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aleksandrvk [35]
3 years ago
15

Zoey purchased a new car in 1992 for \$28,000$28,000. The value of the car has been depreciating exponentially at a constant rat

e. If the value of the car was \$9,600$9,600 in the year 1996, then what would be the predicted value of the car in the year 1998, to the nearest dollar?
Mathematics
2 answers:
Andreas93 [3]3 years ago
7 0

Answer:

5621

Step-by-step explanation:

elena-s [515]3 years ago
3 0
400$
Explanation:
In 1992, the price is 28000$ and 9600$ in 1996 so in 4 years the value the car lost is 18400$
Dividing 18400 by 4 years we get 4600 depreciation value per year.
Between 1996 and 1998 there is 2 years
So in 1998 the value of the car will be:
9600 (value in 1996) - 2x4600 = 400$
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You have D dollars to buy fence to enclose a rectangular plot of land (see figure at right). The fence for the top and bottom co
alex41 [277]

The perimeter of the rectangular plot of land is given by the expression below

P=2x+2y

On the other hand, since the available money to buy fence is D dollars,

\begin{gathered} D=4(2x)+3(2y) \\ \Rightarrow D=8x+6y \\ D\rightarrow\text{ constant} \end{gathered}

Furthermore, the area of the enclosed land is given by

A=xy

Solving the second equation for x,

\begin{gathered} D=8x+6y \\ \Rightarrow x=\frac{D-6y}{8} \end{gathered}

Substituting into the equation for the area,

\begin{gathered} A=(\frac{D-6y}{8})y \\ \Rightarrow A=\frac{D}{8}y-\frac{3}{4}y^2 \end{gathered}

To find the maximum possible area, solve A'(y)=0, as shown below

\begin{gathered} A^{\prime}(y)=0 \\ \Rightarrow\frac{D}{8}-\frac{3}{2}y=0 \\ \Rightarrow\frac{3}{2}y=\frac{D}{8} \\ \Rightarrow y=\frac{D}{12} \end{gathered}

Therefore, the corresponding value of x is

\begin{gathered} y=\frac{D}{12} \\ \Rightarrow x=\frac{D-6(\frac{D}{12})}{8}=\frac{D-\frac{D}{2}}{8}=\frac{D}{16} \end{gathered}<h2>Thus, the dimensions of the fence that maximize the area are x=D/16 and y=D/12.</h2><h2>As for the used money,</h2>\begin{gathered} top,bottom:\frac{8D}{16}=\frac{D}{2} \\ Sides:\frac{6D}{12}=\frac{D}{2} \end{gathered}<h2>Half the money was used for the top and the bottom, while the other half was used for the sides.</h2>

7 0
1 year ago
Two equations are shown:
vekshin1
Y=24  Y-12=12  Y=12+12  Y=24

(X-12) = 12

X = 12+12
X=24
5 0
3 years ago
10 x 1/2 + (-6) (-3)
torisob [31]
Equation

10x1/2+(-6) (-3)

Answer

23
5 0
2 years ago
Plezzzzzwzzzzzzzz help
strojnjashka [21]

Answer:

3 - a

Step-by-step explanation:

Given that when you add two numbers together the result is 3.

The greater of the number is given as a.

Let "x" represent that lesser number.

Thus:

a + x = 3

To make x the subject of the formula. Subtract a from both x.

a + x - a = 3 - a

x = 3 - a

Therefore, the expression that represents the lesser number, x, is:

3 - a

8 0
2 years ago
What is the solution of √1-3x = x+3 ?<br><br><br>​
Vadim26 [7]

Answer:

{-1, -8}

Step-by-step explanation:

Please enclose "1 - 3x" inside parentheses so the reader will know that you want the square root of all of "1 - 3x".

Squaring both sides of the given equation, we get:

1 - 3x = x^2 + 6x + 9, or  x^2 + 6x + 8 + 3x, or

x^2 + 9x + 8 = 0.  Factoring, we get:  (x + 8)(x + 1) = 0, so that the solutions are {-1, -8}.

5 0
3 years ago
Read 2 more answers
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