PLEASE HELP 100 POINTS!!! PLEASE DON'T ANSWER IF YOU DON'T KNOW!!
Alana and Kelsa are training for a marathon. To prepare for this marathon they have been training and tracking their progress periodically.

In the first week of training Alana ran an average of 20 minutes per mile. Later, in week seven of training she ran an average of 14 minutes per mile.

In the first week of training Kelsa ran an average of 15 minutes per mile. Later, in week five of training she ran an average of 13 minutes per mile.

Assuming that Alana and Kelsa continue to train and improve their times at the same rate your task is to determine which week they will have the same average minutes per mile. We will assume that the relationship is linear as they will be training for a maximum of 43 weeks. To complete this task follow the steps below.

1. Determine the equation of a line in standard form that represents Alana’s training progress. Her progress corresponds to the points (1, 20) and (7,14).

2. Determine the equation of a line in standard form that represents Kelsa’s training progress. Her progress corresponds to the points (1, 15) and (5,13)

3. Solve the system of equations (you must show all your work to receive full credit).

4. In which week will Alana and Kelsa have the same average minutes per mile?

5. If Alana and Kelsa continue to train until week 30, what will their times be?

6. Do you believe a linear model best represents the relationship of the time of the runners and the weeks that passed?(Hint: look at question 5). What do you think this says about problems in the real world? Justify your thoughts in 3-4 sentences.

Answers

Answer 1

Answer: Alana's training experience in (weeks, minutes per mile) is (1, 12) and (5, 6).

Kelsa's training experience is (1, 10), (11, 5).

Find:

A linear equation in standard form that describes Alana's experience

A linear equation in standard form that describes Kelsa's experience

A solution to the pair of linear equations

The week in which the number of minutes per mile is the same

Minutes per mile for Alana and Kelsa at week 25

Comment on the use of a linear model in this context

Solution:

Please note that in parts 1 and 2 a "standard form" linear equation has a positive leading coefficient and the numbers have no common factor.

1. A linear equation can be written from two points (x1, y1) and (x2, y2) as ...

... (y2 -y1)(x -x1) -(x2 -x1)(y -y1) = 0

Using the given points in order, this becomes

... (6-12)(x -1) -(5 -1)(y -12) = 0 . . . . above equation with values filled in

... -6x +6 -4y +48 = 0 . . . . . . . . . . eliminate parentheses

... 3x +2y -27 = 0 . . . . . . . . . . . . . divide by -2 to make x-coefficient positive

... 3x +2y = 27 . . . . . . . . . . . . . . . . Alana's training experience

2. In similar fashion, we can write the equation for Kelsa's experience.

... (5 -10)(x -1) -(11 -1)(y -10) = 0

... -5x +5 -10y +100 = 0 . . . . . . eliminate parentheses

... x +2y -21 = 0 . . . . . . . . . . . . . divide by -5

... x +2y = 21 . . . . . . . . . . . . . . . . Kelsa's training experience

3. We note that both equations have the term 2y, so we can subtract the second equation from the first to eliminate that term:

... (3x +2y) -(x +2y) = (27) -(21)

... 2x = 6 . . . . . . . simplify

... x = 3 . . . . . . . . divide by 2

... 3·3 +2y = 27 . . . substitute x=3 into Alana's equation

... 2y = 18 . . . . . . . . subtract 9

... y = 9 . . . . . . . . . . divide by 2

The solution is (weeks, minutes) = (x, y) = (3, 9).

4. The solution of part 3 tells us both have an average time of 9 minutes per mile in week 3 of training.

5. Substituting x=25 into the equations of parts 1 and 2, we get ...

... 3·25 +2y = 27

... y = (27 -75)/2 = -24 . . . . Alana's time per mile at week 25

... 25 + 2y = 21

... y = (21 -25)/2 = -2 . . . . . Kelsa's time per mile at week 25

6. A linear model makes no sense in this context. At some point a linear equation for minutes per mile will always have a value of 0. We know that marathon runners will never have a time of zero minutes per mile. Under the best of conditions, we expect training to improve time toward some asymptotic limit determined by body mechanics. A linear model is completely inappropriate for describing such training effects. Not every real-world problem is appropriately represented by a linear equation.

Step-by-step explanation:


Related Questions

PLEASE HELP ME IM DESPERATE!!!
I WILL GIVE BRAINLIST TO THE BEST ANSWER!!!
ALSO I NEED YOU TO TELL ME HOW TO DO IT!!!

