The table below shows that the number of miles driven by Lily is directly proportional to the number of gallons she used. Gallons Used Miles Driven 37 754.8 47 958.8 50 1020 What is the constant of proportionality between the number of miles driven and the number of gallons used?
Answers
Answer:
20.4
Step-by-step explanation:
Constant of proportionality, k, is given as [tex] \frac{y}{x} [/tex].
Given that number of miles driven by Lily is directly proportional to the number of gallons she used, therefore the constant of proportionality between the number of miles driven and the number of gallons used can be determined by using any given pair from the table of values.
Using, (50, 1020),
constant of proportionality (k) = [tex] \frac{1020}{50} = 20.4 [/tex].
The constant of proportionality is 20.4 miles per gallon.
A linear equation is in the form:
y = mx + b
where y, x are variables, m is the slope of the line and b is the y intercept.
Let y represent the distance driven in miles for x galloons.
From the table, using the points (37, 754.8) and (50, 1020):
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1} (x-x_1)\\\\y-754.8=\frac{1020-754.8}{50-37}(x-37)\\\\y-754.8=20.4(x-37)\\\\y=20.4x[/tex]
Therefore the constant of proportionality is 20.4 miles per gallon.
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Related Questions
Determine whether each equation represents
proportional relationship. If it does, identify the
constant of proportionality.
a. y = 0.5x - 2
b. y = 1,000x
c. y=x+1
Answers
Answer:
b) y = 1,000x
If this incorrect sorry
Brandon bought a jacket on sale for $36. If the jacket originally cost $60, what was the percentage discount for the cost of the jacket?
Answers
Answer:
40% discount
Step-by-step explanation:
To find this remember the formula [tex]\frac{discount amount}{original price} = \frac{percent discount}{100}[/tex]
To find the discount amount subtract $36 from $60 which is $24.
[tex]\frac{24}{60} = \frac{x}{100}[/tex] next you have to cross multiply
24*100 = 2400 and 60*x = 60x
Now you have the equation 2400 = 60x
Divide both sides by 60 to isolate the variable
x = 40
please help question eleven
Answers
The length of a rectangle is 6 ft longer than its width.
If the perimeter of the rectangle is 44 ft, find its area.
Answers
Answer:
112 ft square
Step-by-step explanation:
Perimeter=2l+2w
l=w+6
Perimeter=2(w+6)+2w
44=2w+12+2w
44=4w+12
32=4w
8=w
l=8+6
l=14
area=lw
area=14x8
area=112 ft square
You and a friend take pictures at a motocross event. Your camera can take 24 pictures in 3.75 seconds. Your friend's camera can take 36 pictures in 4.5 seconds. Evaluate the expression (36 divided by 4.5)/(24 divided by 3.75) to find out how many times faster your friend's camera is than your camera. GIVING BRAINLIST!
Answers
Answer:
bro
Step-by-step explanation:
bro i have no idea
help plsplspls !! :)
Answers
Answer:
I want to say it's -69/100
Step-by-step explanation:
Hope that helps!
Find the x−and y−intercepts.
4x − 2y = −8
The x−intercept is
.
The y−intercept is
.
Answers
Answer:
(4,-8/5)
Step-by-step explanation:
.............
Answer:
x=y-4/2
Step-by-step explanation:2x-y=-4
2x-4=-8/2
2x=4+4
2x=4-4
Find the quotient of -36 / -6
Answers
Answer:
6
Step-by-step explanation:
-36/-6 = 6
Answer:
The answer is positive 6.
Step-by-step explanation:
Hope this helps!
You want to enlarge the picture by a factor of 4 from its current size of 5 inches by 7 inches what is the size of the enlarged picture
Answers
Answer:
20 inches by 28 inches
Step-by-step explanation:
The current size of the picture is 5 inches by 7 inches
If we want to enlarge the picture by a factor of 4, the perimeter will also increase by the factor of 4.
New dimension = 4(old dimensions)
= 4(5 inches by 7 inches)
= 20 inches by 28 inches
Hence, the size of the enlarged picture is 20 inches by 28 inches.
if y=4x+3 were changed to y=-4x+3, how would the graph of the new funtion compare to the original
Answers
Answer:
graph would go to the left 4 units instead of to the right 4 units then up 3
Step-by-step explanation:
read above
Which equation, when solved, glves 8 for the value of x?
5
7
3
3
OA. 2x+ź= 4x+14
OB. 1-9=34-12
OC 41-2=15-4
OD. *-7= x+14
Reset
Ne
Answers
Answer:
C.
