an electrition charged $70 for 2 hours of work and 115 for 5hours of work write an equtionto find the cost for y and xk

1 answer:

7 0

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

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

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.

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Triangle XYZ was dilated by a scale factor of 2 to create triangle ACB and cos ∠X = 2 and 5 tenths over 5 and 59 hundredths.

Maru [420]

Based on the above, the Triangle XYZ and ACB are known to be similar triangles since tanX = tanA = 5 over 2 and 5 tenths;

Hence:

AC = 2 x XY
CB = 2 x YZ

<h3>What is the triangle about?</h3>

From the question given; Triangle XYZ is known to have been dilated by a scale factor of 2 to form a type of triangle known as triangle ACB, So therefore, XYZ and ACB are known to be the same or similar triangles.

Since Angles Y and C are known to both measure 90 degrees, and angles A and X are said to be congruent. Therefore:

tanX = tanA = 5 over 2 and 5 tenths

AC = 2 x XY

CB = 2 x YZ

For part B:

cosX=Base/Hypotenuse

cos A=AC/AB

AC = 2.05

AB = 5.59

Therefore, Based on the above, the Triangle XYZ and ACB are known to be similar triangles since tanX = tanA = 5 over 2 and 5 tenths;

Hence: