Answers
Answer:
[tex]\huge\boxed{\dfrac{x^2+9^2}{x-3y}+\dfrac{6xy}{3y-x}=x-3y}[/tex]
Step-by-step explanation:
Domain:
[tex]x-3y\neq0\Rightarrow x\neq3y[/tex]
[tex]\dfrac{x^2+9y^2}{x-3y}+\dfrac{6xy}{3y-x}=\dfrac{x^2+9y^2}{x-3y}+\dfrac{6xy}{-(x-3y)}\\\\=\dfrac{x^2+9y^2}{x-3y}-\dfrac{6xy}{x-3y}=\dfrac{x^2+9y^2-6xy}{x-3y}\\\\=\dfrac{x^2-2(x)(3y)+(3y)^2}{3y-x}=\dfrac{(x-3y)^2}{3y-x}\\\\=\dfrac{\bigg[-1(3y-x)\bigg]^2}{3y-x}=\dfrac{(-1)^2(3y-x)^2}{3y-x}\\\\=\dfrac{1(x-3y)(x-3y)}{x-3y}=x-3y[/tex]
Used:
The distributive property: a(b + c) = ab + ac
(a - b)² = a² - 2ab + b²
Related Questions
What is the solution set to the inequality m-7>-2(m+0.5)?
Select a ray. Move the point on the ray to the correct place on the number line.
Answers
The solution set to the inequality m-7>-2(m+0.5) is all real numbers greater than -0.75.
What is real numbers?Real numbers are the set of all rational and irrational numbers, which includes all positive and negative numbers, fractions, decimals, and integers. They are represented on the number line and are composed of an infinite amount of numbers between any two given numbers.
This can be represented graphically on a number line by selecting a ray starting at -0.75 and extending infinitely in the positive direction. The point on the ray at -0.75 represents the boundary between the solution set and the numbers not included in the solution set.
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I have a few math problems I need help with so they're all in picture form (and in separate questions). I'd appreciate it if they were explained to me, but it is not a requirement.
Answers
Answer:
In those questions you asked, we can use equation to find the answer but the 1st question's x did not get an exact value so you can do no solution. Thank you
3. A car can accelerate at a rate of 0.5 meters per second squared if it is already moving forwards at an initial velocity of 6 meters per second.
a. Write a differential equation for velocity. Write an initial condition for the velocity.
b. Solve the initial value problem you wrote in (a) to find a formula for velocity.
c. Use the formula for the velocity you found in (b) to write an initial value problem for the car’s position. Assume that the car is initially at position 0.
d. Solve the initial value problem you wrote in (c) to find a formula for the position of the car.
e. How fast is the car going after 30 seconds?
Answers
Using the relation between acceleration, velocity and distance, it is found that:
a) The differential equation for the velocity is: [tex]\frac{dV}{dt} = 0.5[/tex]
b) The formula for the velocity is given by: V(t) = 0.5t + 6.
c) The initial value problem to find the position is: [tex]\frac{dS}{dt} = 0.5t + 6, S(0) = 0[/tex]
d) The formula for the position of the car is S(t) = 0.25t² + 6t.
e) The car is at a velocity of 21 m/s after 30 seconds.
What is the relation between acceleration, velocity and distance?We have that:
The velocity is the integral of the acceleration.The position is the integral of the velocity.For item a, we have that the acceleration is constant of 0.5 m/s², hence the differential equation for the velocity is:
[tex]\frac{dV}{dt} = 0.5[/tex]
For item b, we apply separation of variables, and find the velocity as follows:
[tex]\frac{dV}{dt} = 0.5[/tex]
[tex]\int dV = \int 0.5 dt[/tex]
V(t) = 0.5t + v(0).
v(0) is the initial velocity and is the constant of integration, hence:
The formula for the velocity is given by: V(t) = 0.5t + 6.
For item c, we have that the position is the integral of the velocity, hence:
The initial value problem to find the position is: [tex]\frac{dS}{dt} = 0.5t + 6, S(0) = 0[/tex]
For item d, applying separation of variables, we have that:
[tex]\frac{dS}{dt} = 0.5t + 6[/tex]
[tex]\int dS = \int (0.5t + 6) dt[/tex]
S(t) = 0.25t² + 6t + s(0).
