A student needs to borrow $9,000 to pay for college. She can get the loan at an APR of 10% to be paid off in monthly installments over the next 4 years.

If she decides to pay the loan off in monthly installments over 3 years instead of 4 years at the given APR, how much money will she save altogether? Round your answer to the nearest cent.)

Answer:

Step-by-step explanation: Reformatting the input :

Changes made to your input should not affect the solution:

(1): "x2" was replaced by "x^2".

Rearrange:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

p*(x)-((2*x^2-9*x+7)*(x-2))=0

STEP

1

:

Equation at the end of step 1

px - (((2x2 - 9x) + 7) • (x - 2)) = 0

STEP

2

:

Trying to factor by splitting the middle term

2.1 Factoring 2x2-9x+7

The first term is, 2x2 its coefficient is 2 .

The middle term is, -9x its coefficient is -9 .

The last term, "the constant", is +7

Step-1 : Multiply the coefficient of the first term by the constant 2 • 7 = 14

Step-2 : Find two factors of 14 whose sum equals the coefficient of the middle term, which is -9 .

-14 + -1 = -15

-7 + -2 = -9 That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -7 and -2

2x2 - 7x - 2x - 7

Step-4 : Add up the first 2 terms, pulling out like factors :

x • (2x-7)

Add up the last 2 terms, pulling out common factors :

1 • (2x-7)

Step-5 : Add up the four terms of step 4 :

(x-1) • (2x-7)

Which is the desired factorization

Equation at the end of step

2

:

px - (2x - 7) • (x - 1) • (x - 2) = 0

STEP

3

:

Equation at the end of step 3

px - 2x3 + 13x2 - 25x + 14 = 0

STEP

4

:

Solving a Single Variable Equation:

4.1 Solve px-2x3+13x2-25x+14 = 0

In this type of equations, having more than one variable (unknown), you have to specify for which variable you want the equation solved.

We shall not handle this type of equations at this time.

Supplement : Solving Quadratic Equation Directly

Solving 2x2-9x+7 = 0 directly

Earlier we factored this polynomial by splitting the middle term. let us now solve the equation by Completing The Square and by using the Quadratic Formula

Parabola, Finding the Vertex:

5.1 Find the Vertex of y = 2x2-9x+7

Parabolas have a highest or a lowest point called the Vertex . Our parabola opens up and accordingly has a lowest point (AKA absolute minimum) . We know this even before plotting "y" because the coefficient of the first term, 2 , is positive (greater than zero).

Each parabola has a vertical line of symmetry that passes through its vertex. Because of this symmetry, the line of symmetry would, for example, pass through the midpoint of the two x -intercepts (roots or solutions) of the parabola. That is, if the parabola has indeed two real solutions.

Parabolas can model many real life situations, such as the height above ground, of an object thrown upward, after some period of time. The vertex of the parabola can provide us with information, such as the maximum height that object, thrown upwards, can reach. For this reason we want to be able to find the coordinates of the vertex.

For any parabola,Ax2+Bx+C,the x -coordinate of the vertex is given by -B/(2A) . In our case the x coordinate is 2.2500

Plugging into the parabola formula 2.2500 for x we can calculate the y -coordinate :

y = 2.0 * 2.25 * 2.25 - 9.0 * 2.25 + 7.0

or y = -3.125

Parabola, Graphing Vertex and X-Intercepts :

Root plot for : y = 2x2-9x+7

Axis of Symmetry (dashed) {x}={ 2.25}

Vertex at {x,y} = { 2.25,-3.12}

x -Intercepts (Roots) :

Root 1 at {x,y} = { 1.00, 0.00}

Root 2 at {x,y} = { 3.50, 0.00}

3 Solving 2x2-9x+7 = 0 by the Quadratic Formula .

According to the Quadratic Formula, x , the solution for Ax2+Bx+C = 0 , where A, B and C are numbers, often called coefficients, is given by :

- B ± √ B2-4AC

x = ————————

2A

In our case, A = 2

B = -9

C = 7

Accordingly, B2 - 4AC =

81 - 56 =

25

Applying the quadratic formula :

9 ± √ 25

x = —————

4

Can √ 25 be simplified ?

Yes! The prime factorization of 25 is

5•5

To be able to remove something from under the radical, there have to be 2 instances of it (because we are taking a square i.e. second root).

√ 25 = √ 5•5 =

± 5 • √ 1 =

± 5

So now we are looking at:

x = ( 9 ± 5) / 4

Two real solutions:

x =(9+√25)/4=(9+5)/4= 3.500

or:

x =(9-√25)/4=(9-5)/4= 1.000

Answer:

388 or 288

Step-by-step explanation:

this week in total = 100

4 more ( + ) 3 times ( x ) last

- - - - - -

100 - 4 = 96

96 x 3 = 288

either subtract or add

288 - 100 = 188

or add

288 + 100 = 388

hope this helps !

it may right or wrong :)

To divide a mixed number by a fraction, we need to convert the mixed number into an improper fraction and then multiply it by the reciprocal of the fraction.

