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3 years ago

What is the x-coordinate of the solution to the system?

Mathematics

1 answer:

Alex787 [66]3 years ago

3 0

Answer:

D. -3

Step-by-step explanation:

Graph the two equations, find where they intersect, (-3,7), find the x-coordinate. (-3)

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Write the equation of the perpendicular bisector of . Point B is located at (–3, 1), and point C is located at (1, 5).

maxonik [38]

The equation of perpendicular bisector of BC is

$y=-x+2$

Further explanation:

A perpendicular bisector passes through the mid-point of a line so to get an ordered pair from which the perpendicular bisector will pass we need to find the mid-point of BC.

$Mid-point = (\frac{x_1+x_2}{2} , \frac{y_1+y_2}{2} )\\Here\\(x_1,y_1) = (-3,1)\\(x_2,y_2) = (1,5)\\Putting\ values\ in\ formula\\M = (\frac{-3+1}{2} , \frac{1+5}{2} )\\= (\frac{-2}{2} ,\frac{6}{2})\\= (-1, 3)$

So the perpendicular bisector will pass through (-1,3)

Let m1 be the slope of BC

Then

$m_1 = \frac{y_2-y_1}{x_2-x_1} \\=\frac{5-1}{1+3} \\=\frac{4}{4}\\ =1$

Let m2 be the slope of perpendicular bisector

We know that the product of slopes of perpendicular lines is -1.

$m_1.m_2 = -1\\1*m_2 = -1\\m_2 = -1$

The standard form of point-slope form of line is:

$y=mx+b$

Putting the value of slope of bisector we get

$y=(-1)(x)+b\\y=-x+b$

To find the value of b, put the ordered pair (-1,3) in the equation

$3 = -(-1) +b\\3= 1+b\\3-1 =b\\b=2\\$

Putting the values of m and b in standard form

$y=-x+2$

Hence the equation of perpendicular bisector of BC is

$y=-x+2$

Keywords: Perpendicular bisector, Point-slope form

Learn more about point-slope form at:

#LearnwithBrainly

6 0

3 years ago

Solve |2x + 1| = 10<br> {9/2, 11/2}<br> {-9/2, 9/2}<br> {-11/2, 9/2}

prisoha [69]

The answer is -11/2, 9/2

Explanation

You have to rewrite the absolute value equation as two separate equations.
2x+1=10
2x+1=-10

Then you solve for X in each equation.
2x+1=10 would give you 9/2

2x+1=-10 would give you -11/2

So your final solutions would be x1= -11/2 x2= 9/2

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3 years ago

Lily solve the equation 3x-10= -3x+8. The explanation of her process is shown. Select the text that shows an error in her proces

MrMuchimi

Answer:sbutaraction property of equality

Step-by-step explanation:

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3 years ago

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lara [203]

Step-by-step explanation:

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3 years ago

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DochEvi [55]

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Sally works for in a week = 16 hours.

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