Be sure that you show all of your work to reach your answer. Each step must be on a separate line. Your method to reach your answer must be clear and include explanations.

Be sure to only round at the last step for your final answer.


You plan to purchase a house for $525,000 and you will make a 20% down payment. You are evaluating two mortgages a 30-year fixed mortgage at 2.72% and a 15-year fixed mortgage at 2.25%. Your goal is to have a monthly payment that fits within your budget.

a. Which mortgage will give you the lowest monthly payment? What will that payment be? How much less will this be than the other monthly mortgage payment?

b. Assuming you take the full term of the mortgage, which mortgage will result in you paying the most interest? What will that interest be? How much more will this be than the interest on the other mortgage?

R= regular monthly payment
p= amount financed, or principal
r= rate written as a decimal
n= number of payments per year
t= number of years

Needs to be easy to read.

Answer:

0.23

Step-by-step explanation:

5y+14=27y+9

14-9=27y-5y

5=22y

dividing through by 22

y=0.23

[tex]\huge\boxed{4x}[/tex]

Start by simplifying the power.

[tex](5x)^3=5^3x^3=125x^3[/tex]

[tex]\dfrac{500x^4}{125x^3}[/tex]

Cancel out the common factor of [tex]125[/tex].

[tex]\dfrac{4x^4}{x^3}[/tex]

Finally, cancel out the common factor of [tex]x^3[/tex].

[tex]\boxed{4x}[/tex]

The equivalent fraction of 12/25 is 24/50

The fraction is given as:

Fraction = 12/25

Multiply the fraction by 1

Fraction = 12/25 * 1

Express 1 as 2/2

Fraction = 12/25 * 2/2

Evaluate the product

Fraction = 24/50

Hence, the equivalent fraction of 12/25 is 24/50

Read more about fractions at:

https://brainly.com/question/10354322

#SPJ1

The equations are the same when the line goes through the origin. y = mx + b is a more general form of y = mx. Therefore, Renee is correct.

The given statement is "The equations are the same when the line goes through the origin. y = mx + b is a more general form of y = mx".

The point where the reference axes in a coordinate system meet. The values of coordinates are normally defined as zero.

The equation of the line is y = mx + b.

If the line goes through the origin, then b = 0, so y = mx + b is y = mx + 0 or y = mx.

The equations are the same when the line goes through the origin. y = mx + b is a more general form of y = mx. Therefore, Renee is correct.

To learn more about the equation of the line visit:

https://brainly.com/question/21511618.

#SPJ1

The value of the car decreases by $1430 per year over 5 years

The given parameters are:

So, the ordered pair is (0, 13,755)

In (a), we have:

The difference in the amounts is

Difference = 13755 - 1811

Difference = 11944

So, the ordered pair is (1, 11,944)

We have:

5 year depreciation = $7,150

The difference in the amounts is

Difference = 13755 - 7150

Difference = 6605

So, the ordered pair is (5, $6,605)

This is calculated as:

m = (y2 - y1)/(x2 - x1)

Over 1 year, we have:

m = (13,755-11,944)/(0-1)

m =-1811

Over 5 years, we have:

m = (13,755-6605)/(0-5)

m =-1430

The average rate of change over 5 years is -1430

This means that the value of the car decreases by $1430 per year

Read more about average rates of change at:

https://brainly.com/question/23715190

#SPJ1

Missing information in the question

Total Cash Price: $13,755

1 year depreciation: $1,811

5 year depreciation: $7,150

A constant function is exactly that - constant - meaning it exhibits no change whatsoever with respect to any change in its input. If [tex]f(x) = 1[/tex], then it doesn't matter what value of [tex]x[/tex] I give you, the value of [tex]f(x)[/tex] will always be nothing other than 1.

That the derivative of such a function is zero follows immediately from the definition of the derivative. If [tex]c\in\Bbb R[/tex] and [tex]f(x) = c[/tex], then

[tex]f'(x) = \displaystyle \lim_{h\to0}\frac{f(x+h)-f(x)}h = \lim_{h\to0} \frac{1 - 1}h = \lim_{h\to0}\frac0h = 0[/tex]

The constants 0.693 is the natural log of 2 and the constant 2.303 is the multiplicative factor of converting log of a number to the natural log of that same number.

It follows from the task content that the calculation involves the use of the half-life of radioactive materials formula.

