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yKpoI14uk [10]
3 years ago
6

The value of a painting recently sold at an auction is expected to increase in value over time. The function v(t)=12,000(1.15)^t

represents the value of the painting, v(t), at time t, where t is the measure in years since the painting was sold at an auction.
Which of the following statements provide a correct interpretation of the function representing the value of the painting? SELECT ALL THAT APPLY.

A. The painting was sold at the auction 1.15 years ago.
B. The painting value was 1.15 at the time it was sold at the auction.
C. Each year the painting increases its value by 15 percent.
D. The painting was sold at the auction 12,000 years ago.
E. The painting's value was 12,000 at the time it was sold at the auction.
F. Each year the painting increases its value by 12,000 percent
Mathematics
1 answer:
tensa zangetsu [6.8K]3 years ago
8 0
This is an exponential equation with a starting value of 12000 and an increase of 15% each years.

The following are true:

C. Each year, it increases by 15%

E. The painting's value was 12,000 at the time is was sold.
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Answer:

z+372=160

Step-by-step explanation:

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If the endpoints of the diameter of a circle are (−8, −6) and (−4, −14), what is the standard form equation of the circle? A) (x
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Answer:

\large\boxed{A.\ (x+6)^2+(y+10)^2=20}

Step-by-step explanation:

The standard form of an equation of a circle:

(x-h)^2+(y-k)^2=r^2

(h, k) - center

r - radius

We have the endpoints of the diameter of a circle (-8, -6) and (-4, -14).

The midpoint of a diameter is a center of a circle.

The formula of a midpoint:

\left(\dfrac{x_1+x_2}{2},\ \dfrac{y_1+y_2}{2}\right)

Substitute:

x=\dfrac{-8+(-4)}{2}=\dfrac{-12}{2}=-6\\\\y=\dfrac{-6+(-14)}{2}=\dfrac{-20}{2}=-10

We have h = -6 and k = -10.

The radius is the distance between a center and the point on a circumference of a circle.

The formula of a distance between two points:

d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}

Substitute (-6, -10) and (-8, -6):

r=\sqrt{(-8-(-6))^2+(-6-(-10))^2}=\sqrt{(-2)^2+4^2}=\sqrt{4+16}=\sqrt{20}

Finally we have

(x-(-6))^2+(y-(-10))^2=(\sqrt{20})^2\\\\(x+6)^2+(y+10)^2=20

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Step-by-step explanation:

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Given:

u varies directly with the square of p and inversely with d.

To find:

The equation for the given situation.

Solution:

If y is directly proportional to x, then

y\propto x

If y is inversely proportional to x, then

y\propto \dfrac{1}{x}

It is given that u varies directly with the square of p and inversely with d. So,

u\propto \dfrac{p^2}{d}

It can be written as:

u=k\dfrac{p^2}{d}

Where, k is the constant of proportionality.

Therefore, the required equation is u=\dfrac{kp^2}{d}.

6 0
3 years ago
15PTS QUICK
lana66690 [7]

Answer:

Option B

40x + 50y = 130

5x - 4y = 16

Option C

20x + 25y = 65

-20x + 16y = 64

Step-by-step explanation:

we have

4x+5y=13 ----> equation a

10x-8y=-32 ----> equation b

we know that

If two system of equations are equivalent, then their solution is the same

Part 1)

step 1

Multiply by 10 equation a both sides

10(4x+5y)=10(13)

40x+50y=130 ----> equation a'

step 2

Divide by 2 equation b both sides

(1/2)(10x-8y)=(1/2)(-32)

5x-4y=-16 ----> equation b'

so

The system of equations a and b and the system of equations a' and b' are equivalent

therefore

The system of equations a' and b' have the same solution as the given system

Part 2)

step 1

Multiply by 5 equation a both sides

5(4x+5y)=5(13)

20x+25y=65 ----> equation a'

step 2

Multiply by -2 equation b both sides

-2(10x-8y)=-2(-32)

-20x+16y=64 ----> equation b'

so

The system of equations a and b and the system of equations a' and b' are equivalent

therefore

The system of equations a' and b' have the same solution as the given system

6 0
3 years ago
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