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Answer

Number of years 1               2            3

House 1 (value in dollars) 249,000 253,980 259,059.60

House 2 (value in dollars) 249,000 256,000 263,000

House 1: exponential function

House 2: linear function

House 1: f(x) = 249,000 * (1.02)^(x-1)

→ f(3) = 249,000 * (1.02)³⁻¹ = 249,000 * (1.02)² = 259,059.60

House 2: f(x) = 249,000 + 7,000(x-1)

→ f(3) = 249,000 + 7,000(3-1) = 249,000 + 7,000(2) = 249,000 + 14,000 = 263,000

House 1:

f(45) = 249,000 * (1.02)⁴⁵⁻¹ = 249,000 * (1.02)⁴⁴ = 249,000 * 2.39 = 595,110

House 2:

f(45) = 249,000 + 7,000(45-1) = 249,000 + 7,000(44) = 249,000 + 308,000 = 557,000

House 1 will have a greater value than House 2 after 45 years.

Step-by-step explanation:

Hope this helps, if not let me know and I will fix it.

Part A

The value for house 1 follows an exponential growth function since the value is increasing by 2% each year. This is because we multiply each value by 1.02 to get the next year's value.

In contrast, house 2's value increases by the same amount each year (7000 per year)

This fixed amount it increases directly leads to house 2 having linear growth.

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Part B

The equation for house 1's value is y = 249000(1.02)^x

This is in the form y = ab^x, where a = 249000 is the starting value and b = 1.02 is the growth rate factor.

We can think of 1.02 as 1+0.02 to represent the 2% growth.

In other words, 1.02 = 1+r solves to r = 0.02 = 2%

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The equation for the second home's value is y = 7000x+249000

The slope m = 7000 tells us how the value is going up per year.

The y intercept b = 249000 is the original home value (when x = 0).

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Part C

Let's plug x = 45 into each equation mentioned in part B

For home 1, we have

f(x) = 249000(1.02)^x

f(45) = 249000(1.02)^45

f(45) = 607,025.697

f(45) = 607,025.70

So that's the value of home 1 after 45 years of constant 2% growth per year

For the second home, we have,

f(x) = 7000x+249000

f(45) = 7000*45+249000

f(45) = 564,000

So there is a significant difference. This difference is 607,025.70 - 564,000 = 43,025.70 dollars.

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Answer:

-27k^4 +12k^3+16k^2+56k

---------------------

(9k-4)(2k+7)      

Step-by-step explanation:

8k                  3k^3

---------   -  -----------

9k-4             2k+7

Get a common denominator

8k *(2k+7)          3k^3 *(9k-4)

---------      -           -----------

(9k-4)(2k+7)        (9k-4)(2k+7)

Combine

8k *(2k+7) -3k^3 *(9k-4)

---------------------

(9k-4)(2k+7)        

Distribute

16k^2+56k -27k^4 +12k^3

---------------------

(9k-4)(2k+7)      

-27k^4 +12k^3+16k^2+56k

---------------------

(9k-4)(2k+7)        

Answer:

[tex]opposite\approx 70.02[/tex]

Step-by-step explanation:

The triangle in the given problem is a right triangle, as the tower forms a right angle with the ground. This means that one can use the right angle trigonometric ratios to solve this problem. The right angle trigonometric ratios are as follows;

[tex]sin(\theta)=\frac{opposite}{hypotenuse}\\\\cos(\theta)=\frac{adjacent}{hypotenuse}\\\\tan(\theta)=\frac{opposite}{adjacent}[/tex]

Please note that the names ([tex]opposite[/tex]) and ([tex]adjacent[/tex]) are subjective and change depending on the angle one uses in the ratio. However the name ([tex]hypotenuse[/tex]) refers to the side opposite the right angle, and thus it doesn't change depending on the reference angle.

In this problem, one is given an angle with the measure of (35) degrees, and the length of the side adjacent to this angle. One is asked to find the length of the side opposite the (35) degree angle. To achieve this, one can use the tangent ([tex]tan[/tex]) ratio.

