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2 years ago

We have 10 gallons of gas in the car. We use 1 5/8 gallons each hour. How many hours of gas do we have?

Mathematics

1 answer:

Sindrei [870]2 years ago

8 0

You have a little over 6 hours of gas.

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The value of

marusya05 [52]

$\large\underline{\sf{Solution-}}$

We have to find out the value of the fraction.

Let us assume that:

$\sf \longmapsto x =2 + \dfrac{1}{2 + \dfrac{1}{2 + \dfrac{1}{2 + ... \infty} } }$

We can also write it as:

$\sf \longmapsto x =2 + \dfrac{1}{x}$

$\sf \longmapsto x =\dfrac{2x + 1}{x}$

$\sf \longmapsto {x}^{2} =2x + 1$

$\sf \longmapsto {x}^{2} - 2x - 1 = 0$

Comparing the given equation with ax² + bx + c = 0, we get:

$\sf \longmapsto\begin{cases} \sf a =1 \\ \sf b = - 2 \\ \sf c = - 1 \end{cases}$

By quadratic formula:

$\sf \longmapsto x = \dfrac{ - b \pm \sqrt{ {b}^{2} - 4ac } }{2a}$

$\sf \longmapsto x = \dfrac{2 \pm \sqrt{ {( - 2)}^{2} - 4(1)( - 1)} }{2 \times 1}$

$\sf \longmapsto x = \dfrac{2 \pm \sqrt{4 + 4} }{2 \times 1}$

$\sf \longmapsto x = \dfrac{2 \pm \sqrt{8} }{2}$

$\sf \longmapsto x = \dfrac{2 \pm2 \sqrt{2} }{2}$

$\sf \longmapsto x = 1 \pm\sqrt{2}$

$\sf \longmapsto x = \begin{cases} \sf 1 + \sqrt{2} \\ \sf 1 - \sqrt{2} \end{cases}$

But "x" cannot be negative. Therefore:

$\sf :\implies x = 1 + \sqrt{2}$

So, the value of the fraction is 1 + √2.

4 0

2 years ago

No. Zachary should have drawn the first two arcs with the compass centered at B.

qaws [65]

Answer:

what's the question.. I'll help

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2 years ago

Which of the following is a type of data that is likely to be normally distributed?

kkurt [141]

It is either A or D, but I think it’s A

8 0

2 years ago

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What is the simplified expression for this ?

schepotkina [342]

Answer:

I think it is 14.1421356237. I needed you can round it down to 14.14.

5 0

2 years ago

Evaluate each expression when n = 4 and b = 7

alexgriva [62]

Answer:

1. 5 2. 31 3. 55

Step-by-step explanation:

1. 2(4)-3=8-3=5

2. 4(7)+3=28+3=31

3. 3(4)+8(7)-13=12+56-13=56-1=55

4 0

2 years ago

Read 2 more answers