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3 years ago

Can someone please help me with this.

Mathematics

1 answer:

ad-work [718]3 years ago

4 0

Answer:

Step-by-step explanation:

1.Distribute

12x - 66 + 15 =21

2.Add the numbers

12x-51=21

3.Add 51 to both sides of the equation

12x -51 +51 = 21+51

4.Simplify

12x=72

5. Divide both sides of the equation by the same term

12x/12 = 72/12

6. Divide the numbers

x=6

And you have your answer x=6

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5. (01.07) Solve 3x - x + 2 = 12. (1 point)

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Answer:

x = 5

Step-by-step explanation:

Simplify. First, combine like terms:

3x - x + 2 = 12

(3x - x) + 2 = 12

(2x) + 2 = 12

2x + 2 = 12

Isolate the variable, x. Note the equal sign, what you do to one side, you do to the other. Do the opposite of PEMDAS.

PEMDAS =

Parenthesis

Exponents (& Roots)

Multiplication

Division

Addition

Subtraction

& is your order of operation.

First, subtract 2 from both sides:

2x + 2 (-2) = 12 (-2)

2x = 12 - 2

2x = 10

Next, divide 2 from both sides:

(2x)/2 = (10)/2

x = 10/2

x = 5

5 is your answer for x.

Check: Plug in 5 for x in the equation. Solve:

3(5) - (5) + 2 = 12

15 - 5 + 2 = 12

10 + 2 = 12

12 = 12 (True)

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The equation in slope-intercept form for the line that passes through the point ( -1 , -2 ) and is perpendicular to the line − 4 x − 3 y = − 5 is $y = \frac{3}{4}x - \frac{5}{4}$

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The slope intercept form is given as:

y = mx + c ----- eqn 1

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Given that the line that passes through the point ( -1 , -2 ) and is perpendicular to the line − 4 x − 3 y = − 5

Given line is perpendicular to − 4 x − 3 y = − 5

− 4 x − 3 y = − 5

-3y = 4x - 5

3y = -4x + 5

$y = \frac{-4x}{3} + \frac{5}{3}$

On comparing the above equation with eqn 1, we get,

$m = \frac{-4}{3}$

We know that product of slope of a line and slope of line perpendicular to it is -1

$\frac{-4}{3} \times \text{ slope of line perpendicular to it}= -1\\\\\text{ slope of line perpendicular to it} = \frac{3}{4}$

Given point is (-1, -2)

Now we have to find the equation of line passing through (-1, -2) with slope $m = \frac{3}{4}$

Substitute (x, y) = (-1, -2) and m = 3/4 in eqn 1

$-2 = \frac{3}{4}(-1) + c\\\\-2 = \frac{-3}{4} + c\\\\c = - 2 + \frac{3}{4}\\\\c = \frac{-5}{4}$

$\text{ substitute } c = \frac{-5}{4} \text{ and } m = \frac{3}{4} \text{ in eqn 1}$

$y = \frac{3}{4} \times x + \frac{-5}{4}\\\\y = \frac{3}{4}x - \frac{5}{4}$

Thus the required equation of line is found

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