Doug purchased land for $8,000 in 1995. The year value of the land depreciated by 4% each year thereafter. Use an exponential function to find the approximate value of the land in 2002.

Answer:

a = 3

b = 2

c = 0

d = -4

Step-by-step explanation:

Form 4 equations and solve simultaneously

28 = a(2)³ + b(2)² + c(2) + d

28 = 8a + 4b + 2c + d (1)

-5 = -a + b - c + d (2)

220 = 64a + 16b + 4c + d (3)

-20 = -8a + 4b - 2c + d (4)

(1) + (4)

28 = 8a + 4b + 2c + d

-20 = -8a + 4b - 2c + d

8 = 8b + 2d

d = 4 - 4b

Equation (2)

c = -a + b + d + 5

c = -a + b + 4 - 4b+ 5

c = -a - 3b + 9

28 = 8a + 4b + 2c + d (1)

28 = 8a + 4b + 2(-a - 3b + 9) + 4 - 4b

28 = 6a - 6b + 22

6a - 6b = 6

a - b = 1

a = b + 1

220 = 64a + 16b + 4c + d (3)

220 = 64(b + 1) + 16b + 4(-b - 1 - 3b + 9) + 4 - 4b

220 = 60b + 100

60b = 120

b = 2

a = 2 + 1

a = 3

c = -3 - 3(2) + 9

c = 0

d = 4 - 4(2)

d = -4

Step-by-step explanation:

Step 1:  Solve using the first point

(2, 28)

[tex]28 = a(2)^3 + b(2)^2 + c(2) + d[/tex]

[tex]28 = 8a + 4b + 2c + d[/tex]

Step 2:  Solve using the second point

(-1, -5)

[tex]-5 = a(-1)^3 + b(-1)^2 + c(-1) + d[/tex]

[tex]-5 = -a + b - c + d[/tex]

Step 3:  Solve using the third point

(4, 220)

[tex]220 = a(4)^3 + b(4)^2 + c(4) + d[/tex]

[tex]220 = 64a + 16b + 4c + d[/tex]

Step 4:  Solve using the fourth point

(-2, -20)

[tex]-20 = a(-2)^3 + b(-2)^2 + c(-2) + d[/tex]

[tex]-20 = -8a + 4b - 2c + d[/tex]

Step 5:  Combine the first and fourth equations

[tex]28 - 20 = 8a - 8a + 4b + 4b + 2c - 2c + d + d[/tex]

[tex]8 = 8b + 2d[/tex]

[tex]8 - 8b = 8b - 8b + 2d[/tex]

[tex](8 -8b)/2 = 2d/2[/tex]

[tex]4 - 4b = d[/tex]

Step 6:  Solve for c in the second equation

[tex]-5 + 5 = -a + b - c + d + 5[/tex]

[tex]0 + c = -a + b - c + c + d + 5[/tex]

[tex]c = -a + b + d + 5[/tex]

Step 7:  Substitute d with the stuff we got in step 5

[tex]c = -a + b + (4 - 4b) + 5[/tex]

[tex]c = -a + b + 4 - 4b + 5[/tex]

[tex]c = -a - 3b + 9[/tex]

Step 8:  Substitute d and c into the first equation

[tex]28 = 8a + 4b + 2(-a - 3b + 9) + (4 - 4b)[/tex]

[tex]28 = 8a + 4b - 2a - 6b + 18 + 4 - 4b[/tex]

[tex]28 - 22 = 6a - 6b + 22 - 22[/tex]

[tex]6 / 6 = (6a - 6b) / 6[/tex]

[tex]1 + b = a - b + b[/tex]

[tex]1 + b = a[/tex]

Step 9:  Substitute a, b, and c into the third equation

[tex]220 = 64(1 + b) + 16b + 4(-(1 + b) - 3b + 9) + (4 - 4b)[/tex]

[tex]220 = 64 + 64b + 16b + 4(-1 - b - 3b + 9) + 4 - 4b[/tex]

[tex]220 - 100 = 60b + 100 - 100[/tex]

[tex]120 / 60 = 60b / 60[/tex]

[tex]2 = b[/tex]

Step 10:  Find a using b = 2

[tex]a = b + 1[/tex]

[tex]a = (2) + 1[/tex]

[tex]a = 3[/tex]

Step 11:  Find c using a = 3 and b = 2

[tex]c = -a - 3b + 9[/tex]

[tex]c = -(3) - 3(2) + 9[/tex]

[tex]c = -3 - 6 + 9[/tex]

[tex]c = 0[/tex]

