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 =

Maria Made Two Batches Of Fruit Punch. The Table At The Right Shows How Many Quarts Of Juice She Used

Answers

Answer 1

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

Complete the equation of the line through (2, 1) and (5, -8). Use exact numbers. y =​

Answers

Answer:

Step-by-step explanation:

given: (2,1) & (5-8)

first find the slope,

m= (Y2-Y1) / (X2-X1)    

m=(-8-1)/(5-2)

m=(-9)/(3)

m=-3

we have y=-3x+b

use any point to sub in x and y

1=-3(2)+b

1+6=b

b=7               therefore, y=-3x+7 is the equation

Answer:

y = - 3x + 7

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Calculate m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (2, 1) and (x₂, y₂ ) = (5, - 8)

m = [tex]\frac{-8-1}{5-2}[/tex] = [tex]\frac{-9}{3}[/tex] = - 3 , then

y = - 3x + c ← is the partial equation

To find c substitute either of the 2 points into the partial equation

Using (2, 1 ), then

1 = - 6 + c ⇒ c = 1 + 6 = 7

y = - 3x + 7 ← equation of line

Solve for x given the lines are parallel.
(7x - 8)
62°

Answers

Answer:

The answer is 0 ✌

Step-by-step explanation:

70 - 8 =62°

What are the answers?

Answers

Answer:

Step-by-step explanation:

I need the statements please.

If a relation has more numbers in its range than in its domain, what has to be true?

Answers

Answer:

Both the domain and range are the set of all real numbers. For the absolute value function f(x)=|x| f ( x ) = | x | , there is no restriction on x . ... For the cubic function f(x)=x3 f ( x ) = x 3 , the domain is all real numbers because the horizontal extent of the graph is the whole real number line. this is the best i can do if its not helpful i guess u can ask ur teacher.

In 2018, researchers examined a random sample of 1455 "disadvantaged" Australian school children (children aged 6 – 15 from rural and outer suburban areas) and found that 4.3% of them were nearsighted. In 2014, the rate of nearsightedness among such children was 3.5%. Is this strong evidence that the parameter has changed since 2018?

Answers

Answer:

No, this is not a strong evidence that the parameter has changed since 2018. This is because, there are so many factors that could have led to the fall in percentage of "disadvantaged school students" from the initial 3.5% to 4.3%.

Some of the factors could be reduction in the number of disadvantaged students, sample size considered being considered as well as the geographic location upon which the random sampling was made.

Step-by-step explanation:

Which line has a slope of 1/2 and passed through (2,-4)

Answers

The Answer is: “D” step by step explanation:

the width of a rectangle is ycm and its length is y+2 cm. if the perimeter of the rectangle is 32cm what is the width of the rectangle​

Answers

Answer:

[tex]\huge\mathtt{{\colorbox{silver}{ANSWER~~~↴}}}[/tex]

ꜰɪʀꜱᴛ ᴡᴇ ᴡʀɪᴛᴇ ᴛʜᴇ ɢɪᴠᴇɴ↴

⇒WIDTH = Y cm

⇒LENGTH =( y+2 )cm

⇒PERIMETER = 32cm

▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃

solution ↴

perimeter of rectangle = 2 ( length + width)

[tex]32cm = 2( (y +2) +y )cm \\ \frac{32}{2} cm = 2y + 2cm \\ 16cm = 2y - 2cm \\ 16 cm- 2 cm=2y\\ 14cm = 2y \\ y = \frac{14cm}{2} \\ y = 7cm

[/tex]

☛ so the width of the rectangle is 7cm

so we all done :D

▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃

Question 18
1 pts
If JKLM is an isosceles trapezoid, solve for x.
(8x – 23)
(6x + 11)°
M
L
HELPPP

Answers

Answer:

Step-by-step explanation:

J and K are equal

8x - 23 = 6x + 11            Add 23 to both sides

8x = 6x + 11 + 23           Combine the right

8x = 6x + 34                  Subtract 6x from both sides

8x - 6x = 34                   Combine the left

2x = 34                           Divide by 2

x = 34/2

x = 17

=================================

M and L are both supplementary to J and K respectively.

J = 8x - 23

J = 8*17 - 23

J = 136-23

J = 113

K = 113

===================================

M + 113 = 180

M = 180 - 113

M = 67

L = 67

Ben ,Cam and Justin are lumberjacks. The number of trees they chop down is given by b+2c+3j where b is the number of hours Ben some spendsI chopping, c is the number of hours Cam spends chopping and j is the number of hours Justin spends chopping.

Answers

Answer:

26 trees

Step-by-step explanation:

Ben, Cam, and Justin are lumberjacks. The number of trees they chop down is given by b+2c+3j where b is the number of hours Ben spends chopping, c is the number of hours Cam spends chopping, and j is the number of hours Justin spends chopping. How many trees do they chop down after Ben spends 8 hours chopping, Cam spends 3 hours chopping, and Justin spends 4 hours chopping?

