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3 years ago

7(y – 8) + 24 = x(y – 6)

Mathematics

1 answer:

ICE Princess25 [194]3 years ago

8 0

Answer:y = y = (32 - 6x)/(7 - x)

Step-by-step explanation:

1. Distribute -> 7y - 56 + 24 = xy - 6x

2. Add Like Terms -> 7y - 32 = xy - 6x

3. Collect Like Terms -> 7y - xy = 32 - 6x

4. Factor Out the "y" -> y(7 - x) = 32 - 6x

5. Divide Out the Left "x" -> y = (32 - 6x)/(7 - x)

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A function g is defined by g(x)=50−2x. If x increases by 7, by how much does g(x) decrease?

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Answer: g(x) decreases by 7

Step-by-step explanation:

Simple algebra and substitution of variables for the number can help you to solve the problem,

g(7)=50-2(7)

g(7)=50-14

g(7)=36

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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]

Answer:

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

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

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

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

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

Each problem is worth 10 points each. (For each problem show your work and give a brief explanation of how you solved your probl

maxonik [38]

It’s a big problem it’s deserve 20 points you can’t play people make it fair

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3 years ago

What is the value of x, when -2(2+3(x+5))=-64?

Amiraneli [1.4K]

Answer:

x = 5

I hope this helps!

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