Step 12:  Find d using b = 2

[tex]d = 4 - 4b[/tex]

[tex]d = 4 - 4(2)[/tex]

[tex]d = 4 - 8[/tex]

[tex]d = -4[/tex]

Answer:  [tex]a = 3, b = 2, c = 0,d = -4[/tex]

Step-by-step explanation:

Area of the parallelogram=bh

b=20cm

h=12cm

Area=12*20=240cm²

Answer:

[tex](-\frac{1}{4}, \frac{5}{8} )[/tex]

Step-by-step explanation:

If you label the points on the axes, it will show that point K is actually on [tex]\frac{5}{8}[/tex] not [tex]\frac{3}{4}[/tex]

is there a picture to this??

Answer:

D

Step-by-step explanation:

Solving for each equation:

A: True.

[tex]\frac{n}{2} +3 *4 = \frac{n}{2}+12\\\\\frac{n}{2} + 12 = \frac{n}{2} + 12[/tex]

B: False.

[tex]\frac{1}{3}z+\frac{2}{3}z * 9 = 9z\\\\\frac{1}{3} z+6z = 9z[/tex]

C: True, given that y = 1

[tex]-8y +4.3y + 3.7 = 0\\\\-3.7y = -3.7[/tex]

D: True, given that b = 6.66667

[tex]12-1.8b+1.8b=1.8b\\12 = 1.8b[/tex]

E: True.

[tex]\frac{m}{8} + 7(\frac{m}{8} ) =m\\\\\frac{m}{8} + (\frac{7m}{8} )= m\\\\\\\frac{8m}{8} = m\\[/tex]

Answer:

= 40%

Step-by-step explanation:

Original price = 100%

Discount = Op - Np = $49.99 - $29.99 = $20

If $49.99 = 100%

What about $20 = ?

= (20 x 100) ÷ 49.99

= 2000 ÷ 49.99

= 40.008

= 40%

Answer:it is 1/2

Hopefully this helps

Answer:

Event A: stops on red

Event B: stops on yellow

Find P(A or B)

1/2

Answer:

368 square feet of orange paint.

292 square feet of grey paint.

Step-by-step explanation:

Here is a picture of my work that you can follow to show how i did it. hope this helps!

Answer:

8+i

Step-by-step explanation:

Answer:

8 + 1 i

if im wrong soooooorrrrrrryyyyyy

Step-by-step explanation:

Answer: rolling a six sided die☞︎Fiona forest research

Hearts suit☞︎Althea class representative

Spinner☞︎ Jenny marbles

Step-by-step explanation:

Answer:

Fiona= die

Althea=cards

Jenny=Spinner

Step-by-step explanation:

starting off Fiona has three which can evenly go into six.

Althea has 13 options which matches with the number of suits in the hearts

the Jenny would be spinner because 5 times 2 is 10

Answer

Step-by-step explanation:

To find the area of a shape multiply its height by its width. For a square  you only need to find the length of one of the sides (as each side is the same length) and then multiply this by itself to find the area.

please mark me as brainliest.

Answer:

[tex]7 units^2[/tex]

Step-by-step explanation:

You can split this irregular shape into a square and a trapezoid.

The formula for a square is:

[tex]A=lw[/tex]

The formula for a right trapezoid:

[tex]A=\frac{1}{2} (h)(a+b)[/tex]

Area of square:

[tex]A=(2)(2)\\A=4[/tex]

Area of right trapezoid:

[tex]A=\frac{1}{2} (2)(1+2)\\A=3[/tex]

Add up the individual areas to find the overall:

4 + 3 = 7

Answer:

see below

Step-by-step explanation:

Let w = width

L = length = w+5

The area is l*w

A = (w+5)*w

A = w^2 +5w

Answer:

1

Step-by-step explanation:

The maximum value of sin(x) is 1.

When x = 90 degrees sinx = 1.

Answer:

Its B C

Step-by-step explanation:

on edge2020

Step-by-step explanation:

You can make a table of values to find the points that belong to the line and then draw the line through those points. Here are some: (-6, -2), (0, -1), and (6, 5). You can use any value for x in your table. Hope this helps!

Answer:

Step-by-step explanation:

put a point in at negative 1 first; that is the y value.

Then, go up 1 then to the right six points. that should result in the next point being at (0,6).

Keep going and draw a line

Answer:

A.) Never meet.