[tex]tan(\theta)=\frac{opposite}{adjacent}[/tex]

Substitute,

[tex]tan(35)=\frac{opposite}{100}[/tex]

Inverse operations,

[tex]tan(35)=\frac{opposite}{100}[/tex]

[tex]100(tan(35))=opposite[/tex]

Simplify,

[tex]100(tan(35))=opposite[/tex]

[tex]70.02\approx opposite[/tex]

Answer:

See step by Step

Step-by-step explanation:

Both are correct. As long as we undo the operations that was given from the original term to both sides until we get the variable by itself., any way can be applied.

Both, Spencer and Jeremiah are correct. We can verify this by testing their methods.

Spencer's method:

[tex]6x - 2 = - 4x + 2[/tex]

[tex]6x - 2 + 4x= - 4x + 2 + 4x[/tex]

[tex]10x - 2 = 2[/tex]

[tex]10x = 2 + 2[/tex]

[tex]10x = 4[/tex]

[tex]x = \frac{4}{10} [/tex]

[tex]x = 0.4[/tex]

Jeremiah's method:

[tex]6x - 2 = - 4x + 2[/tex]

[tex]6x - 2 - 6x = - 4x + 2 - 6x[/tex]

[tex] - 2 = - 10x + 2[/tex]

[tex] - 2 - 2 = - 10x[/tex]

[tex] - 4 = - 10x[/tex]

[tex] \frac{ - 4}{ - 10} = x[/tex]

[tex]0.4 = x[/tex]

As seen, we get the correct answer by using Spencer's and Jeremiah's method. So, we can say that they both are correct.

Answer:

14.9 degrees

Step-by-step explanation:

For this problem you can use Tan∅=o/a and solve for the angle:

15.7 / 59 = 0.2661

Then use inverse tangent of 0.2661 to get 14.9.

Answer:

(0,1) is not the solution to the equation

Step-by-step explanation:

Given:

−3x − 8y = −8 (1)

y = 2 − x ​ (2)

Substitute (2) into (1)

−3x − 8y = −8 (1)

- 3x - 8(2 - x) = -8

- 3x - 16 + 8x = -8

- 3x + 8x = -8 + 16

5x = 8

x = 8/5

Substitute x = 8/5 into (2)

y = 2 − x ​ (2)

= 2 - 8/5

= (10-8) / 5

= 2/5

y = 2/5

Solution to the equation:

(x, y) = (8/5, 2/5)

Therefore,

(0,1) is not the solution to the equation

Answer:

56 different outfits

Step-by-step explanation:

Answer:

626

Step-by-step explanation:

So 62 fewer right so 688 combined- 62 cheeseburger =626 hamburger

Given:

The expression is:

[tex]b^2+20b[/tex]

To find:

The a monomial so that the trinomial may be represented by a square of a binomial.

Solution:

If an expression is [tex]x^2+bx[/tex], then be need to add square of half of coefficient of x, i.e., [tex]\left(\dfrac{b}{2}\right)^2[/tex] in the given expression to make in perfect square.

We have,

[tex]b^2+20b[/tex]

Here, coefficient of b is 20,so wee need to add square of half of coefficient of b, i.e., [tex]\left(\dfrac{20}{2}\right)^2[/tex].

[tex]\left(\dfrac{20}{2}\right)^2=10^2[/tex]

[tex]\left(\dfrac{20}{2}\right)^2=100[/tex]

Therefore, we need to add 100 to make [tex]b^2+20b[/tex] a perfect square binomial.

Answer: 3172

Step-by-step explanation:

Answer:

180

Step-by-step explanation:

Answer:

false.

Step-by-step explanation:

A conditional statement is something like:

If P, then Q.

This means that if a given proposition P is true, then another proposition Q is also true.

An example of this is:

P = its raining

Q = there are clouds in the sky.

So the conditional statement is

If its raining, then there are clouds in the sky.

A biconditional statement is:

P if and only if Q.

This means that P is only true if Q is true, and Q is only true if P is true.

So, using the previous propositions we get:

Its raining if and only if there are clouds in the sky.

This statement is false, because is possible to have clouds in the sky and not rain.

(this statement implies that if there are clouds in the sky, there should be rain)

Then we could see that for the same propositions, the conditional statement is true and the biconditional statement is false.

Then these statements are not logically equivalent.

The statement is false.

