[tex]r=\frac{5i\sqrt{2} }{4}, -\frac{5i\sqrt{2} }{4}[/tex] or simply just say ± [tex]\frac{5i\sqrt{2} }{4}[/tex].
Hope this helps!
Answer:
[tex]r=\dfrac{5\sqrt{2}}{4}}\:i\:,\quad \;\;r=-\dfrac{5\sqrt{2}}{4}}\:i[/tex]
Step-by-step explanation:
To solve the given equation, rearrange the equation to isolate r.
Given equation:
[tex]0=-16r^2-50[/tex]
Add 16r² to both sides of the equation:
[tex]0+16r^2=-16r^2-50+16r^2[/tex]
[tex]16r^2=-50[/tex]
Divide both sides of the equation by 16:
[tex]\dfrac{16r^2}{16}=\dfrac{-50}{16}[/tex]
[tex]r^2=-\dfrac{25}{8}[/tex]
[tex]\textsf{For\;\:}x^2=f\left(a\right)\textsf{\:the\:solutions\:are\:\:}x=\pm\sqrt{f\left(a\right)}[/tex]
[tex]r=\pm\sqrt{-\dfrac{25}{8}}[/tex]
[tex]\textsf{Apply\;the\:radical\:rule:}\;\:\sqrt{-a}=\sqrt{a}\sqrt{-1}[/tex]
[tex]r=\pm\sqrt{\dfrac{25}{8}}\sqrt{ -1}[/tex]
[tex]\textsf{Apply\;the\:imaginary\:number\:rule:}\;\:\sqrt{-1}=i[/tex]
[tex]r=\pm\sqrt{\dfrac{25}{8}}\:i[/tex]
[tex]\textsf{Apply\;the\:radical\:rule:}\:\:\sqrt{\dfrac{a}{b}}=\dfrac{\sqrt{a}}{\sqrt{b}},\:\quad \:a\ge 0,\:b\ge 0[/tex]
[tex]r=\pm\dfrac{\sqrt{25}}{\sqrt{8}}\:i[/tex]
Simplify the numerator and denominator of the fraction:
[tex]r=\pm\dfrac{5}{2\sqrt{2}}\:i[/tex]
Rationalise the denominator by multiply the numerator and denominator by √2:
[tex]r=\pm\dfrac{5\cdot\sqrt{2}}{2\sqrt{2}\cdot \sqrt{2}}\:i[/tex]
[tex]r=\pm\dfrac{5\sqrt{2}}{4}}\:i[/tex]
Therefore, the solutions to the given equation are:
[tex]r=\dfrac{5\sqrt{2}}{4}}\:i\:,\quad \;\;r=-\dfrac{5\sqrt{2}}{4}}\:i[/tex]
a stack of books is 61 inches high. how high is it in feet and inchess
Answer: 5.08333 repeating three
Find the distance between the two points.
(-4,-5)
(4,2)
√ [?]
Enter the number that
goes beneath the
radical symbol.
Enter
By using distance formula, it can be calculated that-
Distance between (-4, -5) and (4, 2) is [tex]\sqrt{113}[/tex] units
What is distance formula?
Distance formula is used to find the distance between two coordinates.
If the points are [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex], then distance is calculated by the formula
d = [tex]\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex]
The points are (-4, -5) and (4, 2)
Distance between (-4, -5) and (4, 2) = [tex]\sqrt{(-4-4)^2+(-5-2)^2}[/tex]
= [tex]\sqrt{64 + 49}\\\sqrt{113}[/tex]units
Distance between (-4, -5) and (4, 2) is [tex]\sqrt{113}[/tex] units
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Akin's salary is 20% less than Shola's and Shola spent 45% of his salary on accommodation leaving him with #550. How much is Akin's salary?
Answer:
$800
Step-by-step explanation:
Let's say that Shola's salary is x dollars. This means that Akin's salary is 0.8x dollars, because his salary is 20% less than Shola's salary.
Since Shola spent 45% of his salary on accommodation, he had 0.55x dollars left, or $550. This means that we can write the equation 0.55x = 550.
To solve for x, we can divide both sides of the equation by 0.55 to get x = 1000. This means that Shola's salary is $1000, and since Akin's salary is 20% less than Shola's, his salary is 0.8 * 1000 = $800. Therefore, Akin's salary is $800.
X-3y = 16 4x-y=9
I’m so confused
Answer:
x = 1, y = -5.
