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3 years ago

∠C and ∠D are vertical angles with m∠C=−2x+90 and m∠D=x−30 . What is m∠D ?

1 answer:

5 0

∠C = ∠ D (vertical angles

C= -2x + 90
D= x-30

Since C = D , Then -2x + 90 = x-30

-2x - x = - 30 - 90

-3x = -120

3x = 120 and x = 40°. Now replace x by 40 in any of the equality, say :
D = x-30 ; D = 40 - 30 and D = 10°

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Maria's height while jumping on a a trampoline can be modeled by the equation h=-16t^2+18t+5. Where t=time in seconds and h=heig

Vadim26 [7]

Answer:

10.06 ft

Step-by-step explanation:

Maria's maximum height will occur when her velocity reaches zero (0). This means that she has stopped ascending and is about to begin descent.

The equation for the height reached by Maria on the trampoline is given as:

$h=-16t^2+18t+5$

To find her maximum height, we first have to find the time it will take her to get to that height and corresponding velocity (zero).

Her velocity can be found by differentiating her height i.e. dh/dt:

$v = \frac{dh}{dt} = -32t + 18$

Therefore, when v = 0:

$0 = -32t+ 18\\\\=> 32t= 18\\\\t = 18 / 32 = 0.5625 secs$

It takes her 0.5625 seconds to get to her maximum height.

Therefore, her height at that time (0.5625 seconds) is:

$h=-16(0.5625)^2+18(0.5625)+5\\\\h = -16 * (0.3164) + 10.125+5\\\\h = -5.0624 + 15.125\\\\h = 10.06 ft$

Therefore, her maximum height is 10.06 ft.

3 0

3 years ago

Find the area of the shape shown below.

mina [271]

Answer:

28 square units

Step-by-step explanation:

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3 years ago

Find the midpoint of the line segment shown below.

balu736 [363]

Answer:

x²-6x+y²-4y=-4

Step-by-step explanation:

We know the circle equation stands like this:

(x-a)² + (y-b)² = R²

and (a,b) is center

and R stands for Radius

so in this case:

center = (3,2)

R = 3

(x-3)² + (y-2)² = 9

x²-6x+9 + y²-4y+4=9

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2 years ago

An assistant cook peeled 18 potatoes in 6 minutes. At this rate, how many potatoes can he peel in 50 minutes?

malfutka [58]

Answer:

$150$ potatoes

Step-by-step explanation:

Since the assistant can peel $18$ potatoes in $6$ minutes, we know that he can peel $\frac{18}{6}=3$ potatoes in $1$ minute. Therefore, he will be able to peel $3*50=150$ potatoes in $50$ minutes. Hope this helps!