Willard Hudson took out a simple interest loan of $6,000.00 at 10 percent interest for 24 months. His monthly payment is $276.60 After 4 payments the balance is $5,082.21. He pays off the loan when the next payment is due. What is the interest? What is the final payment? How much is saved by paying the loan off early?​

Answer: 24

Step-by-step explanation:

3x + 9 = 5x - 3

9 = 2x - 3

12 = 2x

x = 6

6 * 4  =24

4x = 24

Answer:

The answer is below

Step-by-step explanation:

Find the dimensions of the rectangle of maximum area with sides parallel to the coordinate axes that can be inscribed in the ellipse 4x² + 16y² = 16

Solution:

Given that the ellipse has the equation: 4x² + 16y² = 16

let us make x the subject of the formula, hence:

4x² + 16y² = 16

4x² = 16 - 16y²

Dividing through by 4:

x² = (16 - 16y²)/4

x² = 4 - 4y²

Taking square root of both sides:

[tex]x=\sqrt{4-4y^2 }\\[/tex]

The points of the rectangle vertices is at (x,y), (-x,y), (x,-y), (-x,-y). Hence the rectangle has length and width of 2x and 2y.

The area of a rectangle inscribed inside an ellipse is given by:

Area (A) = 4xy

A = 4xy

[tex]A=4(\sqrt{4-4y^2} )y\\\\A=4y\sqrt{4-4y^2}=4\sqrt{4y^2-4y^4} \\\\The\ maximum\ area\ of\ the\ rectangle\ is\ at\ \frac{dA}{dy}=0\\\\ \frac{dA}{dy}=4(\frac{4-8y^2}{\sqrt{4-4y^2} } )\\\\4(\frac{4-8y^2}{\sqrt{4-4y^2} } )=0\\\\4-8y^2=0\\\\8y^2=4\\\\y^2=1/2\\\\y=\frac{1}{\sqrt{2} }\\\\x=\sqrt{4-4(\frac{1}{\sqrt{2} })^2}=\sqrt{2}[/tex]

Therefore the length = 2x = 2√2, the width = 2y = 2/√2

9514 1404 393

Answer:

  1)  c, f

  2) a, e

  3) b, d

Step-by-step explanation:

If you think about the units associated with a coordinate (feet, for example), then you may recognize the following

a) each difference is of "feet", so each difference will have units of "feet". The ratio of "feet" to "feet" cancels the units, leaving a pure number. In this case, it is called "steepness" in selection e. Steepness is given by the slope formula (2).

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b) The difference in parentheses has units of "feet" (as in (a)), so the square will be "square feet". The sum of two of those will still be "square feet" and the square root of that will be "feet". The units of the formula are those of distance, or length, matching selection d. Distance is given by the distance formula (3).

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c) The form shown is an ordered pair. That is the same as the representation of a coordinate point, selection f. Coordinates of a point are given by the midpoint formula (1).

Step-by-step explanation:

let the angles be ' 7x, 8x and 5x'

as we know, the sum of all the angles of a triangle is 180 degree, so,

7x + 8x + 5x = 180

20 = 180

x = 180/2

x = 90 degrees

7x = 7 × 90 = 630 degree

8x = 8 × 90 = 720 degrees

5x = 5 × 90 = 540 degrees

therefore, 5x is the smallest degrees

Answer:

3[tex]\sqrt{5}[/tex]

Answer:

3

Step-by-step explanation:

_+(-4) = -1

_-4 = -1

_ = 3

Answer:

9

Step-by-step explanation:

Move the variable to the other side of the equation

144 ÷ 16 = a

9 = a

Check:

144 ÷ a = 16 (Correct)

Answer:

300 feet

Step-by-step explanation:

Answer:

4.24

Step-by-step explanation:

the calculator says otherwise (but yea its 4.24

Answer: the initial number of water lily’s

Step-by-step explanation:

the value 1.106 represents the population increase rate

edge 2021

The value 3.915 represents the initial population of water lilies

The standard exponential equation is given as y = ab^x

where;

