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3 years ago

10

It takes Ben 32 minutes to run 3 miles. At this rate, how long will it take him to run 8 miles?

1 answer:

morpeh [17]3 years ago

3 0

96 minutes because of

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$180^o-112^o=68^o$

$\left\{\begin{array}{ccc}2x+3y=68&|\cdot(-15)\\30x+11y=112\end{array}\right\\\underline{+\left\{\begin{array}{ccc}-30x-45y=-1020\\30x+11y=112\end{array}\right}\\.\ \ \ \ \ \ \ -34y=-908\ \ \ |:(-34)\\\\.\ \ \ \ \ \ \ \ \ \ \ y=\dfrac{908}{34}\to y=\dfrac{454}{17}\\\\2x+3\cdot\dfrac{454}{17}=68\ \ \ \ |\cdot17\\\\34x+1362=1156\ \ \ \ |-1362\\34x=-206\ \ \ \ |:34\\\\x=-\dfrac{206}{34}\to x=-\dfrac{103}{17}\\\\ \left\{\begin{array}{ccc}x=-\dfrac{103}{17}\\\\y=\dfrac{454}{17}\end{array}\right$

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3 years ago

Determine if the sequence is arithmetic. If it is, find the term named in the problem.

Brums [2.3K]

Answer:

$a_{39}$ <em>= 279</em>

Step-by-step explanation:

$a_{n}$ = $a_{1}$ + (n - 1)d

d = $a_{2}$ - $a_{1}$

~~~~~~~~~

d = - 17 + 25 = - 9 + 17 = - 1 + 9 = 8

$a_{39}$ = - 25 + 8(39 - 1) = 279

$a_{39}$ <em>= 279</em><em> </em>

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