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Helga [31]
3 years ago
11

An isosceles trapezoid with a perimeter of 42 inches. Each of the congruent non parallel sides is 5 inches long, and the trapezo

id is 3 inches tall. How long are the two parallel sides?
A. 10 in, 22 in
B. 16 in, 16 in
C. 10 in, 16 in
D. 12 in, 20 in
Mathematics
1 answer:
Ratling [72]3 years ago
8 0

Answer:

Longer - 20 in and Shorter - 12 in

Step-by-step explanation:

We know that when we subtract the shorter side from longer we get two cuts named  x:

2 x = a - b  => a - b = 2 x

One of this section ( x ) with height ( h ) and lateral (congruent non parallel) side ( c ) make right triangle, from which we get:

x² = c² - h²  and c = 5 in, h = 3 in

x² = 5² - 3² = 25 - 9 = 16 => x = √16 = 4 => x = 4 in

Now we will replace x = 4  in the equation  a - b = 2 · 4 = 8 and get first equation of the system.

a - b = 8

We also know that the formula for calculating perimeter is:

P = a + b + 2 c  where P = 42 in and c = 5 in

a + b = 42 - 2 · 5 = 42 - 10 = 32

Now  we get the second equation of the system:

a + b = 32

a - b = 8  

When we add first equation to the second we get:

2 a = 40 => a = 40 / 2 = 20 => a = 20 in

When we replace a = 20 in the first equation we get:

20 + b = 32  => b = 32 - 20 = 12 => b = 12 in

God with you!!!

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Answer:

It will take the boulder approximately 4.28 seconds to hit the road

Step-by-step explanation:

The given height of the cliff from which the boulder falls, h = 90 feet

The equation that can be used to find the time it takes the boulder to fall is h = u·t + (1/2)·g·t²

Where;

h = The height of the cliff = 90 ft.

u = The initial velocity of the boulder = 0 m/s (The boulder is assumed to be at rest when it falls)

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Plugging in the values gives;

90 = 0 × t + (1/2)×9.81×t² = 4.905·t²

∴ t = √(90/4.905) ≈ 4.28

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7 0
3 years ago
Help with 5b please . thank you.​
Allushta [10]

Answer:

See explanation

Step-by-step explanation:

We are given f(x)=ln(1+x)-x+(1/2)x^2.

We are first ask to differentiate this.

We will need chain rule for first term and power rule for all three terms.

f'(x)=(1+x)'/(1+x)-(1)+(1/2)×2x

f'(x)=(0+1)/(1+x)-(1)+x

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We are then ask to prove if x is positive then f is positive.

I'm thinking they want us to use the derivative part in our answer.

Let's look at the critical numbers.

f' is undefined at x=-1 and it also makes f undefined.

Let's see if we can find when expression is 0.

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So we should see increasing values of f when we up the value for x after 0.

Plugging in 0 gives: f(0)=ln(1+0)-0+(1/2)0^2=0.

So any value f, after this x=0, should be higher than 0 since f(0)=0 and f' told us f in increasing after x equals 0.

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