2. The table shows distance, y, that Mario runs in x minutes.
Mario’s Running Speed
Time,
(min) Distance,
(mi)
7 1
21 3
35 5

(a) Based on the information in the table, write an equation that can be used to model the relationship between the time (x) and distance (y). Show your work.
(b) What is the rate of change for this linear relationship? Show your work.
(c) What is Mario’s distance given that he ran for 70 minutes? Show your work.

Answers

Answer 1

Answer:

Equation: y = ⅐x

Rate of change: ⅐

Distance = 10 miles

Step-by-step explanation:

Given

The information in the above table

Solving (a): The equation

To get the equation, we need to first calculate the slope (m)

Take any two corresponding values of x and y

(x1,y1) = (7,1)

(x2,y2) = (21,3)

m = (y2 - y1)/(x2 - x1)

m = (3 - 1)/(21 - 7)

m = 2/14

m = ⅐

The equation is calculated using

y - y1 = m(x - x1)

Substitute values for m, x1 and y1

y - 1 = ⅐(x - 7)

y - 1 = ⅐x - 1

Add 1 to both sides

y = ⅐x

Solving (b) Rate of change:

The calculated slope in (a) above represents the rate of change.

So:

Rate of change = Slope = ⅐

Solving (c): Distance when time is 70 minutes

This implies that x = 70

Substitute 70 for x in y = ⅐x

y = ⅐ * 70

y = 10 miles


Related Questions

Which of the following is a biconditional statement?
Question 17 options:

A)

If x ≠ 5 then x2 ≠ 25

B)

If x2 = 25, then x = 5 or x = –5

C)

x = 5 if x2 = 25

D)

x = 5 if and only if x + 5 = 10

Answers

It is D

I just took the test and got it right

The biconditional statement is x = 5 if and only if x + 5 = 10.

Option D is the correct answer.

What is an expression?

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

Biconditional statement.

This means,

The statement and its converse are both true.

Now,

x = 5 if and only if x + 5 = 10

This shows that both the statement and its converse are true.


Thus,

x = 5 if and only if x + 5 = 10 is a biconditional statement.

Learn more about expressions here:

https://brainly.com/question/3118662

#SPJ2

Are these proportional?
Yes | No

Answers

Answer:

yes

Step-by-step explanation:

multiply 6 for the numerators and denominaters

Answer:

Yes they are proportional

Step-by-step explanation:

May I please have brainliest?

In the diagram, lines m and n are parallel. What is the measure of w?

Answers

Answer:

35 degrees

Pleaase seek help u need to be smarter than this giv me brainilest

Salvador is 15 years older than Elizabeth. In 6 years, the sum of their ages will be 87. How old are they now?​

please include and explantation

Answers

Answer:

????

Step-by-step explanation:

 

Write a fraction that is equal to 5

Answers

Answer:

5/1

Step-by-step explanation:

For which equation does x = 2?

Answers

Answer:

what are the equations

Step-by-step explanation:

I need help with 10 please!!!!!!!

Answers

From the graph, [tex]y=mx+b[/tex] and m < 0 (The slope right here is less than 0.)

That means cut ( b ) and ( d ) choice, they both are wrong.

Now look at ( a ) and ( c ).

For ( a ) It's just f(x) = -2x but the graph that's shown here intercepts y-axis at (0,2).   f(x) = -2x is just slope and intercepts y-axis at (0,0)

So the answer is ( c )

A rectangular garden is divided into four sections. Some dimensions are shown in the diagram, and the distance from
point A to point Cis 16 ft.
12 it
8
15 ft
What is the distance from point A to point B in feet?
A. 8ft B.7ft c.9ft D.6ft

Answers

Answer:9 ft

Step-by-step explanation:

The requried measure of the AB is given as 7ft. Option B is correct.

What are Pythagorean triplets?  

In a right-angled triangle, its sides, such as hypotenuse, and perpendicular, and the base is Pythagorean triplets.

Here,
From the diagram, applying Pythagoras' theorem to the right rectangle,
BC² = 15² - 12²
BC² = 81
BC = 9

Now,
AC = 16
AB + BC = 16
AB + 9 = 16
AB = 7 ft

Thus, the requried measure of the AB is given as 7ft. Option B is correct.