Since s(0) = 0, we have that:
The formula for the position of the car is S(t) = 0.25t² + 6t.
The velocity after 30 seconds is of:
v(30) = 6 + 0.5(30) = 21.
The car is at a velocity of 21 m/s after 30 seconds.
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A portfolio has a risk free rate of 3.5%, an expected return of 12.9%, and a sharpe ratio measure of 2.99. Find the standard deviation of the portfolio return.
Answers
The standard deviation of the portfolio return is 3.14%
What is Sharpe ratio?
Sharpe ratio measures the by extent to which the risk of an investment portfolio is compensated as it indicates the return per unit of risk inherent in the portfolio whereas the standard deviation measures the risk of expected return of the portfolio.
It should be noted that the Sharpe ratio can be determined as the expected return of the portfolio minus the risk-free rate of return divided by the standard deviation of the portfolio.
Sharpe ratio=(expected return-risk-free rate)/standard deviation
Sharpe=2.99
expected return=12.9%
risk-free rate=3.5%
standard deviation=unknown(assume it is x)
2.99=(12.9%-3.5%)/x
2.99*x=9.40%
x=9.40%/2.99
x=3.14%
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Translate the figure 2 units legt and 4 units down. What are the coordinates of the image?
Answers
Answer:
[tex]A_{new}=(-3,0)\\B_{new}=(0,-1)\\C_{new}=(1,-4)\\D_{new}=(-3,-5)[/tex]
Step-by-step explanation:
Looking at the diagram, you can see and determine the following points, write them down:
A=(-1,4)
B=(2,3)
C=(3,0)
D=(-1,-1)
Translating 2 units left means x changes by (-2)
Translating 4 units down means y changes by (-4)
Old Point + Point Change = New Point
[tex]A_{old}+T=A_{new}\\A_{old}=(-1,4)\\T=Translation=(-2,-4)\\A_{old}+T=(-1,4)+(-2,-4) = A_{new}=(-3,0)[/tex]
[tex]B_{old}=(2,3)\\C_{old}=(3,0)\\D_{old}=(-1,-1)\\T=(-2,-4)\\B_{new}=(2,3)+(-2,-4)=(0,-1)\\C_{new}=(3,0)+(-2,-4)=(1,-4)\\D_{new}=(-1,-1)+(-2,-4)=(-3,-5)[/tex]
Which system of inequalities represents the graph?
y−6≤−11x
y+3x≤−4
−2x+3y<15
y−6≤−11x
y+3x≥−4
−2x+3y>15
y+11x≥6
y+4≥−3x
−2x+3y>15
y+11x≥6
y+4≤−3x
−2x+3y<15
Answers
The system of inequalities that represents the graph are:
y−6≤−11x
y+3x≥−4
−2x+3y>15
Option B
This is further explained below.
What is a system of equalities?Generally, The term "set of simultaneous equations" refers to a finite collection of equations in the subject of mathematics, all of which are looking for the same solution.
A system of equations or an equation system is a name that is sometimes used to refer to this kind of collection of equations.
In conclusion,
y−6≤−11x
y+3x≥−4
−2x+3y>15
represents the graph
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What type of number is √14? (square root of 14) Multiple answers can be selected.
A. Rational
B. Irrational
C.Natural
D. Whole
F. Integer
Answers
Square root of 14=3.74, which is not an integer making it an irrational number
Answer:
B. Irrational
Step-by-step explanation:
The √14 = 3.74 recurring. This isn't an integer and therefore can't be written as a fraction. Therefore it's an irrational number.
Whereas, if it was √16 which equals 4, the answer would be rational as it is an integer which can be written as a fraction such as 4/1 or 8/2 etc.
The mass of the Earth is about 6,000,000,000,000,000,000,000,000 kg. The mass of a human toddler's brain is about 400 grams. SHOW ALL WORK
(a) What is the mass of the Earth written in scientific notation?
(b) What is the mass of a toddler’s brain in scientific notation?
(c) In comparing the measurements in Parts (a) and (b), what else must be done before a comparison is made?
(A) = 6 x 10^24
(B) = 4 x 10^2
(C) but i need help on C cause I think you have to combine the kg and grams but I dont know how
Answers
Step-by-step explanation:
that's why it is so important to always write also the units a number represent.
and for a fully nice scientific notation you write also at least 1 digit after the decimal point.
(a) 6.0 × 10²⁴ kg
(b) 4.0 × 10² g
now,
1 kg = 1000 g ("kilo" means 1000)
so, in order to be able to compare the 2 numbers, you have to bring both numbers to the same unit. either both to kg or both to g.
6.0 × 10²⁴ kg = 6.0 × 10²⁴ × 1000 g = 6.0 × 10²⁷ g
or
4.0 × 10² g = 4.0 × 10² / 1000 kg = 4.0 × 10^-1 kg
once you have both showing the same unit, you can truly compare them.
complete exercises 22 - 24.
X
h(x)
-3
-24
-2
0
-1
8
0
6
1
0
2
-4
4
18
13. Two of the zeros of h(x) are listed in the table. Between which two values of x does the Intermediate
Value Theorem guarantee that a third value of x exists such that h(x) = 0? Explain your reasoning.
Answers
Answer:
send the image of the exercise
7th-grade question
4. If a snail can move 3/10 of a meter every 1/12 hour, what is the speed of
the snail, in meters per hour?
A. 1/40
B. 5/18
C. 1 1/2
D. 18/5
Answers
Answer:
18/5 which also equals 3 3/5 would be the answer
Graph the image of the pre-image shown below, translated 4 units to the right, and 8 units down.
PLEAS ANSWER QUICK ASAP
Answers
The image of the transformation on the graph are (7, -7), (7, -2) and (-1, -14)
How to plot the graph of the function?The graph represents the given parameter
On the graph, we have the coordinates of the triangle to be
(3, 1), (3, 6) and (-5, -6)
The transformation rule is given as
Translated 4 units to the right, and 8 units down.
Mathematically, the transformation rule is given as
(x, y) = (x + 4, y - 8)
When the above transformation rule is applied to the coordinates of the triangle, we have
(3 + 4, 1 - 8), (3 + 4, 6 - 8) and (-5 + 4, -6 - 8)
Evaluate the sum and the difference
So, we have
(7, -7), (7, -2) and (-1, -14)
Next, we plot the image of the transformation on the graph
See attachment for the image of the transformation of the triangle on the graph
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Mercury is 5.8 x 10^7 km from the sun. Neptune is 4.5 x 10^10 km from the sun. How much further is Neptune from the sun than Mercury?
Divide the distances: (4.5 x 10^10)/(5.8 x 10^7)-.76 x 10^3=7.6 x 10^2
Subtract the distances by getting the same power of 10: (4.5 x 10^10) - (5.8 x 10^7)-(4.5 x 10^10)-(.0058 x 10^10) = 44.99 x 10/10km
Add the distances together: (5.8 x 10^7) 4.5 x 10^10) - 10.3 x 10^17-1.03 x 10^18km
Multiply the distances: (5.8 x 10^7) x (4.5 x 10^10) = (5.8 x 4.5) x (10^17)-26.1 x 10^17-2.61 x 10^16
Answers
The distance of Neptune from the sun than Mercury will be B. Subtract the distances by getting the same power of 10: (4.5 x 10^10) - (5.8 x 10^7)-(4.5 x 10^10)-(.0058 x 10^10) = 44.99 x 10/10km.
How to calculate the value?From the information, Mercury is 5.8 x 10^7 km from the sun and Neptune is 4.5 x 10^10 km from the sun.
It should be noted that since we want to find the difference, therefore, we've to subtract.
Therefore, distance of Neptune from the sun than Mercury will be Subtract the distances by getting the same power of 10: (4.5 x 10^10) - (5.8 x 10^7)-(4.5 x 10^10)-(.0058 x 10^10) = 44.99 x 10/10km.
In conclusion, the correct option is B.
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In an effort to keep low-wage workers' salaries commensurate with the cost of living, a number of states have amended their constitutions to allow the minimum wage to be adjusted with inflation.
You are the accountant for a company that owns a chain of 16 fast food restaurants in a state which adjusts the minimum wage for inflation. Each restaurant employs 55 workers, each averaging 20 hours per week at the current federal minimum wage, $7.25 per hour.
(d)
How much in "additional wages" will the company have to pay out next year at the adjusted rate (in $)? (Round your answer to the nearest dollar.)
Answers
The "additional wages" that the company will have to pay out next year at the inflation-adjusted rate of 7.5% (in $) is $494,208.
What is the inflation-adjusted pay rate?The inflation-adjusted pay rate is the rate after adjusting for inflation.
Data and Calculations:The number of fast-food restaurants = 16
The number of workers per restaurant = 55
Average weekly hours per worker = 20 hours
The number of weeks per year = 52
The current federal minimum wage per hour = $7.25
The total hours worked by the workers = 915,200 hours (16 x 55 x 20 x 52)
Total current wages = $6,635,200 (915,200 x $7.25)
Inflation rate = 7.5%
Inflation-adjusted wage rate = $7.79 ($7.25 x 1.075)
Total wages for next year = $7,129,408 ($7.79 x 915,200)
Additional wages next year = $494,208 ($7,129,408 - $6,635,200)
Thus, the "additional wages" that the company will have to pay out next year at the inflation-adjusted rate of 7.5% (in $) is $494,208.
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Is 14 a factor of 3,024
Answers
Answer:
Yes, 14 × 216 = 3024
Step-by-step explanation:
Which set of ordered pairs does not represent a function?
OA) { (-2,5), (-4,6), (1,2), (6,5)}
O B) { (-7,-5), (-9,4), (9,4), (1,-6)}
O c) { (5,-6),(5,9),(0,3), (-7,-9)}
D) {(5,2), (-1,-1), (-8,-1), (-7,1)}
Answers
Answer:
Answer for this question is C because, 1 input has 2 outputs. And that's why C doesn't represent a function.
1. Given the following set of values, what two numbers would you subtract to find the interquartile range?
17 21 19 23 16
22 19 20 24 18
22 minus 18
22 minus 16
O24 minus 16
24 minus 19
Answers
The two numbers that you would subtract to find the interquartile range (IQR) of the set of values are: A. 22 - 18.
What is the Interquartile Range of a Data Set?The interquartile range (IQR) = Upper quartile (Q3) = lower quartile (Q1).
Given the data set, 17, 21, 19, 23, 16, 22, 19, 20, 24, 18, we have the following:
Upper quartile (Q3): 22 (center of the second half of the data)
Lower quartile (Q1): 18 (the middle/center of the first part of the data)
Interquartile range (IQR) = 22 - 18
Interquartile range (IQR) = 4
Therefore, the two numbers that you would subtract to find the interquartile range (IQR) of the set of values are: A. 22 - 18.
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Ian measures 9 kg of rice. One kilogram is approximately equal to 2.2 pounds. Which measurement represents the number of pounds of rice?
Answers
By using multiplication, we get that the number of pounds of rice will be 19.8 pounds.
We are given that:
1 kg of rice = 2.2 pounds of rice.
We need to find the number of pounds of rice in 9 kg of rice.
So, we will use the operation of multiplication to covert the units from kg into pounds.
So, we get that:
9 kg of rice = 2.2 × 9 pounds of rice
9 kg of rice = 19.8 pounds of rice.
Therefore, by using multiplication, we get that the number of pounds of rice will be 19.8 pounds.
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7. y = x + 5
8. y=x-7
9. y=x-b
Solve for x: ax + b = c.
Answers
X= c/a - b/a for the last one
Help me solve this question
Answers
Answer:
x = -26
Step-by-step explanation:
[tex](f-g)(x)=\frac{4}{x-3}-\frac{3}{x+5}=\frac{3}{x^2 +2x-15} \\ \\ \frac{4(x+5)-3(x-3)}{x^2 +2x-15} \\ \\ =\frac{4x+20-3x+9}{x^2 +2x-15}=\frac{3}{x^2 +2x-15} \\ \\ \frac{x+29}{x^2 +2x-15}=\frac{3}{x^2+2x-15} \\ \\ x+29=3 \\ \\ x=-26[/tex]
This is in the domain of the equation, and is thus a solution.
At 6 AM the temperature was -6 Fahrenheit between 6 AM and 3 PM. The temperature‘s rose 11° between 3 PM and midnight the temperatures fell 7° write a number sentence that shows how to find the temperature at midnight then write the midnight temperature.
Answers
The number sentence is 5 - 7 and temperature at midnight is equal to -2°F .
What is algebra ?
Algebra is a branch of mathematics that deals with various symbols and the arithmetic operations such as addition , subtraction , etc.
The temperatures are given at different time of a day. It is given that the final temperature was the temperature that existed at midnight. Firstly temperature rise between 6 AM and 3PM by 11° from - 6 °F at 6 AM and then between 3PM and midnight it fell by 7°.
So , we can show these variations as follows :
At 6AM temperature = - 6 °F
Between 6AM and 3 PM temperature rose by 11° , so temperature at 3 PM will be :
= - 6 + 11
= 5 °F
Between 3PM and midnight the temperature fell by 7° , so the number sentence will be :
= 5 - 7
And the temperature at midnight will be :
= -2°F
Therefore , the number sentence is 5 - 7 and temperature at midnight is equal to -2°F .
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Guys this is an important question do NOT PUT A RANDOM ANSWER OR WRITE RANDOM THINGS
It’s annoying man
Answers
Answer: 1/7
Step-by-step explanation:
The total amount of cars that had AC problems is 30+20=50. The total amount of cars is 30+20+200+100=350. 50/350 = 1/7
Rochelle had an important swim meet coming up, so she made a schedule for herself for extra practice. She practiced for 609 minutes over a 3-week time span to get herself ready. She spent the same amount of time practicing each week. What is the constant of proportionality (k) between the number of minutes Rochelle practiced (m) and the number of weeks she spent practicing (w)?
Answers
Over the course of three weeks, she practiced for 609 minutes to become ready. The constant of proportionality is k=203.
Given that,
Rochelle planned out additional practice because she was getting ready for a big swim meet.
Over the course of three weeks, she practiced for 609 minutes to become ready. Every week she practiced for the same amount of time.
We have to find the constant of proportionality (k) between Rochelle's weekly practice time (w) and the number of minutes she practiced each week (m).
3 week =609 minutes
3w=609m
1w=609m/3
1w=203m
For 1 week she practiced 203 minutes.
Now,
Constant of proportionality is
m=kw
203=k(1)
k=203
Therefore, the constant of proportionality is k=203.
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Identify a pattern in the given list of numbers. Then use this pattern to find the next number. (More than one pattern might exist, so it is possible that
there is more than one correct answer.)
31, 27, 23, 19, 15,
Answers
Answer:
pattern: numbers decrease by 4next number: 11Step-by-step explanation:
You want the next number in the sequence 31, 27, 23, 19, 15, ... such that it follows the same pattern.
Sequence patternsIt is often useful to look at the differences between successive terms of a sequence. This can quickly reveal a pattern if the sequence is polynomial or exponential.
Here, the differences are ...
27 -31 = -4
23 -27 = -4
19 -23 = -4
15 -19 = -4
It appears reasonable to assume that the pattern is that each term is 4 less than the previous one.
Next termThe number that is 4 less than 15 is ...
15 -4 = 11
The next number in the pattern is 11.
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The midpoint of AB is M(3, -1). If the coordinates of A are (5, 1), what are the
coordinates of B?
Answers
The coordinate of B is (1,-3)
In coordinate system mid point is the point which is exactly at the middle
The coordinates of point A are (5,1)
The coordinate of mid point M are (3,-1)
It is to be noted that mid point divides both sides in the ratio 1:1
We are required to find the coordinates of point B
Let the coordinates of B be (x,y)
For mid points, section formula further simplifies to
m's x coordinate= (a's x coordinate + b's x coordinate)/2
m's y coordinate = (a's y coordinate + b's y coordinate)/2
therefore,
3 = (5+x)/2
6=5+x
x=6-5 =1
-1 = (1+y)/2
-2 =1+y
y=-3
Hence the coordinates of B are (x,y) which is (1,-3)
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Two in-line skaters, Nell and Kristin start from the same point and skate in the same direction.Nell skates at 8 mile per hour and Kristin skates at 10 miles per hour. if they can keep up the pace for 4.5 hours, how far apart will they be at the end of the time?
