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bagirrra123 [75]
2 years ago
8

TWENTY POINTS!!! Baxter is thinking about buying a car for $18,500. The table below shows the projected value of two different c

ars for three years. Number of years 1 2 3 Car 1 (value in dollars) 17,390 16,346.60 15,365.80 Car 2 (value in dollars) 17,500 16,500 15,500 Part A: What type of function, linear or exponential, can be used to describe the value of each of the cars after a fixed number of years? please explain your answer:)
Mathematics
1 answer:
Anika [276]2 years ago
7 0
Part A: Linear function

explanation:
The table for the value of the two cars with time are given as follows;
Years Car 1 Car 2
1 18,500 18,500
2 17,390 17,500
3 16,500 16,346.6
Plotting the give data, we have;
From the plot of the data, the function that can be used to describe the values of both cars after a fixed number of years is a linear function

Hope this helps a bit
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Which statement describes function composition with respect to the commutative property? Given f(x) = x² – 4 and g(x) = x – 3, (
Paraphin [41]

Answer:

The correct option are;

f(x) = x² - 4 and g(x) = x - 3, (f ο g)(2) = -3 and (g ο f)(2) = -3, so the function is commutative

Given f(x) = 4·x and g(x) = x², (f ο g)(x) = 4·x² and (g ο f)(x) = 16·x²

So the function is not commutative

Step-by-step explanation:

For the equations f(x) = x² - 4 and g(x) = x - 3, we have;

(f ο g)(x) = f(g(x)) = (x - 3)² - 4 = x² - 6·x + 9 - 4 = x² - 6·x + 5

At x = 2, we have;

(f ο g)(2) = f(g(2)) = 2² - 6×2 + 5 = - 3

Similarly, we have;

(g ο f)(x) = g(f(x)) = x² - 4 -3 = x² - 7

At x = 2, we have;

(g ο f)(2) = g(f(2)) = 2² - 7 = 4 - 7 = -3

Therefore, by commutative property, we have that the result of an operation does not change by changing the order of the operands such that we have;

a + b = b + a or a·b = b·a from which we have resolved also the following operation is commutative

(f ο g)(2) = (g ο f)(2)

Similarly given f(x) = 4·x and g(x) = x², (f ο g)(x) = 4·x² and (g ο f)(x) = 16·x²

So the function is not commutative

(f ο g)(x) = f(g(x)) = 4·x²

(f ο g)(x) = 4·x²

(g ο f)(x) = g(f(x)) = (4·x)² = 16·x²

(g ο f)(x) = 16·x²

∴ (f ο g)(x) = 4·x² ≠ (g ο f)(x) = 16·x²

(f ο g)(x)  ≠ (g ο f)(x) the function is not commutative.

8 0
2 years ago
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$36 for 4 baseball hats; $56 for 7 baseball hats are they equivalent
Arlecino [84]
36/4 = 9 per hat
56/7 = 8 per hat

no, they are not equivalent
5 0
2 years ago
RS=2x-8, ST= 11, RT= x+10
swat32

Answer:

X=7 ST=11 RT=17

Step-by-step explanation:

RT=RS+ST. RS= 2(7)-8. ST=11

X+10=2x-8+11. =14-8=6. RT= x+10

X+10=2x+3. RS=6. 7+10=17

10=x+3. RT=17

X=7

4 0
1 year ago
A piece of paper is to display ~128~ 128 space, 128, space square inches of text. If there are to be one-inch margins on both si
Grace [21]

Answer:

The dimensions of the smallest piece that can be used are: 10 by 20 and the area is 200 square inches

Step-by-step explanation:

We have that:

Area = 128

Let the dimension of the paper be x and y;

Such that:

Length = x

Width = y

So:

Area = x * y

Substitute 128 for Area

128 = x * y

Make x the subject

x = \frac{128}{y}

When 1 inch margin is at top and bottom

The length becomes:

Length = x + 1 + 1

Length = x + 2

When 2 inch margin is at both sides

The width becomes:

Width = y + 2 + 2

Width = y + 4

The New Area (A) is then calculated as:

A = (x + 2) * (y + 4)

Substitute \frac{128}{y} for x

A = (\frac{128}{y} + 2) * (y + 4)

Open Brackets

A = 128 + \frac{512}{y} + 2y + 8

Collect Like Terms

A = \frac{512}{y} + 2y + 8+128

A = \frac{512}{y} + 2y + 136

A= 512y^{-1} + 2y + 136

To calculate the smallest possible value of y, we have to apply calculus.

Different A with respect to y

A' = -512y^{-2} + 2

Set

A' = 0

This gives:

0 = -512y^{-2} + 2

Collect Like Terms

512y^{-2} = 2

Multiply through by y^2

y^2 * 512y^{-2} = 2 * y^2

512 = 2y^2

Divide through by 2

256=y^2

Take square roots of both sides

\sqrt{256=y^2

16=y

y = 16

Recall that:

x = \frac{128}{y}

x = \frac{128}{16}

x = 8

Recall that the new dimensions are:

Length = x + 2

Width = y + 4

So:

Length = 8 + 2

Length = 10

Width = 16 + 4

Width = 20

To double-check;

Differentiate A'

A' = -512y^{-2} + 2

A" = -2 * -512y^{-3}

A" = 1024y^{-3}

A" = \frac{1024}{y^3}

The above value is:

A" = \frac{1024}{y^3} > 0

This means that the calculated values are at minimum.

<em>Hence, the dimensions of the smallest piece that can be used are: 10 by 20 and the area is 200 square inches</em>

3 0
1 year ago
At the start of the week, Monique’s savings account had a balance of $326. She made a $45 withdrawal each day for seven days. Du
sammy [17]

Answer:

Step-by-step explanation:

45 times 7= 315

326-315=11

125 times 2=250

250+11=261

so the answer is C. $261

6 0
2 years ago
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