Eric is a real estate agent. He makes a 5% commission on each house he sells. Last month, Eric sold three houses. The sale price of each house is shown in the table. House saleAmount House 1 $55,000 House 2$105,525 House 3 $35,200 How much did Eric earn last month? Enter your answer in the box .

Answer:

Part 1) [tex]A=36(\pi-2)\ cm^2[/tex]

Part 2) [tex]P=6(\pi+2\sqrt{2})\ cm[/tex]

Step-by-step explanation:

Part 1) Find the area

we know that

The area of the shape is equal to the area of a quarter of circle minus the area of an isosceles right triangle

so

[tex]A=\frac{1}{4}\pi r^{2}-\frac{1}{2}(b)(h)[/tex]

we have that the base and the height of triangle is equal to the radius of the circle

[tex]r=12\ cm\\b=12\ cm\\h=12\ cm[/tex]

substitute

[tex]A=\frac{1}{4}\pi (12)^{2}-\frac{1}{2}(12)(12)[/tex]

[tex]A=(36\pi-72)\ cm^2[/tex]

simplify

Factor 36

[tex]A=36(\pi-2)\ cm^2[/tex]

Part 2) Find the perimeter

The perimeter of the figure is equal to the circumference of a quarter of circle plus the hypotenuse of the right triangle

The circumference of a quarter of circle is equal to

[tex]C=\frac{1}{4}(2\pi r)=\frac{1}{2}\pi r[/tex]

substitute the given values

[tex]C=\frac{1}{2}\pi (12)[/tex]

[tex]C=6\pi\ cm[/tex]

The hypotenuse of right triangle is equal to (applying the Pythagorean Theorem)

[tex]AC=\sqrt{12^2+12^2}[/tex]

[tex]AC=\sqrt{288}\ cm[/tex]

simplify

[tex]AC=12\sqrt{2}\ cm[/tex]

Find the perimeter

[tex]P=(6\pi+12\sqrt{2})\ cm[/tex]

simplify

Factor 6

[tex]P=6(\pi+2\sqrt{2})\ cm[/tex]

Answer:

36(π-2)cm^2 is area

Perimeter is 6(π+2√2)

Step-by-step explanation:

Answer:

i don't know

Step-by-step explanation:

Answer:

y = - 4x + 2

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 )

Here m = - 4, thus

y = - 4x + c ← is the partial equation

To find c substitute (- 1, 6) into the partial equation

6 = 4 + c ⇒ c = 6 - 4 = 2

y = - 4x + 2 ← equation of line

Answer:

192

Step-by-step explanation:

20% of 240 is 48

240-48 = 192

Answer:

192

Step-by-step explanation:

20%/100% x 240 =48

His cholesterol level now will be 240 - 48 = 192

Answer:

f^-1 (x)=-x-1

Step-by-step explanation:

y=-x-1

x=-y-1

-y=x+1

y=-x-1

Jordan it a bigger number

Answer:

Therefore Perimeter of Rectangle ABCD is 4 units

Step-by-step explanation:

Given:

ABCD is a Rectangle.

A(-6,-4),

B(-4,-4),

C(-4,-2), and

D (-6,-2).

To Find :

Perimeter of Rectangle = ?

Solution:

Perimeter of Rectangle is given as

[tex]\textrm{Perimeter of Rectangle}=2(Length+Width)[/tex]

Length = AB

Width = BC

Now By Distance Formula  we have'

[tex]l(AB) = \sqrt{((x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2} )}[/tex]

Substituting the values we get

[tex]l(AB) = \sqrt{((-4-(-6))^{2}+(-4-(-4))^{2} )}[/tex]

[tex]l(AB) = \sqrt{((2)^{2}+(0)^{2} )}=2\ unit[/tex]

Similarly

[tex]l(BC) = \sqrt{((-4-(-4))^{2}+(-2-(-4))^{2} )}[/tex]

[tex]l(BC) = \sqrt{((0)^{2}+(2)^{2} )}=2\ unit[/tex]

Therefore now

Length = AB = 2 unit

Width = BC = 2 unit

Substituting the values  in Perimeter we get

[tex]\textrm{Perimeter of Rectangle}=2(2+2)=2(4)=8\ unit[/tex]

Therefore Perimeter of Rectangle ABCD is 4 units

Answer:

Therefore Perimeter of Rectangle ABCD is 4 units

Step-by-step explanation:

Given:

ABCD is a Rectangle.