Answers
At the end of 4.5 hours, Nell and Kristin will be at a distance of 9 miles apart.
Here, we are given that Nell and Kristin start from the same point and skate in the same direction.
Speed of Nell = 8 miles per hour
Time for which he skates = 4.5 hours
Thus, the distance travelled by Nell will be-
Distance = Speed × time
= 8 × 4.5
= 36 miles
Similarly, Speed of Kristin = 10 miles per hour
Time for which he skates = 4.5 hours
Thus, the distance travelled by Kristin will be-
= 10 × 4.5
= 45 miles
Thus, the distance between them will be-
45 - 36 = 9 miles.
Thus, at the end of 4.5 hours, Nell and Kristin will be at a distance of 9 miles apart.
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Nell and Kristin, two inline skaters, begin at the same location and move in the same direction. While Kristin skates at 10 miles per hour, Nell skates at 8 miles per hour. 5 miles apart will they be at the conclusion of the 4.5 hours if they maintain their current rate.
Distance =Rate x time ....... d=rt
The difference in the distances traveled will be how far apart they are 12(2.5)-10(2.5)=2(2.5)=5 miles apart
Note that you can find their individual distances and subtract those to get the same answer:
Nell: distance =10(2.5)=25 miles
Kristin: distance =12(2.5)=30$ miles
30-25=5 miles apart
Distance is the sum of an object's movements, regardless of direction. Distance may be defined as the amount of space an item has covered, regardless of its beginning or finishing position.
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Write a numerical expression for 15 minus the sum of 6 and 7
Answers
Answer:
15-(6+7)
Step-by-step explanation:
Answer:
15 - (6+7)
Step-by-step explanation:
Answer this question please
Answers
Error: They failed to account for when x-5 is negative.
Solution:
[tex]|x-5|<20 \\ \\ -20<x-5<20 \\ \\ \boxed{-15<x<25}[/tex]
Peter Sam and Ben run on a round track Peter takes hundred seconds Sam take 110 seconds and ben takes 120 seconds to run a round if they start together when will they meet again ?
Answers
Answer:
when one of them is done
Step-by-step explanation:
you can't meet together because you don't run fast the
Lori ran 5/3 miles Monday, 15/4 miles Tuesday, 9/2 miles Wednesday,
3/5 on Thursday and 2/5 miles on Friday. What is the average number of miles
Lori ran per day this week?
Answers
15/4 = 3.75 miles
9/2 = 4.5 miles
3/5 = 0.6 miles
2/5 = 0.4 miles
1.67+3.75+4.5+0.6+0.4 = 10.92/5 = 2.18 miles
Find the present value of a loan with a MONTHLY payment of $530.65 and an interest rate of 5.90% APR over 29 years, compounded MONTHLY.
Give your answer to 2 decimal places.
Answers
One person took a loan A monthly payment is $530.65. An interest rate is 5.90%. APR is over 29 years. The present value of a loan is 100.69.
Given that,
One person took a loan
A monthly payment is $530.65
An interest rate is 5.90%
APR is over 29 years.
We have to find the present value of a loan
The formula for present value of a loan is
The present value (PV) formula is used in finance to determine the present worth of money received in the future. The compound interest formula serves as the foundation for the present value formula (PV formula). The formula for compound interest is,
PV = [tex]\frac{FV}{(1+\frac{r}{n)} ^{nt}}[/tex]
Where,
PV=present value
FV=future value
r= rate of interest
n=When frequently the amount compounds
t=time
Given FV=$530.65
r= 5.90% =0.059
t=29 years
n=1(Due to the amount's annual compounding).
PV=[tex]\frac{530.65}{(1+\frac{0.059}{1})^{1\times29} }[/tex]
PV=[tex]\frac{530.65}{(1+0.059)^{29}}[/tex]
PV=[tex]\frac{530.65}{(1.059)^{29}}[/tex]
PV=[tex]\frac{530.65}{5.27}[/tex]
PV=100.69
Therefore, The present value of a loan is 100.69.
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