Given:

b + 2c + 3j

Where,

b = number of hours Ben spends chopping

c = number of hours Cam spends chopping

j = number of hours Justin spends chopping

Substitute the below into the given expression

b = 8 hours

c = 3 hours

j = 4 hours

b + 2c + 3j

= 8 + 2(3) + 3(4)

= 8 + 6 + 12

= 26 trees

They chopped down 26 trees altogether

[Image: Vertical number line ranging from negative 5 to 5.]

On this number line, zero represents sea level. Plot the following points based on the description provided.

• -3 1/2

[Image: Vertical number line ranging from negative 5 to 5.]

On this number line, zero represents sea level. Plot the following points based on the description provided.

• opposite of –5

Answers

Answer:

Positive 5.

Step-by-step explanation:

Opposite of negative 5 is positive 5.

The point will be on the positive side, which is above sea level. So it will be on 5 above the zero.

Answer:positive 5

Step-by-step explanation:

equations with variables on both sides: decimals & fractions, 6d - 11/2 = 2d - 13/2

Answers

Step-by-step explanation:

i work in paper sheet please see it

Final Answer: [tex]d = -\frac{1}{4}[/tex]

Steps/Reasons/Explanation:

Question: Equations with variables on both sides: decimals & fractions, [tex]6d - \frac{11}{2} = 2d - \frac{13}{2}[/tex].

Step 1: Subtract [tex]2d[/tex] from both sides.

[tex]6d - \frac{11}{2} - 2d = -\frac{13}{2}[/tex]

Step 2: Simplify [tex]6d - \frac{11}{2} - 2d[/tex] to [tex]4d - \frac{11}{2}[/tex].

[tex]4d - \frac{11}{2} = -\frac{13}{2}[/tex]

Step 3: Add [tex]\frac{11}{2}[/tex] to both sides.

[tex]4d = -\frac{13}{2} + \frac{11}{2}[/tex]

Step 4: Simplify [tex]-\frac{13}{2} + \frac{11}{2}[/tex] to [tex]-1[/tex].

[tex]4d = -1[/tex]

Step 5: Divide both sides by [tex]4[/tex].

[tex]d = -\frac{1}{4}[/tex]

~I hope I helped you :)~

An angle measures 130.4° more than the measure of its supplementary angle. What is the measure of each angle?

Answers

Answer: 24.8 and 155.2

Step-by-step explanation:

x+x+130.4=180

2x=49.6

x=24.8

Answer:

155.2

Step-by-step explanation:

let x be the supplimentary angle

then the angle is

130.4+x

we have

 

130.4+x+x=180

2x=49.6

multiply both sides with 2

x=24.8

then the angle is

130.4+24.8

155.2

8 more than a third of a number

Answers

Answer:

8 + 1/3n

Step-by-step explanation:

The admission fee at a museum is $5 for children and $16 for adults. Yesterday, 800 people came to the museum and $8400 was collected. How many children and how many adults came to the museum?

Answers

(c + a = 800)5
5c + 16a = 8400
5c + 5a = 4000
Subtract
11a = 4400
a = 400
There were 400 children and 400 adults

Given h(x) = 3x + 4, find h(-1).

Answers

Plug in -1 for x
h(-1) = 3(-1) + 4
h(-1) = -3 + 4
Solution: h(-1) = 1

The value of h(-1) for the given funciton  h(x) = 3x + 4 will be 1.

What is a function?

A certain kind of relationship called a function binds inputs to essentially one output.

A function can be regarded as a computer, which is helpful.

The machine will only accept specified inputs, described as the function's domain, and will potentially produce one output for each input.

In other words, the function is a relationship between variables, and the nature of the relationship defines the function for example y = sinx and y = x +6 like that.

Given the function  h(x) = 3x + 4

If we want to calculate the value of the function at a certain point then we need to keep that point in the function.

So,

Value of function at = -1 will be

h (-1) = 3(-1) + 4

h(-1) = 1

Hence "  The value of h(-1) for the given funciton  h(x) = 3x + 4 will be 1".

For more about the function,

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For the equation
y - 3 = 2(x + 4),
the line has a slope of 2 and contains what point?
O (3,-4)
O (-3,-4)
0 (-4,-3)
O (-4.3)

Answers

We can use the equation of tangent as a structure.

[tex]y - f(a) = f'(a)(x - a)[/tex]

Our f(a) is y-point and Our a is x-point..

Looking back at the equation, our f(a) would be 3 and a would be - 4

Therefore the answer is (-4,3)

Rewrite as a simplified fraction 2.67 repeating

Answers

265/99, is what I think but I’m not sure

An isosceles triangle has two sides of equal length, a, and a base, b. The perimeter of the triangle is 15.7 inches, so the equation to solve is 2a + b = 15.7.
Which lengths make sense for possible values of b? Check all that apply.
–2 in.
0 in.
0.5 in.
2 in.
7.9 in.

