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NikAS [45]
3 years ago
5

Joe and Linda have the opportunity to purchase a new home. The house in Glen Oaks is currently worth $250,000 but is predicted t

o be worth $270,000 in a year. What is the rate of appreciation for the house from one year to the next?
Mathematics
1 answer:
Dmitry [639]3 years ago
7 0

You can work out the percentage change and that would help you work out the rate of appreciation :)

The formula is ((new value - old value)/old value) * 100.

So you do \frac{270,000 - 250,000}{250,000} \times 100 = 8\%

Therefore the rate of appreciation is 8% p/a.

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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

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
PLEASE HELP ASAP I WILL MARK AS BRAINLIEST
zimovet [89]

Answer:

The triangle because the other shapes have a square in them, also FYI you got your name in the photo

Step-by-step explanation:

4 0
3 years ago
29. Determine the value of x.<br> abc<br> X + 42°<br> 147°<br> 2x
suter [353]

Answer:

x=35

Step-by-step explanation:

180-147=33 (angles in a straight line)

33+3x+42=180 (angles in a triangle)

3x+42=147

147-42=105

105/3=35

5 0
2 years ago
A motorist traveled 311 miles on 12 gallons of gas. To the nearest tenth, how many miles can the motorist travel on one gallon o
Alina [70]
D. 311 divided by 12 = 25.91
The nearest tenth would be 25.9
3 0
3 years ago
Read 2 more answers
What’s the answer for y= (x-2)^2 +2 {x&lt;4.5}
stealth61 [152]

Answer:

x<4.5

Step-by-step explanation:

y =(x-2)^2 +2 {x<4.5}

add the power and then divide by 2 you get 4.5

8 0
3 years ago
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