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11111nata11111 [884]
2 years ago
5

Find the equation that represents the relationship between the variables.

Mathematics
1 answer:
galben [10]2 years ago
3 0

to get the equation of any straight line, we simply need two points off of it, hmmm let's use (0 , 10) and (8 , 30) from the table

(\stackrel{x_1}{0}~,~\stackrel{y_1}{10})\qquad (\stackrel{x_2}{8}~,~\stackrel{y_2}{30}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{30}-\stackrel{y1}{10}}}{\underset{run} {\underset{x_2}{8}-\underset{x_1}{0}}}\implies \cfrac{20}{8}\implies \cfrac{5}{2}

\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{10}=\stackrel{m}{\cfrac{5}{2}}(x-\stackrel{x_1}{0}) \\\\\\ y-10=\cfrac{5}{2}x\implies y=\cfrac{5}{2}x+10

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Nastasia [14]

Answer:

Pipe 1 alone fills a tank in 10 min

Pipe 2 alone fills the tank in 20 min

If both are turned on together, how long will it take to fill the tank???

Pipe 1 fills at the RATE of 1/10th tank per min

Pipe 2 fills at the RATE of 1/20th tank per min

Pipe 1 + Pipe 2 fills at the rate of 1/10+1/20 or 3/20th tank per min

Let x= time to fill the tank

(3/20)(x)=1 Where 1 denotes a full tank (Multiply both sides by 20)

3x=20

x=6 2/3 min----------both working together

NOW YOUR PROBLEM

Let x= amount of time for smaller pipe to fill the tank

Then (x-5)=amount of time for larger pipe to fill the tank

NOW HERE'S WHERE THE RECIPROCAL COMES IN:

The smaller pipe fills the tank at the RATE of 1/x cu units per min

The larger tank fills the tank at the RATE of 1/(x-5) cu units per min

Together, they fill the tank at the rate of 1/x+(1/(x-5)) cu units per min

But now we are told that together the fill the tank in 11 1/9 minutes. so our equation to solve is:

(1/x+(1/(x-5))(11 1/9)=1 where 1 denotes a full tank. In fact, in each of the above reciprocals, the 1 denotes a full tank.

So, dividing both sides by 11 1/9, we get:

1/x+(1/(x-5)=1/(11 1/9)-------------- which is your equation

I assume that you have no problems solviing this eq.

Hope this helps----ptaylor

Step-by-step explanation:

7 0
3 years ago
Find the hypotenuse of a right triangle with legs measuring 4 and 5ft
tangare [24]
The hypotenuse would be square root of 41
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4 years ago
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Viktor [21]
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3 years ago
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Lena [83]

The value of h(8) in h(x)= 6x - 17 is 31

<h3></h3>

What are functions:

Functions relate input and output. Therefore, a function takes elements from a set (the domain) and relates them to elements in a set (range).

h(x)= 6x - 17

Let's find h(8)

h(8) = 6(8) - 17

h(8) = 48 - 17

h(8) = 31

learn more on function here:brainly.com/question/15615479?referrer=searchResults

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Answer:

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