Step-by-step explanation:
X-3y = 16 Equation (1)
4x- y = 9 Equation (2)
We can solve this by the Method of Elimination.
One way is to multiply the second equation by -3, as follows:
-3(4x - y = 9)
= -12x + 3y = -27 Call this equation (3)
Now if we add equation (3) to equation (1) we eliminate the y terms:
x - 3y = 16
-12x + 3y = -27 Adding:
-11x + 0 = -11
-11x = -11
x = -11/-11 = 1
Finally, we find the value of y by substituting x = 1 into equation (2):
4(1) - y = 9
-y = 9 - 4
-y = 5
y = -5.
So, the answer is x = 1, y = -5.
or we can write it as an ordered pair (1, -5).
Hope this helps.
Answer:
x=1 and
y= -5
Create an inequality with 0-9
Answer:
The inequality form is 0≤x≤9 0 ≤ x ≤ 9 .
Plot the GNP series, gnp, and then test for a unit root against the alternative that the process is explosive. State your conclusion.
Hint: [in R]
library(astsa)
library(tseries)
head(gnp)
print(gnp)
there are about millions of multinational and national companies which are working for the better Gross National Product(GNP).
The United States is super power and has multiple resources to maintain itself and the over all economic system. As, there are about millions of multinational and national companies which are working for the better Gross National Product(GNP). As, there is agriculture, car manufacturer, and the military industry for improving and adding the value to the over all GNP of the United States.
The Oil and gas sector is the one major factor for the development of the United State's GNP(Gross National Product). As, the exports of the region is well known to be very high and generates more revenue for the over all system as well.
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Kanoi can weed a garden in 40 minutes. Ale'a can weed the same garden in 50 minutes. How long would it take for Kanoi and Ale'a to weed the same garden together? (Round to the nearest hundredth)
Kanoi and Ale'a can weed the same garden together in 22.22 minutes
How to find the time it will take to weed the garden togetherRate of work refers to amount to of work completed at a given time
Information from the question include
Kanoi can weed a garden in 40 minutes
Kanoi's rate = 1/40 per minute
Ale'a can weed the same garden in 50 minutes
Ale'a rate = 1/50 per minute
When both are working together the rate will be
1/40 per minute + 1/50 per minute
= 9/200 per minute
The time is solved
1 / 9/200
= 200/9
= 22.2222 minutes
= 22.22 minutes to the nearest hundredth
The time it will take both of them to weed is 22.22 minute
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Select each expression that has a sum of 4 4/12 A 3 1/5 + 1 3/7. B 1 11/12 + 2 1/4. C 1 3/6 + 1 1/2 + 1 3/4. D 1 1/3 + 1 1/2 + 2 1/3. E 3/6 + 1 2/4 + 2 1/3
Find the equation of a line that passes through the points (-4,-3) and (4,-1)
Answer:
y=x/4 - 2
Step-by-step explanation:
First, find the slope:
m=(y2-y1)/(x2-x1) ==> slope formula where m=slope
(x1, y1), (x2, y2) ==> (x1=-4, y1=-3) and (x2=4, y2=-1)
Now plug in known values back into the slope formula:
m=(-1-(-3))/(4-(-4))
m=(-1+3)/(4+4)
m=2/8 ==> simplify
m=1/4
y=mx+b ==> slope-intercept equaiton form
-1=(1/4)(4)+b ==> plug in the slope, m=1/4, and a known coordinate: (4,-1)
-1=1+b ==> simplify
-1-1=1-1+b ==> solve for b
b=-2
y=(1/4)x+(-2) ==> plug in b=-2 and m=1/4 back into y=mx+b
y=x/4 - 2
Given m
|| n, find the value of x and y.
(8x+1)°
Z
(4y+3)
(9x-16)°
m
72
Use photo for better explanation PLEASE HELP
Answer:
(x, y) = (17, 10)
Step-by-step explanation:
You want the values of x and y given three angles written in terms of x and y at a transversal crossing parallel lines.
Corresponding anglesAngles at lower right of the points of intersection are corresponding angles, and are congruent:
(9x -16)° = (8x +1)°
x = 17 . . . . . . . . . . . . . divide by °, add 16-8x
Linear pairThe marked angles at the bottom form a linear pair, so are supplementary.