Step-by-step explanation:

It’s A they never meet

Answer:

A. 3,864 ft²

B. 1,319.585 ft²

C. 2,544.415 ft²

Step-by-step explanation:

Area of triangle:

½ × 92 × 84

3864 ft²

Area of circle:

pi × r²

3.14 × 20.5²

1319.585 ft²

Difference:

3864 - 1319.585

2544.415 ft²

Answer:

B. 0.9%

Step-by-step explanation:

If the diameter of the meteor is 750 miles, then its radius is 750/2 = 375 miles

The radius of the earth is 3959 miles

Assuming that both bodies are spherical, their surface are:

meteor's surface: π*r² = π*375² = 441786.467 miles²

Earth's surface: π*3959² = 49240321.1 miles²

If 49240321.1 miles² represents 100% then 441786.467 miles² represents:

49240321.1 miles² / 100% = 441786.467 miles² / x%

x = 441786.467/49240321.1*100

x = 0.9%

Answer:

B) 0.9%

Step-by-step explanation:

Answer:

C. (3x^2+4)(x+3)

Step-by-step explanation:

3x^3+9x^2+4x+12

=(3x^3+9x^2)+(4x+12)

=3x^2(x+3)+4(x+3)

=(3x^2+4)(x+3)

Therefore, C. (3x^2+4)(x+3)

The correct factor of the polynomial is,

⇒ (x + 3) (3x² + 4)

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

We have to given that;

The expression is,

⇒ 3x³ + 9x² + 4x + 12

Now, We can factor the polynomial as;

⇒ 3x³ + 9x² + 4x + 12

⇒ 3x² (x + 3) + 4 (x + 3)

⇒ (x + 3) (3x² + 4)

Thus, The correct factor of the polynomial is,

⇒ (x + 3) (3x² + 4)

Learn more about the mathematical expression visit:

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Answer:

B

Step-by-step explanation:

The equation that satisfies the above table is y = 8[tex](\frac{1}{2})^{x}[/tex]

Given,

Table between x and y .

Here,
To get the equation between x and y first justify the data given in the table.

So,

When,

x = -3 , y = 64

x = -2 , y = 32 .

In the equation  y = 8[tex](\frac{1}{2})^{x}[/tex] substitute the values of x and check for y .

Put x = -3 ,

y = 8[tex](1/2)^{-3}[/tex]

y = 8 * 8

y = 64

Thus it satisfies the value given in the table .

So the correct equation will be Option B .

Know more about equations,

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Answer:

340

Step-by-step explanation:

442 / 13 = 34

34 × 10 = 340

Answer:

340

Step-by-step explanation:

442 / 13 = 34

34 × 10 = 340

Answer:

g = -13

Step-by-step explanation:

5(g-2)+g=6(g-4)

5g - 10 + g = 6g - 24

5g + g - 6g = -24 + 10

6g - 6g = -13

g = -13

Answer:

x = 4

Step-by-step explanation:

5x-50=30-15x

5x +15x =30+50

20x= 80

Divide both sides of the equation by 20

x = 4

I hope it helps

Answer:

The number of meal combinations, She has to choose:

N = 3 x 4 x 3 =36

Hope this helps!

:)

Answer:

129 1/3

Step-by-step explanation:

According to Alcumus, "There are 20 square posts which are not on a corner, so there are $20/4=5$ square posts on each side, not including the corner posts. Including the corner posts, there are 7 posts on a side, which means that there are 6 five-foot gaps between posts. Altogether the length of a side is $7\left(\frac{1}{3}\right)+6(5)=32\frac{1}{3}$ feet. The perimeter of the square is four times the side length, so the perimeter is $4\cdot 32\frac{1}{3}=\boxed{129\frac{1}{3}}$ feet."

The outer perimeter is 129 1/3 feet.

The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.

For Example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.

12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.

As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.

This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.

Given:

Twenty-four 4-inch wide square posts are evenly spaced with 5 feet.

So, there are $20/4

                   =5$ square posts on each side, not including the corner posts.

and, including the corner posts, there are 7 posts on a side, which means that there are 6 five-foot gaps between posts.

Then, the length of a side is

= 7 1/3 + 6(5)

= 32 1/3 feet

and, The perimeter of the square

= 4 x 32 1/3

= 129 1/3 feet

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Answer:

The horizontal asymptote is x-axis

Step-by-step explanation:

The horizontal asymptote is the y axis not x axis

Answer:

Step-by-step explanation:

(20+10)*3/2 = 45

Answer:

45 ft squared

Step-by-step explanation:

Area of a trapazoid = a plus b divuded by 2 times h

20 plus 10 divided by 2 equals 15

then 15 times 3 equals 45