A(-6,-4),

B(-4,-4),

C(-4,-2), and

D (-6,-2).

To Find :

Perimeter of Rectangle = ?

Solution:

Answer:

Step-by-step explanation:

picture to help

Answer: I can't draw it but i answered

Step-by-step explanation:

To draw a model for 1/6 you would have draw six shapes of any kind. Then you would only fill one of them.

Answer:

Option D: y = 4x + 16

Step-by-step explanation:

Given the line:  y - 1 = 4(x + 3)  ⇒  y = 4x + 13

The slope of the given line = m = 4

The required line is parallel to the given line

So, the slope of the required line = m = 4

So, the general equation of the required line: y = 4x + c

Where c is constant represents y-intercept

To find the value of c, substitute with the point (4,32)

At x = 4 y = 32

∴ 32 = 4 * 4 + c

∴ c = 32 - 16 = 16

∴ y = 4x + 16

The answer is option D: y = 4x + 16

Answer:true

Step-by-step explanation:

5x-3(2x-4)=

1) solve the parentheses

5x-6x-12=0

2) we just can rest the X

5x-6x=X

3) X-12=0

4) The order of factors does not alter the product

12-X=0

Answer:

True

Step-by-step explanation:

5x − 3(2x − 4)

Expand

5x - 6x + 12

-x + 12

12 - x

( ) are called "parentheses" or "brackets "

Whatever is inside the ( ) needs to be treated as a "package".

So when multiplying: multiply by everything inside the "package".

Multiplying negatives has special rules: a negative times a positive gives a negative, but multiplying two negatives gives a positive:

In that case −3 · -5 = +15 (a positive answer)

Answer:

Step-by-step explanation:

x = first angle

y = second angle

z = third angle

x + y + z = 180

The sum of the measures of the second and third angles is twice the measure of the first angle.    ---->       y + z = 2x

The third angle is 12 more than the second.  ---->    z = y + 12

Use substitution to find each variable. Since z is already isolated/by itself, plug it into the other equation

y + z = 2x    Plug in (y + 12) for z

y + (y + 12) = 2x      Simplify

2y + 12 = 2x    Divide 2 on both sides

y + 6 = x          Isolate "y"

y = x - 6         Next you could plug this into z = y + 12, so that z has the x variable

z = y + 12

z = x - 6 + 12

z = x + 6

Now that you have y and z, you can do this:

x + y + z = 180

x + (x - 6) + (x + 6) = 180     Simplify

3x = 180    Divide 3 on both sides

x = 60             Now that you found x, plug it into the other equations to find y and z

y = x - 6

y = 60 - 6

y = 54

z = x + 6

z = 60 + 6

z = 66

x = 60°

y = 54°

z = 66°          [sorry if this is confusing]

PROOF

x + y + z = 180

60 + 54 + 66 = 180

180 = 180

The problem can be solved by setting up and solving a system of equations based on the information given in the problem. Using these equations, we are able to establish a relationship between the angles and thus calculate their individual measures.

To solve this problem, we need to set up and solve a system of equations based on the information provided. We know from the problem that:

First, let's substitute z = y + 12 into the other two equations:

We now substitute x = y + 6 into the equation x + 2y = 168 to find the values of x and y and hence z.

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Answer:

20

Step-by-step explanation:

Answer:

20

Step-by-step explanation:

Answer:

15

Step-by-step explanation:

First subtract the remainder from 403 to get 390. then divide 390 by 26 to get 15.

The number used by Justin used to divide 403 to get a quotient of 26 with a remainder of 13 is 15.

