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Dafna11 [192]
2 years ago
15

1/2x-9=-25 what is your answer

Mathematics
1 answer:
Elodia [21]2 years ago
4 0
First, let's only the expression with x stay on the let side: let's add 9 to both sides of the equation.

\frac{1}{2} x-9+9=-25+9
which is
\frac{1}{2}x=-16


now, let's multiply everything by 2:

\frac{2}{2} x=-16*2
x=-32


so the answer is -32!

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Simplify both sides if needed. The left-hand side needs simplification.

4(x - 6) \leq -2x + 6
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All is left to do is add and subtract to get the x variable all alone.

4x - 24  \leq -2x + 6
6x - 24  \leq  6    <-- Add 2x to both sides
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x           \leq 5    <-- Divide both sides by 6

In order to be in the solution set, x has to be less than or equal to 5.

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Lines 3x-2y+7=0 and 6x+ay-18=0 is perpendicular. What is the value of a?
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\boxed{\sf a = 9 }

Step-by-step explanation:

Two lines are given to us which are perpendicular to each other and we need to find out the value of a . The given equations are ,

\sf\longrightarrow 3x - 2y +7=0

\sf\longrightarrow 6x +ay -18 = 0

Step 1 : <u>Conver</u><u>t</u><u> </u><u>the </u><u>equations</u><u> in</u><u> </u><u>slope</u><u> intercept</u><u> form</u><u> </u><u>of</u><u> the</u><u> line</u><u> </u><u>.</u>

\sf\longrightarrow y = \dfrac{3x}{2} +\dfrac{ 7 }{2}

and ,

\sf\longrightarrow y = -\dfrac{6x }{a}+\dfrac{18}{a}

Step 2: <u>Find </u><u>the</u><u> </u><u>slope</u><u> of</u><u> the</u><u> </u><u>lines </u><u>:</u><u>-</u>

Now we know that the product of slope of two perpendicular lines is -1. Therefore , from Slope Intercept Form of the line we can say that the slope of first line is ,

\sf\longrightarrow Slope_1 = \dfrac{3}{2}

And the slope of the second line is ,

\sf\longrightarrow Slope_2 =\dfrac{-6}{a}

Step 3: <u>Multiply</u><u> </u><u>the </u><u>slopes </u><u>:</u><u>-</u><u> </u>

\sf\longrightarrow \dfrac{3}{2}\times \dfrac{-6}{a}= -1

Multiply ,

\sf\longrightarrow \dfrac{-9}{a}= -1

Multiply both sides by a ,

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Divide both sides by -1 ,

\sf\longrightarrow \boxed{\blue{\sf a = 9 }}

<u>Hence </u><u>the</u><u> </u><u>value</u><u> of</u><u> a</u><u> </u><u>is </u><u>9</u><u> </u><u>.</u>

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B-y is the another factor
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