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morpeh [17]
2 years ago
10

Can anyone answer this question? I'll be giving 100 points, and mark brainliest to the best answer!!

Mathematics
2 answers:
Temka [501]2 years ago
8 0

Answer:

see below

Step-by-step explanation:

<APR and < PRD are  alternate interior angles, when lines APB and CRD are parallel, alternate interior angles are equal

<APR = < PRD

62+x =115

Subtract 62 from each side

62+x-62 = 115-62

x =53

nasty-shy [4]2 years ago
4 0
X=53 here is your answer and plsss mark me as a brainliest
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The vertices of a parallelogram are A(x1, y1), B(x2, y2), C(x3, y3), and D(x4, y4). Which of the following must be true if paral
Iteru [2.4K]

The answer is really none of the above, because all of these have divisions by difference in x, and there are perfectly fine rectangles where those will mean dividing by zero.

To do the problem the way they want us to, we note segments with the same slope are parallel (or collinear); segments with slopes which multiply to -1 are perpendicular.

Let's figure out what each choice is trying to tell us by translating it into parallel and perpendicular. Remember A is point 1, ...

A. ((y_4-y_3)/(x_4-x_3)= (y_3-y_2)/(x_3-x_2)) and ((y_4-y_3)/(x_4-x_3)×(y_3-y_2)/(x_3-x_2))=-1

translated, that's CD║BC and CD⊥BC - contradictory; second half right

B. (y_4-y_3)/(x_4-x_3)= (y_2-y_1)/(x_2-x_1) and ((y_4-y_3)/(x_4-x_3)×(y_2-y_1)/(x_2-x_1))=-1

CD ║ AB and CD ⊥ AB - only the parallelogram half is right

C. (y_4-y_3)/(x_4-x_3)= (y_2-y_1)/(x_2-x_1) and (y_4-y_3)/(x_4-x_3)×(y_3-y_2)/(x_3-x_2)=-1

CD║AB and CD⊥BC - that's TRUE

D. (y_4-y_3)/(x_4-x_3)= (y_3-y_1)/(x_3-x_1) and (y_4-y_3)/(x_4-x_3)×(y_2-y_1)/(x_2-x_1)=-1

CD║AC and CD⊥AB - nope

Answer: C

The way I'd get the proper expression is with the dot product.

A parallelogram is a rectangle when adjacent sides are perpendicular. It only takes one right angle to make them all right.

Two sides are perpendicular when the dot product of their direction vectors is zero. All the answers have y_4 - y_3 so one side is CD. The other side must be BC or AD; AD would give y_4 - y_1 terms which don't appear among the answer, so let's go with BC.

The direction vectors are

D-C = (x_4 - x_3, y_4 - y_3)

C-B = (x_3 - x_2, y_3 - y_2)

For perpendicularity we need a zero dot product:

0 = (D-C)\cdot(C-B) = (x_4 - x_3)(x_3 - x_2) + (y_4 - y_3)(y_3 - y_2)

- (x_4 - x_3)(x_3 - x_2) = (y_4 - y_3)(y_3 - y_2)

That's the correct expression, given it's a parallelogram, to demonstrate it's a rectangle. The divisions make it iffy.

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3 years ago
Are cracks in rock mechanical or chemical weathering
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Answer: Chemical weathering
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A right angle intersects a line at point M.Which statement is true about angles 1 and 2They are congruent.
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Step-by-step explanation:

4 0
3 years ago
A=1/4 and b=6.<br><br> −8ab=
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Answer:

When a=\frac{1}{4} and b=6:

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Step-by-step explanation:

-8ab can be seen as -8×a×b. Insert the given values:

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Simplify multiplication from left to right:

-8*\frac{1}{4} \\\\\frac{-8}{1} *\frac{1}{4} =\frac{-8}{4} =-2

Insert and solve:

-2*6=-12

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Instructions: Solve the following equation for the variable given.
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x = -1

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