Division is theartimetic process used to divide a number into equal parts using another number. The sign used to denote division is ÷.

In order to detemine the number used to divide 403, take the following steps:

Subtract 13 from 403 = 403 - 13 = 390

Now divide 390 by 26: 390 / 26 = 15

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Answer:16 books

Step-by-step explanation:

Final answer:

Julian bought 8 books and received a free book with each purchase, resulting in 16 books altogether by the end of the year.

Explanation:

The question is asking how many books Julian would have altogether if he bought 8 books and received a free book with each purchase this year. To solve this, we need to consider that for every book purchased, he gets an additional book without cost. Therefore, Julian gets 2 books each time he makes a purchase for one book. As he bought 8 books, we simply need to double that amount to account for the free books he received.

To calculate: 8 books purchased × 2 = 16 books altogether.

Julian would have a total of 16 books by the end of the year after his purchases and receiving the complementary books.

Answer: irs

Step-by-step explanation:

Banks give interest on savings accounts to encourage consumers to deposit and retain their money in the bank

Banks give interest on savings accounts to encourage consumers to deposit and retain their money in the bank.

Banks can attract and maintain consumer cash by providing interest, which they can then use to lend to other people or invest in various financial operations.

Paying interest on savings accounts assists banks in maintaining liquidity, generating money, and developing a mutually beneficial relationship.

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Answer: y = 3

Step-by-step explanation:

Two lines are said to be parallel if they have the same slope. All we need to do is to find the slope of each line . The formula for finding slope is given as :

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

For the first line

[tex]x_{1}[/tex] = 11

[tex]x_{2}[/tex] = 2

[tex]y_{1}[/tex] = y

[tex]y_{2}[/tex] = 0

substituting into the formula , we have

m = [tex]\frac{0 - y}{2 - 11}[/tex]

m = [tex]\frac{-y}{-9}[/tex]

m = [tex]\frac{y}{9}[/tex]

Also Finding the slope of the second line we have

[tex]m_{2}[/tex] = [tex]\frac{2-5}{-2 - 7}[/tex]

[tex]m_{2}[/tex] = [tex]\frac{-3}{-9}[/tex]

[tex]m_{2}[/tex] = [tex]\frac{1}{3}[/tex]

Since the two lines are parallel , we will equate their slope , that is

[tex]\frac{y}{9}[/tex] = [tex]\frac{1}{3}[/tex]

3y = 9

y = 3

Answer:

The correct answer is C. 4 -6

Step-by-step explanation:

Let's solve the operation given, this way:

(7 - 11/) + (-3 + 5/)

7 - 11 - 3 + 5=

12 - 14 = - 2

After resolving the parenthesis, adding and subtracting the result of thhe operation is - 2

The correct answer is C. 4 -6

Answer: Should Be 0.01

Step-by-step explanation: It’s Asking How Thick it is and never asked when So it would automatically mean from the start therefore it’s 0.01 cm thick

Answer:

g (x) = 2 ^ (x + 2)

Step-by-step explanation:

For this case the transformation of f (x) is given by

g (x) = 2 ^ (x + 2)

To prove it, we must verify that equality is met by replacing the ordered pairs shown in the function g (x)

For (-2,1)

g (-2) = 2 ^ ( -2 + 2)

g(-2)=1

For (-1,2)

g (-1) = 2 ^ ( -1+ 2)

g(-1)=2

For (0,4)

g (0) = 2 ^ ( 0+ 2)

g(0)=4

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Answer:

f−1(f(x)) = f(f−1(x)) = x

Step-by-step explanation:

Follow this simple example using the function f(x) = x + 2

f(x) = x + 2

NOw we find the inverse function f^(1)(x).

y = x + 2

x = y + 2

y = x - 2

f^(-1)(x) = x - 2

The inverse function is f^(-1)(x) = x - 2

Now we do the two compositions of functions:

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

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

Both are equal to x.