Answer:

NMHGJMHBNKJ6T76 5745

Step-by-step explanation:

7657457657776767

Answer:

y - 2 = 36(x - 4)

Step-by-step explanation:

The equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b) a point on the line

Here m = 36 and (a, b ) = (4, 2 ) , then

y - 2 = 36(x - 4) ← equation of line

Answer:

36 spuare units

Step-by-step explanation:

A= 1/2 b*h

b=8

h=9

A=1/2(8*9)

A=1/2(72)

A=36

Answer:

hey mate

plz mark it as brainliest

Answer:

Step-by-step explanation:

e) 3√2 (-3√6 -2 -6)

3√2 (-3√6 - 8)

-9√12 - 24√2

-9√(2^2 * 3) - 24√2

-18√3 - 24√2

or

6(-3√3 - 4√2)

f) -5√2 (3 + 2√2 - 6 - 1)

-5√2(-4 + 2√2)

20√2 - 20

or

20(√2 - 1)

Answer:

factors are 1,2,3,4,6,8,12,24

Answer:

Option (d), (e) and (f) are correct.

Step-by-step explanation:

In triangle MNP, angle P = 90 degree

Cos M = 7 / 12

Now according to the right angle triangle

[tex]NP^2 = NM^2 - PM^2\\\\NP^2 = 12^2 - 7^2\\\\NP = \sqrt95[/tex]

Now

[tex]Sin M = \frac{sqrt95}{12}\\\\Cos N = \frac{95}{12}[/tex]

Answer:

5 3/5

Step-by-step explanation:

3 1/2 * 1 3/5

Change to  improper fractions

(2*3+1)/2  * (5*1+3)/5

7/2 * 8/5

56/10

Change back to a mixed number

50/10 +6/10

5 +3/5

5 3/5

Answer: experimental

Step-by-step explanation:

Experimental research design refers to a research that is conducted with a scientific approach whereby two sets of variables are used. It adheres to the scientific research design.

An experimental research design consist of an hypothesis, a variable which the researcher can manipulate and variables which can be measured. Based on the information given, the experimental research design is used.

Answer:

5y=4x

Step-by-step explanation:

Hello,

[tex](211)_x=(10110)_2\\\\2*x^2+x+1=22\\\\2x^2+x-21=0\\\Delta=1+4*2*21=169=13^2\\x=\dfrac{-1+13}{4}= 3\\or\\x=\dfrac{-1-13}{4}\ may\ not\ be\ negative\\\\[/tex]

x=3

Answer:

Step-by-step explanation:

The graph of a quadratic function is a U-shaped curve called a parabola. One important feature of the graph is that it has an extreme point, called the vertex. If the parabola opens up, the vertex represents the lowest point on the graph, or the minimum value of the quadratic function.

Answer:

36.7

Step-by-step explanation:

180 - 102.9 - 40.4= 36.7

The measure of the third angle of the given triangle after applying the angle sum property of a triangle is 36.7 degrees.

The measures of the two angles of a triangle are 102.9 and 40.4.

We need to find the measure of the third angle.

The angle sum property of a triangle states that the sum of all three interior angles of a triangle is 180 degrees.

If A, B, and C are the interior angles we have,

A + B + C = 180.

Consider the three interior angles to be A, B, and C.

We are given two angles 102.9 and 40.4.

Let  A = 102.9,  B = 40.4.

and C = angle to be measured.

Now,

Applying the angle sum property of a triangle.

We have,

A + B + C = 180

102.9 + 40.4 + C = 180

143.3 + C = 180

C = 180 - 143.3

C = 36.7 degrees.

After applying the angle sum property of a triangle we got the measure of the third angle as 36.7 degrees.

Learn more about the measurement of angles in a triangle here:

https://brainly.com/question/27681289

#SPJ2

Answer:

Reese's love peanut butter and chocolate

hope it helps u

plz mark it as brainliest

Answer:

26

Step-by-step explanation:

We have the average rate of change on the interval [a,b] as

f(b)-f(a)/(b-a)

b = 1 and a = -4

f(b) = f(1) = -2(1)^3 -5 = -2-5 = -7

f(a) = f(-4) = -2(-4)^3 -5 = 128 -5 = 123

so we have;

(123 + 7)/(1+4) = 130/5 = 26