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lana [24]
2 years ago
9

11. Given Triangle GHI with G(7, 0), H (-5, 5) and I (1, 9), find the slope of a line perpendicular to HI.

Mathematics
1 answer:
elena-14-01-66 [18.8K]2 years ago
5 0
First, you need to find the slope of HI.

Find two points. (On the line)

(-5,5) (1,9) I’m just going to use the points for H and I.

Plug it into the slope formula.

M= (y2-y1)/(x2-x1)

M= (9-5)/(1-(-5) Switch the sign to be positive, two negatives equal a positive.

M= 4/6

Now, you just need to find the opposite reciprocal for the slope of the perpendicular line.

Flip 4 and 6. Make it negative.

-6/4

Simplify.

-3/2 or -1.5

I hope this helps!
~kaikers
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Answer:

a) There is no solution to the equation.

b) Solution: x = 16

Step-by-step explanation:

Hi there!

a) Let´s write the equation:

√(x + 5) - 9 = -12

add 9 to both sides of the equation

√(x + 5) = -12 + 9

√(x + 5) = -3

Square both sides of the equation

x + 5 = 9

Subtract 5 to both sides

x = 9 - 5

x = 4

Let´s check the solution:

√(x + 5) - 9 = -12

√(4 + 5) - 9 = -12

√9 - 9 = -12

3 - 9 = -12

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Then x = 4 is not a solution to the equation.

b) Let´s write the equation:

√(4x - 7) = √(3x + 9)

square both sides of the equation  

4x - 7 = 3x + 9

subtract 3x and add 7 to both sides of the equation

4x - 3x = 9 + 7

x = 16

Let´s check the solution:

√(4x - 7) = √(3x + 9)

x = 16

√(4(16) - 7) = √(3(16) + 9)

√57 = √57

Then x = 16 is the solution to the equation

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