Michelle would like to know how much of her loan payments will go toward interest. She has a $124,500 loan with a 5.9% interest rate that is compounded monthly. The loan has a term of 10 years. Calculate the total amount of interest that Michelle will pay over the course of the loan.

Answer:

Step-by-step explanation:

Answering a comes from simplification, and answering b and c are done all in one step: completing the square on the quadratic that results from a.

(a)  If Martina has 240 m of fencing and is only utilizing one side for the length and 2 sides for the width, the perimeter formula is

240 = x + 2w where x is a length and w is the width. Solving this for w in terms of x:

240 - x = 2w so

[tex]w=120-.5x[/tex] The area for a rectangle is L * W, so our area using the lengths we have is

A(x) = x(120 - .5x) and we simplify:

A(x) = 120x - .5x²  That's the answer to a.

Now for b and c, we will complete the square on this to get the vertex.

Begin by factoring out the -.5:

[tex]A(x)=-.5(x^2-240x)[/tex] Now we take half the linear term, square it and add it both inside the parenthesis and outside the parenthesis. Our linear term is 240. Half of 240 is 120, and 120 squared is 14400:

[tex]A(x)=-.5(x^2-240x+14400)+7200[/tex] (The 7200 comes from multiplying the 14400 times the -.5; -.5 times 14400 is -7200 so to balance things out, we have to add 7200).

The perfect square binomial that results from this is

A(x) = -.5(x - 120)² + 7200. From this we determine that our vertex is

(120, 7200). The 120 is the value of x, the length we are asked to find in b; the 7200 is the max area we are asked to find in c.

The required solutions are,,
(a) area = 240x - 2x²
(b) the side adjacent to the rivers gives the maximum length of the field.
(c) the maximum area could be 6400-meter square.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
length of the field is x,
The perimeter of the field, = 240
x + x + width = 240
width = 240 - 2x
now,
(a)
area of the field,
= length * width,

= x(240-2x)
= 240x - 2x²

Similarly,
(b) the side adjacent to the rivers gives the maximum area of the field.
(c) the maximum area could be 6400-meter square.

Thus, the required solutions are mentioned above.

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Answer:

21%

Step-by-step explanation:

Percentage reduction is (999.99-789.99)/(999.99)=21%

Answer:

Step-by-step explanation:

3-(2x-5)=-4(x+2)

We simplify the equation to the form, which is simple to understand

3-(2x-5)=-4(x+2)

Remove unnecessary parentheses

3-2x+5=-4*(x+2)

Reorder the terms in parentheses

3-2x+5=+(-4x-8)

Remove unnecessary parentheses

+3-2x+5=-4x-8

We move all terms containing x to the left and all other terms to the right.

-2x+4x=-8-3-5

We simplify left and right side of the equation.

+2x=-16

We divide both sides of the equation by 2 to get x.

x=-8

Answer:

x < - 8

Step-by-step explanation:

Given

3 - (2x - 5) < - 4(x + 2) ← distribute parenthesis on both sides

3 - 2x + 5 < - 4x - 8

- 2x + 8 < - 4x - 8 ( add 4x to both sides )

2x + 8 < - 8 ( subtract 8 from both sides )

2x < - 16 ( divide both sides by 2 )

x < - 8

Answer:

Hello,

Answer 2

Step-by-step explanation:

7=2*0+7

9=2*1+7

11=2*2+7

13=2*3+7

15=2*4+7

17=2*5+7

y=2*x+7

An other way:

[tex]points\ ( 0,7)\ and\ (1,9)\\\\\Delta\ y=9-7=2\\\Delta\ x=1-0=1\\\\\\y-7=(x-0)*2\\\\y=2x+7\\[/tex]

The complete equation is [tex]y = 2x+7[/tex].

An equation is a condition on a variable such that two expressions in the variable should have equal value.

Substitution means replacing the variables (letters) in an algebraic expression with their numerical values.

