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WITCHER [35]
4 years ago
5

What is the solution of the equation? 4(y + 2) =32

Mathematics
2 answers:
ehidna [41]4 years ago
6 0
Hey there!
For the left side, we are going to use the distributive property, which means:
a(b+c) = ab+ac
Therefore, we have:

4y + 8 = 32

Subtract 8 from both sides.

4y = 24

Divide both sides by 4 to get:

y = 6

I hope this helped you! :)

galben [10]4 years ago
3 0
So you are solving for 'y'

You would follow this order so first look for Parentheses. You have some so you multiple 4 times everything in the parentheses.
4(y + 2)
4 and why can't really combine so you would just have 4y.

Then you would multiply 4 by 2 which is 8.

Your new equation should be...
4y + 8 = 32
You do not have exponents so the next thing to do is try to get 'Y' by itself.

You would minus 8 from both sides to cancel it out and your new equation should be...
4y = 24
The last thing to do is devide by 4 on both sides.

The answer will be
y = 6
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The equation h(t) = -16t² + 80t + 64 represented the height, in feet, of a potato t seconds after it has been launched.
Lyrx [107]

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Part A) The potato hit the ground at t=5.70 seconds (see the explanation)

Part B) The potato is 40 feet off the ground at the time t=5.28 seconds (see the explanation)

Step-by-step explanation:

we have

h(t)=-16t^2+80t+64

where

h(t) is the height of a potato in feet

t is the time in seconds

Part A)  Write an equation that can be solved to find when the potato hits the ground. Then solve the equation

we know that

When the potato hit the ground, the value of h(t) must be equal to zero

so

For h(t)=0

-16t^2+80t+64=0

Solve the quadratic equation

The formula to solve a quadratic equation of the form

ax^{2} +bx+c=0

is equal to

x=\frac{-b\pm\sqrt{b^{2}-4ac}} {2a}

in this problem we have

-16t^2+80t+64=0

so

a=-16\\b=80\\c=64

substitute in the formula

t=\frac{-80\pm\sqrt{80^{2}-4(-16)(64)}} {2(-16)}

t=\frac{-80\pm\sqrt{10,496}} {-32}

t=\frac{-80+\sqrt{10,496}} {-32}=-0.70

t=\frac{-80-\sqrt{10,496}} {-32}=5.70

therefore

The potato hit the ground at t=5.70 seconds

Part B) Write an equation that can be solved to find when the potato is 40 feet off the ground. Then solve the equation

For h(t)=40 ft

substitute in the quadratic equation

-16t^2+80t+64=40

-16t^2+80t+24=0

Solve the quadratic equation

we have

a=-16\\b=80\\c=24

substitute in the formula

t=\frac{-80\pm\sqrt{80^{2}-4(-16)(24)}} {2(-16)}

t=\frac{-80\pm\sqrt{7,936}} {-32}

t=\frac{-80+\sqrt{7,936}} {-32}=-0.28

t=\frac{-80-\sqrt{7,936}} {-32}=5.28

therefore

The potato is 40 feet off the ground at the time t=5.28 seconds

3 0
3 years ago
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