Step-by-step explanation:
5/4x-2=3/2x-4
5/4x-3/2x = -4+2
(multiply both sides by 4)
5x-6x=-16+8
-x=-8
(multiply by -1)
x=8
Answer:
C
Step-by-step explanation:
[tex]\frac{5x}{2} +\frac{7}{2} =\frac{3x}{4} +14\[/tex] isolate the terms with the variable x
[tex]\frac{5x}{2} -\frac{3x}{4} =14-\frac{7}{2}[/tex] get the same denominator and combine like terms
[tex]\frac{10x-3x}{4} = \frac{28-7}{2}[/tex] solve
[tex]\frac{7x}{4} =\frac{21}{2}[/tex] crossmultiply and solve for x
[tex]x=\frac{4*21}{7*2} =6[/tex] so is not the first option
try second
[tex]\frac{5x}{4} -9=\frac{3x}{2} -12[/tex] same steps as before
[tex]\frac{5x-6x}{4}=9-12\[/tex]
[tex]\frac{-x}{4} =\frac{-3}{1}[/tex] so x=12 not the second option
try third option
[tex]\frac{5x}{4} -2=\frac{3x}{2} -4[/tex]
[tex]\frac{5x-6x}{4} =2-4[/tex]
[tex]\frac{-x}{4} =\frac{-2}{1}[/tex] so x=8
Ther are 5,290 students at Highline College. If each college classroom holds 50 students, how
many classrooms are needed at Highline College. This is an Order of operation question btw
Answers
50 students per classroom
Then
5,290/50 = 105.8
They need 106 classrooms
What is the point-slope form of a line with slope 4/5 that contains the point
(-2, 1)?
A. y+1 = 4/5(x-2)
B.y+1 = 4/5(x + 2)
C. y-1 = 4/5 (x+2)
D. y-1 =4/5 (x-2)
SUBMIT
Answers
Awnser: Its D uhm yea...
Step-by-step explanation:
The point-slope form of a line is (y-y1)=m(x-x1). Therefore, option C is the correct answer.
Given that, slope (m)=4/5 and the point on line=(-2, 1).
What is the point-slope form of a line formula?A slope is, a numerical measure of a line's inclination relative to the horizontal. In analytic geometry, the slope of any line, ray, or line segment is the ratio of the vertical to the horizontal distance between any two points on it (“slope equals rise over run”).
The point-slope form of a line formula is (y-y1)=m(x-x1).
Now, (y-1)=4/5(x+2).
Therefore, option C is the correct answer.
To learn more about the point-slope form of a line visit:
https://brainly.com/question/12743204.
#SPJ2
What is the absolute value of the number indicated on the number line below?
A. -2 2/3
B. 2 2/3
C. -2 1/2
D. 2 1/2
Answers
Answer:
D, because in between -3 and -2 is -2 1/2, and absolute values are not negative, so the answer is 2 1/2, or D
Answer:
C.
Step-by-step explanation:
what is 1/8 as a percentage ?HELP
Answers
Answer:
12.5%
Step-by-step explanation:
Write 18 as a percent. Divide 1 by . Therefore, the fraction 18 is equivalent to 12.5% .
12. An initial amount of 100 grams of the radioactive isotope thorium-234 decays according
to
A(t) = 100e^-0.02828t
where t is in years. How long will it be before half of the initial amount has disinte-
grated?
Answers
Answer:
Radioactive half-life An initial amount of 100 g of the radioactive isotope thorium-234 decays according to Q ( t ) = 100 e − 0.02828 t where t is in years.
Step-by-step explanation:
-5x-18y=-28 and -10x+9y=-11 solve elimination
Answers
Answer:
[tex]\mathrm{The\:solutions\:to\:the\:system\:of\:equations\:are:}[/tex]
[tex]x=2,\:y=1[/tex]
Step-by-step explanation:
Given the equations
[tex]-5x-18y=-28[/tex]
[tex]-10x+9y=-11[/tex]
solving the system of the equation by elimination method
[tex]\begin{bmatrix}-5x-18y=-28\\ -10x+9y=-11\end{bmatrix}[/tex]
[tex]\mathrm{Multiply\:}-5x-18y=-28\mathrm{\:by\:}2\:\mathrm{:}\:\quad \:-10x-36y=-56[/tex]
[tex]\begin{bmatrix}-10x-36y=-56\\ -10x+9y=-11\end{bmatrix}[/tex]
[tex]-10x+9y=-11[/tex]
[tex]-[/tex]
[tex]\underline{-10x-36y=-56}[/tex]
[tex]45y=45[/tex]
[tex]\begin{bmatrix}-10x-36y=-56\\ 45y=45\end{bmatrix}[/tex]
solve 45y=5 for y:
[tex]45y=45[/tex]
[tex]\frac{45y}{45}=\frac{45}{45}[/tex]
[tex]y=1[/tex]
[tex]\mathrm{For\:}-10x-36y=-56\mathrm{\:plug\:in\:}y=1[/tex]
solve [tex]-10x-36\cdot \:1=-56[/tex] for x:
[tex]-10x-36\cdot \:1=-56[/tex]
[tex]-10x-36=-56[/tex]
Add 36 to both sides
[tex]-10x-36+36=-56+36[/tex]
[tex]-10x=-20[/tex]
[tex]\frac{-10x}{-10}=\frac{-20}{-10}[/tex]
[tex]x=2[/tex]
[tex]\mathrm{The\:solutions\:to\:the\:system\:of\:equations\:are:}[/tex]
[tex]x=2,\:y=1[/tex]John is hanging 146 feet of Halloween lights on the sides of his rectangular fence that encloses his property. The length is five feet less than five times the width. Find the length of the fencing.
