Mathematics Middle School

The variables x and y vary directly. Use the values to find the constant of proportionality, k. Then write an equation that relates x and y.

y=72; x=3

Answers

Answer 1

y = kx

Replace y and x to solve for k:

72 = 3k

Divide both sides by 3:

k = 24

Now replace k with 24:

y = 24x

Answer 2

The proportionality constant [tex]k=\frac{1}{24}[/tex], and the equation that relates [tex]x[/tex] and [tex]y[/tex] is [tex]x=\frac{1}{24}y\text{ or } y=24x[/tex]

Since [tex]x[/tex] and [tex]y[/tex] are related by direct proportion,

[tex]x \text{ }{\displaystyle \propto}\text{ }y \implies x=ky[/tex]

where [tex]k[/tex] is our proportionality constant. To find the value of [tex]k[/tex], substitute the values [tex]x=3\text{ and } y=72[/tex] into the formula, and solve for [tex]k[/tex].

[tex]x=ky\\\implies 3=72k\\\implies k=\frac{1}{24}[/tex]

Thus the equation that relates [tex]x[/tex] and [tex]y[/tex] is

[tex]x=\frac{1}{24}y\text{ or } y=24x[/tex]

Learn more about direct proportion here: https://brainly.com/question/908424

Related Questions

Question down below! 15 points and brainliest if you answer the question!

Answers

It’s the second option- no the triangles are not similar

Answer:

no

Step-by-step explanation:

3/4 is not eqal to 8/10

because in similar ratio of same sides are equal

help again. take ur time no rush. thank u to every one who answers my questions. u are appreciated i promise.

Answers

Answer:

52°

Step-by-step explanation:

If it is a right triangle, one interior angle is 90°, and we are also given the interior angle of 38°. The sum of any triangles interior angles will always be 180°.

90 + 38 = 128

180 - 128 = 52

The third angle is 52°

Answer:

52°

Step-by-step explanation:

they do too much with these hard questions

Answers

Answer:

it's either B or D but you would have to do the math

Step-by-step explanation:

i believe it is D but i don’t know how to do the math on here

Sally's mother wants to buy a cell phone. The price of the cell phone she wants increased this week from $200 to $240. What is the percent increase in the price of the cell phone?

Answers

Answer:

20 percent

Step-by-step explanation:

200 divided by 5 is 40

Ok so 200 + 40 is 240 but the percentage increase is 20% because because the new value is greater than the old value.

A can of grapefruit juice concentrate is 13 fluid oz. The recipe calls for a ratio of 2 cans of concentrate to 5 cans of cold water. How big of a pitcher do you need to make one batch of juice?

Answers

Answer:

You need a pitcher that can fit 91 fluid ounces.

Step-by-step explanation:

13 times 2 = 26

13 times 5 = 65

65 + 26 = 91

A pitcher that can hold 91 fluid ounces

Hope that helps

Answer all parts in the question below. Be sure to show all your work. Remember NO WORK, NO CREDIT EVEN IF THE ANSWER IS CORRECT!!!

13. A car travels 30 ⅕ miles in ⅔ of an hour. What is the average speed, in miles per hour, of the car?

Answers

I'm sorry I need the points lol anyways I hope you got the answer to it

Help me if you can it would be so helpful

Answers

Answer:135.80

Step-by-step explanation:

Find 40 percent of 97 then have an answer of 135.8 and add an zero because it’s money

Answer: $38.80


Multiply .4 by 97

This equals 38.80


The final cost of the sofa is 97-38.80= 58.20

plssssssssssssss help

Answers

What are the 7 & 9 for? Obviously, you had info from somewhere else for the 9 & 7 if they are THE ONLY NUMBERS here

r 2x-6+3=6x-5 please help

Answers

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[tex]2x - 6 + 3 = 6x - 5[/tex]

[tex]2x - 3 = 6x - 5[/tex]

[tex]6x - 5 = 2x - 3[/tex]

Add sides 5

[tex]6x - 5 + 5 = 2x - 3 + 5[/tex]

[tex]6x = 2x + 2[/tex]

Subtract sides 2x

[tex] - 2x + 6x = - 2x + 2x + 2[/tex]

[tex]4x = 2[/tex]

Divide sides by 4

[tex] \frac{4x}{4} = \frac{2}{4} \\ [/tex]

[tex]x = \frac{1}{2} \\ [/tex]

_________________________________

CHECK :

[tex]2( \frac{1}{2} ) - 3 = 6( \frac{1}{2} ) - 5 \\ [/tex]

[tex]1 - 3 = 3 - 5[/tex]

[tex] - 2 = - 2[/tex]

Thus the solution is correct....

