Need help!!
An individual borrowed $95,000 at an APR of 5%.
which will be paid off with monthly payments of $ 450 for 25 years.
Of the total amount​ paid, what percentage is paid toward the principal and what percentage is paid for​ interest?

Answers

Answer 1

Percentage of amount paid towards principal = 70.37%

Percentage of amount paid towards interest = 29.63%

What is APR?

APR is abbreviation Annual Percentage Rate. APR is estimate cost over a year of borrowing, It is expressed in percentage of the money borrowed. The higher it is, the more expensive to borrow. The lower it is, the cheaper it'll be to borrow.

Given,

Principal amount (P) = $95000

APR (R) = 5% = 0.05

Time (T)= 25 years

Amount paid monthly $450 for 25 years

There are 12 payments every year for 25 years

No. of payments,

12 × 25 = 300.

Total amount paid

3000 × $450 = $135000.

Amount paid toward Principal = $95,000

In percentage

= (95000/135000)×100

= 70.37%

Toward Interest = $135000 - $95000 = $40000

In percentage

= (95000/135000)×100

= 29.63%

Hence, 70.37% of amount is paid toward principal and 29.63% is paid for interest.

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Answer 2

Answer:

Step-by-step explanation:

To determine what percentage of the total amount paid is applied towards the principal and interest, we first need to calculate the total amount paid over the 25-year term.

The monthly payment can be calculated using the formula for a loan payment:

P = (r(PV)) / (1 - (1+r)^(-n))

where P is the monthly payment, r is the monthly interest rate (APR / 12), PV is the present value of the loan (or the amount borrowed), and n is the total number of payments (25 years * 12 months/year = 300).

Plugging in the given values, we get:

P = (0.05/12 * $95,000) / (1 - (1+0.05/12)^(-300)) = $536.82

This means that the total amount paid over the 25-year term is:

Total amount paid = 300 * $536.82 = $161,046

The amount borrowed (or the principal) is $95,000. Therefore, the amount of interest paid over the 25-year term is:

Total interest paid = $161,046 - $95,000 = $66,046

To find the percentage of the total amount paid that is applied towards the principal, we can divide the principal by the total amount paid and multiply by 100:

Percentage of total amount paid towards principal = ($95,000 / $161,046) x 100% = 59.03%

To find the percentage of the total amount paid that is applied towards interest, we can divide the interest paid by the total amount paid and multiply by 100:

Percentage of total amount paid towards interest = ($66,046)


Related Questions

A dentist’s office and parking lot are on a rectangular piece of land. The area (in square meters) of the land is represented by x^2+x−30.

Write a binomial that represents the width of the land.


b. Find the area of the land when the length of the dentist’s office is 20 meters.

Answers

Answer:

a. (x-5) meters

b. 390 m²

Step-by-step explanation:

A. We get the equation x²+x-30.

We need to find two factors of 30, which equals 1.
6 and -5 are factors of 30.
Now, we can see that (x-5) and (x+6) are the equations. (x+6) cannot be applied, so the answer is (x-5)


B. We can substitute x with 20, and when we plug it in, we get 390 meters.

simple workingo ut :)

Answers

Answer:     b = 82°

To solve for angle b, calculate using the given angles and the straight angle theorem.

Straight Angle Theorem

The straight angle theorem is a rule that says all straight lines are 180°.

Since the angle formed by XY is a straight line, it is also equal to 180°.

XY is divided into three separate angles, a, b and c.

If we add a, b, and c, it will equal to 180°.

Write an equation

XY = a + b + c                              XY is the sum of a, b, and c.

180° = 46° + b + 52°                     Substitute what we know.

To solve for b using this equation, isolate.

180° - 46° = 46° + b + 52° - 46°   Subtract 46° on both sides.

134° = b + 52°

134° - 52° = b + 52° - 52°             Subtract 52 on both sides.

82° = b                                         Keep the variable on the left.

b = 82°                                         Final answer.

Therefore, angle b is 82°.

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Please show your work step by step thank you:
9w=93;w=10
10 (is;is not) a solution

Answers

Answer:

Step-by-step explanation:

9w=93w=10

We move all terms to the left:

9w-(93w)=0

We add all the numbers together, and all the variables

-84w=0

w=0/-84

w=0

   

A regular pentagon has an area of 315.25 square meters, and each side of the pentagon measures 9.7 meters. What is the length of an apothem of the pentagon? Enter your answer in the box.

Answers

The length of the apothem of the pentagon is 12.96 meters .

What is apothem ?
In geometry, the apothem of a polygon is the distance from the center of the polygon to the midpoint of one of its sides. For a regular polygon (a polygon with all sides and angles equal), the apothem is the perpendicular distance from the center of the polygon to one of its sides.

Explanation:
The formula for the area of a regular pentagon is:

A = (1/2)P × a

where A is the area, P is the perimeter, and a is the apothem.

To solve for the apothem, we need to rearrange the formula and solve for a:

a = (2A) / P

The perimeter of a regular pentagon is given by:

P = 5s

where s is the length of each side.

Substituting the given values, we get:

P = 5s = 5(9.7) = 48.5

A = 315.25

a = (2A) / P = (2 × 315.25) / 48.5 = 12.96

Therefore, the length of the apothem of the pentagon is 12.96 meters (rounded to two decimal places).

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Answer:

Step-by-step explanation:

its 13

At the Crown Interior Pizza Hat location in Faridabad, a report showed that 431 out of 778 orders were for delivery. What is the minimum sample size needed to have a 4 percentage point error for the proportion of orders that were carry-out?


*If you used a program on the graphing calculator or formula can you specify which ones please?

Answers

Answer:

Step-by-step explanation:

To determine the minimum sample size needed to have a 4 percentage point error for the proportion of orders that were carry-out, we can use the following formula:

n = (Z^2 * p * q) / E^2

where:

n is the sample size we want to determine

Z is the z-score associated with the desired level of confidence (let's assume a 95% confidence level, so Z = 1.96)

p is the estimated proportion of orders that were carry-out (we don't know this yet, so we'll use 0.5 as a conservative estimate)

q is 1 - p (i.e., the estimated proportion of orders that were delivery)

E is the desired margin of error (in this case, 0.04)

Using the given information, we can estimate that the proportion of orders that were carry-out is:

p = 1 - 431/778 = 0.446

Then, plugging in the values into the formula, we get:

n = (1.96^2 * 0.446 * 0.554) / 0.04^2 ≈ 602.25

Rounding up to the nearest whole number, the minimum sample size needed is 603.

Note that I used the formula for sample size calculation based on a finite population, since the total number of orders is known (778). If we used the formula for an infinite population, the result would be very similar (around 604). I calculated this by hand, without using any calculator program, but you could use a calculator or a spreadsheet to perform the calculations more efficiently.

At the moment Mr Finn pays £700 per month in rent.
His landlord has informed that this will increase by 5% for the next two years and by 8% after that.
What will Mr Finn's rent be in three years' time if he stays in his current accommodation?
(4)

Answers

Mr. Finn's rent in the next 3 years will be £ 833.49

Finding increased rent:

To find the rent, calculate how much it will increase in the first and in the second year by using calculating percentages individually or using the compound interest formula. From the find total rent for next years. Using the total rent in the second year find the rent in 3rd year.

Here we have

The rent paid by Mr. Finn is £700 per month in rent.

His landlord informed him that rent will increase by 5% for the next two years and by 8% after that.

The rent in the 1st year = 700 + 5% of 700

= 700 + (5/100) 700

= 700 + 35 = 735  

In the second year again the rent will increase by 5%

The total rent in the second year = 735 + 5% of 735

= 735 + 36.75 = 771.75

After 2 years, the increment will be 8%

So, The total rent in the 3rd year year = 771.75 + 8% of 771.75

= 771.75 + (8/100) 771.75

= 833.49

Therefore,

Mr. Finn's rent in the next 3 years will be £ 833.49

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Study the table below and answer the questions that follows.
YearNominalGDP(£)
(in billions)
GDP Deflator
2000=100
Population
(million)
2012750104.045.0
2013325112.050.0
2014910121.054.0
i.Calculate the growth (percentage change) innominal GDP from 2012to 2013(2marks)
ii.What was the real GDP in 2012 and 2013 (2marks)
iii.By how much did the real GDP grow (2marks)
iv.If changes in the standard of living can be measure by changes in real capita; GDP,didthe
growth in nominal and realGDP rise the standard of living in this economy from 2012to
2013 (2marks)
v.Explain the reasons for the changes in the standards of living that you have found ​

Answers

The real GDP per capita increased by 28% from 2012 to 2013.