Step 1: Convert the mixed number to an improper fraction:

7 5/6 = (6 * 7 + 5) / 6 = 47/6

Step 2: Multiply the improper fraction by the reciprocal of the fraction:

47/6 ÷ 2/3 = 47/6 * 3/2

Step 3: Simplify the fraction if possible:

47/6 * 3/2 = (47 * 3) / (6 * 2) = 141/12

Step 4: Simplify the fraction further, if necessary:

141/12 can be simplified by dividing both the numerator and denominator by their greatest common divisor, which is 3:

141/12 = (141 ÷ 3) / (12 ÷ 3) = 47/4

Therefore, 7 5/6 ÷ 2/3 is equal to 47/4 or 11 3/4.

Answer:

The answer is 68

Step-by-step explanation:

Plug -5 into each x value then solve.

Answer:

35.775

Step-by-step explanation:

So, 53 is the amount of ccs that makes a 40% solution.

How can we find the ccs of 27% solution?

Well, we should first find teh amount of ccs per 1%.

To do this, divide 53 by 40:

53/40

=

1.325

Now multiply this by 27 to get the amount of ccs for 27%:

27*1.325

=

35.775

Hope this helps! :)

Answer:

D. 36ft

Step-by-step explanation:

Answer:

the real answer is 24 :)

Step-by-step explanation:

The function represented by the graph is f(x) = ln(0.5x).

The graph displays a diminishing curve that begins above the x-axis and moves closer to it as x grows.

Logarithmic functions most  typically take this structure of graph.

Only f(x) = ln(0.5x), where ln stands for the natural logarithm, is one of the many functions that can express a logarithm.

The inverse of the exponential function with base e is the natural logarithm, which has a base of e (about 2.718).

The rate at which the function decrements is determined by the 0.5 coefficient in ln(0.5x).

The argument of the logarithm (0.5x) as it  grows as x increases, causes the function to approach the x-axis more slowly.

This is consistent with how the graph in the provided graphic behaves.

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A proportional relationship has the form:

Then, we notice that the only expression that have this form are A and C.

Answer:

no solution

Step-by-step explanation:

If you end up with a false equality, then the initial statement is false, meaning that there are no solutions.

This is the hypergeometric not the binomial.

Based on separate trials, a binomial random variable frequently models sampling with replacement. Based on non-independent trials, hypergeometric random variables frequently simulate sampling without replacement.

The hypergeometric distribution: When should we utilize it? It is employed when attempting to estimate the likelihood of attaining a specified number of successes from a particular sample size without replacement.

The number of times an event happens in a fixed number of trials is described by both the binomial distribution and the hypergeometric distribution.

Hence, we can say that this is the hypergeometric not the binomial.

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Answer:

791,800

Step-by-step explanation:

Answer: 791800

Step-by-step explanation:

$450 if you need the process ask me will give it to you

Step-by-step explanation:

I guess, the silent request here is that there will be no wire left after the 10th square.

and I guess, the following square does not reuse one side of the previous square. all squares are "standalone".

T stands for area ? well, ok.

when the side length doubles, the area quadruples (the area is side×side, and factor 2 × factor 2 = factor 4). but the perimeter still only doubles.

T1 = x × x = x²

T2 = x×2 × x×2 = x² × 4 = T1 × 4

Tn = Tn-1 × 4 = T1 × 4^(n-1) = x² × 4^(n-1)

so, Tn/Tn-1 = 4

but the geometric series for the perimeter is

p1 = 4x

pn = pn-1 × 2 = x × 2^(n+1)

and pn/pn-1 = 2

the sum of a finite geometric series with n elements is

s = p1 × (1 - r^(n))/(1 - r)

r is the common factor. in our case it is 2.

and we have 10 elements.

so, we know

8184 = 4x × (1 - 2^(10))/(1 ‐ 2) = 4x × (1-2¹⁰)/-1 =

= 4x × -1023 / - 1 = 4x × 1023

2046 = x × 1023

x = 2046/1023 = 2 cm

so, now finally for iii)

T10 (the last, biggest square) = x² × 4⁹ = 4×4⁹ = 4¹⁰ =

= 1,048,576 cm²

Answer:

a)

S+G=525

G=S+75

b) See attached pictures

c) S=$225 and G=$300

The point where both graphs meet each other is the point where both equations will be true when having the same S and G values. This is, this is the point where both conditions given by the problem are the same.

Step-by-step explanation:

a) For the first part of the problem, the addition of both amounts will give us the total, so the first equation is:

S+G=525.

On the second equation we need to add 75 to sharon's amount to figure Geordi's amount, so we get:

G=S+75

b) In order to graph the system of equations, we need to find two points for each of the equations. It would be a good idea to solve the first equation for g, so our system of equations would be:

G=525-S

G=S+75

First Equation:

You can pick any value you like for S, for example: S=0 and then substitute it into the equation to get te first G-value:

G=525-0

so G=525.

