Answer:
To factor a trinomial of the form ax^2 + bx + c, you can use the following steps:
Step-by-step explanation:
To factor a trinomial of the form ax^2 + bx + c, you can use the following steps:
Find a factor pair of ac that has the sum of b. For example, if a = 2, b = -7, and c = -21, then the factor pair for -42 (2 * -21) that has the sum of -7 is (-7, -6).
Rewrite bx as a sum of those factors. In the example, -7x = -7x + (-6x).
Factor out the GCF (greatest common factor) from the two groups of terms. In the example, (2x - 7)(x - 6) = 2x(x - 6) - 7(x - 6) = 2x^2 - 14x + 12x - 42 = 2x^2 - 2x - 42.
Write the original trinomial as the product of two binomials. In the example, the trinomial 2x^2 + -7x + -21 can be factored as (2x - 7)(x - 6)
So the final factorization is (2x - 7)(x - 6)
Short Answer
Note: Your teacher will grade your responses to questions 24–25 to ensure you receive proper credit for your answers.
Classify the triangle by its angles and its sides. Explain how you knew which classifications to use.
A triangle has sides measuring 8, 11, and 12 and angles measuring 45 degrees, 65 degrees, and 70 degrees.
not drawn to scale
This triangle is an acute triangle because all three angles measure less than 90 degrees.
It is also a scalene triangle because all three sides have different lengths. I know this because an acute triangle is defined as a triangle where all three angles measure less than 90 degrees and a scalene triangle is defined as a triangle where all three sides have different lengths.
According to the lengths of sides, triangles can be classified into :
Scalene.
Isosceles.
Equilateral.
Different Types of Triangles Based on Angles are :
Acute-angled. Obtuse-angled. Right-angled.
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given: m||n, angle 1 is congruent to angle 3
prove: k||L
The complete proof of the parallel lines k and l is:
m || n ⇒ Given∠1 ≅ ∠3 ⇒ alternate interior angle theorem∠1 ≅ ∠3 ⇒ Given∠2 ≅ ∠3 ⇒ Transitive Propertyk || l ⇒ ProvedHow to determine the proof of the anglesThe complete question is added as an attachment
With the given information and the image attached below, we can state that the two lines are parallel
Then go ahead to use the angle theorems and transitive properties to complete the proof
So, the complete proof is:
Statement Reasonm || n ⇒ Given∠1 ≅ ∠3 ⇒ alternate interior angle theorem∠1 ≅ ∠3 ⇒ Given∠2 ≅ ∠3 ⇒ Transitive Propertyk || l ⇒ ProvedRead more about congruence proof at:
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a model of a flagpole has a scale of 1in:12ft. The flagpole is 174 feet tall. How tall is the model flagpole
Answer:12 feet
Step-by-step explanation:
In triangle ABC. AD is a median. P and q are the midpoints of AB and AD respectively. If ar (ABC) = 72cm ^ 2 then ar (APQ) =?
The area of the ar (APQ) = 18 cm ^ 2 for the given triangle ABC.
Define the term median of triangle?A line segment from such a vertex here to middle of the other side is what is meant by a median. When the vertex is just an angle in a right triangle and the non-congruent angle about an isoceles triangle, it also functions as an angle bisector.Given that:
AD is ABC's median, ABC will be divided into two distinct triangles by AD.We are aware that a triangle's middle separates that into two triangles with equal areas. Triangle ABC's median is AD, and ABD's median is PQ.Then, area (ΔABD) = area (ΔADC)
And, area (ΔABD) = 1/2 area (ABC) eq.....(i)
Thus, In ΔABD, PQ is the median, as PQ are the mid points on AB and AD respectively.
Then,
ar (APQ) = 1/2 ar(ΔABD)
ar (APQ) = 1/2 × [1/2 ar(ABC)] ....... (Use eq (i))
ar (APQ) = 1/4 ar(ΔABC)
ar (APQ) = 1/4 *72 cm ^ 2
ar (APQ) = 18 cm ^ 2
Thus, the area of the ar (APQ) = 18 cm ^ 2 for the given triangle ABC.
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A dartboard has a radius of 9 inches. How much area covers the dartboard in which you can land?
According to the area of circle, the area covers the dartboard in which you can land is 254.34 square inches.
In math the term called area of circle is defined as the process of π multiplied by the square of the radius and area of a circle(A) when the radius 'r' is given is πr² here the value of π is approx. 3.14 or 22/7.
Here we know that the dartboard has a radius of 9 inches.
And the value of area covers the dartboard in which you can land is calculated as,
Where the value of r is 9, then the area is calculated as,
=> A = π(9)²
When we expand the terms, then we get,
=> A = π x 81
Apply the value of π as 3.14, then we get,
=> A = 3.14 x 81
=> A = 254.34
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4 3/7 ÷ 1/7
What is it?
Answer: 31
Step-by-step explanation:
4 3/7 = 31/7
31 × 7 = 217
7 × 1 = 7
217/7 = 31
Evaluate 12.3v + 11.7w when v=3 and w=4.
Answer:
83.7
Step-by-step explanation:
Substitute v = 3 and w = 4:
[tex]\displaystyle{12.3 \cdot 3 + 11.7 \cdot 4}\\\\\displaystyle{= 36.9 + 46.8}\\\\\displaystyle{= 83.7}[/tex]
Therefore, the value is 83.7
If RS is an altitude of ARPQ, m/RSP = (5x+40)°, and PR = x - 1, find PR.
A. 6
B. 8
C. 9
D. 10
Please select the best answer from the choices provided
OA
OB
The length of segment PR is given by the following option:
How to obtain the segment angle?The angle measure of the altitude is given as follows:
m < RSP = 5x + 40º.
The altitude of the triangle is always going to form a right angle, with measure of 90º, hence the value of x is obtained as follows:
5x + 40 = 90
5x = 50
x = 50/5
x = 10.
The length of segment PR is given as follows:
PR = x - 1.
As the value of x is of x = 10, the numeric length of the segment is given as follows:
PR = 10 - 1
PR = 9.
Meaning that the correct option is given by option C.
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the variable bwght gives the birthweight of the baby (in ounces). what is the difference in average birthweight between smoking mothers and non- smoking mothers?
The difference in average birthweight between smoking mothers and non- smoking mothers is, mothers who smoke cigarettes during pregnancy have, on average, lower birthweight children.
When cigs=0, the bwght is 119.77 ounces.
The average birth weight of the baby when the mother is not a smoker is 119.77 ounces.
When cigs=20,
bwght = 119.77 − 0.514(20) = 109.49,
The bwght is 109.49 ounces.
However, as more cigarettes are smoked, the birthweight of the baby decreases at the rate of 0.5138 ounce for every additional cigarette smoked per day.
Obviously, mothers who smoke cigarettes during pregnancy have, on average, lower birthweight children.
So, The difference in average birthweight between smoking mothers and non- smoking mothers is, mothers who smoke cigarettes during pregnancy have, on average, lower birthweight children.
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If f(x)=-5(2x+1) and f(x)=-35, find x
Answer: x = 3
Step-by-step explanation:
Set the two equal to each other.
-5 (2x+1) = -35
-5 x 2x = -10x , -5 x 1 = -5
-10x -5 = -35
Add 5 to both sides.
-10x = -30
Divide both sides by -10.
x = 3
Caroline has 32 marbles. Caroline gives 3/8 of the marbles to Leon
The two Caroline's marbles are hence blue.
What happens to the denominator when you multiply fractions?Adding a whole number to the numerator multiplies it. No change is made to the denominator. In the simplest possible way, simplify the product. The denominator stays the same since a whole number's denominator is 1, when expressed in fractional form.
The denominator stays the same since a whole number's denominator is 1, when expressed in fractional form.
Adding a whole number to the numerator multiplies it. No change is made to the denominator. In the simplest possible way, simplify the product. The denominator stays the same since a whole number's denominator is 1, when expressed in fractional form.
3 Caroline's marbles are blue.
In line with the assertion made:
16 marbles total, 1/8 of which are blue belong to Caroline.
16 marbles are included in the total.
Blue portions of them
calculate the proportion of blue marbles in Caroline's collection.
marbles that are blue in number =1/8 * 16 = 2.
The two Caroline's marbles are hence blue.
The complete question is,
Caroline has sixteen marbles. eight of them are blue. what proportion of Caroline's marbles are blue?
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5. Write the negation of each of the following statements:
a. R: Ron went to school.
b. S: A triangle has 3 sides.
c. T: x=9
d. U: 20 is a multiple of 3.
The negation of the following statements are a. R: Ron did not go to school. b. S: A triangle does not have 3 sides. c. T: x ≠ 9 d. U: 20 is not a multiple of 3.
What is negation?It's vital to know the opposite of a particular mathematical statement from time to time in mathematics. This practice is known as "negating" a claim. Remember that if a claim is true, then the negation must be false.
The negation of the following statements is:
a. R: Ron did not go to school.
b. S: A triangle does not have 3 sides.
c. T: x ≠ 9
d. U: 20 is not a multiple of 3.
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Given triangle A-C-D and triangle C-D-F, what is FD?
Can i Get some help? 5 stars!
The measure of FD = 16.001 units
Consider following diagram.
We can observe that ΔABE and ΔACD are similar triangles.
By definition of similar triangle the sides of ΔABE and ΔACD must be in proportion.
AB/AC = AE/AD
Let us assume that AB = x
x/(x + 12) = 6/15
15x = 6(x + 12)
15x = 6x + 72
9x = 72
x = 8
So, AB = 8 units
And AC = 12 + 8
AC = 20 units
Consider right triangle ΔACD
Here, AC = 20, AD = 15
Using Pythagoras theorem,
AC² = AD² + CD²
CD = [tex]\sqrt{AC^2 - AD^2}[/tex]
CD = [tex]\sqrt{20^2 - 15^2}[/tex]
CD = 13.23 units
For right triangle CDF,
Using Pythagoras theorem,
FD² = CD² + CF²
FD² = 13.23² + 9²
FD = 16.001
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HELPPPPPPPPP
What is the value of x?
Enter your answer as a decimal in the box.
Check the picture below.
HELPPP THIS IS SO HARD FOR ME!!!
yall amazing <33
Answer:
7/20
Step-by-step explanation:
Answer:
The shaded area is equal to [tex]\frac{7}{20}[/tex]
Step-by-step explanation:
The full circle has a value of 1.
We know that 1/4 and 2/5 of the circle are not shaded and we are asked for the shaded area.
We can use 1-(1/4)-(2/5) to find the shaded area.
1-1/4=3/4
3/4-2/5=15/20-8/20=7/20
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the starting salaries of individuals with an mba degree are normally distributed with a mean of $35,000 and a standard deviation of $8,000. what percentage of mbas will have starting salaries of $24,000 to $46,000?
The percentage of M.B. A's will have starting salaries of $24,000 to $46,000 is 83.09.
Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one. Probability has been introduced in Maths to predict how likely events are to happen. The meaning of probability is basically the extent to which something is likely to happen. This is the basic probability theory, which is also used in the probability distribution, where you will learn the possibility of outcomes for a random experiment. To find the probability of a single event to occur, first, we should know the total number of possible outcomes.
[tex]$$\begin{aligned}& \mu=\$ 35,000 \\& \sigma=\$ 8,000\end{aligned}$$[/tex]
we need to calculate probability for
[tex]& P(24000 < x < 46,000)\\ \\& =P\left(\frac{24000-35,000}{8,000} < \frac{x-\mu}{\sigma} < \frac{46,000-35,000}{8000}\right)\\ \\& =P(-1.37 < z < 1.315) \\\\& =P(z < 1.37)-P(z < -1.37)[/tex]
[tex]& =0.9147-0.0853[/tex] [tex]=0.9162-0.0838 \\[/tex]
[tex]& =0.8294[/tex] [tex]=0.8324 \\[/tex]
[tex]& =82.94 \% \\[/tex] [tex]& =83.09[/tex]
Therefore, the percentage of M.B. A's will have starting salaries of $24,000 to $46,000 is 83.09.