How to find the percentage from the total value?

Suppose the value of which a thing is expressed in percentage is "a'

Suppose the percent that considered thing is of "a" is b%

Then since percent shows per 100 (since cent means 100), thus we will first divide the whole part in 100 parts and then we multiply it with b so that we collect b items per 100 items(that is exactly what b per cent means).

We need to Write the percent as a fraction in simplest form

16.24%

So, we can rewrite it as;

16.24 / 100

16 and 24/100 or 16 6/25

So the percent as a fraction is 16 6/25

We are given that;

The table with GDP deflator and population

Now,

i. The percentage change in nominal GDP from 2012 to 2013 can be calculated as follows:

[(Nominal GDP in 2013 - Nominal GDP in 2012) / Nominal GDP in 2012] x 100

= [(112 - 75) / 75] x 100

= 49.33%

Therefore, nominal GDP grew by 49.33% from 2012 to 2013.

ii. Real GDP is nominal GDP adjusted for inflation. To find real GDP, we need to use the GDP deflator:

Real GDP (in billions) = Nominal GDP (in billions) / (GDP Deflator / 100)

In 2012: Real GDP = 75 / (50 / 100) = £150 billion

In 2013: Real GDP = 112 / (54 / 100) = £207.41 billion

iii. The percentage change in real GDP from 2012 to 2013 can be calculated as follows:

[(Real GDP in 2013 - Real GDP in 2012) / Real GDP in 2012] x 100

= [(207.41 - 150) / 150] x 100

= 38.27%

Therefore, real GDP grew by 38.27% from 2012 to 2013.

iv. To determine if the growth in nominal and real GDP increased the standard of living, we need to look at the change in real GDP per capita. Real GDP per capita is calculated by dividing real GDP by the population:

Real GDP per capita in 2012 = 150 / 50 = £3 billion

Real GDP per capita in 2013 = 207.41 / 54 = £3.84 billion

The percentage change in real GDP per capita can be calculated as follows:

[(Real GDP per capita in 2013 - Real GDP per capita in 2012) / Real GDP per capita in 2012] x 100

= [(3.84 - 3) / 3] x 100

= 28%

Therefore, by the percentage the answer will be 28% from 2012 to 2013.

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A car rental agency charges $39.99 per day, x, and $0.18 per mile to rent a car. Aaron needs to rent a car for at least 2 days. He can spend no more than $150. Which system of inequalities can be used to find the number of miles, y, Aaron can drive the car?
A X ≤ 2 39.99x+0.18y≥ 150
B. X 22 39.99x+0.18y 150.
C. X ≤ 2 0.18x +39.99y ≤ 150
D. X 22 0.18x +39.99y ≤ 150​

Answers

Answer:208 mi

 Step-by-step explanation:

If David rents the car for four days,

that's an up-front costof 4 × 23.95 = $95.80.

The other cost depends on the distance (d) he drives.

The equation for his total cost (C) isC = 0.26d + 95.80If David has needs a budget

of $150, then

150 = 0.26d + 95.80- 95.80 from each side54.20 =

0.26d ÷ 0.26d = 208.5

David can't drive that extra 0.5 mi without going over his budget.He can drive 208 whole miles.

Can you help on this math problem

Answers

Answer:

k = 11.7

Step-by-step explanation:

Constant of Proportionality

When two quantities y and x are proportional to each other, they are related by the proportionality equation
y = kx
where k is known as the constant of proportionality

The y axis is Money earned in $

x axis is time worked in hours

The relationship is y = kx and we are asked to find k

The constant of proportionality for this graph is nothing but the slope of the graph.