(4y +3)° = 180° -(9x -16)°
4y +3 = 180 -9(17) +16 = 43 . . . . . . use 17 for x and simplify
4y = 40 . . . . . . subtract 3
y = 10 . . . . . . divide by 4
Use the given values of n and p to find the minimum usual value u - 20 and the maximum usual value u + 20. Round your answer to the nearest hundredth unless otherwise noted. n = 108 p = 0.24
The minimum usual value, μ-2σ is 17.8 and the maximum usual value, μ+2σ is 54.04
How to find the minimum and maximum usual values?From the information, n = 108, p = 0.24
minimum usual value μ-2σ
maximum usual value μ+2σ
Find the mean, μ:
μ = np = 108 × 0.24 = 35.92
Find the variance, n(1-p):
n(1-p) = 108 ×( 1-0.24) = 82.08
Find the standard deviation, σ:
σ = √82.08 = 9.06
minimum usual value, μ-2σ:
μ-2σ = 35.92 - (2×9.06) = 17.8
maximum usual value, μ+2σ:
μ+2σ = 35.92 + (2×9.06) = 54.04
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find the dimensions of a rectangle with area 64000 m2 whose perimeter is as small as possible. (give your answers in increasing order, to the nearest meter.)
the dimensions of a rectangle with area 64000 m2 whose perimeter is as small as possible. (give your answers in increasing order, to the nearest meter.)Length: 200 m and Width: 320 m
The area of a rectangle is given by the formula A = lw, where l is the length and w is the width. To find the dimensions of a rectangle with an area of 64000 m2 and a perimeter that is as small as possible, we can use the formula P = 2l + 2w. We can use this to create an equation with the area and solve for l and w: 64000 = lw, and 2l + 2w = P (min). Solving for l and w, we get l = 200 m and w = 320 m. Thus, the dimensions of the rectangle with an area of 64000 m2 and a perimeter that is as small as possible are 200 m by 320 m.
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Solve for f.
f 3 = 8
f =
suppose baby kittens' weights are normally distributed with a mean of 12.3 and a standard deviation of 2.2. the z-score tells you how many units above the average (if z-score is positive) or below the average (if z-score is negative) any particular baby kitten's weight is. find the baby kitten weight that corresponds to the following z-scores given below. hint: use the formula x
X-μ Use the formula Z where is the mean, o is the standard deviation, and X is the baby kitten σ weight. a. Z= 1.98, X = b. Z-2.87, X =
X-μ Use the formula Z where is the mean, o is the standard deviation, and X is the baby kitten σ weight. a. Z= 1.98, X = b. Z-2.87, X ,,a. X = 16.786 , b. X = 8.014
To find the baby kitten weight corresponding to the given z-scores, we use the formula X = μ + Zσ, where μ is the mean, σ is the standard deviation, and Z is the z-score. For the first z-score of 1.98, we substitute the values and solve for X. X = 12.3 + (1.98)(2.2) = 16.786. For the second z-score of 2.87, we substitute the values and solve for X. X = 12.3 + (2.87)(2.2) = 8.014. Therefore, the baby kitten weights corresponding to the given z-scores are 16.786 and 8.014, respectively.
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assume victoria's indifference curves are bowed outward but her indifference curves satisfy the other three properties of indifference curves. as victoria moves from right to left along the horizontal axis, her marginal rate of substitution
The marginal rate of substitution (MRS) is a measure of how much of one good an individual is willing to give up in exchange for another good. In other words, it represents the slope of the indifference curve at a given point.
If Victoria's indifference curves are bowed outward, it means that as she moves from right to left along the horizontal axis, the MRS will decrease. This is because as she consumes more of one good, she becomes less willing to give up units of the other good in exchange. The MRS will continue to decrease until it reaches its minimum value at the point where the indifference curve is tangent to the budget line.
It's important to note that the MRS will only decrease if Victoria's indifference curves satisfy the other three properties of indifference curves:
Higher indifference curves represent a higher level of utility.Indifference curves do not intersect.Indifference curves are downward sloping.If Victoria's indifference curves do not satisfy these properties, it is not possible to accurately determine the behavior of her MRS as she moves from right to left along the horizontal axis.
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a linear equation is graphed to the left. which of the following equations combines with the graphed equation to create a system of equations whose solution set is comprised of the points
To get the equation which combines with the graphed equation to create a system of equations whose solution set is comprised of the points (−1,−5) and (3,3) we need to plug the points into each equation choice.
Therefore , this is the first step to solve this equation.
The equations of degree 1 are known as linear equations.
These are the equations which are defined for a straight line in a coordinate system.