According to the question.

We have a table which shows the relation between x and y.

Let the missing term be a and b.

The the given equation becomes

[tex]y = ax + b[/tex]

For finding the value of a and b.

Substitute x = 0 and y = 7 in equation y = ax + b.

[tex]\implies 7 = a(0) + b\\\implies b = 7[/tex]

Again, substitute  x = 1 and y = 9 in the equation y = ax+ b

[tex]\implies 9 = a(1) +b\\\implies 9 = a + 7\\\implies a = 2[/tex]

substitute the value of a and b in the equation y = ax + b.

[tex]\implies y = 2x+ 7[/tex]

Therefore, the complete equation is [tex]y = 2x+7[/tex].

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Answer:

A) 4x^2+20x+25=(2x)^2+2*(2x)*5+5^2=(2x+5)^2

Area=(side)^2, side=sqrt(area)=sqrt((2x+5)^2)=2x+5

B) 4x^2-9y^2=(2x-3y)(2x+3y), these are the dimensions of the rectangle

A) The length of each side of the square is (2x + 5).

B) The dimensions of the rectangle are (2x - 3y) and (2x + 3y).

Used the concept of a quadratic equation that states,

An algebraic equation with the second degree of the variable is called a Quadratic equation.

Given that,

Part A: The area of a square is [tex](4x^2 + 20x + 25)[/tex] square units.

Part B: The area of a rectangle is [tex](4x^2 - 9y^2)[/tex] square units.

A) Now the length of each side of the square is calculated by factoring the area expression completely,

[tex](4x^2 + 20x + 25)[/tex]

[tex]4x^2 + (10 + 10)x + 25[/tex]

[tex]4x^2 + 10x + 10x + 25[/tex]

[tex]2x (x + 5) + 5(2x + 5)[/tex]

[tex](2x + 5) (2x+5)[/tex]

Hence the length of each side of the square is (2x + 5).

B) the dimensions of the rectangle are calculated by factoring the area expression completely,

[tex](4x^2 - 9y^2)[/tex]

[tex](2x)^2 - (3y)^2[/tex]

[tex](2x - 3y) (2x + 3y)[/tex]

Therefore, the dimensions of the rectangle are (2x - 3y) and (2x + 3y).

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Answer:

Option C

Step-by-step explanation:

f(1) = -8

f(2) = -5/2×-8 = -20

f(3) = -5/2×-20 = -125

.

.

.

So option C is the answer

Answer:

C.  a1 = -8

an = an-1 * 5/2  for n >1

Step-by-step explanation:

-8, -20, -50, –125, 625,...

We need to find the common ratio

Take the second  term and divide by the first term

-20/-8 = 5/2

Take the third term and divide by the second term

-50/-20 = 5/2

The common ratio is 5/2

A geometric sequence is

an = a1 * r^(n-1)

an = -8 *(5/2)^(n-1)

We can also write a recursive formula

a1 = -8

an = an-1 * 5/2  for n >1

Answer:

[tex](f-g)(x)[/tex]

[tex]f(x)-g(x)[/tex]

[tex]x^{2} -6x-27-x+9[/tex]

[tex]x^{2} -7x-18[/tex]

----------------------

[tex](f*g)(x)[/tex]

[tex]=f(x)g(x)[/tex]

[tex](x^{2} -6x-27)(x-9)[/tex]

[tex]=x^{3} -15x^{2}+27x+243[/tex]

----------------------

[tex]\frac{f}{g} (x)[/tex]

[tex]\frac{x^{2} -6x-27}{x-9}[/tex]

[tex]\frac{(x-9)(x+3)}{x-9}[/tex]

[tex]x+3[/tex]

-----------------------

[tex](f+g)(x)[/tex]

[tex]f(x)+g(x)[/tex]

[tex]=x^{2} -6x-27+x-9[/tex]

[tex]=x^{2} -5x-36[/tex]

------------------------

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------------------------

Step-by-step explanation:

Tan² theta = sec² theta - 1

Cot² theta = cosec² theta - 1

Tan²+Cot² = sec²-1+cosec²-1

= sec²+cosec²-2

Please find attached herewith the solution of your question.