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Find the values of x and y.
Answer: (30, 5)
Step-by-step explanation:
Since the 3 red angles are equal, then they are all 60 degrees, which shows that the triangle is equilateral. Therefore, 8y = 40, so y = 5
Also, since BD = BC, triangle BDC is isosceles. We know that angle BDC = 180 - 60 = 120, so 2x = 60 and x = 30
(x, y) = (30, 5)
I need help with this question o can’t seem to solve this one.
Each can hold 330 milliliters of sparkling water. Layla buys 6-pack of sparkling water. Which sentence about the amount of sparkling water Layla buys is true?
A) Layla bought 20mL less than 2 L
B) Layla bought 120mL less than 2 L
C) Layla bought 20mL less than 20 L
D) Layla bought 120mL less than 20 L
I need help solving this and can you show me by step by step how to solve and thank you
For the given situation sentence represents amount of the sparkling water bought by Layla is given by :
Option A). Layla bought 20milliliters less sparkling water than 2 liters.
Sparkling water in each pack is equal to 330 milliliters
Number of packs of sparkling water bought by Layla is equal to 6 packs
Amount of sparkling water in 6 packs = 330 milliliters
⇒ Amount of sparkling water in 6 packs = ( 330 × 6 ) milliliters
⇒ Amount of sparkling water in 6 packs = ( 1980 ) milliliters
1 liter = 1000milliliters
⇒ 2 liter = 2000milliliters
1980 is less than 2 liters
Difference between 1980milliliters and 2 liters
2000 - 1980 = 20milliliters
Therefore, sentence which represents the given situation of sparkling water bought by Layla is option A) Sparkling water bought by Layla is 20ml less than 2L.
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(2)
a) Solve 15n > 12n + 18
+
o
b) n is an integer and -2
Write down the possible values of n,
from smallest to largest.
All values must be separated by commas. Eg
(3)
. 5 =
Total marks: 5
Solution of the given inequalities based on integer 'n' is given by :
a. Value of 'n' for 15n > 12n + 18 is n > 6.
b. All the possible integer value of 'n' for -2 <n + 3 ≤ 4 are -4, -3, -2, -1, 0.
a. Solution of the expression 15n > 12n + 18 is :
15n > 12n + 18
Subtract 12n from both the sides ,
⇒ 15n - 12n > 12n - 12n + 18
⇒ 3n > 18
Divide by 3 from both the sides,
⇒ 3n/3 > 18 /3
⇒ n > 6
b. -2 <n + 3 ≤ 4
where 'n' is an integer
⇒ -2 -3 < n + 3 -3 ≤ 4 -3
⇒ -5 < n < 1
All the possible values of 'n' smallest to largest are:
-4, -3, -2, -1, 0.
Therefore, the answer of the questions based on integers 'n' are :
a. 15n > 12n + 18 ⇒ n > 6.
b. All possible integers of 'n' are -4, -3, -2, -1, 0.
The above question is incomplete , the complete question is:
a) Solve 15n > 12n + 18
b) n is an integer and -2 <n + 3 ≤ 4
Write down the possible values of n, from smallest to largest.
All values must be separated by commas. Eg. .... , .... , .....
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188 fewer than B is 330
The value of the expression or equation is 142
What is an algebraic expression?An algebraic expression is an expression built up from constant algebraic numbers, variables, and the algebraic operations (addition, subtraction, multiplication, division and exponentiation by an exponent that is a rational number)
The algebraic word problem says:
188 fewer than B is 330
Express in equation form to have
B-188 = 330
Making B the subject of the formula
B = 330+188
B=510
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For what values of the variable does each of the following expressions make sense?
sqrt -(6-x) pls help
The value of the equation is A = √ ( -6 + x )
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
Substituting the values in the equation , we get
A = √ - ( 6 - x ) be equation (1)
On simplifying the equation , we get
Remove the parentheses for addition or subtraction
A = √ ( -6 + x )
when the value of A = 0
√ ( -6 + x ) = 0
Taking squares on both sides of the equation , we get
-6 + x = 0
Adding 6 on both sides of the equation , we get
x = 6
Therefore , the value of x is 6
Hence , the equation is A = √ ( -6 + x )
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Write a number story in which the answer is ¹³୵₂₀.