So the first ordered pair would be (0,525)

You can do the same with a different S-value to get a second point to plot:

S=100

G=525-100

G=424

so the second ordered pair would be (100,424)

and now you can plot the points on the graph and connect them with a straight line.

See attached picture.

Second Equation:

The same procedure is followed for the second equation, in this case I used the same S-values, but you can use different values if you wish, so the two points to plot were:

(0,75)

(100,175)

and the graph looks like the one attached.

c)

In order to figure out how much each person earned, we need to find the point where the two graphs meet each other (see attached picture) in this case the point will be located at (225,300)

This means that Sharon earned a total of $225 while Geordi earned a total of $300.

S=$225 and G=$300

The point where both graphs meet each other is the point where both equations will be true when having the same S and G values. This is, this is the point where both conditions given by the problem are the same.

Answer: 3583.37 ≈ 3500

Step-by-step explanation:

Answer: 48 qt

Step-by-step explanation:

The conversion factor between pints and quarts is two which means there are 2 pints in every quart. divide the number of pints by two to find the number of quarts.

96/2 = 48

EX: 24 pints = 12 quarts

24/2 =12

EX 8 quarts = 16 pints

The same rule works in reverse but instead of dividing you multiply.

8x2 = 16

Answer:

the answer is either 20 or 4 ..

Answer:

C

Step-by-step explanation:

AP Classroom

Answer:

28

Step-by-step explanation:

4,8,12,16,20,24,28. +4 every time

Answer:

28

Step-by-step explanation:

multiples of 4: 4,8,12,16,24,28

Answer:

Step-by-step explanation: [-2.19] = -3

[3.67] = 3

[-0.83] = -1

The domain of this function is a group of real numbers that are divided into intervals such as [-5, 3), [-4, 2), [-3, 1), [-2, 0) and so on. This explains the domain and range relations of a step function.

This can be generalized as given below:

[x] = -2, -2 ≤ x < -1

[x] = -1, -1 ≤ x < 0

[x] = 0, 0 ≤ x < 1

[x] = 1, 1 ≤ x < 2

Answer:

y = - \(\frac{3}{2}\) x

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

with (x₁, y₁ ) = (- 2, 3) and (x₂, y₂ ) = (0, 0) ← 2 points on the line

m = \(\frac{0-3}{0-(-2)}\) = \(\frac{-3}{0+2}\) = - \(\frac{3}{2}\) , then

y = - \(\frac{3}{2}\) x + c ← is the partial equation

to find c substitute either of the 2 points into the partial equation

using (0, 0 )

0 = - \(\frac{3}{2}\) (0) + c = 0 + c , so

c = 0

y = - \(\frac{3}{2}\) x + 0 , that is

y = - \(\frac{3}{2}\) x

Answer: D) 54 inches = 1 1/2 yards

explanation: 1 1/2 yards = 54 inches.

Answer:

See attached to see my markings

PTO and RTS are vertical angles, so they are congruent.

Thus, triangle PSM is congruent to triangle ROM by ASA congruence

16 ounces is equivalent to 453.6g when rounding to nearest tenth.

What is rounding off ?

Rounding off means a number is made into simpler form by keeping its value fixed but closer to the next number.

To round off the number to the nearest tenth we need to look at the hundredths place digit. If the digit is 1, 2, 3, 4 then we don't have to do anything, if the digit is 5, 6, 7, 8, 9 we must round up.

here the given data is :

1 ounce = 28.35 grams

Conversion of ounce to grams :

This is the conversion of a mass unit from ounce to grams. Given that 1 ounce is equal to 28.35 grams, let us calculate how grams would be in 16 ounces.

The easiest way about this is simply multiply 16 by 28.25g

1 ounce = 28.35 grams

16 ounce = x

x = 16 x 28.25

x= 453.6 g

From the calculations above, 16 ounces is equivalent to 453.6g.

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The two types of frequency distributions are Discrete Frequency Distribution and Grouped Frequency Distribution

The two types of frequency distributions are;

When the data consists of discrete, separate values, this sort of distribution is used. It displays the frequency or number of occurrences of each value.

The data is often expressed in a table with two columns: one for distinct values and another for the frequencies of those values.

This distribution is utilized when the data is continuous and has a wide range of values. It entails categorizing the data into intervals or classes and then calculating the frequency of values that fall within each interval.

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Answer:

4/15

Step-by-step explanation:

2/5 drive

1/3 bus

and rest walk

fraction of those who walk is 1-(2/5+1/3)

2/5+1/3=(6+5)/15=11/15

15/15-11/15=4/15

Answer:

The answer you want is indeed, (C).

8.04

ED2021

Answer:

C) 8.04

Step-by-step explanation:

edge 2023

Answer:

Third answer.

Step-by-step explanation:

To simplify, we can factor 'x' from the equation, giving us:

\(\frac{x(1)}{x(4 + x)} = \frac{1}{x+4}\)

However, we must put a domain restriction to ensure that the denominator will not equal 0. This means that 'x+ 4' cannot equal zero. Therefore, x ≠ -4.

The third answer is correct.