Slope can be found by taking any two points on the graph, determining the difference in y values and dividing by the difference in corresponding x values;

Two points have been chosen for us:
(3, 35.1) and (7, 81.9)

Difference in y values = 81.9 - 35.1 = 46.8 (also known as rise)

Difference in x values = 7 - 3 = 4 (also known as run)

Slope = k = rise/run = 46.8/4 = 11.7

Therefore k = 11.7

Answer: k = 11.7

Step-by-step explanation: hope this helps0^0

Let U= {q,r,s,t,u,v,w,x,y,z}, A={q,s,u,w,y}, B={q,s,y,z}, and C= {v,w,x,y,z} A n (B U C)

Answers

The value of A n (B U C) = {q, s, w, y} for the given sets.

What is intersection of sets?

A set is a clearly defined group of things in mathematics. We may define several operations on sets and look at their attributes, unlike numbers. An operation in set theory is a task that involves combining different sets in order to create a new set with unique attributes.

The set containing all elements shared by sets A and B is the intersection of the two sets.

The given sets are:

U= {q,r,s,t,u,v,w,x,y,z}, A={q,s,u,w,y}, B={q,s,y,z}, and C= {v,w,x,y,z}

The value of (B U C) depicts all the terms in B and C:

(B U C) = {q, s, y, z, v, w, x}

The value of A n (B U C) depicts all the common terms in set A and B U C:

A n (B U C) = {q, s, w, y}

Hence, the value of A n (B U C) = {q, s, w, y} for the given sets.

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Determine the set of x-values where f(x) =

Answers

The set of x-values where f(x) is continuous is all real numbers except x=1, interval notation is (-∞, 1) U (1, ∞).

What are the set of x-values?

The function f(x) is a rational function, which is continuous for all x-values except those that make the denominator 0.

Thus, to find the set of x-values where f(x) is continuous, we need to find the values that make the denominator x-1 equal to 0:

x - 1 = 0

x = 1

Therefore, the set of x-values where f(x) is continuous is all real numbers except x=1. We can write this set in interval notation as:

(-∞, 1) U (1, ∞)

which means the set of all x-values less than 1, combined with the set of all x-values greater than 1.

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Graph by writing equations in slope intercept form.

Answers

Answer:

1) y = -1x+-1 and 2) y = -1x+-1

Step-by-step explanation:

Slope Intercept Form: y = mx+b (m is slope and b is y-intercept)

1) 8x+8y=-8

8y = -8x+-8

y = -1x+-1

2) 3x+3y =-3

3y = -3x+-3

y = -1x+-1

What is the equation of the line that goes through the points (4, 7) and (5, 9)?
(Choose all correct answers)
Oy-9=x-5
Oy-9=2(x - 5)
Oy-7= 2(x - 1)
Oy-4=x-7

Answers

Answer:

y - 7 = 2(x - 4)

Step-by-step explanation:

The equation of the line that goes through the points (4, 7) and (5, 9) is y - 7 = 2(x - 4). To find the equation of the line, you can use the point-slope form of the equation, which is y - y1 = m(x - x1), where m is the slope of the line and (x1, y1) is a given point on the line. In this case, the given points are (4, 7) and (5, 9), and the slope is m = 2. Therefore, the equation of the line is y - 7 = 2(x - 4).

What is the slope of the line that passes through the point (6.24) and the origina
KINA
m=4
SEES
m
m=0
m = undefined

Answers

Answer:

slope = 4

Step-by-step explanation:

calculate the slope m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (6, 24 ) and (x₂, y₂ ) = (0, 0 )

m = [tex]\frac{0-24}{0-6}[/tex] = [tex]\frac{-24}{-6}[/tex] = 4

Harold and Marie went scuba diving. Harold dove to a depth of
45 feet below sea level. Marie dove to a depth that was 15 feet
above Harold. Which equation can be used to find Marie's depth,
in feet?
A 45-15 = 30
B (-45) + (-15) = -60
C (-45) +15=-30
D 45-(-15) = 60

Answers

Answer: The answer is  (A)

Step-by-step explanation:

You insure your home for $125,000. You want to be safe and add coverage on the contents, so you take 55% on the contents. How much coverage will you have on the contents of your home?

Answers

The amount of coverage that you will have on the contents of your home would be = $68,750

How to calculate the amount of coverage for contents of your home?