Given the exponential equation y = 3.915(1.106^x

On comparison, we can see that;

a  = 3. 915

This shows that the value 3.915 represents the initial population of water lilies

Learn more on exponential equation here: https://brainly.com/question/2456547

Answer:

x=9

Step-by-step explanation:

13+14=3x

27=3x

27/3=x

9=x

Answer:

4.5 (j + m) + 27

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

(x+4)(3x^2-7)

multiply and get 3x^3 +12x^2 -7x -28 which is anwser choice b

Answer:

C

Step-by-step explanation:

Answer:

- AB is similar to YZ because all the sides from triangle ABC got multiplied by 3/4, and 40 times 3/4 = 30.

- AC is similar to YX because 50 times 3/4 = 37.5.

- CB is similar to XZ because 60 times 3/4 = 45.

hope this helps!

Answer:

Step-by-step explanation:

b = 10

Substitute b in every equation below and compare the results

A. 2(b + 4) = 16

B.  2(b + 2) = 40

C. 3(b - 2) = 24

D. 2(8 + b) = 42

E. 3(b - 4) = 20

Answer:

C. 3(b - 2) = 24..

Answer:

C) n=5

Step-by-step explanation:

6n+13=43

6n+13-13=43-13

6n=30

6n/6=30/6

n=5

Answer:

Your answer is c

Step-by-step explanation:

Here you go mate

Step 1

6n+13=43  Equation/Question

Step 2

6n+13=43  Simplify

6n+13=43

Step 3

6n+13=43  Subtract 13 from sides

6n=30

Step 4

6n=30  Divide sides by 6

5

Answer

n=5

Hope this helps

Answer:

Its oka linden

Step-by-step explanation:

Just cause

Answer:

It will read the same at F = -40.

Step-by-step explanation:

The relation between fahrenheit and celsius is given by the following equation:

[tex]C = \frac{5(F-32)}{9}[/tex]

At what temperature will a Fahrenheit thermometer read the same as a Celsius thermometer?

This is F for C = F. So

[tex]C = \frac{5(F-32)}{9}[/tex]

[tex]F = \frac{5(F-32)}{9}[/tex]

[tex]9F = 5F - 160[/tex]

[tex]4F = -160[/tex]

[tex]F = -\frac{160}{4}[/tex]

[tex]F = -40[/tex]

It will read the same at F = -40.

Answer:

it's 78<C. < means less than

Answer:

don't know what you need

Step-by-step explanation:

Answer:

50°

Step-by-step explanation:

the angles should add up to 180. there is a 90° angle abd a 40° angle which adds up to 130. 180-130 gives you rour missing angle if 50°.

Answer:

apples cost a total of 2.16

cherrys cost a total of 9.05

Step-by-step explanation:

1.35*1.6=2.16

3.62*2.5=9.05

Answer:

Hey

Step-by-step explanation:

Where is the question

Answer:

126 degrees

Step-by-step explanation:

The sum of adjacent side of the rectangle is 180 degrees

Hence <1 + <4 = 180 degrees

Given

<4 = 54 degrees

<1 = 180 - <4

<1 = 180 - 54

<1 = 126degrees

Hence the value of <1 is 126 degrees

Answer:

None or 12 depending on what the question is. See explanation below.

Step-by-step explanation:

If the number is 1248:

A single number cannot have a GCF. The GCF has be for at least two numbers.

If the numbers are 12 and 48, then the GCF can be calculated.

Since 12 is a factor of 48, then the GCF of 12 and 48 is 12.

In general, to calculate the GCF do this:

To calculate it, find the prime factors of 12 and 48.

12 = 2^2 * 3

48 = 2^4 * 3

GCF is the product of common factors with lower exponent.

GCF = 2^2 * 3 = 12

9514 1404 393

Answer:

 13 : 33

Step-by-step explanation:

  hearts : all shapes = hearts : (hearts + circles) = 13 : (13 +20) = 13 : 33