Hence, the constant 0.693 is the real number value of ln(2). Additionally, the constant 2.303 as used by convention is used to convert log value of a number x to its natural log value. Hence,. it follows that the relation which holds true is; ln(x) = 2.303 × log(x).

Read more on natural log;

https://brainly.com/question/305900

#SPJ1

Point F is on line a, so it does represent Josiah's distance at a certain time. Also, point F is below line b, so it represents a distance that is less than Chana's distance. This is a distance-time graph problem.

Recall that Josiah had a head start of 10 meters and he skates at 2 meters per second.

Since Y is the function that represents the distance in meters from the finished line, by observation, it is clear to see that all the factors that are related to his race are adequately represented in:

y = 10 + 2x

Where 10 is the head start in meters

2 is the rate at which he skates per second; and

x is the unknown amount of time in seconds.

Given that the point F sits over 25 seconds,

that is F(y) = 10 + 2 * 25

= 60 meters.

Hence, Point F is on line a, so it does represent Josiah's distance at exactly 25 seconds.

Learn more about distance-time graphs at:
https://brainly.com/question/4931057
#SPJ1

Answer:

1.090909090909091

Step-by-step explanation:

12/11 = 1.090909090909091

W = 1.090909090909091

Answer:

w = [tex]\frac{12}{11}[/tex]

Step-by-step explanation:

11w = 12 ( isolate w by dividing both sides by 11 )

w = [tex]\frac{12}{11}[/tex]

Round this however your teacher instructs.

=================================================

Work Shown:

mu = 830 = mean

sigma = 96.7 = standard deviation

x = 915 = given raw score we want to convert

z = (x - mu)/sigma

z = (915 - 830)/(96.7)

z = (85)/(96.7)

z = 0.8790072 approximately

Based on the calculations, Tart & Sweet's total profit from April to June is equal to -2 dollars.

A bar chart can be defined as a type of chart that is used for the graphical representation of a data set, especially by using rectangular bars or vertical columns.

In order to determine Tart & Sweet's total profit, we would simply add the amount of money (in dollars) generated from April to June as follows:

Total profit = -8 + 2 + 4

Total profit = -$2.

Read more on bar chart here: https://brainly.com/question/24741444

#SPJ1

The solution to the system of equations is x = 0.5, y = 0

The system of equations is given as:

y = 2x-1

4x + y=2

Substitute y = 2x-1  in 4x + y=2

4x + 2x-1  =2

Evaluate the like terms

6x = 3

Divide by 6

x = 0.5

Substitute x = 0.5 in y = 2x-1

y = 2 * 0.5 - 1

Evaluate

y = 0

Hence, the solution to the system of equations is x = 0.5, y = 0

Read more about system of equations at:

https://brainly.com/question/13729904

#SPJ1

The area of the shaded region is 29.5 square yards.

The following calculations are to be done:

Area of the triangle:

Base of the triangle is

= 5 + 4

= 9 yard.

Height of the triangle = 6 + 5  

Height of the triangle= 11 yards.

The area of the triangle is,

[tex]\ Area \ of \ the\ rectangle=\frac{1}{2} \times height\times base[/tex]

[tex]\ Area \ of \ the\ rectangle=\frac{1}{2}\times 9\times 11[/tex]

= 49.5 square yards.

Area of the rectangle:

[tex]=Length\times width[/tex]

[tex]=4\times 5[/tex]

= 20 square yards.

Now finally the shaded region should be

= 49.5 square yards - 20 square yards

= 29.5 square yard

Therefore we can conclude that the area of the shaded region is 29.5 square yards.

To learn more about the rectangle visit:

brainly.com/question/2773823

#SPJ1

it's B why they need me to write something long the answer is ez B

Step-by-step explanation:

it f common sense

The measure of the exterior angle x is 90°.

We need to find the measure of the exterior angle x.

An exterior angle of a triangle is equal to the sum of its two opposite non-adjacent interior angles.

Now, x°=∠A+∠B

⇒x°=30°+60°=90°

Therefore, the measure of the exterior angle x is 90°.

To learn more about the exterior angle visit:

https://brainly.com/question/2406986.

#SPJ1

From the statements and reasons given below as regards the Isosceles Triangle, we have been able to prove that; ∆BAM ≅ ∆CAN

Isosceles Triangle means that two sides of the triangle are equal and also 2 angles are equal.

