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Thepotemich [5.8K]
3 years ago
7

Line M passes through points (2,-5) and (4, -3). Line N passes through points (-4, -8) and (-6,-6). Are lines M and N perpendicu

lar? Explain.
A. No, the lines are not perpendicular because the product of their slopes equals -1.

B. Yes, the lines are perpendicular because the product of their slopes equals-1.

C. No, their lines are not perpendicular because the product of their slopes does not equal-1.

D. Yes, the lines are perpendicular because the product of their slopes does not equal -1.
Mathematics
1 answer:
melamori03 [73]3 years ago
6 0

Answer:

Yes, the lines are perpendicular because the product of their slopes equals -1 ⇒ B

Step-by-step explanation:

The product of the slopes of the perpendicular lines is -1

So to prove that the lines are perpendicular let us find their slopes

The rule of the slope is:

m=\frac{y2-y1}{x2-x1} , where (x1, y1) and (x2, y2) are two points on the line

∵ Line M passes through points (2, -5) and (4, -3)

∴ x1 = 2 and x2 = 4

∴ y1 = -5 and y2 = -3

→ By using the rule of the slope above

∴ m=\frac{-3-(-5)}{4-2}=\frac{-3+5}{2}=\frac{2}{2}

∴ The slope of line M is 1

∵ Line N passes through points (-4, -8) and (-6, -6)

∴ x1 = -4 and x2 = -6

∴ y1 = -8 and y2 = -6

→ By using the rule of the slope above

∴ m=\frac{-6-(-8)}{-6-(-4)}=\frac{-6+8}{-6+4}=\frac{2}{-2}

∴ The slope of line N is -1

∵ 1 × -1 = -1

∴ The product of the slopes of lines M and N is -1

∴ Lines M and N are perpendicular

∴ Yes, the lines are perpendicular because the product of their

   slopes equals -1.

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4(c + d) -3c + 5d when c=1.5 and d= -6.2
patriot [66]

Answer:

-54.3

Step-by-step explanation:

4(1.5−6.2)−4.5−31

=(4)(−4.7)−4.5−31

=−18.8−4.5−31

=−23.3−31

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2 years ago
Triangle CDE is an isosceles triangle with angle d congruent to angle E if CD= 4x+9, DE= 7x-5, CE= 16x-27, find x and the measur
Montano1993 [528]
ANSWER

x = 3
CD= 21 \: units
DE= 16 \: units

CE= 21 \: units



EXPLANATION

It was given that ∆CDE is an isosceles triangle.

The length of the sides are given in terms of x as follows.

CD=4x+9


DE=7x-5


CE=16x-27



It was also given that, angle D is congruent to angle E.


This implies that, side CD and CE are equal.


Thus,

|CD|  =  |CE|
In terms of x, we have;

4x + 9 = 16x - 27


We group like terms to get,

16x - 4x = 9 + 27

12x = 36

Divide both sides by 12 to get,

x =  \frac{36}{12}

\therefore \: x = 3


The length of the sides are;

CD=4(3)+9 = 21 \: units

DE=7(3)-5 = 16 \: units


CE=16(3)-27 = 21 \: units
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Answer:

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