Answers
Answer:
1347 feet in the space of the suns house
Step-by-step explanation:
find the slope of a line to the line perpendicular to the line containing the points (3,-7) and (4,-3)
Answers
Answer:
4
Step-by-step explanation:
m = y2 - y1/x2 - x1
y = -3 - -7 = -3 + 7 = 4
x = 4 - 3 = 1
m = 4/1
answer should be 4... If i am correct hope that helps
a pharmacist measured 70 mL of medication by difference starting with 100 mL. He noted that the graduate used contained 35 mL of glycerin. Calculate the percentage of error incurred in the measurement.
Answers
i dont have time to do it right now but here is the percent error equation!
help pls (picture attached)
Answers
Answer:
an = 5 . n - 5
a50 = 245
Step-by-step explanation:
equation: an = 5 . n - 5, with n=0, 1, 2, ...
a50 = 5.50 - 5 = 250 - 5 = 245
Is the point (16,20) on line ℓ?
Answers
Answer:
YES
Step-by-step explanation:
Find the equation of the line written as, y = kx. The graph shows a proportional relationship between y and x.
Constant of proportionality/unit rate/slope (k) = rise/run = ⁵/4.
Substitute ⁵/4 in y = kx
We would have:
y = ⁵/4x.
Using the equation of the line, we can know if a given point is on the line by plugging the value of x and y coordinates of the point into the equation. If it makes the equation true, then it is a point on the line. If it doesn't make the equation true, then it isn't a point on the line.
Let's plug in (16, 20) into y = ⁵/4x.
Thus substitute x = 16 and y = 20, we have:
[tex] 20 = \frac{5}{4}(16) [/trex]
[tex] 20 = (5)(4) [/trex]
[tex] 20 = 20 [/trex]
It makes the equation true. Therefore, the point, (16, 20) is a point on line l.
Which two division sentences result in the same quotient?
0.148 ÷ 0.02
1.48 ÷ 0.02
1.48 ÷ 0.2
148 ÷ 2
Answers
Answer:
the first and third one
Step-by-step explanation:
Think About the Process You have 20 quarters. You find 40% more quarters in your room. Then
you go shopping and spend 75% of the total number of quarters. Write an expression to represent
the total number of quarters you take with you shopping. Calculate, in dollars, the amount of money
you have left.
What expression represents your total number of quarters?
O A. 20 +(20 - 0.75)
OB. 20+ (20 = 40)
OC. 20+ (20 x 40)
OD. 20+(20 x0.40)
Answers
Answer:
A. 1.4*20 quarters
B.14
Step-by-step explanation:
A: 1.you start with 20 quarters= 20*1
2.you find 40% of twenty quarters in your room= 4/100*20=0.4*20
3.20*1+20*0.4= 20*1.4
B:20*1.4=28
28*50/100=14
Solve each equation algebraically. 2/3x( - 4)=20
Answers
Answer:
Step-by-step explanation:
2/3x(-4)=20
2/3x*4=20
8/3x=20
8/3x/8/3= 20/8/3
0.83 but 3 is repeting
A graph of an inequality includes an open circle and an
arrow pointing left. Explain how you would use that
information to choose which symbol to use to write an
inequality
Answers
Answer: Since the circle is open, the symbol must be < or="">, because the boundary point is not included. The arrow points left, so the solution set includes all values less than the boundary point. I would use < in="" my="">
Step-by-step explanation:
Sample Response
The information that should be selected for symboling the equality function since the boundary point is not involved.
What is an inequality function?It is the relation type where it can graph and show any kind of relationship. rather drawing the lines for linking the dots here we have to shade the large areas for the graph.
Also, there is open circle so here the symbol should be like < or=""> since the boundary point is not involved. Also, the point of arrow should be in left hand side, so it should be lower than the boundary point.
Learn more about circle here: https://brainly.com/question/2031248
Divide: 2 divided 1/2
2
16
8
4
Answers
Answer:
4
Step-by-step explanation:
2 / 1/2. Flip it. 2*2 which is 4
Hope this helps plz mark brainliest if correct :D
10 + -6 please help me find the answer thanks everyone for helping
Answers
Answer:
4
Step-by-step explanation:
10+-6 is the same as 10-6.
You can see this because there is a addition and subtraction symbol in the middle. You can use the KCC (keep, change, change) method to change the symbols from 10+-6 to 10-6. (You keep the 10, change the subtraction and addition symbols).
Answer: its 4
Step-by-step explanation: Because if you put it on a number line from 0 to 10. go right 10 times. then for -6 you go back left 6 times. and get 4. or just 10 - 6 = 4
A recipe for tropical punch calls for 2 cups of pineapple juice and 3 cups of orange juice. Jo creates a drink by mixing 3 cups of pineapple juice with 4 cups of orange juice
Answers
Answer:
Okay?
Step-by-step explanation:
How long would it take the two trains to meet?
Answers
Answer: 2.5 hours.
Step-by-step explanation:
