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3 years ago

12

Find AM in the parallelogram

1 answer:

n200080 [17]3 years ago

5 0

Answer:

AM = 6

Step-by-step explanation:

Using the property of a parallelogram

• The diagonals bisect each other

MO is a diagonal, hence

AM = AO = 6

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You know the measure of the exterior angle which forms a linear pair with the vertex angle. Describe two ways you can find measu

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Answer:

Step-by-step explanation:

A linear pair are two given angles whose sum is equal to $180^{o}$ .

Let the exterior angle be represented by $x^{o}$ , and the three interior angles of the triangle be represented by $a^{o}$ , $b^{o}$ and $c^{o}$ .

Assume that the vertex angle $c^{o}$ is the linear pair to the exterior angle $x^{o}$ .

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Thus,

i. $a^{o}$ + $b^{o}$ = $x^{o}$ (sum of two opposite interior angles is equal to an exterior angle)

⇒ $a^{o}$ = $x^{o}$ - $b^{o}$

Also,

$b^{o}$ = $x^{o}$ - $a^{o}$

But,

$a^{o}$ + $b^{o}$ + $c^{o}$ = $180^{o}$ (sum of angles in a triangle)

⇒ $c^{o}$ = $180^{o}$ - ( $a^{o}$ + $b^{o}$ )

and

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ii. $a^{o}$ + $b^{o}$ + $c^{o}$ = $180^{o}$ (sum of angles in a triangle)

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3 years ago

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3 years ago

Benjamin threw a rock straight up from a cliff that was 48 ft above the water. If the height of the rock h, in feet, after t s

fomenos

Answer: It will take 4 seconds for the rock to hit the water.

Step-by-step explanation:

Given : Benjamin threw a rock straight up from a cliff that was 48 ft above the water.

If the height of the rock h, in feet, after t seconds is given by the equation

$h = -16 t^2+ 52 t + 48$

To find : Time taken for the rock to hit the water.

When rock hit the water height becomes zero , i.e. put h = 0 , we get

$-16 t^2+ 52 t + 48 =0$

Divide equation by 2 , we get

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The Laue of x for ax²+bx+c =0 is $x=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}$

So , $t=\frac{-26\pm\sqrt{(26^{2}-4(-8)(24))}}{2(-8)}$

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Since t cannot be negative , so t= 4

Hence, it will take 4 seconds for the rock to hit the water.

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3 years ago