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Ok so if this is basic algebra it should be x=-1

First combine like terms:

you can add 6 and 3 in 2x-6+3

2x-9=6x-5

Second get x alone:

you can add 9 to both sides and get

2x=6x+4

then you can subtract 6 from both sides which would leave you

-4x=4

finally divide -4 from both sides and you get

x=-1

I hope this helps! Have a nice day or night :)


Help me pls I’m begging

Answers

Answer:

1. -4,-3,-1,0,4,5,6

2.-15,-12,-5,-2,0,8,9

Step-by-step explanation:

good luck!!! if that’s not right lmk

can anyone help me on this?

Answers

Answer:

First row is -2,0,-1,0,2,1. Second row is 15,5,-15,9,9,3. and they are in the correct order I put them in. The first number is the first equation.

Step-by-step explanation:

A block of clay contains twenty 4 - ounce portions of clay. Ceramics teacher wants to use the block to make as many spheres of clay as possible. Each weighing ⅖ pound. How Many spheres can the class make

Answers

Answer:

12.5

Step-by-step explanation:

20 x 4 = 80

80 ÷ 16 = 5

5 ÷ 2/5 = 12.5

Using 24 ounce portions of clay, maximum they can make 3 spheres.

Given that, a block of clay contains 24 ounce portions of clay.

What is metric conversion?

Metric Conversion refers to the conversion of the given units to desired units for any quantity to be measured.

We know that, 1 pound = 16 ounces

So, 1 ounce = 1/16 pound

Then 24 ounce = 24/16

= 1.5 pound

Here, each sphere of clay weighing 2/5 = 0.4 pounds

Number of spheres = 1.5/0.4

= 3.75

Maximum 3 spheres

Therefore, using 24 ounce portions of clay, maximum they can make 3 spheres.

To learn more about the metric conversion visit:

brainly.com/question/21244256.

#SPJ2

Can someone please explain the Slope formula? Don't quite get it. I'm working on edge Physical science grade 8

Answers

Answer:

ok is that a question or not but if it is i may be help u

Answer:What About y = mx + b ? You may already be familiar with the "y=mx+b" form (called the slope-intercept form of the equation of a line). It is the same equation, in a different form! The "b" value (called the y-intercept) is where the line crosses the y-axis.

Step-by-step explanation:

Find the expressions that have a quotient of 7 R12. choose all that apply

A. 362÷50
B.408÷60
C.492÷50
D.432÷60
E420÷60
F.502÷70

Answers

Answer:

Try D. I am not exactly sure but let's hope it works.

Step-by-step explanation:

Answer:

Its D.

Step-by-step explanation:

Almost 100% sure

Brainliest to the correct answer. Im stuck more on the question rather than the problem solving at hand if you know what i mean(if not just answer the question pls)

Answers

Answer:

0.17

Step-by-step explanation:

the answer is 0.17
have a good day!

I need help ASAP!!!!!!!! PLEASE CORRECT ANSWER!
A student writes an incorrect step while checking if the sum of the measures of the two remote interior angles of triangle ABC below is equal to the measure of the exterior angle.

A triangle ABC is shown. The base of the triangle extends into a straight line. The angle formed between this straight line and the edge of the triangle is marked as w. The angle adjacent to w is marked as z, and the other two angles inside the triangle are marked as x and y.
Step 1: m∠x + m∠y + m∠z = 180 degrees (sum of angles of a triangle)
Step 2: m∠w − m∠z = 90 degrees (corresponding angles)
Step 3: Therefore, m∠x + m∠y + m∠z = m∠w + m∠z
Step 4: So, m∠x + m∠y = m∠w

In which step did the student first make a mistake and how can it be corrected? (5 points)

Select one:
a. Step 1; it should be m∠x + m∠y + m∠z = 180 degrees (sum of corresponding angles)
b. Step 2; it should be m∠w + m∠z = 180 degrees (supplementary angles)
c. Step 1; it should be m∠x + m∠y + m∠z = 90 degrees (corresponding angles)
d. Step 2; it should be m∠w + m∠z = 90 degrees (alternate exterior angle)

Answers

Answer:

Step 2 D

Step-by-step explanation: Hopes this helps

Answer:

D is wrong

Step-by-step explanation:

Took the test

Pre-Algebra FLVS :)

help please and thank you!

Answers

Answer:

12 ounces.

Step-by-step explanation:

Dividing 48 by 4 gives you 12.

PLEASE MAKE SURE HELP ME!