Learn  more about Pythagorean triplets here:

brainly.com/question/22160915

#SPJ2

Alex is writing statements to prove that the sum of the measures of interior angles of triangle PQR is equal

Answers

Answer:

here

Step-by-step explanation:

Alex is writing statements to prove that the sum of the measures of interior angles of triangle PQR is equal to 180°. ... Triangle PQR has vertex P on line n and vertices Q and R on line m. Angle QPR is 80 degrees. Segment PQ makes 40 degrees angle with line n and segment PR makes 60 degrees angle with line n.

Answer:

Angle PQR measures 40 degrees

Step-by-step explanation:

No explanation took the test got it right.

Little late but, oh well, better late than never.

Fihd the area of the triangle.
6
8
square units

Answers

Answer:

area of triangle is

[tex]\frac{1}{2} * b*h\\\\\frac{1}{2} *6*8\\\\6*4=24[/tex]

Lin swims 10 laps in the pool in 25 minutes.
How many minutes per lap is that?
I am not good at math (о´∀`о)

Answers

Answer:

The answer is 2.5 minutes per lap.

Step-by-step explanation:

Divide the number of minutes by the amount of laps:

25/10 = 2.5

To check your answer, multiply 2.5 my the amount of laps.

2.5 x 10 = 25

I hope this helped you! If it did, please consider rating, pressing thanks, and/or giving my answer 'Brainliest.' Have a wonderful day. :)

Answer:

40 seconds per lap

Step-by-step explanation:

10 divided by 25 is 0.4

So im pretty sure the anser is 40 secounds

Sorry if im wrong- im not that great at math eaither I just used a calculator.

Given the set of test scores: 71, 75, 80, 81, 81, 84, 89, 93. If a score of 50 is added to the data set, which statement is true? Select all that apply. Choose all that apply:
The mean decreases.

The median decreases.

The standard deviation increases.

The range increases.​

Answers

Answer:

The standard deviation increases, it's mean, medium and mode, if you put them in order and then go through and get your middle number it'll be 81.

If a score of 50 is added to the data set,

The standard deviation increases.

The range increases.​

What is mean?

"It is the average of all elements of the data set."

What is median?

"It is the middle number in a sorted list of numbers."

Formula to calculate the standard deviation:

[tex]SD=\sqrt{\frac{\sum{(x-M)^{2}} }{N} }[/tex]

where, SD is the population standard deviation

N : the size of the population

x : each value from the data

M : the mean of the data

Formula to calculate the range of the data:

range = maximum value - minimum value

For given situation,

Consider the original set of test scores: 71, 75, 80, 81, 81, 84, 89, 93

N = 8

range R = 93 - 71

⇒ R = 22

Mean M = (71 + 75 + 80 + 81 + 81 + 84 + 89 + 93)/8

⇒ M = 654/8

⇒ M = 81.75

Now, we find the median K

First we sort given data set: 71, 75, 80, 81, 81, 84, 89, 93

The middle numbers are 81 and 81

So, the median is the average of 81, 81

So, K = 81

Now, we calculate the standard deviation.

[tex]SD=\sqrt{\frac{[(71-81.75)^{2}+(75-81.75)^{2}+...+(89-81.75)^{2}+(93-81.75)^{2}] }{8} }[/tex]

⇒ SD = 6.61

Consider, the set of test scores with 50 added to the data set.

N = 9

range R = 93 - 50

⇒ R = 43

Mean M =  (71 + 75 + 80 + 81 + 50 + 81 + 84 + 89 + 93)/9

⇒ M = 704/9

⇒ M = 78.22

Now, we find the median K

First we sort given data set: 50, 71, 75, 80, 81, 81, 84, 89, 93

The middle number is 81.

So, the median is K = 81

Now, we calculate the standard deviation.

[tex]SD=\sqrt{\frac{[(71-81.75)^{2}+(75-81.75)^{2}+...+(50-81.75)^{2}+(93-81.75)^{2}] }{9} }[/tex]

⇒ SD = 11.76

So, we can observe that if a score of 50 is added to the data set, the correct statements are:

The standard deviation increases.

The range increases.​

Learn more about mean, standard deviation, median, range here:

https://brainly.com/question/17998130

#SPJ2


After a 15% increase, a town has 115 people. What was the population before the increase?

Answers

Answer:

100 people

Step-by-step explanation:

Population Of People=115Percentagencrease=15%

The New Population corresponds to 115%

(That is 100+15)

We want to find the population that corresponds to 100% that is the original population.