Now, we are told that triangle ABC is an Isosceles and as such, AB and AC are congruent.

We are given that BM and NC are congruent. Now, due to the fact that Triangle AMN is an isosceles triangle, it means that the sides AM and AN are congruent to each other.

Thus, from the proofs above and from the definition of the isosceles Triangle, we can say that triangles BAM and CAN are congruent.

Read more about Isosceles Triangle at; https://brainly.com/question/1475130

#SPJ1

Answer & Step-by-step explanation:

To prove ∆BAM ≅ ∆CAN:

1. Given that ∆ABC is an isosceles triangle with base BC, and BM = CN, we know that AB = AC.

2. Using the Side-Angle-Side (SAS) congruence criterion, we can show that ∆ABM and ∆ACN are congruent.

3. Therefore, corresponding angles ∠BAM and ∠CAN are congruent.

4. Similarly, ∠BMA and ∠CNA are congruent.

5. By showing that corresponding angles in ∆ABM and ∆ACN are congruent, we can conclude that ∆BAM ≅ ∆CAN.

To prove ∆AMN is an isosceles triangle:

1. From the given information, we know that BM = CN.

2. By proving ∆BAM ≅ ∆CAN, we have shown that ∠BAM ≅ ∠CAN.

3. Since ∠BAM and ∠CAN are congruent, we can conclude that ∠BAN ≅ ∠CAM using the Transitive Property of Congruence.

4. By establishing that ∠BAN ≅ ∠CAM, we can conclude that ∆AMN is an isosceles triangle because it has two congruent angles.

Answer:

4 quarts of milk

Step-by-step explanation:

4 quarts = 1 gallon

so, melissa needs to buy 4 quarts

The table represents an exponential function given by:

[tex]f(x) = 24*(1/2)^x[/tex]

Here we have the table:

x    f(x)

0    24

1      12

2      6

3       3

First, notice that for each unit that x increases, the value of f(x) decreases by its half.

This is clearly an exponential equation, whose base must be equal to (1/2).

And because when x = 0, f(0) = 24, we know that the initial value of the function is 24.

Then the exponential function is:

[tex]f(x) = 24*(1/2)^x[/tex]

Such that:

[tex]f(0) = 24*(1/2)^0 = 24\\\\f(1) = 24*(1/2)^1 = 12\\\\f(2) = 24*(1/2)^2 = 24*(1/4) = 6\\\\f(3) = 24*(1/2)^3 = 24*(1/8) = 3[/tex]

Concluding, the table represents an exponential function.

If you want to learn more about exponential functions:

https://brainly.com/question/11464095

#SPJ1

Step-by-step explanation:

[tex]f(x) = 3 {x}^{2} + 2x + 4[/tex]

[tex] \: [/tex]

[tex]f(2) = 3. {2}^{2} + 2.2 + 4[/tex]

[tex]f(2) = 3.4 + 4 + 4[/tex]

[tex]f(2) = 12 + 8[/tex]

[tex]f(2) = 20 \\ [/tex]

[tex] \: [/tex]

[tex]f(a + h) = 3 {(a + h)}^{2} + 2.(a + h) + 4[/tex]

[tex]f(a + h) = 3( {a}^{2} + 2ah + {h}^{2} ) + 2a + 2h[/tex]

[tex]f(a + h) = 3 {a}^{2} + 6ah + 3 {h}^{2} + 2a + 2h + 4[/tex]

[tex]f(a + h) = 3 {a}^{2} + 3 {h}^{2} + 6ah + 2a + 2h + 4[/tex]

Evaluating the given algebra fraction (x - 1)²/(1 - x)² at x = 0 gives; 1

We want to evaluate the algebra fraction;

(x - 1)²/(1 - x)² at x = 0.