The total amount of money that was insured for the house = $125,000

The percentage of insurance that was left for the contents of the house = 55% of insurance.

That is;

= 55/100 × $125,000

= 6875000/100

= $68,750.

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which polynomial represents the difference below 12x^3+7x+3-(3x^7+4x)

Answers

Answer:

The polynomial that represents the difference of 12x^3+7x+3 and 3x^7+4x is 12x^3-3x^7+7x-4x.

Sampling considerations. A statistics class has 10 graduate students and 40 undergraduate students. You want to randomly sample 10% of the students in the class. One graduate student and four undergraduate students are selected at random. Which of the following is not correct? and why?
(a) Because each student has a 10% chance of being selected, this is a simple random sample.
(b) Because each sample includes exactly one graduate student and four undergraduate students, this is not a random sample.
(c) It is possible to get a sample that contains only graduate students.
(d) It is possible to get a sample that contains only undergraduate students.

Answers

The option that is incorrect is option (b) Because each sample includes exactly one graduate student and four undergraduate students, this is not a random sample.

Simple random sample:

A simple random sample is a type of probability sampling method used in statistics, where each member of a population has an equal chance of being selected for the sample.

In other words, in a simple random sample, every possible sample of a given data will have has an equal probability of being selected from the population.

Here we have

A statistics class has 10 graduate and 40 undergraduate students.

We want to randomly sample 10% of the students in the class.

Even though one graduate student and four undergraduate students are selected at random, the percentage selecting both categories is the same.

Hence, this is a simple random sample.

Therefore,

The option that is incorrect is option (b) Because each sample includes exactly one graduate student and four undergraduate students, this is not a random sample.

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can someone explain, answer, and give formulas for all the numbered points as well as the letters above? 100 POINTS

Answers

The correctly matched pairs are mentioned below.

What is algebraic expression?

An algebraic expression is a combination of terms both constants and variables. For example -

2x + 3y + z

3x + y

Given is to match the correct pairs given below.

{ 1 } -

47, 41, 35, 29, 23   →   a{n} = a{1} + (n- 1)d

{ 2 } -

7, -21, 63, -189, 567   →   a{n} = a{1}rⁿ⁻¹

{ 3 } -

[tex]$A = P(1 + 0.025/12)^{12t}[/tex]   →   A = [tex]$P(1 + r/n)^{nt}[/tex]

{ 4 } -

An 18 - month invest on $10 at 5%.   →   A = P[tex]$e^{rt}[/tex]

{ 5 } -

Investments and loans -

Simple interest : I = PrtCompound interest : A = P[tex]$e^{rt}[/tex]Continuous Compound interest : A = [tex]$P(1 + r/n)^{nt}[/tex]

Therefore, the correctly matched pairs are mentioned above.

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Data from www.centralhudsonlabs.com determined the mean number of insect fragments in 225-gram chocolate bars was 14.4, but three brands had insect contamination more than twice the average. Assume the number of fragments follows a Poisson distribution.
a. If you consume a 225-gram bar from a brand at the mean contamination level, what is the probability of no insect contaminants?
b. Suppose you consume a bar that is one-fifth the size tested (45 grams) from a brand at the mean contamination level. What is the probability of no insect contaminants?
c. If you consume seven 28.35 gram (one-ounce) bars this week from a brand at the mean contamination level, what is the probability that you consume one or more insect fragments in more than one bar?
d. Is the probability of contamination more than twice the mean of 14.4 unusual, or can it be considered typical variation? Explain.

Answers

a. The probability of no insect contaminants in a 225-gram bar from a brand at the mean contamination level can be found using the Poisson probability formula:


[tex]P(X = 0) = \frac{ (e^{-λ})(λ^0)}{0!} = \frac{(e^{-14.4})(14.4^0)}{0!}= 0.000000831[/tex]


b. If you consume a bar that is one-fifth the size tested (45 grams) from a brand at the mean contamination level, the mean number of insect fragments would be one-fifth of 14.4, or 2.88. The probability of no insect contaminants can be found using the Poisson probability formula:


[tex]P(X = 0) = \frac{(e^-λ)(λ^0)}{0!} = \frac{(e^-2.88)(2.88^0)}{0!} = 0.056032[/tex]

c. If you consume seven 28.35 gram (one-ounce) bars this week from a brand at the mean contamination level, the mean number of insect fragments would be (7 * 28.35/225) * 14.4 = 5.4336.