A linear equation is one that describes a straight line. The general form of a linear equation is y= mx + b, where m denotes the slope and b its y-intercept.
Note:
The complete question is ,
A linear equation is graphed to the left. Which of the following equations combines with the graphed equation to create a system of equations whose solution set is comprised of the points (−1,−5) and (3,3)?
WHAT IS THE FIRST STEP IN SOLVING THIS PROBLEM?
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Choose the correct solution graph for the inequality.
7x+2≥30 or 2x-3≤-11 PLEASE HELP I HAVE 2 HOURS
Answer:
Therefore, the correct solution graph for the inequality is a line with no solution. This means that there is no value of x that satisfies both inequalities at the same time.
Step-by-step explanation:
To solve this inequality, we need to consider the two separate cases of 7x+2≥30 and 2x-3≤-11 separately.For the first case, 7x+2≥30, we can rewrite the inequality as 7x≥28, which simplifies to x≥4. This means that the solution for this inequality is x≥4.For the second case, 2x-3≤-11, we can rewrite the inequality as 2x≤-8, which simplifies to x≤-4. This means that the solution for this inequality is x≤-4.To find the combined solution for both inequalities, we need to take the intersection of these two solutions. The intersection of x≥4 and x≤-4 is the empty set, which means that there is no solution that satisfies both inequalities
Which statement proves that parallelogram KLMN is a rhombus?
d. The slope of KM is 1 and the slope of NL is -1.
The midpoint of both diagonals is (4 1/2, 5 1/2), the slope of RP is 7, and the slope of SQ is -1/7
Answer: D is the right answer .The slope of KM is 1 and the slope of NL is –1.
A rhombus is a parallelogram whose all sides are equal. Its diagonals perpendicularly bisect each other.
i.e. product of its slope should be -1.
[∵if one line is perpendicular to the other lines then product of its slope should be -1.]
Slope of KM= 1
Slope of NL= -1
Product of slope of diagonals=1×-1=-1
∴diagonals of given parallelogram perpendicularly bisect each other.
Therefore, it is a rhombus.
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How do you know that segment AD is congruent to segment BC ? Lesson (2-1)
Two line segments are said to be congruent if, regardless of their orientation or position, their lengths are the same.
What are congruent Triangles ?If the matching sides and angles of two triangles are the same length, then the triangles are said to be congruent.
What are Two congruent Sides ?Two sides that are the same length make up an isosceles triangle .In addition, it contains two equal-sized angles located across from the two sides of equal length. A triangle with three identical sides is called an equilateral triangle.
So
According to the given information
Segment AD = Segment BC
Two line segments are said to be congruent if, regardless of their orientation or position, their lengths are the same.
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Match each data set with its range.
The range of the data set are
{10.2, 3.8, 21.9, 33.4, 31.8, 17.2} = 29.6
{0.5, 0.65, 0.22, 0.11, 0.47, 0.55, 0.55, 0.71} = 0.6
{6, 2, 14, 11, 28, 10, 19, 15, 11} = 26
The first data set is
{10.2, 3.8, 21.9, 33.4, 31.8, 17.2}
The range is the difference between the highest value and the smallest value
The highest value = 33.4
Lowest value = 3.8
The range = 33.4 - 3.8
= 29.6
The second data set is
{0.5, 0.65, 0.22, 0.11, 0.47, 0.55, 0.55, 0.71}
The highest value = 0.71
Lowest value = 0.11
The range = 0.71 - 0.11
= 0.6
The third data set is
{6, 2, 14, 11, 28, 10, 19, 15, 11}
Highest value = 28
Lowest value = 2
The range = 28 - 2
= 26
Therefore, the range of the each data set has been found
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Simplify each algebraic expression by combining like terms.
2x+ (9+x) -6
Answer:
3x +3
Step-by-step explanation:
You want to simplify 2x+ (9+x) -6.
Like termsLike terms have the same constellation of variables. Here, there are terms containing x, and terms not containing x.
2x+ (9+x) -6 = (2 +1)x +(9 -6) = 3x +3
The simplified expression is 3x +3.