Therefore Original Population;

[tex] \frac{100}{115}\times {115}{} [/tex]

[tex]100 \: people[/tex]

Kayla hikes 25 meters in 13.7 seconds. Which of the following closest to how far she will hike in 6 minutes, if she maintains the same pace

Answers

Answer:

197.28 meters in 6 minutes

Step-by-step explanation:

13.7 seconds ÷ 25 meters = 0.548 meters in 1 second

6 minutes = 360 seconds (6 minutes x 60 seconds in every minute = 360 seconds)

0.548 meters in 1 second x 360 seconds = 197.28 meters in 6 minutes

Hopefully this helped! Sorry if wrong. You are loved and you are beautiful/handsome!

-Bee

Mr. & Mrs. Martin drove 200 miles in September. They drove 2 times as many miles in November as they did in September. They drove 2 times as many miles in October as they did in November. How many miles did Mr. & Mrs. Martin drive in October?

Answers

they drove 800 miles in October

Question:

Mr. & Mrs. Martin drove 200 miles in September. They drove 2 times as many miles in November as they did in September. They drove 2 times as many miles in October as they did in November. How many miles did Mr. & Mrs. Martin drive in October?

Answer:

200 miles x 2 = 400 miles in September  400 x 2 = 800 in october

Find the distance between the points (-3, -6) and (1, -2).

Answers

Answer: -3 - 1 = -4

Your Answer I think is -4 Hope This helps If I'm Wrong I apoligize.

Help and please do not report I got an practice thing from my tutor, so it's not a quiz.

Answers

Answer:

The answer is D. II 1 > -2 and III -2< 1 Hopefully this is helpful!

Step-by-step explanation:

25
50
75
100
y
5
10
15
20
Write an equation to represent the proportional relationship.

Answers

x=5y i think
i apologize if it’s wrong

Nine hundred light bulbs are packaged and shipped to a retail store. Thirteen percent of the light bulbs arrive broken. Which equation can be used to find the number of light bulbs that were broken? StartFraction 13 times 9 Over 100 times 9 EndFraction = StartFraction 117 Over 900 EndFraction StartFraction 13 times 9 Over 900 times 9 EndFraction = StartFraction 117 Over 8100 EndFraction StartFraction 100 divided by 9 Over 900 divided by 9 EndFraction = StartFraction 11.1 Over 100 EndFraction StartFraction 900 divided by 9 Over 13 divided by 9 EndFraction = StartFraction 100 Over 1.4 EndFraction

Answers

Answer:

3

Step-by-step explanation:

Answer:

3

Step-by-step explanation:

plese help
plese
plese

Answers

B 25% percent because 15/60 is 25
Answer: C
15 seats were empty, so 45 out of 60 seats were taken. 45 divided by 60 is 0.75, which is 75%

I can't help solve my friends problems,I got too much to do help him out please

Answers

Answer:

the ask a question about the question isnt working

Step-by-step explanation:

but can you zoom in its really glitchy and blurred from far away

Yeah I would also need it zoomed in please.

A spinner is divided into eight equal-sized sections, numbered from 1 to 8, inclusive. What is true about spinning the spinner one time? Select three options. S = {1, 2, 3, 4, 5, 6, 7, 8} If A is a subset of S, A could be {1, 2, 3}. If A is a subset of S, A could be {7, 8, 9}. If a subset A represents spinning a number less than 4,then A = {1, 2, 3, 4}. If a subset A represents the complement of spinning an odd number, then A = {2, 4, 6, 8}.

Answers

Answer: A, B, and E

Step-by-step explanation:

The true statements are (A) A could be {1, 2, 3} and (B) A could be {1, 2, 3, 4}, where A  is a subset of S

How to determine the true statements?

The sample space is given as:

S = {1, 2, 3, 4, 5, 6, 7, 8}

The possible subsets of S are as follows:

Even numbers = {2,4,6,8}Odd numbers = {1,3,5,7}Any number or group from 1 to 8, inclusive

Using the above highlights, the possible set of A are:

A could be {1, 2, 3}. A = {1, 2, 3, 4}.

Hence, the true statements are (A) and (B)

Read more about spinners at:

https://brainly.com/question/3765462

#SPJ2

e length of a rectangle is five times its width. If the area of the rectangle is 320in, find its perimeter.