The probability of consuming one or more insect fragments in more than one bar can be found using the Poisson probability formula and the complement rule:


[tex]$$\begin{aligned}& P(X>1) \\& =1-P(X \hat{a} 1) \\& =1-\left[\left(e^{-} \hat{I}\right)\left(\hat{I}^0\right) / 0 !+\left(e^{-} \hat{I}\right)\left(\hat{I}^1\right) / 1 !\right] \\& =1-\left[\left(e^{-} 5.4336\right)\left(5.4336^0\right) / 0 !+\left(e^{-} 5.4336\right)\left(5.4336^1\right) / 1 !\right] \\& =0.994784\end{aligned}$$[/tex]

d. The probability of contamination more than twice the mean of 14.4 can be found using the Poisson probability formula and the complement rule:

[tex]P(X > 28.8) = 1 - P(X ≤ 28.8) \\= 1 - ∑(e^-λ)(λ^x)/x!\\ = 1 - 0.999999999999999 \\= 0.000000000000001[/tex]


This probability is extremely small, so it can be considered unusual and not typical variation.

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please help me with this

here is the picture is just one question

Answers

Note that the equation for the parent function y=x² stretched horizontally by a factor of 4 and shifted down 5 units is given as follows: y = (1/16)x² - 5

What is the rationale for the above response?

Note that a parent function is a simple, basic function from which other more complex functions can be derived by applying transformations.

To stretch the graph horizontally by a factor of 4, we divide x by 4, which gives:

y = (1/16)x²

To shift the graph down 5 units, we subtract 5 from the whole function, which gives:

y = (1/16)x² - 5

Therefore, the equation for the parent function y=x^2 stretched horizontally by a factor of 4 and shifted down 5 units is:

y = (1/16)x² - 5

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Answer please, I'll give brainliest

Answers

Answer:

1st one

Step-by-step explanation:

Answer: A. (2/5,-3)

Step-by-step explanation:

in order to find the solution to the set of equations, you need to find one variable first, lets fing y first

10x+3y=-5

10x = -5 - 3y

x = (-5 -3y)/10

substitute this in for x in the other equation

-5((-5 - 3y)/10) -4y = 10

(25 + 15y)/10 -4y = 10

25/10 + 15y/10 -4y = 10

make all fractions on the left side

25/10 + 15y/10 - 40y/10 = 10

combine

25/10 -25y/10 = 10

multiply both sides by 10 to get rid of the denominator

25 - 25y = 100

combine like terms

-25y = 75

divide

y = -3

plug y into the first equation to find x

10x + 3(-3) = -5

10x -9 = -5

10x = 4

x = 4/10

simplify

x = 2/5

hope this helps!

y=100000(0.25)^8 exponential decay​

Answers

y=100000(0.25)^8 exponential decay​ is 1.526.

How to find the exponential decay​?

The formula represents exponential decay with a decay factor of 0.25 and an initial value of 100,000. To evaluate the formula, you can simply substitute 8 for the variable x (since the formula has y in terms of x) and calculate the result:

y = 100000(0.25)^8

y = 100000(0.00001525878906)

y ≈ 1.526

Therefore, the value of y for x = 8 is approximately 1.526. This means that after 8 units of time, the initial value of 100,000 has decayed to around 1.526.

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Find the value of x from the adjoining figure​

Answers

The value of x from the adjoining figure​ given as pentagon is 85°.

What is angle?

An angle is a geometric figure formed by two rays, or lines, that share a common endpoint, called the vertex. The measure of an angle is typically expressed in degrees, radians, or other units of angular measurement, and it represents the amount of rotation between the two rays. Angles are often used in geometry, trigonometry, physics, and other fields to describe the orientation of objects and the relationships between them. Some common types of angles include acute angles (less than 90°), obtuse angles (greater than 90°), and right angles (exactly 90°).

Here,

This is a pentagon with sum of angle as 540 degrees.