Answer:
Step-by-step explanation:
well, it will be 13/20 because you can't simplify our ya
Answer:no answer
Step-by-step explanation:no explanation help
A company is offering a bank account. The value, in dollars, of the account, is represented by the function A(t)=50,000(1.02)^t, where t represents the number of years since the account was first opened. Determine the average rate of change of the account value from t = 0 to t = 5. Express your answer in the nearest cent. PLS HELP!!!
The average rate of change of the account value from t = 0 to t = 5 is the change in the account value divided by the change in time, or (A(5) - A(0))/(5 - 0).
We can substitute the given function into the equation:
A(t) = 50,000(1.02)^t
So,
A(5) = 50,000(1.02)^5
and
A(0) = 50,000(1.02)^0
Now we can substitute these values in the equation of average rate of change:
(A(5) - A(0))/(5 - 0) = (50000(1.02)^5 - 50000(1.02)^0) / (5-0)
This simplifies to
(50000(1.02)^5 - 50000) / 5
Which is approximately equal to 67,622.05
So the average rate of change of the account value from t = 0 to t = 5 is approximately 67,622.05.
The histogram summarizes the percentage of people in each state and the District of
Columbia who identify as Hispanic or Latino. Use the drop-down menus to describe the
distribution of percentages shown in the histogram.
The histogram's smallest and greatest ranges, 0 to 4.9 and 45 to 49.9, respectively, represent the percentage of residents in each state and the District of Columbia who identify as Hispanic or Latino.
What is percentage?The histogram's smallest and greatest ranges, 0 to 4.9 and 45 to 49.9, respectively, represent the percentage of residents in each state and the District of Columbia who identify as Hispanic or Latino.
Percentage refers to quantifying anything per 100, as the word indicates.You can get the percentage, for instance, by dividing your score by 100.
Given: The histogram summarizes the proportion of persons who identify as Hispanic or Latino in each state and the District of Columbia,
The x-axis displays the population's frequency, while the y-axis displays the population's Hispanic or Latino proportion.
Consider the graph to determine the narrowest range possible,
The smallest possible range = 0 - 4.9
Calculate the broadest range feasible while keeping in mind the graph,
The largest possible range = 45 - 49.9
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Please help with this problem!
A constraint is a restriction or limitation on the possible solutions of a problem or system. In the context of a system of inequalities, a constraint is an inequality that must be satisfied by any solution of the system. A system of inequalities is a set of multiple inequalities that must all be satisfied simultaneously. Solving a system of inequalities involves finding the set of all possible solutions that satisfy all of the constraints. This can be done graphically by graphing the inequalities and finding the intersection of their solution sets, or algebraically by isolating the variables and solving for their values.
159.12 divided by 6.8 give evidence.
After divide, the value of quotient is 23.4.
What is Division method?Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications. For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.
We have to given that;
⇒ 159.12 divided by 6.8
Now, We can divide the numbers as;
⇒ 159.12 divided by 6.8
⇒ 159.12 ÷ 6.8
⇒ 23.4
Thus, The value of quotient = 23.4
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Find the missing angles measurements. Please show your steps.
If m∠DAC = 65°, m∠DAC and m∠BCA can be classified as alternate interior angles. And m∠BCA = 65°.
What is alternate interior angles of a rectangleAlternate interior angles of a rectangle are congruent, which implies they are equal in measure and are formed by the intersection of the opposite sides of the rectangle.