Answers

Answer:

4

Step-by-step explanation:

We are asked to find a slope whilst given a graph.

To solve for slope, we must pick two coordinate points that are not decimals and following the formula of rise over run, which in basic terms y over x.

So based on what I see, I can see (1, 1) and (2, 5).

The rise over run is as followed :

[tex]\frac{y2 - y1}{x2 - x1}[/tex]

2 and 1 meaning the first and second number within the coordinate, so substitute :

[tex]\frac{5 - 1}{2 - 1}[/tex]

[tex]\frac{4}{1}[/tex]

Divide :

[tex]4[/tex]

4 is our slope.

Which equations best describes the graph of a line that has a slope of - 1/2 and passes through the point (2,-3)? O y = 2x +4 O 2x +y=24 Ov--x-4 O y = x + 2​

Answers

Answer:

The equation which best describes the graph of a line that has a slope of - 1/2 and passes through the point (2,-3) will be:

y = -1/2x - 2

Step-by-step explanation:

The slope-intercept form of the line equation

[tex]y = mx+b[/tex]

where

m is the slopeb is the y-intercept

In our case, we are given

The slope m = -1/2

Point (2, -3)

now substituting m = -1/2 and (2, -3) in the slope-intercept form of the line equation to determine the y-intercept

[tex]y = mx+b[/tex]

-3 = -1/2(2) + b

-3 = -1 + b

b = -3 + 1

b = -2

now substituting m = -1/2 and b = -2 in the slope-intercept form of the line equation

y = mx + b

y = -1/2x + (-2)

y = -1/2x - 2

Therefore, the equation which best describes the graph of a line that has a slope of - 1/2 and passes through the point (2,-3) will be:

y = -1/2x - 2

3.1= -5.9+x, x=?
what does this answer to

Answers

Answer:

6-2=3

Step-by-step explanation:

5234.9

Answer:

x = 9

Step-by-step explanation:

3.1= -5.9+x

x - 5.9 = 3.1

x - 5.9 + 5.9 = 3.1 + 5.9

x = 9

Find the value
of 6y^2 - 24y - 51 when y=-2

Answers

Answer:

21

Step-by-step explanation:

6(y^2) - 24y -51 = 6 4 - 24y - 51

(6 4) - (24y) - 51 = 24 - -48 - 51

(24 - -48) - 51 = 72 - 51

72 - 51 = 21

1. - 9 - 28 = -9+
Need answers

Answers

Answer:



-37=-9

hope this help

chris worked 3 1/2 hours at his uncles farm. He was paid 8$ for every 1/4 hour he worked. How much money did chris make

Answers

Answer:

$112

Step-by-step explanation:

So first figure out how much he makes an hour

8*4 is 32.

32*3 1/2 is $112

The amount that Chris will make will then be $112.

The first thing to do is to divide 3 1/2 by 1/4. This will be:

= 3 1/2 / 1/4

= 7/2 × 4/1

= 14

Now we'll then multiply 14 by $8. This will be:

= $8 × 14

= $112

The amount made will be $112.

Read related link on:

https://brainly.com/question/19965204

Which equation is equivalent to 15 +80 ?

Answers

Answer:

is a lot of them

Step-by-step explanation:

94+1, 95+0, 79+16

Answer: 5(3+16)

Step-by-step explanation:

5x(3+16) = (3+16= 19) = 5 x 19 = 95 which is equivalent to 15 + 80 = 95

brainliest plz

Can someone help me pls and thank you!

Answers

Answer:

yes

Step-by-step explanation:

if you add 2+3 it will be five and 6+5 equals 11 so yes

Answer:

Yes.

Step-by-step explanation:

6+2+3=11

8+3=11

Therefore, both equations are equal.

Type the missing number in this sequence:
-5,
-30,
-180,

-6,480

Answers

-1,080, because they are all being multiplied by 6 :)

help a girl out pls!!!!

Answers

Answer:

Your answer would be D!

Step-by-step explanation:

10-x=-2x what is it ???

Answers

Answer:

x = - 10

Step-by-step explanation:

Given

10 - x = - 2x ( add 2x to both sides )

10 + x = 0 ( subtract 10 from both sides )

x = - 10

is the point 15,4 a solution to the system?
y=2x+4

Answers

Answer:

y8

Step-by-step explanation:

PLEASE HELP ME I WILL GUVE BRAINLIEST I REALLY NEED HELP

Answers

The word solution means the value that makes the equation true. 88 is the solution because it makes he equation true.