50+x=180

x=130°

x+80+120+125+130=540

x=540-455

x=85°

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find the equation of the line perpendicular to x=7 through point (4,-3)

Answers

Answer:

y= -3

Step-by-step explanation:

Because the only line that does through 4,-3 is y =-3

Solve for d.
d+5≥6 solve one step liner inequality

Answers

The range of value for d is d ≥ 1

What is inequality?

Inequality, In mathematics is a statement of an order relationship. Greater than, greater than or equal to, less than, or less than or equal to—between two numbers or algebraic expressions.

Greater than is >

Greater then or equal to is ≥

less than <

less then or equal to ≤

d + 5≥ 6

add the additive inverse of 5 to both sides

d+5+(-5) ≥ 6+(-5)

d ≥ 6-5

d ≥ 1

therefore the range of value of d is d ≥ 1

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What is the value of t in the figure?

Answers

The interior angles of the triangle are in terms of t=15.

what are interior angles ?

In a polygon, an interior angle is an angle formed by two adjacent sides of the polygon inside the polygon. For example, in a triangle, the interior angles are the angles formed by the three sides of the triangle inside the triangle.

The formula for the sum of the interior angles of a polygon with n sides is:

(n-2) x 180 degrees

In other words, to find the sum of the interior angles of a polygon, you take the number of sides, subtract 2, and then multiply the result by 180 degrees.

For example, a triangle has 3 sides, so the sum of its interior angles is:

(3-2) x 180 = 1 x 180 = 180 degrees



Given by the question:
The sum of the interior angles of a triangle is 180 degrees. Therefore:

w + x + y = 180

(5t + 3) + (3t + 7) + 50 = 180

8t + 60 = 180

8t = 120

t = 15

So the value of t is 15.

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need help with part b

Answers

The image of the polygon after the rotation is added as an attachment

How to determine the image of the polygon

From the question, we have the following coordinates that can be used in our computation:

(1, 0), (2, 0), (0, 2) and (2, 2)

The location of point G is

G = (3, -1)

To rotate about point G, we start by subtracting the points from G

So, we have

[(1, 0), (2, 0), (0, 2) and (2, 2)] - (3, -1)

This gives

(-2, 1), (-1, 1), (-3, 3) and (-1, 3)

The rule is 90 degrees clockwise rotation

This is represented as

(x, y) ⇒ (y, -x)

So, we have

(-2, 1), (-1, 1), (-3, 3) and (-1, 3) ⇒ (1, 2), (1, 1), (3, 3) and (3, 1)

Next, we plot (1, 2), (1, 1), (3, 3) and (3, 1)

See attachment for the image of the transformation

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Please help this is due soon!
Use the lucky guess method to find the general equation of
[tex]\frac{dy}{dt} = y + 3t[/tex]

Answers

The solution to the ordinary differential equation y' - y = 3 · t is the equation [tex]y(t) = C\cdot e^{t} + A\cdot t + B[/tex], where C, A and B are real numbers.

How to determine the general solution to a first order linear non-homogeneous ordinary differential equation

Differential equations are equations that involves functions and its derivatives. In this case we have an example of a first order linear non-homogeneous ordinary differential equation, whose standard form is introduced below:

y' - y = 3 · t

Given the linearity of the differential equation, the solution of the differential equation is the sum of the homogeneous component and the particular component. First, we must determine the homogeneous component:

y' - y = 0

y' = y

dy / dt = y

dy / y = dt

∫ dy / y = ∫ dt

ln y = t + C

[tex]y = C \cdot e^{t}[/tex], where C is the integration constant.

Second, find the particular component:

f(t) =3 · t → yP(t) = A · t + B, where A, B are real coefficients.

Third, write the complete solution:

[tex]y(t) = C\cdot e^{t} + A\cdot t + B[/tex]

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In your first semester of college you took 13 credit hours and earned a GPA of 2.13. In your second semester your Gpa of 2.34 was based on 12 credit hours. Your third semester GPA was 3.00 Based on 17 hours. Calculate overall GPA for the three semesters.

Answers

Answer:

below

Step-by-step explanation:

[ 2.13 * 13   +  2.34 * 12  +  3.00 * 17 ] / ( 13 + 12 + 17) = 2.54 GPA

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