Answer:3x+3
Step-by-step explanation:
First we remove the parenthesis because they are not needed in an addition problem to make it 2x+9+x-6
Then we sort and combine like terms, [2x+x]+[9-6]
After that, you add the coefficients of the the first term, which makes 3x and subtract 6 from 9 to get 3
This then leads you to 3x+3
Blue Skies Inc. is a retail gardening company that is piloting a new strategic initiative aimed at increasing gross profit. Currently, the company’s gross profit is 25% of sales, and its target gross profit percentage is 30%. The company’s current monthly sales revenue is $600,000. The new initiative being piloted is to produce goods in-house instead of buying them from wholesale suppliers. Its in-house production process has two procedures. The makeup of the costs of production for Procedure 1 is 40% direct labor, 45% direct materials, and 15% overhead. The makeup of the costs of production for Procedure 2 is 60% direct labor, 30% direct materials, and 10% overhead. Assume that Procedure 1 costs twice as much as Procedure 2.
The Cost make up of procedure 1 is $280000.
Cost make up of procedure 2 is 140000
What is the cost make up?The cost makeup will be calculated thus:
Cost make up of procedure 1
Labour (40%) 112000
Materials (45%) 126000
Overhead (15%) 42000
Total =[280000
Cost make up of procedure 2
Labour ( 60%) 84000
Materials (30%) 42000
Over head (10%) 14000
Total 140000
Working note:
Sales $600000
Less: Gross profit (sale *30%) $ 180000
COGS $420000
Procedure 1 ( COGS *2/3) $ 280000
Procedure 2 (COGS * 1/3) $ 140000
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Complete question
Blue Skies Inc. is a retail gardening company that is piloting a new strategic initiative aimed at increasing gross profit. Currently, the company’s gross profit is 25% of sales, and its target gross profit percentage is 30%. The company’s current monthly sales revenue is $600,000. The new initiative being piloted is to produce goods in-house instead of buying them from wholesale suppliers. Its in-house production process has two procedures. The makeup of the costs of production for Procedure 1 is 40% direct labor, 45% direct materials, and 15% overhead. The makeup of the costs of production for Procedure 2 is 60% direct labor, 30% direct materials, and 10% overhead. Assume that Procedure 1 costs twice as much as Procedure 2.
Determine what the cost of labor, materials, and overhead for both Procedures 1 and 2 would need to be for the company to meet its target gross profit.
Use Elimination for the answer on both :)
The value of x and y after solving the equation -5x - 10y = 30 and - 3x + 3y = 27 by elimination method is -6 and 3 respectively.
What is the equation?A formula known as an equation uses the equals sign to denote the equality of two expressions.
Given:
-5x - 10y = 30 and - 3x + 3y = 27
Solve by using the elimination method,
Divide the equation - 3x + 3y = 27 by 3 and equation -5x - 10y = 30 by 5 on both sides,
(- 3x + 3y) / 3 = 27 / 3 and (-5x - 10y) / 5 = 30 / 5
-x + y = 9 and -x - 2y = 6
Subtract equation
-x + y = 9 - (-x - 2y = 6)
-x + y - 9 = x - 2y - 6
y = 3
and - x + 3 = 9, x = -6
Therefore, the value of x and y after solving the equation -5x - 10y = 30 and - 3x + 3y = 27 by elimination method is -6 and 3 respectively.
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f(x)=7-2x
g(x)=x+3
find (fog^-1)(5)
3 is the value of (fog⁻¹)(5) for functions f(x)=7-2x and g(x)=x+3.
What is a function?A relation is a function if it has only One y-value for each x-value.
Given that the functions are f(x)=7-2x and g(x)=x+3.
We need to find the value of (fog⁻¹)(5)
g⁻¹(x)=x-3.
By composite functions
f(g⁻¹)(x)=7-2(x-3)
f(g⁻¹)(x)=7-2x+6
Now plug in the value of x as 5
f(g⁻¹)(5)=7-2(5)+6
=7-10+6
=-3+6
=3
Hence, the value of (fog⁻¹)(5) is 3.
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t: w = 7:2
p:r = (4t+w) : (t +9w)
Calculate the ratio p : r.
Give your answer in its simplest form.
The ratio of p:r is 6/5
What is ratio?A ratio can be described as the comparison of two or more numbers which indicates their sizes in relation to one another.
From the information given, we have that;
t: w = 7:2
We have that;
t =7w = 2p:r = (4t+w) : (t +9w)Now, substitute the values into the formula
p = 4t + w
p = 4(7) + 2
expand the bracket
p = 28 + 2
Add the values
p = 30
r = t + 9w
r = 7 + 9(2)
expand the bracket
r = 25
The ratio, p:r
p:r = 30/25
p: r = 6/5
Hence, the value is 6/5
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Determine whether the system of equations is consistent or inconsistent and if it is independent or dependent.