Now, let us first break down the expression to get;

[(x - 1) * (x - 1)]/[(1 - x) * (1 - x)]

At x = 0, we have;

[(0 - 1) * (0 - 1)]/[(1 - 0) * (1 - 0)]

⇒ (-1 * -1)/(1 * 1)

⇒ 1

Read more about Algebra Fractions at; https://brainly.com/question/24705296

#SPJ1

The amount of wrapping paper he need to cover the shoebox is 190 square inches

The formula for calculating the surface area of a box is expressed as:

SA = 2(lw + wh + lh)

where

l is the length

w is the width

h is the height

Given the following parameters

l = 10in

w = 5in

h =3in

Substitute

S = 2(10*5 + 5*3 + 10*3)

S = 2(50+15+30)

S = 2(95)

S = 190 square inches

Hence the amount of wrapping paper he need to cover the shoebox is 190 square inches

Learn more on surface area of box here: https://brainly.com/question/26161002

#SPJ1

Answer:

Step-by-step explanation:

F = [tex]\frac{mv^2}{r}[/tex]

mv² = Fr

m = [tex]\frac{Fr}{v^2}[/tex]

[tex]\huge\boxed{\textsf{D.}\ 57^\circ}[/tex]

We know that angles 1 and 2 are supplementary angles that add up to 180 degrees.

Solve for angle 2:

[tex]\begin{aligned}\angle1+\angle2&=180^\circ\\123^\circ+\angle2&=180^\circ\\123^\circ-123^\circ+\angle2&=180^\circ-123^\circ\\\angle2&=57^\circ\end{aligned}[/tex]

We also know that angles 2 and 6 are corresponding angles, so they are equal to each other. This means that angle 6 is also 57 degrees.

For more information on this topic, search the Internet. There are many great resources on transversal lines and angles out there that expand on the few details I shared here.

Answer:

76 sqcm.

Step-by-step explanation:

2(5 x 2) + 2(5 x 4) + 2(4 x 2) = 2(10) + 2(20) + 2(8)
                                             =  20 + 40 + 16
                                             =  76

The measure of both the interior angles are 70 and 110 degree.

Lines they never intersect with each other and the distance between them always remains same are called parallel lines.

It is given that

Line l and m are parallel lines and are intersected by a transversal ,n

Interior angles of the same side are (2x−8) degree and (3x−7) degree

Applying the property of interior angles of parallel lines

2x -8 + 3x - 7 = 180 degree

5x -15 = 180

5x = 195

x = 39 degree

Both the angles have measure of

2 * 39 - 8 = 70 degree

3 * 39 -7 = 110 degree

Therefore the measure of both the angles are 70 and 110 degree.

The complete question is

Two parallel lines l and m are cut by a transversal  n . If the interior angles of the same side of n are (2x−8) degree and (3x−7) degree  , find the measure of each of these angles.

To know more about Parallel Lines

https://brainly.com/question/16701300

#SPJ1

The non-extraneous solutions are -6 and -5.

By checking these solution values in the original equation.

[tex](x+6)^{1/2}-5=x+1\\(x+6)^{1/2}=x+6\\((x+6)^{1/2})^2=(x+6)^2\\x+6=x^2+12x+36\\0=x^2+11x+30\\(-11+(11^2-4(1)(30))^{1/2})/2\\(-11+((1)^{1/2})/2\\(-11+1)/2=-5\\(-11-1)/2=-6\\((-6)+6)^{1/2}-5=(-6)+1\\(0^{1/2})-5=-5[/tex]

Thus, -6 is non-extraneous.

[tex]((-5)+6)^{1/2}-5=(-5)+1\\(1^{1/2})-5=-4\\1-5=-4\\-4=-4[/tex]

Thus, -5 is non-extraneous.

Learn more about non-extraneous solutions;

https://brainly.com/question/7536891

#SPJ1

The expression that represents a complex number is the one in the second option.

[tex]\frac{2}{3} + \sqrt{-\frac{27}{28} }= \frac{2}{3} + \sqrt{\frac{27}{28} } i\\[/tex]

Remember that the complex number i is given by:

[tex]i = \sqrt{-1}[/tex]

So we have complex numbers when we have negative arguments inside of square roots.

In this particular case, the only option with a negative argument on a square root is on the second option:

[tex]\frac{2}{3} + \sqrt{-\frac{27}{28} } \\\\\frac{2}{3} + \sqrt{-1} *\sqrt{\frac{27}{28} } \\\\\frac{2}{3} + \sqrt{\frac{27}{28} } i\\[/tex]

We conclude that the correct option is the second one.

If you want to learn more about complex numbers:

https://brainly.com/question/10662770

#SPJ1

Answer:

(2)/(3)+\sqrt(-(27)/(28))

Step-by-step explanation:

Plato/Edmentum