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:
PLEASE HELP ME IM DESPERATE!!!
I WILL GIVE BRAINLIST TO THE BEST ANSWER!!!
ALSO I NEED YOU TO TELL ME HOW TO DO IT!!!
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
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 - 2Step-by-step explanation:
The slope-intercept form of the line equation
[tex]y = mx+b[/tex]
where
m is the slopeb is the y-interceptIn 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 - 23.1= -5.9+x, x=?
what does this answer to
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
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
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
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 ?
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!
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
help a girl out pls!!!!
Answer:
Your answer would be D!
Step-by-step explanation:
10-x=-2x what is it ???
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
Answer:
y8
Step-by-step explanation:
PLEASE HELP ME I WILL GUVE BRAINLIEST I REALLY NEED HELP
Evaluate the expression for r = 0 and s = –14. Simplify your answer.
r − s
s
=
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.
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
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
Answer:
the answer for this problem would be 24 dollars.
PLZ HELP ME !!!!!!!!!!! what is -3+5=11.6
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
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
Answer:
y=-1x+2
or
y=-x+2
y=mx+b
substitute
you get y=-1x+2
What slope would be parallel to the following line? y=4x+3
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=
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
PLEASE HELP I WILL GIVE BRANLIEST TO WHO ANSWERS FIRST
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?
What is 3/4 x 6 , simplified .
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°
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!!!!
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.
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?
Answer:
About 45% increased