Evaluate the expression for r = 0 and s = –14. Simplify your answer.

r − s
s
=

Answers

14 is the answer

Step-by-step explanation:

0+14=14

Luke has a board 56 of a yard long. He needs to cut the board into 5 equal sections. Use the expression to find the length of each section. Each section is yard long.

Answers

Answer:

11.2

Step-by-step explanation:

56 divided by 5

The smaller triangle is dilated to create the larger triangle. The center of
dilation is plotted, but not labeled

Answers

to create a larger plot you need to dilation it

PLS HELP ASAP rob is saving money for a new mp3 player. For every $15 he saves $8. On Sunday he earns $45 how much does he save

Answers

Answer:

the answer for this problem would be 24 dollars.

PLZ HELP ME !!!!!!!!!!! what is -3+5=11.6

Answers

Answer:

The answer is 2 not 11.6

Step-by-step explanation:

Answer:

23.2

Step-by-step explanation:

-3 + 5=2 2*11.6=23.2

Plz help due tomorrow

Answers

Answer:

1. 2.19g + 0.59b + 1.49p

2. 6.57 + 1.77 + 2.98 = 11.32

Answer:

Part A.)   2.19g + 0.59b + 1.49p

Part B.)   11.32

Step-by-step explanation:

Part A.)  

basically they give you the price for each item in the upper description. Just use g,b,p in terms that they gave you

Part B.)

plug in the amount of fruit per pound for each matching variable

2.19(3) + 0.59(3) + 1.49(2) = 11.32

Write an equation in slope intercept form for: m = - 1 and b = 2

Answers

Answer:

y=-1x+2

or

y=-x+2

y=mx+b

substitute

you get y=-1x+2

y=-x+2


Explanation: Slope intercept form is: y=mx+b. Then you just substitute!

Hope this helps! :)

What slope would be parallel to the following line? y=4x+3

Answers

Answer:

Anything with a 4x for slope. It could be y=4x + any number.

Step-by-step explanation:

28, 30, 24, 96, 33
Mean
Range =
Median =
IQR =
Mode =
Variance
Midrange=
Standard Deviation=

Answers

Answer:

I know some .

median : 24

Step-by-step explanation:

Mean : you add all of them up then divide by how many numbers there are .

range : the biggest number minus the smallest number .

median : the middle number . the middle number is 24 .

I know what is mode but the answer is not in there

Solve for m and q:
m+ 2 = q - 4
5m - 33 = q+1

Answers

Answer: m = 10 and q = 16

hope this helps!!

PLEASE HELP I WILL GIVE BRANLIEST TO WHO ANSWERS FIRST

Answers

56
...................................





Answer:

142

Step-by-step explanation:

you have to break the shape in to squares and find the area of each one by multiplying the sides together and then after you find the area you add all them together

what does y = 3x + 5 look like on a graph?

Answers

It’s gonna cross 5 on the y axis. And it’s increasing by 3 cause that’s the slope. :) hope this helped

What is 3/4 x 6 , simplified .

Answers

Answer:

9/2

Step-by-step explanation:

3/4 x 6 can be thought of as multiplying 3/4 x 6/1

When multiplying fractions, multiply the numerator (top number) with the numerator, and the denominator with the denominator.

3/4 x 6/1 = (3x6)/(4x1)

3/4 x 6/1 = (18)/(4)

3/4 x 6/1 = 9/2

Let me know if this helps!

Answer:

92/

Step-by-step explanation:

3/4×6

18/4

9/2

hope it's helpful ❤❤❤❤

THANK YOU.

#

If the measure of AngleB is 40°, what measures can AngleA and AngleC be? Select the three correct answers. 20° and 30° 30° and 110° 55° and 85° 60° and 90° 70° and 70°

Answers

Answer:

30° and 110°

55° and 85°

70°and 70°

Step-by-step explanation:

Given that :

Angle B = 40°

Sum of angles in a triangle :

Angle (A + B + C) = 180°

A + 40 + B = 180

A + C = 180 - 40

A + C = 140°

From the Given options ;

The sun of the Angles Given must add up to 140°

Hence,

30° and 110° = 140°

55° and 85° = 140°

70°and 70° = 140

PLEASE ANSWER, URGENT!!!!

Answers

Answer:

a)57,600 b)12.5% increase

Step-by-step explanation:

Answer:

Step-by-step explanation:

Plz, help I have no clue how to solve this.

Answers

Answer:  Create equations. Top length=Bottom length

Left side = right side.

Combine like terms and rewrite the equations.  

