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Sav [38]
3 years ago
15

There are 3.79 L in every gallon how many liters of gas does a 13.6 gallon tank hold

Mathematics
1 answer:
Zinaida [17]3 years ago
4 0

Answer:

51.544 L  in our tank

Step-by-step explanation:

We have a 13.6 gallon tank

Our conversion factor is 3.79 L = 1 gallon.  We want liters on top since that is where we want to end up

3.79 L /1 gallon is what we want to use

13.6 * 3.79L/1 gallon = 51.544 L  in our tank

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The points A(1, 4), B(5,1) lie on a circle. The line segment AB is a chord. Find the equation of a diameter of the circle.
tangare [24]

Check the picture below.

well, we want only the equation of the diametrical line, now, the diameter can touch the chord at any several angles, as well at a right-angle.

bearing in mind that <u>perpendicular lines have negative reciprocal</u> slopes, hmm let's find firstly the slope of AB, and the negative reciprocal of that will be the slope of the diameter, that is passing through the midpoint of AB.

\bf A(\stackrel{x_1}{1}~,~\stackrel{y_1}{4})\qquad B(\stackrel{x_2}{5}~,~\stackrel{y_2}{1}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{1}-\stackrel{y1}{4}}}{\underset{run} {\underset{x_2}{5}-\underset{x_1}{1}}}\implies \cfrac{-3}{4} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{slope of AB}}{-\cfrac{3}{4}}\qquad \qquad \qquad \stackrel{\textit{\underline{negative reciprocal} and slope of the diameter}}{\cfrac{4}{3}}

so, it passes through the midpoint of AB,

\bf ~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ A(\stackrel{x_1}{1}~,~\stackrel{y_1}{4})\qquad B(\stackrel{x_2}{5}~,~\stackrel{y_2}{1}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left( \cfrac{5+1}{2}~~,~~\cfrac{1+4}{2} \right)\implies \left(3~~,~~\cfrac{5}{2} \right)

so, we're really looking for the equation of a line whose slope is 4/3 and runs through (3 , 5/2)

\bf (\stackrel{x_1}{3}~,~\stackrel{y_1}{\frac{5}{2}}) \stackrel{slope}{m}\implies \cfrac{4}{3} \\\\\\ \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}{\cfrac{5}{2}}=\stackrel{m}{\cfrac{4}{3}}(x-\stackrel{x_1}{3})\implies y-\cfrac{5}{2}=\cfrac{4}{3}x-4 \\\\\\ y=\cfrac{4}{3}x-4+\cfrac{5}{2}\implies y=\cfrac{4}{3}x-\cfrac{3}{2}

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Refer to the attachment.

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Two isosceles triangles are shown above. If b = 180-4a and a=35, What is the value of c?
Ymorist [56]

Answer:

a=35 given

b=40  

c=110

I couldn't complete see c. Please look at the picture to see what I assumed it to be.

Step-by-step explanation:

Hmmm... I guess a and b are not vertical.

We are given b=180-4a and a=35 so b=180-4(35)=180-140=40.

So b=40.

Isosceles triangles always have congruent base angles.  So let's call both of the base angles in the bottom triangle x.

That means x+x+40=180.

We need to solve this for x.

Combine like terms:

2x+40=180

Subtract 40 on both sides:

2x=140

Divide both sides by 2:

x=140/2

Simplify:

x=70

So I'm assuming that c and it's adjacent angle are sitting on a straightedge together which means 70+c=180.

70+c=180

Subtract 70 on both sides:

c=180-70

Simplify:

c=110

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