Maria made two batches of fruit punch. The table at the right shows how many quarts of juice she used for each batch. Write an equation that relates the proportional quantities. Convince Me! How does the equation change if the amount of grape juice is the independent variable, x, and the amount of apple juice is the dependent variable, y? A table with Apple Juice (x), Grape Juice (y) and Grape Juice/Apple Juice (y/x). The first row has x as 5 and y as 8. The second row has x as 10 and y as 16. In each row, the ratio of Grape Juice to Apple Juice is a blank to be filled. The constant of proportionality is . An equation that represents this proportional relationship is =
Answers
Answer/Step-by-step explanation:
The equation that relates the proportional quantities would take the following form ---› [tex] y = kx [/tex], where,
y = amount of Grape juice (dependent variable)
x = amount of Apple juice (independent variable)
k = constant of proportionality (y/x)
✔️Using any of the given pair, say, (5, 8),
Constant of proportionality = [tex] k = \frac{y}{x} = \frac{8}{5} = 1.6 [/tex]
Substitute k = 1.6 in [tex] y = kx [/tex].
An equation that represents the proportional relationship would be:
[tex] y = 1.6x [/tex]
Or
[tex] y = \frac{8}{5}x [/tex]
How the equation would change if:
y = amount of Apple juice (dependent variable)
x = amount of Grape juice (independent variable)
The constant of proportionality would change, that is using a pair, say, (8, 5),
[tex] k = \frac{y}{x} = \frac{5}{8} = 0.625 [/tex]
Substitute k = 0.625 in [tex] y = kx [/tex].
The equation would now be:
[tex] y = 0.625x [/tex].
Or
[tex] y = \frac{5}{8}x [/tex]
Related Questions
In Exercises 27 and 28, find the domain of the function
represented by the graph. Determine whether the
domain is discrete or continuous. Explain.
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Question 27
The graph on question 27 indicates that there are three points with the locations such as:
(2, 6)(4, 12)(6, 18)In other words, there are three points that lie on the graph with the x-values such as:
{(2, 6), (4, 12), (6, 18)}
We know that the domain includes the set of x-values.
Hence, the domain of the function is:
Domain: {2, 4, 6}Since the points are not connected between them. In other words, there is not a continuous line.
Thus, the function represented on the graph has a discrete domain.
Question 28
The graph on question 27 indicates that the line segment with the end-points (0, 25) and (7, 20).
Since there is a continuous line between the points from x = 0 to x = 7.
Thus, the domain of the line function is:
Domain: {0, 1, 2, 3, 4, 5, 6, 7}As the line segment is a continuous line. Thus, the domain is continuous.
Select the correct answer from each drop-down menu.
Aerial's grandmother gave her $5,500.00 to save for her college education. She went to the bank to open a savings account. The bank told her they had two options available.
Account A will pay 5.5% simple interest until the account is closed.
Account B will pay 4.5% simple interest and if the account is left open for longer than 3 years, then at the end of the third year a bonus account will be opened with $250 that also earns 4.5% for the remainder of the time the initial account is open. When the initial account is closed, the bonus account will be closed as well and the money from the two accounts will be combined.
If Aerial is planning on leaving the money in the account for 4 years and then withdrawing all funds, then account
is the better choice earning her
more.
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If Aerial is planning on leaving the money in the account for 4 years and then withdrawing all funds, then account B is the better choice earning her $41.25 more.
Dolly and Willie's scores are shown. Dolly claims that she is the better student, but Willie
claims that he is the better student. What statistics make either Dolly or Willie seem like
the better student? Drag and drop the correct word into each box to complete the
explanation.
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Answer:
I have attached a picture below. I hope this helps!
Please help!!
Use the given vectors to find the indicated quantities.
u =(5, - 2), v =(0, 1), w =(-1, -3)
(a) (u • v)w (b) 5u • V
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Part (a)
Lets say we had the two general vectors
u = (a,b)
v = (c,d)
The dot product is
u dot v = a*c + b*d
-------------------
Apply that rule to these specific vectors
u = (5, -2)
v = (0, 1)
So we get
u dot v = 5*0 + (-2)*1
u dot v = 0 - 2
u dot v = -2
Therefore,
(u dot v)*w = -2*(-1, -3)
(u dot v)*w = ( -2*(-1), -2(-3) )
(u dot v)*w = (2, 6)
Answer: (2, 6)
=============================================
Part (b)
u = (5, -2)
5u = 5*(5, -2)
5u = (5*5, 5*(-2))
5u = (25, -10)
5u dot v = (25, -10) dot (0,1)
5u dot v = 25*0 + (-10)*1
5u dot v = 0 - 10
5u dot v = -10
Answer: -10
What angles are they ?
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number 2 is your answer
Answer:
number 2 is your answer
Step-by-step explanation:
2+2+4 because 1+1+1+1=4 easyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyy
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PLEASE HELP!!!