Use the new equations to create a system of equations to solve for x and y.

Once you have x and y, you can substitute those in the expressions for the lengths of the parallelogram.

You should end up with top and bottom lengths of 10. The sides are 9.

Step-by-step explanation:

3x-5 = 18 -2y . Rewrite as 3x + 2y = 23

x+4 = 21 -3y    Rewrite as  x + 3y = 17

The system of equations is

3x + 2y = 23   and  x + 3y = 17 . To solve by substitution, multiply the second equation by -3   It becomes  -3x-9y= -51  Add the equations so the x terms cancel. Solve for y

3x + 2y = 23

-3x - 9y = -51

0  -7y  = - 28  Divide both sides by -7.   y = 4

Substitute 4 for y,  solve for x

x + 3(4) = 17

x + 12 = 17 . Subtract 12 from both sides   x = 5

Substitute the values of x and y in the expressions

Top: 3x-5    is 3(5) -5  becomes 10

Bottom: 18 -2y  is  18 - 2(4) becomes 10

Left:  x +4   is (5) + 4  becomes 9

Right:  21 - 3y  is  12 -3(4)  becomes 9

Tessa bought stock in a restaurant for $177.00. Her stock is now worth $260.19. What is the percentage increase of the value of Tessa's stock?

Answers

Answer:

About 45% increased

Other Questions
Write an equation in point-slope form for the line that passes through the point with the given slope. point: (4,2) and m=3 Game Stop has 48 video games to sell. If it sells 1/8 of its games each day. how many days will it take to sell all of the games? These headlines identify - A. events that contributed to the formation of political parties B. differences between the views of Alexander Hamilton and John Adams C. conflicts between Congress and the Supreme Court D. President Washington's reasons for favoring political parties During the current year, the Town of Salo Alto recorded the following transactions related to its property taxes: Levied property taxes of $3,300,000, of which 2 percent is estimated to be uncollectible. Collected current property taxes amounting to $2,987,500. Collected $26,500 in delinquent taxes and $2,400 in interest and penalties on the delinquent taxes. These amounts had been recorded as Deferred Inflows of Resources in the prior year. Imposed penalties and interest in the amount of $3,750 but only expects to collect $3,100 of that amount. None is expected to be collected this year or within 30 days of year-end. Reclassified uncollected taxes as delinquent. These amounts are not expected to be collected within the first 60 days of the following fiscal year. Makabubuo ng maikling sanaysay hinggil sa Batas ni Hammurabi at sa kasalukuyang batas Please help due today I have a pile of socks which contains 12 white socks, 12 black socks, and 12 red socks. How many socks must I take from the pile to be certain that I have at least one matching pair? *ANSWER ASAP!!!, I WILL GIVE BRAINLIEST*How is the judicial branch of government different from the others?a.) It was created much later than the others.b.) It is passive and independent.c.)Its power has decreased over time. HELP I HAVE TIME LIMIT | Wa. State History Full year 7thWomen suffragists gained victory in 1920, afterA: international sanctions caused the country to give women the vote.B: President Wilson declared that all states must give women the vote.C: enough states ratified the Nineteenth Amendment, giving women the vote.D: both houses of Congress agreed to extend the vote to all women. Use simple interest to find the ending balance$14,000 at 6% for 9 years Use the drop-down menus to select the names of the labeled structures. A: B: C: Your daughter is currently 10 years old. You anticipate that she will be going to college in 8 years. You would to have $136,000 in a savings account to fund her education at that time. If the account promises to pay a fixed interest rate of 3% per year, how much money do you need to put into the account today to ensure that you will have $136,000 in 8 years how can I solve this problem? What is the equation of the line that is parallel to thegiven line and has an x-intercept of -3? Evaluate 6 (4). (10 point) 10 2 24 2 A group of people attempt to bake the largest vegan cake the used 17 kilograms of cocoa powder which is about one-tenth the amount of dates. How many kilograms of cocoa powder and dates do they use? 3How many solutions does the system of equations below have?1y = 8x +y = 8x +fo7.Answer:one solutionno solutionsone solutionInfinitely manysolutions Describe the colonists soldiers Spanish please help !Matching: Match the Spanish reflexive verbs with their English Translation. I WILL GIVE BRAINIST Imagine you are going to lead a discussion about the first chapter of The True Confessions of Charlotte Doyle. Make a list of possible discussion questions based on specific passages from the text. What questions do you have? Were you confused by anything? Are there certain events or moments that are worth talking about in detail? List three questions with their corresponding passages in your journal.