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Mathematics

2 answers:

KiRa [710]3 years ago

7 0

Answer:

Step-by-step explanation:

replace y with 8

2(8)+7

16 + 7

Rufina [12.5K]3 years ago

6 0

Answer:

Step-by-step explanation:

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Write an equation of the line that passes through (18, 2) and is parallel to the line 3y−x=−12

miskamm [114]

keeping in mind that parallel lines have the same exact slope, hmmmm what's the slope of the line above anyway?

$\bf 3y-x=-12\implies 3y=x-12\implies y=\cfrac{x-12}{3}\implies y = \cfrac{x}{3}-\cfrac{12}{3} \\\\\\ y = \stackrel{\stackrel{m}{\downarrow }}{\cfrac{1}{3}}x-4\qquad \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}$

so we're really looking for the equation of a line whose slope is 1/3 and runs through (18,2)

$\bf (\stackrel{x_1}{18}~,~\stackrel{y_1}{2})~\hspace{10em} \stackrel{slope}{m}\implies \cfrac{1}{3} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{2}=\stackrel{m}{\cfrac{1}{3}}(x-\stackrel{x_1}{18}) \\\\\\ y-2=\cfrac{1}{3}x-6\implies y=\cfrac{1}{3}x-4$

3 0

3 years ago

A 16-inch candle is lit and burns at a constant rate of 0.8 inches per hour. Let t represent the number of hours since the candl

Tamiku [17]

Answer:

<h2>See the explanation.</h2>

Step-by-step explanation:

The initial length of the candle is 16 inch. It also given that, it burns with a constant rate of 0.8 inch per hour.

After one hour since the candle was lit, the length of the candle will be (16 - 0.8) = 15.2 inch.

After two hour since the candle was lit, the length of the candle will be (15.2 - 0.8) = 14.4 inch. The length of the candle after two hours can also be represented by {16 - 2(0.8)}.

Hence, the length of the candle after t hours when it was lit can be represented by the function, $f(t) = 16 - 0.8t$ . $f(t) = 0$ at t = 20.