Considering the diagonal AC from one corner of the rectangle to the opposite corner, the angles formed at the intersection of the non-parallel sides will be congruent
Therefore, the angles m∠DAC and m∠BCA are alternate interior and m∠DAC = m∠BCA, which makes m∠BCA = 65°
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WILL MARK BRAINLIEST!! function g is the result of these transformations on the parent sine function: •vertically stretch by a factor of 3 •horizontal shift left pi/2 units • vertical shift down 4 units. Substitute the values of A, C, and D to complete the equation modeling function g
By substituting the values of A, C, and D, the equation modelling the function is g(x) = 3·sin(x - π/2) - 4.
From the question, we have the following information;
The vertical distance of the sine function = 3 × The parent function
∴ A = 3
Given that the horizontal shift left = π/2 units (from an online source with a similar question)
The vertical shift down = 4 units
The given function g is g(x) = A·sin(x + C) + D
Where,
A is the amplitude = The maximum displacement from the rest or equilibrium position = 3
C is the horizontal shift = -π/2 (The negative sign is for the shifting to the left)
D is the vertical shift = -4 (The negative sign is for a shift in the downward direction)
Therefore, the equation modelling the function is g(x) = 3·sin(x - π/2) - 4.
--The given question is incomplete; the complete question is
"Enter the correct answer in the box. Function g is the result of these transformations on the parent sine function:
Vertical stretch by a factor of 3.
Horizontal shift left units.
vertical shift down 4 units.
Substitute the values of A, C, and D to complete the equation modelling function g. g(x) = Asin(x + C) + D."--
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how many inches is a feather
Answer: 4-6 inches
Step-by-step explanation: Hope this helps
Answer:
Feathers are 214 in or less
Step-by-step explanation:
Belinda is thinking about buying a house for $249,000. The table below shows the projected value of two different houses for three years:
Number of years 1 2 3
House 1 (value in dollars) 253,980 259,059.60 264,240.79
House 2 (value in dollars) 256,000 263,000 270,000
Part A: What type of function, linear or exponential, can be used to describe the value of each of the houses after a fixed number of years? Explain your answer. (2 points)
Part B: Write one function for each house to describe the value of the house f(x), in dollars, after x years. (4 points)
Part C: Belinda wants to purchase a house that would have the greatest value in 45 years. Will there be any significant difference in the value of either house after 45 years? Explain your answer, and show the value of each house after 45 years. (4 points)
A)
House 1 value is an exponential function.
House 2 value is a linear function.
B)
House 1:
f(x) = 253,980 x
House 2:
f(x) = 256,000 + 7000x
C)
House 1 will have the greatest value.
The significant difference in the value of either house after 45 years is $168844
The value of house 1 after 45 years:
f(45) = $739844
The value of the house 2 after 45 years:
f(45) = $571000
What is a function?A function is a relationship between inputs where each input is related to exactly one output.
Example:
f(x) = 2x + 1
f(1) = 2 + 1 = 3
f(2) = 2 x 2 + 1 = 4 + 1 = 5
The outputs of the functions are 3 and 5
The inputs of the function are 1 and 2.
We have,
House 1:
The value of the hours is described by an exponential function.
There is an increase of 2% per year.
f(x) = 253,980 x [tex]1.02^x[/tex]
Where x is the number of years.
House 2:
The value of the hours is described by a linear function.
There is an increase of $7000 per year.
f(x) = 256,000 + 7000x
Where x is the number of years.
Now,
For x = 45,
f(45) = 253,980 x [tex]1.02^x[/tex]
f(45) = 253,980 x [tex]1.02^{45}[/tex]
f(45) = $739843.74
f(45) = $739844 ____(1)
f(x) = 256,000 + 7000x
f(45) = 256,000 + 7000 x 45
f(45) = 256,000 + 315000
f(45) = $571000 ______(2)
From (1) and (2),
House 1 will have the greatest value.
The significant difference in the value of either house after 45 years
= $739844 - $571000
= $168844
The value of house 1 after 45 years:
f(45) = $739844
The value of the house 2 after 45 years:
f(45) = $571000
Thus,
The Part A, Part B, and Part C are given above.
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