The temperature in Country Y is at least 7 degrees colder than in Country X. Write an Inequality and graph it.
Solution:
Let temperature in Country Y be
y
and temperature in Country X be
.
"Temperature in Country Y is is at least 7 degrees colder than in Country X."
At least tells us that the inequality sign is
>=
and that the difference in temperature is at least 7
x-y>=7
x>=7+y
x-7>=y
y =7
in your own words.
2. What are the basic steps to be followed in graphing a two-variable linear inequality?
3. In the solution graph, why is the line
y =7
?
How can you find if a point is a solution to inequality?
Answers
Answer:
1)x-y>7
x>7+y
x-7=y
y =7
If it has to be at least 7 then 7 is less than all of them or equal to it.
2) Step 1: Always start by isolating the variable y on the left side of the inequality.
Step 2: Change the inequality to equality symbol. ...
Step 3: Graph the boundary line from step 2 in the X Y − XY- XY−plane. ...
Step 4: The last step is to shade one side or region of the boundary line.
3) The solution graph is y=7 because there is no possible x or x=0
you can find a point in an inequality in the shaded region of the graph. Any of the points in the shaded region work as a solution of the inequality
Hope I helped!!
can sum one solve this plz
5(7+8)+(89-9)
Answers
Answer:
155
Step-by-step explanation:
• 5(15) + 80
• 75 + 80
• 155
YEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEET ON THE TOES
Answers
Answer:
SEOT EHT NO TEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEY
Step-by-step explanation:
I WILL GIVE BRAINLEST!!!!!!!!
A dress is on sale for 35% off the regular price. Which expression represents the
price of the dress after the discount? D is to represent the regular price of the
dress after the discount.
A. 0.35d
B. 0.65d
C. 1.35d
D. 1.65d
PLZSSSSSS SHOW YOUR WORK PLZSSSSS
Answers
Answer: 0.65d (second choice)
====================================================
Explanation:
If you have a 35% discount, this means you save 35% but still pay 65% of the original price.
Notice how 35%+65% = 100%
Or you can think of it as 100% - 35% = 65%
Then we rewrite 65% into 0.65
If d is the original price, then d*0.65 = 0.65d is the price after the discount.
------------------------------
As a slightly longer alternative method, we can say,
d = original price
discount = 35% of d = 0.35d
final price = d - 0.35d
final price = 1d - 0.35d
final price = (1-0.35)d
final price = 0.65d
Select the correct answer. Which expression is equivalent to the given expression?
Answers
Answer:
B
Step-by-step explanation:
2x times x = 2x²
2x times -6 = -12x
1 times x = x
1 times -6 = -6
= 2x² - 12x + x - 6
= 2x² - 11x -6
6x +8=5x=4
what is the value of x
Answers
Answer:
x = -4/11
Step-by-step explanation:
add the x values.
11x+8=4
subtract 8 from each sides
11x=-4
divide by 11
x=-4/11
Simplify (write in the smallest terms) the following expressions using the laws of exponents and distribution.:))) I WILL GIVE BRAINLIST: )))
Answers
Answer:
What is the equation without it I would say it is g or e
Step-by-step explanation:
−3x^ 2 +6x+9=
factor
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Answer:
the answer in factor form would be
-3(
Hi! whats 6666666 × 727272772
Answers
Answer: 4.8484847e+15
Step-by-step explanation:
Answer:
6666666 × 727272772 = 4,848,484,661,818,152
A family is calculating the cost for one semester of college next year. Each hour of class will cost $155. A scholarship gift of $64 can be deducted from costs. If h is the number of hours taken, and c is the total cost, which equation can be used to calculate the total tuition costs for a semester?
C=89h
C=155h+64
C=155h-64
C=-155h-64
Answers
Answer:
c=155h-64
Step-by-step explanation:
you mulitply the cost of the classes by the amount of hours, then you deduct the scholarship gift(64) from the total and get your total cost of the semester
Arrange the expressions in increasing order of their values.
cos(52.5°)cos(7.5°)
sin(52.5°)cos(7.5°)
sin(52.5°)sin(7.5°)
cos(52.5°)sin(7.5°)
Answers
Answer:
cos(52.5°)sin(7.5°)
sin(52.5°)sin(7.5°)
cos(52.5°)cos(7.5°)
sin(52.5°)cos(7.5°)
In increasing order , the expressions are written as follows , cos(52.5°)sin(7.5°) , sin(52.5°)sin(7.5°) , cos(52.5°)cos(7.5°) , sin(52.5°)cos(7.5°).
What are Expressions ?Statements that have more than one term and a variable is connected to another variable by a mathematical operator are called Expressions.