Answer: f−1(f(x)) = f(f−1(x)) = x

The expression [tex]f^{-1}(f(x)) = f(f^{-1}(x)) = x[/tex]

We are to prove the relationship;

[tex]f^{-1}(f(x)) = f(f^{-1}(x)) = ?[/tex]

To get the unknown, let f(x) = x - 2

Find its inverse:

Let y = x - 2

Replace y with x;

x = y - 2

y = x+2

Hence [tex]f^{-1}x = x+2[/tex]

Next is to get [tex]f(f^{-1}(x))[/tex]

[tex]f(f^{-1}(x))=f(x+2) = (x+2) - 2\\f(f^{-1}(x))= x\\[/tex]

We can conclude that [tex]f^{-1}(f(x)) = f(f^{-1}(x)) = x[/tex]

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Answer: m = 15

Step-by-step explanation:

45 = 30 + m

subtract 30 , from both sides  , that is , -30 should be added to both sides to find the variable

45 - 30 = 30 + m - 30

15 = m

Therefore : m = 15

Answer:

10/16

Step-by-step explanation:

Answer:

17k + -13

Step-by-step explanation:

6k + 11k take the + next to the 6k making it say 6k+11

-3 - 10 take the - next to the 10 making it say -3 - 10

Total Cost = 250 + 60x is the equation that models the given situation

Solution:

Given that, Linda's start up cost for her online jewelery store was $250

She has to pay an additional $60 per month to keep it running

To find: Equation that models this situation

From given,

Start up cost = $ 250

Let "x" be the number of months she keeps the store running

Additional pay per month = $ 60

Thus, the total cost Linda spend to keep the store running is given as:

Total Cost = Startup cost + (Additional pay per month)(number of months)

[tex]Total\ Cost = 250 + 60x[/tex]

Thus the equation that models the given situation is found

Answer:

A

Step-by-step explanation:

supplementary angles add up to 180

angle cgr and kga are vertical angles so they are equal

that makes the two angles in question add up to 180

Answer:

6

Step-by-step explanation:

Answer:

a) (1, -2)

Step-by-step explanation:

The given inequality is y < -|x|

We substitute the point to see which points satisfy the inequality.

For a) (1, -2), we substitute x=1 and y=-2 to get:

-2 < -|1|---------->-2<-1--------->True

For b) (1, -1), we substitute x=1 and y=-1 to get:

-1 < -|1|---------->-1<-1--------->False

For a) (1, 0), we substitute x=1 and y=0 to get:

0 < -|1|---------->0<-1--------->False

The first choice is correct.

Total of 8 kids came to Taylor's party.

Given is Taylor's 8th birthday and there were 47 presents. Each kid brought 10 presents, except for three kids who brought five presents each and two kids who bought one present each.

Assume that [n] students bought 10 presents. Then, we can write -

3 x 5 + 2 x 1 + 10n = 47

15 + 2 + 10n = 47

10n = 30

n = 3

Total kids = 3 + 3 + 2 = 8

Therefore, total of 8 kids came to Taylor's party.

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Answer: Third option:

Step-by-step explanation:

The equation in Slope Intercept form of a line that does not pass through the point (0,0), which is known as "Origin, is the following:

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

Where "m" is the slope of the line and "b" is the y-intercept.

The equation  in Slope Intercept form  of a line that passes through the Origin, is:

[tex]y=mx[/tex]

Where "m" is the slope of the line.

In this case you can observe in the picture attached that the line passes through the point (0,0).

You can also notice that "y" would be the Dependent variable and "x" the Independent variable.

Therefore, the equation of this must have this form:

 [tex]y=mx[/tex]

The only equation that matches with that form, is the one given in the Third option. This is:

[tex]y=2x[/tex]

The linear equation shown in the graph can be written as.

y = 2x

A general linear equation is written as:

y = ax + b

Where a is the slope and b is the y-intercept.

In this graph, we can see that the line intercepts the y-axis at y = 0, so we have:

y = ax

We also can see that the line passes through the point (1, 2), replacing these values in the equation we will get:

2 = a*1

2 = a

Then the linear equation is:

y = 2x

The third option.

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