How do you know if two quantities vary directly?

1 answer:

6 0

Write an equation to model this situation. Then complete the input-output table below; and graph the equation on the coordinate plane provided. If two quantities x and y are directly proportional to one another, (meaning if x is doubled, so is y; if x is tripled, so is y), they show direct variation.

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What percent of 300 is 67?

Sav [38]

The answer would be 22.33 hope this helped

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3 years ago

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Jasper and Corey have saved up a total of $78.00. Jasper has saved 6 dollars more than twice as much as Corey. How much has Core

Novay_Z [31]

Answer:

24 is the answer..for this concept

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3 years ago

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sarah can complete a project in 90 minutes and her sister betty can complete it in 120 minutes if they both work on the project

alukav5142 [94]

Answer:

It will take them approximately 51.43 minutes to complete the project together

Step-by-step explanation:

This is what is called a "shared job" problem.

The best way to work on them is to start by finding the "portion" of the job done by each of the people in the unit of time.

So, for example, Sarah completes the project in 90 minutes, so in the unit of time (that is 1 minute) she completed 1/90 of the total project

Betty completes the project in 120 minutes, so in the unit of time (1 minute) she completes 1/120 of the total project.

We don't know how long it would take for them to complete the project when working together, so we call that time "x" (our unknown).

Now, when they work together completing the entire job in x minutes, in the unit of time they would have done 1/x of the total project.

In the unite of time, the fraction of the job done together (1/x) should equal the fraction of the job done by Sarah (1/90) plus the fraction of the job done by Betty. This in mathematical form becomes:

$\frac{1}{x} =\frac{1}{90} +\frac{1}{120}\\\frac{1}{x} =\frac{4}{360} +\frac{3}{360}\\\frac{1}{x} =\frac{7}{360} \\x=\frac{360}{7} \\x=51.43\,\,min$

So it will take them approximately 51.43 minutes to complete the project together.

8 0

3 years ago

(x÷(y÷z))÷((x÷y)÷z) also the variables are not specified.

Bumek [7]

The answer is: z² .
__________________________
Given: (x÷(y÷z))÷((x÷y)÷z) ; without any specified values for the variables;
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we shall simplify.
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We have:
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(x÷(y÷z)) / ((x÷y)÷z) .
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Start with the first term; or, "numerator": (x÷(y÷z)) ;
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x ÷ (y / z) = (x / 1) * (z / y) = (x * z) / (1 *y) = [(xz) / y ]
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Then, take the second term; or "denominator":
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((x ÷ y) ÷z ) = (x / y) / z = (x / y) * (1 / z) = (x *1) / (y *z) = [x / (zy)]
_________________________________________
So (x÷(y÷z)) / ((x÷y)÷z) = (x÷(y÷z)) ÷ ((x÷y)÷z) =

[(xz) / y ] ÷ [x / (zy)] = [(xz) / y ] / [x / (zy)] =
[(xz) / y ] * [(zy) / x] ;
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The 2 (two) z's "cancel out" to "1" ; and
The 2 (two) y's = "cancel out" to "1" ;
______________________________________________
And we are left with: z * z = z² . The answer is: z² .
______________________________________________

4 0

3 years ago

The measure of one angle is 7 times the measure of its complement.Find each angle measure

aleksklad [387]

let the angles be x and y.
as they are compliment
x+y=90
also given
x=7y

substituting value of x in first equation
7y+y=90
8y=90
therefore
y=11.25
x=7*y=78.75

7 0

3 years ago