Answers

Answer:

1. The first problem is wrong, it should be 0.5(3(15) + 2(20)) because the parentheses make sure that every purchased item is being divided by 2 (multiplying by 0.5 is the same as dividing by 2)

2. The second problem is partially correct. The first two answers you have checked are correct, but the last one is wrong. The third answer should be 6 + 12 instead because that's just a simplified version of 2(3) + 6(2), meaning they are equal

3. I cannot read your answers in the "Why or Why Not" column in the third problem, but the answers you gave in the "Evaluate" and "Does It Work?" columns are all correct.

A number is made up of 2 tens and 5 tenths.

A second number is made up of 6 ones and 8 hundredths.

A third number is made up of 2 tens and 6 hundredths.

A fourth number is made up of 5 ones and 8 tenths.

What is the difference between the greatest number and the least number?

Answers

Answer:

A:25

B:860

C:620

D;85

E:

the difference is 835!
860-25=835

A hot air balloon is at elevation of 650 feet. After it descends 120 feet, what is the elevation of the balloon?

Answers

Answer:

530

Step-by-step explanation:

Answer:

530

Step-by-step explanation:

650-120 decends means that its going down.

helppppppppp meeeeeeeeeeeee

Answers

The first question is (A) you can use demos the graphing calculator to help you with those problems.

That's all I know lol

Answer:

I THINK THE CORDINATES ARE (4,1)

Step-by-step explanation:

I MIGHT BE WRONG AND IF SO I AM SORRY

Help MMEEEE PLKEASEEss.

Answers

Answer:

the answer is180.

Step-by-step explanation:

180 is the answer, hope this helps

rewrite the numbers in order from least
to greatest. -45/10, 3/1000, -0.005, 0.34

Answers

Answer:

-45/10  -  -0.005   - 3/1000   -  0.34

Step-by-step explanation:

-45/10  -  -0.005   - 3/1000   -  0.34

1. How fast does Amy run?

2. Who runs the fastest

3. How fast does John run?

Answers

1. Amy runs 3 meters per second
2. They both run the same
3. John runs 3 meters per second

Answer:

Well. Amys rate is 3m/s. and John's is 3 m/s.

Step-by-step explanation:

No one runs faster than the other. It's equal. or I just read it completely wrong.

i need these asap ill give brainliest

Answers

5 1 4 2 I’m sure and I need at least 20 characters
Why u don’t use seamos?

Divide: 3/4 divided by 2/5

2 and 1/5

3 and 3/4

2 and 3/5

1 and 7/8

Answers

number 4. .75/.4=1.875

Answer:

1 and 7/8

Step-by-step explanation:

[tex]\frac{3}{4}[/tex] ÷ [tex]\frac{2}{5}[/tex]

When dividing you have to flip the second number. When the fraction/number flips the problem will turn into multiplication.

[tex]\frac{3}{4}[/tex] × [tex]\frac{5}{2}[/tex]

Now just multiply them. 3×5 and 4×2

[tex]\frac{15}{8}[/tex]

Simplify the fraction

[tex]1\frac{7}{8}[/tex]

I hope this helps!

Mrs. Canale’s class is selling frozen pizzas to earn money for a field trip. For every pizza sold, the class makes $5.35. They have already earned $182.90 toward their $750 goal. How many more pizzas must they sell to earn $750? Solve this problem first by using an arithmetic approach, then by using an algebraic approach. Compare the calculations you made using each approach

Answers

Answer:

106 more pizzas

Step-by-step explanation:

750-182.90

=567.1

567.1 / 5.35

=106

:) hope that helps

Answer:

170

Step-by-step explanation:

Estimate the percentage: 41 of 122
a. 0.3% c. 43.6%
b. 33.3% d. 3% Explain

Answers

Answer:

33.3%

Step-by-step explanation:

41/122 = approximately 0.333

Multiply this by 100 and you get your percent.

Answer:

b

Step-by-step explanation:

the answer is 33.61 but thats the closest

what was the ratio of sixth graders to fifth grade students on the team?

Answers

Answer: the ratio is 7:8

Step-by-step explanation:

Answer:

7:8 Sry if wrong.

Step-by-step explanation:

The Suarez family paid $15.75 for 3 movie tickets. How much would they have paid for 12 tickets?

Answers

Answer:

$63

Step-by-step explanation:

15.75 / 3 = 5.25

5.25 is what each ticket was worth

5.25 * 12 = 63

Answer:

$63

Step-by-step explanation:

15.75 divided by 3 = 5.25 then 12 * $5.25 = $63

Hope this helps! :>

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