Answers

Answer:

Step-by-step explanation:

Let width of rectangle =X

So length=5x

Given area of rectangle =320inch

Area of rectangle =length ×width

Length×width=320

5X×X=320

5x^2=320

x^2=320/5

x^2=64

So X=√64

Width x= 8inch

Length 5x=5×8

= 40 inch

Perimeter of rectangle =2(length+width)

=2(40+8)

=2(48)

=96inch

Who ever gets it right gets a Brainliest

Answers

Answer:

im pretty sure thats a trench ;_;

Step-by-step explanation:

What's the slope and y-intercept?
Help please!!!

Answers

Answer:

slope of fig 1st(m)= 1/4

y-intercept of 1st fig=-1

slope of fig 2= -1

y-intercept of 2nd fig=2

Step-by-step explanation:

x + 3y = 13
- 3x + 2y = 27 steps on how to solve by substitution

Answers

here x+3y=13

x=13-3y.....1st equation

-3x+2y=27......2nd euation

now putting the value of x from equation 1st in 2nd we will get

-3(13-3y)+2y=27

-49+9y+2y=27

11y=27+49

y=76÷11

y=6.9

now again putting the value of y in equation 1st we get

x=13-3×6.9

x=13-20.7

x=7.7

Please help and leave a small explanation if u want brainliest :)

Answers

Answer:

B is true

Step-by-step explanation:

ratio of all corresponding sides are equal

Answer:

B) Triangle ABC is similar to triangle EFG

Step-by-step explanation:

they are similar eve tho they are not the same size. But they arnt congrent cause they are diffrent sizes.

Multiply two and four-fifths negative five and two-thirds

Answers

The answer is -25/3.



If you need it simplified let me know.

Trina earns $28.50 tutoring for 3 hours. Write an equation relating her earrings "m" to the number of hours "h" she tutors. Assuming the situation is proportional, how much would Trina earn tutoring for 2 hours? For 4.5 hours?

Answers

Answer:

Step-by-step explanation:

28.50/3=9.50 dollars per hour

y=9.50h

Trina earns $19.00 for 2 hours

Trina earns $42.75 for 4.5 hours

Answer:

If Trina earns $28.50 in 3 hours, that means she earns $9.50 per hour.

9.50h = m   --->  earnings = 9.50 x hours

2 hours = 9.50 ( 2) =  $19

4.5 hours = 9.50 ( 4) = $42.75

Step-by-step explanation:

An ice cream shop ordered a box of 700 cones. When they opened the box, they noticed 164 of the cones were broken. How many cones do they have left? *

Answers

Answer:

The answer would be 536 cones.

Step-by-step explanation:

You have to subtract 164 from 700.

700-164=536.

Other Questions
I will give brainiest to who answer please fast Which graph describes the relation {(3, 1), (1, 2), (3, 2), (5, 5)}? Please help :( this is a really complicated question What is the answer to 34.50r+78.50(810-r) What tool of dream analysis says that feelings and urges are hidden inside an event? condensation symbolism projection displacement Urgent please help, I will truly be grateful Solve me a riddle, there is a wall in your path that you can't go through, around, or over. Question 4 of 15 Which was a result of apartheid? A. Nelson Mandela was jailed for 27 years. B. The black population became a minority. C. Hutus and Tutsis engaged in a brutal civil war. D. Blacks gained equal rights under the law. 3.55. :1) = 2/3 4; 2) y = 2x + 6;3) = -1,5 3; 4) y = -1/2x + 1;5) y = 5/3x - 2;6) y = -4/3x + 2; -1/4 [p+16]=2 help me pls girls question who wants to go out ;p If the mRNA codon is CCA, what should be the tRNA anticodon be? And Which amino acid does this make? what is 10m-2?Variables are really hard for me so if anyone can help me with this problem that would be really great HELP!!!!!!!! ALL MY GRADES DEPEND ON THIS!!! 0.5y/4/9 = y+3/8 for the essay please i need it by tonight What reforms happened in Europe:Pls answer Log. 216 = YSolve for Y Do you think that the future of metalcraft is in danger due to the ability of computers to do most of the work? Explain your reasons why or why not.pls have at least 3 sentences! thx! :) The people of which country are called Flemish? Find the slope of the line containing the points (-2,5) and(-2,0).