$\bf \begin{array}{ccll} \stackrel{x}{hours}&\stackrel{y}{cost}\\ \cline{1-2} 2&70\\ 5&115 \end{array}~\hspace{10em}(\stackrel{x_1}{2}~,~\stackrel{y_1}{70})\qquad (\stackrel{x_2}{5}~,~\stackrel{y_2}{115}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{115-70}{5-2}\implies \cfrac{45}{3}\implies 15$

$\bf \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-70=15(x-2)\implies y-70=15x-30 \\\\\\ y=15x+40\impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}$

as you already know, a direct proportional variation has a constant of variation "k", y = kx, which in this case that'd be the slope, namely 15.

7 0

2 years ago

The product of two consecutive negative even integers is 24. Find the largest integer.

natali 33 [55]

Answer:

-4

Step-by-step explanation:

ok negative times negative = positive

and factors of 24 are

1,2,3,4,6,8,12,24

4 x 6 are the two consecutive EVEN numbers

so turn it to negative

-4 x -6 = 24

The largest is -4

3 0

2 years ago

-4 1/2, -5.6, -2 3/8, 2.35 from least to greatest

sweet-ann [11.9K]

Hello!

-2 3/8, -5.6, -4 1/2, 2.35.

Those are ordered from least to greatest!

I really hope you found this helpful! c:

8 0

3 years ago

Simplify by dividing negative three over eight divided by five over nine.

goblinko [34]

Answer:

$\frac{-27}{40}$

Step-by-step explanation:

First we need to write in correct form :

$\frac{-3}{8}:\frac{5}{9}$

We know how to divide fractions. If we can divide numerator by numerator, denominator by denominator, we just do it. In this example we can not do that.

So, we rewrite first fraction and multiply by reciprocal second ( numerator and denominator change place)

$\frac{-3}{8} *\frac{9}{5}$

Now, multiply numerator by numerator, denominator by denominator :

$\frac{-27}{40}$

8 0

2 years ago

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