative slope.
Let's look at the table:
Number of Months Enrolled Total Cost
1 75
2 100
3 125
As the number of months enrolled increases, the total cost increases. Therefore, the graph should have a positive slope. From the given options, the graph that correctly represents this linear relationship is Graph B, which has a positive slope.
Learn more about the topic of Linear relationship here:
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#SPJ3
An art gallery is increasing the asking price of its paintings by 60%. A painting now costs $400.00. How much was the painting before the increase??
$
Answers
Answer:
$250
Step-by-step explanation:
The goal here is to find the cost of the painting BEFORE the 60% increase.
To find the cost of the painting, we must take in the information we already have:
Increase percent: 60%
Original price: unknown
Price after increase: $400
$400 is the price of the painting AFTER the increase has been added. So this equals the cost of the painting before the increase, plus the total amount of the increase (which is 60% of the original price).
The total must be (100% + 60% = 160%) 160% of the original painting price.
To find the original price, we must divide the increased price by the new percentage (160%). But how do we get here?
Well, we have 160% and our (fraction) $400/1%. We will have to switch the 160% and the 1%, giving us..
1% $400/160%
We take 400/160, which is 2.5. But this is only 1% of the original price! We want 100%.
So now, we multiply the 2.5 by 100 to get our answer: $250.
What is the unit rate for canned juice, in cases per minute? Explain how you found this unit rate.
Answers
Answer:
Divide any of the numbers of cases by the corresponding time.
92/2 = 46
138/3 = 46
184/4 = 4
Step-by-step explanation:
Elizabeth wants to buy her mother a pair of pearl earrings for Mother’s Day. The earrings cost $50. The sales tax rate is 7.5%. What is the total amount Elizabeth will have to pay to purchase this gift?
Answers
Answer:
$46.25
Step-by-step explanation:
50 divided by 7.5% equals 3.75
Minus 3.75 from 50 to find the removed amount.
Answer:
Cost of the gift = $53.75
Step-by-step explanation:
Total cost of the gift = cost of the earrings + (cost of the earrings × sale tax)
Cost of the gift = $50 + ($50 × .075) 7.5% = .075
Cost of the gift = $50 + $3.75
Cost of the gift = $53.75
Find the area of the shaded
figure.
Answers
50+8 obv 58
hoping its not wrong i learned this like 5 years ago plzz
Answer:
58 sq. units
Step-by-step explanation:
1. split them into 3 shapes
of course it is possible to count them all out, but the more efficient way would be to find the area of each shape and the add them all up.
2. find the area of rectangle a
so you can split one into a recantagle that separates itself from the 2 squares at the bottom
area formula: L x W
so the length of that rectangle is going to be 5, once you count the scares of that side. the width would be 10 when you count the top side of how wide it is.
5 × 10 = 50
3. find the area of the 2 squares
you don't need to find both, because one you find one, you find the other. so the length for the square would be 2 while the width is 2 as well.
2 × 2 = 4
so the area is 4, for each square.
50 + 4 + 4 = 58
what is the slope of (4,1) and (6,-1)
Answers
Answer:
slope = -1
Step-by-step explanation:
you subtract the y-values (-1-1=-2) then subtract the x-values (6-4=2) then divide the sum of the y-values by the sum of the x-values
[tex]\frac{-2}{2}[/tex] which simplifies to a slope of -1
A standard fair dice is rolled twice. What is the probability of getting an even number on the first roll and any factor of 6 on the other?
Answers
Answer:
1/3
Step-by-step explanation:
Factors of 6 are 1, 2, 3, 6.
Even numbers are 2, 4, 6
3/6 * 4/6 = 12/36 or 1/3
A ball was thrown off of a 32 foot bridge and reached a maximum height of 50 feet after 3 seconds. How long
was the ball in the air?
a. 10 seconds
b. 6 seconds
c. 32 seconds
d. 8 seconds
Answers
What two numbers have a product of -57 and a sum of -16?
Answers
Answer:
-19 and 3
Step-by-step explanation:
-19 x 3 = -57
-19 + 3 = -16
Answer:
Step-by-step explanation: To find the answer to "What two numbers have a product of 57 and a sum of 16?" we first state what we know. We are looking for x and y and we know that x • y = 57 and x + y = 16.
Before we keep going, it is important to know that x • y is the same as y • x and x + y is the same as y + x. The two variables are interchangeable. Which This means that when we create one equation to solve the problem, we will have two answers.