If you have any doubt, please comment.

Answer:

1. No 2. No 3. Yes 4. Yes

Step-by-step explanation:

Compare the value of each digit from the leftmost digit.

please mark this answer as brainlist

3000 people participated in the survey, of which 2790 like some type of drink.

Since in a survey of some people, 73% like to drink tea, 85% like to drink coffee and 65% like to drink tea as well as coffee, if 210 people like neither tea nor coffee, to find the total number of people taken part in the survey and show how many of them like at least one of the given drink, the following calculations must be performed:

-First, it must be determined how many people do not prefer any of the drinks, in percentages, subtracting the 65% who like both from the percentages of each particular drink, and adding these results.

-Therefore, the 210 people who do not like any drink are 7 percent of the total survey. Therefore, to determine the total number of people who participated, the following cross multiplication must be carried out.

3000 - 210 = 2790

Therefore, 3000 people participated in the survey, of which 2790 like some type of drink.

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Answer:

A 3/4

Step-by-step explanation:

Set up equation to find the percentage 2/7 equals:

Variable x = percentage

2/7 = x/100

Cross multiply:

2 × 100 = 7 × x

200 = 7x

Divide:

28.57142... = x

About 30% (I rounded to 30% because it is a nice number to use when all other numbers end in 5 or 0)

If Alexa has about 30% saved, she will need to save about 70% more. Find the solution that is closest to 70%.

A is 3/4 which comes out to 75%. So far, this sounds like the best answer. Let's check the others just in case.

B is 1/2, or 50% which isn't as close as A was to 70%.

C is 1 1/4 which means 125% needs to be saved. This would mean Alexa is in debt and hasn't saved any money which is not the case.

D is 1/4, or 25%. The trick here is that she's saved about 30% so 25% is closest, but we are looking for how much more she needs to save.

We have [tex]f\left(f^{-1}(x)\right) = x[/tex] for inverse functions [tex]f(x)[/tex] and [tex]f^{-1}(x)[/tex]. Then if [tex]f(x) = 2x+5[/tex], we have

[tex]f\left(f^{-1}(x)\right) = 2f^{-1}(x) + 5 = x \implies f^{-1}(x) = \dfrac{x-5}2[/tex]

Then

[tex]f^{-1}(8) = \dfrac{8-5}2 = \boxed{\dfrac32}[/tex]

Step-by-step explanation:

A. gof=g(f(x))

= g(f(6))

=6×6

36

Answer:

Hello,

Step-by-step explanation:

[tex]y^2-x^2+1=50\\y^2=x^2+49\\2\ functions \ :\\\\y=\sqrt{x^2+49} \\\\or\\\\y=-\sqrt{x^2+49} \\[/tex]

Using function concepts, it is found that:

----------------------

The expression is given by:

[tex]y^2 - x^2 + 1 = 50[/tex]

In terms of x, the equation is given by:

[tex]y^2 = 50 + x^2 - 1[/tex]

[tex]y^2 = x^2 + 49[/tex]

[tex]y = \pm \sqrt{x^2 + 49}[/tex]

----------------------

Testing the input x = 0:

[tex]y = \pm \sqrt{0^2 + 49}[/tex]

[tex]y = \pm \sqrt{49}[/tex]

[tex]y = \pm 7[/tex]

Two output values for one input, thus, it is not a function.

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2/3 = 8/12

7/12 = 7/12

3/4 = 9/12

7/12 < 8/12 < 9/12

So, 7/12 < 2/3 < 3/4

Answer:

complementary angles 25

Answer:

3480

Step-by-step explanation:

It always help if you make clear how the state assesses taxes. Usually it is done the way I will do it, but it is no guarantee.

