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3 years ago

How many solutions does the system y = 6x + 6 and y = 6(x + 1) have? Explain your answer.

Mathematics

1 answer:

AlladinOne [14]3 years ago

4 0

Answer:

(-∞,∞)

infinite

Step-by-step explanation:

y= 6x+6; y=6(x+1)

Eliminate the equal sides of each equation and combine

6x+6 = 6(x+1)

solve 6x+6 = 6(x+1) for x

simplify 6(x+1)

apply the distributive property

6x+6 = 6x+ 6*1

multiply 6 by 1

6x+6 = 6x+6

move all terms containing x to the left side of the equation

6=6

and since 6=6, the equation will always be true

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write and equation for the line in point-slope form that passes through (2,-5) and is perpendicular to the line 2x-4y+8=0

Ivenika [448]

bearing in mind that perpendicular lines have negative reciprocal slopes, hmmm what's the slope of the equation above?

$\bf 2x-4y+8=0\implies -4y=-2x-8\implies y = \cfrac{-2x-8}{-4} \\\\\\ y = \cfrac{-2x}{4}-\cfrac{8}{-4}\implies y = \stackrel{\stackrel{m}{\downarrow }}{-\cfrac{1}{2}}x+2\qquad \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array} \\\\[-0.35em] ~\dotfill$

$\bf \stackrel{\textit{perpendicular lines have \underline{negative reciprocal} slopes}} {\stackrel{slope}{-\cfrac{1}{2}}\qquad \qquad \qquad \stackrel{reciprocal}{-\cfrac{2}{1}}\qquad \stackrel{negative~reciprocal}{\cfrac{2}{1}\implies 2}}$

so we're really looking for the equation of a line whose slope is 2 and runs through (2,-5),

$\bf (\stackrel{x_1}{2}~,~\stackrel{y_1}{-5})~\hspace{10em} \stackrel{slope}{m}\implies 2 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-5)}=\stackrel{m}{2}(x-\stackrel{x_1}{2}) \\\\\\ y+5=2x-4\implies y=2x-9$

4 0

3 years ago

If a + b = 15, find the maximum value of a × b

Otrada [13]

Answer: 56

Step-by-step explanation:

8 0

3 years ago

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Anybody help me please!!!!!!!!!!!!!!!

Elodia [21]

Answer:

Reflection over the X axis.

8 0

3 years ago

Find the missing length indicated

zhannawk [14.2K]

Answer:

x = 135

Step-by-step explanation:

The three triangles are similar.

144/y = y/81

y^2 = 144 * 81

y = 12 * 9

y = 108

81^ + 108^2 = x^2

x^2 = 18225

x = 135

8 0

3 years ago

A workman received $110 for working 20 hours. At the same rate of pay, how many hours must he work to earn $187?

Andreyy89

Answer:

He must work 34 hours

Step-by-step explanation:

187×20= 3740

3740÷110= 34

7 0

3 years ago