To solve the problem, we take x + y = 16 and solve it for y to get y = 16 - x. Then, we replace y in x • y = 57 with 16 - x to get this:
x • (16 - x) = 57
Like we said above, the x and y are interchangeable, therefore the x in the equation above could also be y. The bottom line is that when we solved the equation we got two answers which are the two numbers that have a product of 57 and a sum of 16. The numbers are:
5.35425
10.64575
That's it! The two numbers that have a product of 57 and a sum of 16 are 5.35425 and 10.64575 as proven below:
5.35425 • 10.64575 = 57
5.35425 + 10.64575 = 16
HOPE THAT HELP YOU PLS MARK ME BRANLITS PLSSSS
PLEASE HELP NUMBER 3 ASAP ILL GIVE BRAINLIEST THANKS
Answers
Answer:
Sarah gets 2 A's.
Step-by-step explanation:
Sarah's mother gives her $10 for each B she receives. She received 3 B's, so 3x10 is 30. You subtract 80-30. You get 50. She receives $25 for each A. You then divide 50 by 25, and are left with 2. The answer is that Sarah received 2 A's on her report card.
Hope you have a great day,
Ginny
Today Nia completed her sixth hour of training which represents her sixth hour of training, which represents 7.5% of the total number of hours in the training. How many hours will Nia spend in training in all?
Answers
The times spent in training is an illustration of proportions
The times spent in training is 80 hours
The given parameters are:
Time spent = 6 hours
Time spent as a percentage = 7.5%
Let the total time spent in training be x.
The scenario is represented by the following equation
Time spent = Time spent as a percentage * Total Time
So, we have:
6 = 7.5% * x
Express percentage as decimal
6 = 0.075 * x
Divide both sides by 0.075
80 = x
Rewrite as:
x = 80
Hence, the times spent in training is 80 hours
Read more about proportions at:
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If x+1=7, what is the value of x2 + 22 +1?
Answers
Answer:
59
Step-by-step explanation:
x+1 = 7
Subtract 1 from each side
x+1-1 =7-1
x =6
x^2 + 22 +1
6^2 +22+1
36+22+1
36+23
59
Answer:
[tex]x + 1 = 7 \\ x = 7 - 1 = 6 \\ putting \: the \: value \: of \: x = 6 \\ 6 \times 2 + 22 + 1 = 34[/tex]
solve pls brainliest
Answers
Since -15/5 is -3
Direct variation is when y varies exactly with x
A spinner included in a board game has four equally sized sections, as pictured below.
If a player spins and gets a 3, what is the probability they will get 3 on the next spin?
a. 0.25
b. 0.5
c. 0
d. 1
Answers
Answer:
.25
Step-by-step explanation:
Since it's a random and equal chance, you can completely disregard what he got previously. There is always a 1 in 4 chance no matter what. .025 is correct.
9514 1404 393
Answer:
a. 0.25
Step-by-step explanation:
A spinner in an algebra problem is generally considered to have equal probabilities for equal areas. It is also generally considered to have the characteristic that the value produced by the next spin is independent of the value produced by the last spin.
With those assumptions in mind, the probability of getting a 3 is always 0.25. It is never anything else with this 4-section spinner.
Evaluate and simplify the
expression when x=10 and y=7.
?
5+ y
6x
Answers
because 5+7=12 and 6x10=60
is -4.9 bigger or smaller then 3.6
Answers
Answer:
Smaller
Step-by-step explanation:
On the number line, 3.6 is on the right side while -4.9 is on the left side. The closer to the right on the number line, the bigger the number.
Answer:
its smaller because negative numbers are to the left of positive numbers and when a number is to the left of another number its less than
You are taking a true/false quiz with 9 questions. What is the probability of getting all 9 questions correct?
Answers
Answer:
If you guess do this -
.5(9)
Basically about a 4.5% chance of getting all right.
Answer:
Step-by-step explanation:
each question has 2 answer choices, so 1 or the 2 is correct, and to get all 9 in a row correct would be like this
1/2 x 1/2 x 1/2 x 1/2 x 1/2 x 1/2 x 1/2 x 1/2 x 1/2
because theres a 1 in 2 chance of getting each question right, and there are 9 questions
1/2^9 = 0.00195 = 0.195%
Please help me! Thanks in advance
Answers
Answer:
the answer is
Step-by-step explanation:
that im not good with math so good luck
Amy drew a scale drawing of a shopping center. The scale she used was 1 inch : 3 feet. If a bakery in the shopping center is 16 inches wide in the drawing, how wide is the actual bakery?
Answers
Answer:
48 ft
Step-by-step explanation:
We can use ratios to solve
1 inch 16 inches
------------ = -------------
3 ft x ft
Using cross products
1 * x = 3 * 16
x = 48
48 ft
angel why should i be with you again what is 100x23x6
Answers
Answer:
13800
Step-by-step explanation:
:b
A cyclist rode at an average speed of 15 mph for 30 miles. How long was the ride? 0. 5 hours 1 hour 2 hours 3 hours.
Answers
Answer:
2 Hours
Step-by-step explanation:
using the relationship
distance = speed × time, then
time =[tex]\frac{distance}{speed}[/tex] =[tex]\frac{30}{15}[/tex] = 2 hours