3x+y=−5
3y+15=−9x
Multiple choice question.
A)
consistent and dependent
B)
consistent and independent
C)
inconsistent
D)
inconsistent and dependent
Answer:
C) inconsistent
Step-by-step explanation:
3x+y=−5
3y+15=−9x
3x + y = -5
9x + 3y = 15
3x + y = -5
3x + y = 5
The system graphs as two parallel lines.
Answer: C) inconsistent
Determine the value of x that makes Triangle ABC congruent to Triangle XYZ
Solve for 2 sin A sin B =
2 sin A sin B with two angles A and B, 2 sin A sin B = cos (A-B) - cos (A + B). The 2sinasinb formula is equivalent to the difference between the angle sum and the angle difference of the cosine functions. The formula for two sins is two sins A and two sins B: cos (A-B) - cos (A + B).
What is 2SinASinB Identity?
2SinASinB identity is a trigonometric formula and it is used for the simplification of trigonometric expressions. It is also used for evaluating integrals involving trigonometric functions for easy calculation. We can derive the formula for 2SinASinB using the angle sum and angle difference formulas of the cosine function. Using the 2SinASinB formula, we can derive another trigonometric formula for SinA SinB given by, sinA sinB = (1/2)[cos(A - B) - cos(A + B)].
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Consider the matrices
S= 4 1 and T= 0 4
-3 -2 -4 3
Show that multiplication of matrices is not commutative by determining the product matrices ST and TS. Enter your answer by filling in the boxes.
ST= ______ TS= _________
Multiplication of matrices is not commutative by determining the product matrices ST and TS .
Given :
Consider the matrices
S = [tex]\left[\begin{array}{ccc}4&1\\-3&-2\end{array}\right][/tex] and T = [tex]\left[\begin{array}{ccc}0&4\\-4&3\end{array}\right][/tex]
Show that multiplication of matrices is not commutative by determining the product matrices ST and TS.
ST = [tex]\left[\begin{array}{ccc}4&1\\-3&-2\end{array}\right][/tex] [tex]\left[\begin{array}{ccc}0&4\\-4&3\end{array}\right][/tex]
[tex]ST_{11[/tex] = 4 * 0 + 1 * -4 = -4
[tex]ST_{12[/tex] = 4 * 4 + 1 * 3 = 19
[tex]ST_{21[/tex] = -3 * 0 + -2 * -4 = 8
[tex]ST_{22[/tex] = -3 * 4 + -2 * 3 = -18
ST = [tex]\left[\begin{array}{ccc}-4&19\\8&-18\end{array}\right][/tex]
TS = [tex]\left[\begin{array}{ccc}0&4\\-4&3\end{array}\right][/tex] [tex]\left[\begin{array}{ccc}4&1\\-3&-2\end{array}\right][/tex]
[tex]TS_{11[/tex] = 0 * 4 + 4 * -3 = -12
[tex]TS_{12[/tex] = 0 * 1 + 4 * -2 = -8
[tex]TS_{21[/tex] = -4 * 4 + 3 * -3 = -25
[tex]TS_{22[/tex] = -4 * 1 + 3 * -2 = -10
TS = [tex]\left[\begin{array}{ccc}-12&-8\\-25&-10\end{array}\right][/tex]
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3) Suppose you finance a car in the amount of $28,550. The loan is for 7 years with an APR of
8%. What will be the payoff balance of this car loan after 4 years?
The
Answer:
So the payoff balance of the car loan after 4 years will be approximately $22,169.73.
Step-by-step explanation:
payoff balance after 4 years can be calculated using the following formula:
Payoff balance = Principal * (1 + APR/n)^(nt) - [(Principal * (1 + APR/n)^(nt) * (APR/n)) / (1 + APR/n - 1)]
Where:
Principal is the loan amount, which is $28,550 in this case.
APR is the annual percentage rate, which is 8% in this case.n is the number of times per year that interest is compounded, which is usually 12 for monthly compounding.t is the number of years for which the loan is taken, which is 4 years in this case.
Plugging in the values, we get:
Payoff balance = $28,550 * (1 + 0.08/12)^(124) - [($28,550 * (1 + 0.08/12)^(124) * (0.08/12)) / (1 + 0.08/12 - 1)]
Payoff balance = $28,550 * 1.006669^48 - [$28,550 * 1.006669^48 * 0.006669] / 0.006669Payoff balance = $22,169.73