The expression given are
cos(52.5°)cos(7.5°)
sin(52.5°)cos(7.5°)
sin(52.5°)sin(7.5°)
cos(52.5°)sin(7.5°)
To arrange them into increasing order , the value of it has to be determined.
cos(52.5°)cos(7.5°) = 0.6088 * 0.9914 = 0.6036
sin(52.5°)cos(7.5°)= 0.7933*0.9914 = 0.7865
sin(52.5°)sin(7.5°)= 0.7933*0.1305 = 0.1035
cos(52.5°)sin(7.5°)= 0.6088*0.1305= 0.07945
Therefore in Increasing order , the expressions are written as follows , cos(52.5°)sin(7.5°) , sin(52.5°)sin(7.5°) , cos(52.5°)cos(7.5°) , sin(52.5°)cos(7.5°).
To know more about Expressions
https://brainly.com/question/14083225
#SPJ2
Does someone knows how to solve this. Step by step?
Completing the Square:
x^2-6x=15
Answers
Answer:
[tex]x_1=3+2\sqrt{6}[/tex]
[tex]x_2=3-2\sqrt{6}[/tex]
Step-by-step explanation
[tex]\rule{100mm}{0.5mm}[/tex]
[tex]x^2-6x=15[/tex]
[tex]x^2-6x+\left(\dfrac{6}{2}\right)^2-\left(\dfrac{6}{2}\right)^2=15[/tex]
[tex]x^2-6x+3^2=15+3^2[/tex]
[tex]x^2-6x+9=15+9[/tex]
[tex](x-3)^2=24[/tex]
[tex]\sqrt{(x-3)^2} =\sqrt{24}[/tex]
[tex]x-3=\pm2\sqrt{6}[/tex]
[tex]\red{\boxed{x_1=3+2\sqrt{6}}}[/tex]
[tex]\red{\boxed{x_2=3-2\sqrt{6}}}[/tex]
[tex]\rule {100mm}{0.5mm}[/tex]
which expression is equivalent to 1/4m + 3/4m-3/8(m+1)?
Answers
Answer:
5/8m - 3/8
Step-by-step explanation:
1/4 m + 3/4 m - 3/8m - 3/8
to combine m’s, change 1/4 to 2/8. And 3/4 to 6/8.
2/8 m + 6/8m - 3/8 m - 3/8
2/8+ 6/8- 3/8= 5/8
5/8m - 3/8
8. 1/6 + (-7/9)
9. 11 5/7 + 8 1/7
10. 3/12 x 4/21
Answers
Bernie’s estimated that 69% of 242 is 168 is her estimate reasonable
Answers
Answer:
Yes it is.
Step-by-step explanation:
Best way is to use percentages you know when estimating.
We know 50% is half.
50% of 242 is 121.
So it has to be more than 121.
10% of 242 is 24.2 so add that to 121 and you get 145.2
You are 60% so far. You just need 9% more.
Add another 10% which is 24.2 and you get 169.4, which is over but we used 10% instead of 9% so the estimate is reasonable and close.
Joe, Luis, Albert and Lupe want to share 3 oranges so that everyone gets an equal amount. How much orange will each child get? ~PLEASE ANSWER QUICK~
Answers
Answer:
Half an orange
Step-by-step explanation:
It would be half an orange because it says 4 other people. Joe, Luis, Albert, and Lupe. And it says 3 oranges so that everyone would get an equal amount. So if you think about it, theirs no other way to let everyone have an equal piece. So you would have to split them in half and through the left overs away that cant be shared.
please mark as brainly
Original price: $10 New price: $7
Answers
Answer:
what about it??
Step-by-step explanation:
Answer:
WHATS THE QUESTION
Step-by-step explanation:
IF YOU WERE WONDERING IT GOT DISCOUNTED BY 3$, OR 30%
Help will give crown
Answers
Answer:
x y
2 9
3 7
4 5
5 3
Step-by-step explanation:
Answer:
9
7
5
3
The order is from up to down
helpppppp plssssssss
Answers
Answer:
d
Step-by-step explanation:
I THINK
write 13/5 as a mixed number
Answers
Answer:
2 3/5
Step-by-step explanation:
Part B
Choose the inequality that compares the numbers
Choose
Choose
0.25
Answers
I'm sorry but this question is very confusing but I believe you want me to choose 0.25?
<3 Enjoy,
Dea
For the function y = 4x – 2, what is the value of the function when x is equal to -3?
Answers
Answer:
the value of y would be -14
Kris can run 200 meters in 25 seconds at this rate how many meters can he run in 80 seconds?
Answers
Answer:
640
Step-by-step explanation:
200 divided by 25 = 8
which means Kris can run 8 meters per second. 8 times 80 equals 640.
The answers at the bottom are $17.67
$12.22
$15.19
$16.19 in case you can’t see it .
Answers
9514 1404 393
Answer:
$15.19
Step-by-step explanation:
Medicare tax is 1.45%; state tax is 1.5%. Together, these are ...
1.45% +1.5% = 2.95%
of Wallace's salary.
That amount is ...
0.0295 · $515 = $15.19
Answer:
$15.19
Step-by-step explanation:
just cuz