First 3000 = 3000 * 2/100 = 60.00

The next 2000 (excess over 3000) = 2000 * 3/100 = 60

The next 12000 (excess over 5000) = 12000 * 5/100 = 600

The next step would be excess over 12000 = 48000 * 5.75/100 = 2760

That's the way most taxes for federal taxes and state taxes work. What you have to know is this: does the question use the term excess anywhere? Or do your notes.  If you are accustomed to the word then this is the way the question is done.

So the total taxes = 60 + 60 + 600 + 2760 = 3480

Answer:

6.45

Step-by-step explanation:

The answer=2.5*7.5-(2.75+9.55)=18.75-(12.3)=6.45

5/6

Step-by-step explanation:

2/3 is equal to 4/6 and if you add 1/6 + 4/6 you get 5/6

Answer:

Step-by-step explanation:

4/6 is equivalent to 2/3 (Times by two).

Since we now have a fraction with the denominator of 6, we can add 1/6 easily.

4/6 + 1/6 = 5/6

The sum is 5/6

Answer:

a

Step-by-step explanation:

Answer:

Incorrect, it's actually B.

Step-by-step explanation:

Look at the Non-Sporting Group and Herding Group. The sizes of the slices are different (NSG being smaller than HG)

Answer:

Vertex: [tex](-\frac{5}{2} , -\frac{53}{4})[/tex]

Solutions: (0,-7), (1, -1), (2, 7)

I hope this helps!

Answer:

5.4

Step-by-step explanation:

cos(theta) = B/H

cos(75)=x/21, x=5.4

The Predicted time a person will serve is "88.9855 months". A complete solution is provided below.

Given equation is,

→ [tex]\hat{y}=9.309x - 167.012[/tex]

Her age,

→ x = 27.5 years

By substituting the value of "x" in the given equation, we get the predicted time,

hence,

→ [tex]\hat{y}=9.309\times 27.5 - 167.012[/tex]

     [tex]= 255.9975- 167.012[/tex]

     [tex]=88.9855 \ months[/tex]

Thus the above is the right answer

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The Required expression is (x+2) / (x^2+2).

x^2+x-2/x^3-x^2+2x-2

The process in mathematics to operate and interpret the function to make function simple or more understandable called simplify and the process is called simplification.

= (x^2+x-2) / (x^3-x^2+2x-2)

= (x-1)(x+2) / (x^2+2)(x-1)

=(x+2) / (x^2+2)

Thus, The Required expression is (x+2) / (x^2+2).

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Answer: see photo#2

Step-by-step explanation:

Answer:

About 6,785 people will be infected about nine months.

Step-by-step explanation:

We can write an exponential function to represent the situation. The standard exponential function is given by:

[tex]\displaystyle f(x) = a(r)^x[/tex]

Where a is the initial value, r is the rate, and x, in this case, is the time that has passed in months.

3,124 people have already been infected. Thus, our initial value a = 3124.

And an additional 9% will be infected per month. Therefore, our rate r will be 1 + 9% or 1.09.

Hence, our function is:

[tex]\displaystyle f(x) = 3124(1.09)^x[/tex]

Then after nine months, the total amount of infected people will be f(9):

[tex]\displaystyle f(9) = 3124(1.09)^{(9)}[/tex]

Use a calculator:

[tex]\displaystyle f(9) \approx 6785[/tex]

About 6,785 people will be infected about nine months.

Answer:

7,022

Step-by-step explanation:

Answer: B

[tex]tan(N)=\frac{opposite}{adjacent}=\frac{n}{r}[/tex]

Step-by-step explanation:

[tex](\sin{x} - \sin{y})(\sin{x} + \sin{y}) = \sin^2{x} + \sin{x}\sin{y} - \sin{x}\sin{y} - \sin^2{y}[/tex]

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