Answers

Answer:

0.5 in, 2 in

Step-by-step explanation:

It cannot be a negative number, so -2 is out.If we use Pythagorean's theorem ([tex]a^2+b^2=c^2[/tex]), we know that only 0.5 and 2 are correct values of b.

A new pair of boots is priced at $123.75, plus 6% sales tax. What is the total cost of the boots?

Answers

Answer:

131.18

Step-by-step explanation:

Which equation can be used to represent the distance D for the times t given in the table?

Answers

Answer: D

Step-by-step explanation:

If you spend 3$ on 6 apples,what is the unit rate (in dollars) per apple?

Answers

Answer

2 apples per $1

Step-by-step explanation:

because 6 apples cost $3, so take 6 divided by 3 so you get 2 apples per dollar

$Ok so there is $6 per apple

Fiteen packs of fruit snacks cost $3. How much do 5 paxks of fruit snack cost?​

Answers

15/3 = 5/x

15x = 15

X = $1

Allen has a 75 yard spool of yarn. He needs to cut the spool of yarn into 6 1/4
yard pieces of yarn.
How many 6 1/4
yard pieces of yarn can Allen create from the 75 yard spool of yarn?

A. 6 pieces

B. 12 pieces

C. 20 pieces

D. 36 pieces

Answers

Answer:

B. 12 pieces

Step-by-step explanation:

75 / 6 1/4 or 75 / 6.25 = 12

Answer:

b (12)

Step-by-step explanation:

The table below represents a linear function f(x) and the equation represents a function g(x):



Part A: Write a sentence to compare the slope of the two functions and show the steps you used to determine the slope of f(x) and g(x). (6 points)

Part B: Which function has a greater y-intercept? Justify your answer. (4 points)

(10 points)

Answers

Answer:

Step-by-step explanation:

Part A

for f(x) slope between points (-1,-6) and (1,0)

m= y2-y1/x2-x1 = -6-0/-1-1 = -6/-2= 3

for g(x) slope m=4 because we compare to equation y=mx+b the given equation g(x)=4x-5

The slope of f(x) is 3 and the slope g(x) is 4 so the line of g(x) is steeper

part B

The y intercept for g(x) is  (0, -5)

The equation of f(x) can be found

y-y1 =m(x-x1) take any point for example point (1,0)

y-1 =3(x-0)

y=3x+1 so the y-intercept is at (0,1)

The y-intercept for f(x) is greater at y=1 then the one of g(x) at y=-5

A. 2x+5=23
B. x+2+5=23
C. x+x+5=23
D. 5x+2=23

Answers

Answer:

b

Step-by-step explanation:

lucky guess

Answer:

your answer is A

Step-by-step explanation:

if you look at the amount of "x's " you have , you put them together and you will get 2x and you add 5 and your answer 23...

hopefully i was helpful

A recipe for 1 batch of spice mix says, “Combine 3 teaspoons of mustard seeds, 5 teaspoons of chili powder, and 1 teaspoon of salt.” How many batches are represented by the diagram? Explain or show your reasoning.

Answers

Answer:

There is no diagram for our observation. Please refine your question next time.

Step-by-step explanation:

15PTS PLEASE HELP ASAP!
(dont write random answers pls)
look at the pic attached:

Answers

Answer:

Triangle RST is an equilateral triangle.

Step-by-step explanation:

All three sides of the triangle are of equal length, therefore, because an isosceles triangle is when 2 sides of the triangle are the same length, a scalene triangle being when all sides are of different lengths, and a right triangle having a right angle (a 90 degree angle), this only leaves equilateral, all three sides being the same length, like in the triangle shown.

Select the correct answer. What is the value of this expression if h = 8, j = -1, and k = –12?

Answers

Answer:

the answer is 12 thankyou lorcolantro for wasting our time

Step-by-step explanation:

ya lorcolantro you made me F

The value of the given expression j³k/h⁰ at h = 8, j = -1, and k = –12 will be 12 so option (B) will be correct.

What is an expression?

A mixture of variables, numbers, addition, subtraction, multiplication, and division are called expressions.

An expression is a mathematical proof of the equality of two mathematical expressions.

A statement expressing the equality of two mathematical expressions is known as an equation.

Given the expression is

j³k/h⁰

Substituting h = 8, j = -1, and k = –12 into the expression

(-1)³(-12)/(8)⁰ = -1 × (-12)/1 = 12

Hence " The value of the given expression j³k/h⁰ at h = 8, j = -1, and k = –12 will be 12".

To learn more about expression,

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Solve for w.

−(1/4w+8)+8=3

w=134
w = 52
w=−34
w=−12

Answers

Solve for w by simplifying both sides of the equation, then isolating the variable.

D. w = −12

Find the value of x.

Answers

You have to combine your liked terms first
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