Given that f(x) = x2 – 12x + 27 and g(x) = x – 9, find f(x) · g(x) and
express the result in standard form.

Answer:SEE BELOW

Step-by-step explanation:

Average the X and Y coordinates (X,Y)

X = (-8 + 8)/2 = 0

Y = (-9 + 3)/2 = -3

(X,Y) = (0,-3)

Step-by-step explanation:

[tex] \underline{ \underline{ \text{Given \: points}}} : [/tex]

[tex] \underline{ \underline{ \text{To \: find}}} : [/tex]

[tex] \underline{ \underline{ \text{Solution}}} : [/tex]

Let the point G ( -8 , -9 ) be ( x₁ , y₁ ) & H ( 8 , 3 ) be ( x₂ , y₂)

[tex] \boxed{ \sf{Midpoint = (\frac{x_{1} + x_{2}}{2}} \: , \frac{y_{1} + y _{2}}{2} )}[/tex]

⟶ [tex] \tt{( \frac{ - 8 + 8}{2} \:, \frac{ - 9 + 3}{2} ) }[/tex]

⟶ [tex] \tt{( \frac{0}{2} \: , \frac{ - 6}{2}} )[/tex]

⟶ [tex] \tt{(0 \: ,- 3})[/tex]

[tex] \red{ \boxed{ \boxed{ \tt{Our \: final \: answer : \boxed{ \tt{(0 \:, - 3)}}}}}}[/tex]

Hope I helped ! ツ

Have a wonderful day / night ! ♡

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Answer:

b

Step-by-step explanation:

she started in the negatives, and went into a positive y value

Answer: The answer is B. I hoped this helps to you! :D

Step-by-step explanation:

Answer:

Getting through ratio method

100-20=80 percent have to pay

18:80

x:100

cross multiply

80 x x=18 x 100

80x=1800

x=1800/80

x=22.5

So the original price was $22.50

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

If you compare the graph of log₂x and g(x) you can see that the slope increases. The only answer that gives you this is C as D would increase too quickly

Answer:

OC. log2 (2x) I think this is your answer as it is increasing

c

Answer:

round it to 20×10 there's you answer

Answer:

Given:

Sebastian :

Principal(invested)= $7,100

Rate of interest=  8.14% compounded monthly

Eva:

Principal(invested)= $7,100

Rate of interest= 8.12% compounded continuously

Step-by-step explanation:

After 5 years,

In Sebastian case:

Amount= Principal*[tex](1+R/100)^{t}[/tex]

Amount = 7100*[tex](1+8.14/100)^{12*5}[/tex]

Amount= 7100*[tex]1.0814^{60}[/tex]

Amount=7100*109.4415

Amount= $777,034.43

In Eva case,

Amount= Principal*[tex]e^{Rt/100}[/tex]

Amount = 7100*[tex]e^{0.0812*12*5\\}[/tex]

Amount= 7100*130.5818

Amount= $927,130.92

Difference between their money=$927,130.92-777034.43

                                                 =$150,096.49

Eva has $150,096 more money than Sebastian.

Answer:

80

Step-by-step explanation:

Answer:

35w^3 + 44w

Combine Like Terms:

= 35w + 9w + 35w^3 + 25w^3 - 25w^3

= (35w^3 + 25w^3 - 25w^3) +(35w + 9w)

= 35w^3 + 44w

Hope this is right ♡

Answer:

28.274

Step-by-step explanation:

Answer: e

Step-by-step explanation: hope this helps!

Answer:

444 cm squared

Step-by-step explanation:

first multiply 6 by 8 by 18.5, and you will get 888.

But since it's a triangle you would have to divide that by 2.

This will get you 444 cm squared.

Answer:

. yupp

Step-by-step explanation:

Answer:

The answer is 5 1/4 liters in 1 hour.

Step-by-step explanation:

If Ben drinks 3 1/2 liters of tea in only 2/3 of a hour, this is how you calculate it. First of all, Ben is not a human being, like who can drink 3 and a half liters of tea in under a hour. To calculate how much Ben drinks in a hour, first multiply both fractions by 3, you will get 10 1/2 liters in 2 hours. Then, divide both fractions by 2, in which you will get 5 1/4 liters in 1 hour. That's your answer!

Answer:

21/4

Step-by-step explanation:

Divide the two numbers

3 1/2 =7/2 as a improper fraction

7/2 divided by 2/3

7/2 times 3/2

21/4 or 5 1/4

Answer:

correct answer is (3)

Methord in the pic

Answer:

101

Step-by-step explanation:

6 - 5 = 1

1+100=101

k=101

Sorry if I'm incorrect

Answer:

A. There will be 2 layers of cubes in the rectangular prism.

Step-by-step explanation:

height = 2 cm

cube height = 1 cm

so only 2 layer of cube can be in the 2 cm height rectangular prism

Answer:

C

Step-by-step explanation:

Answer:

x = 63; y = 27

Step-by-step explanation:

x + 117 = 180

x = 180 - 117

x = 63

x + y = 90

63 + y = 90

y = 90 - 63

y = 27

Bam! UwU

Lol Hope this helps !

That is a question about angles.

There are two informations in that image that we should to note:

With these two informations we can solve that question. The first step is solve the second equation, and we will find the x value. Finally, we change the x value in the first equation and we find the y value. Let's solve the equations:

[tex]x + 117 = 180\\x = 180 - 117\\x = 63[/tex]

So, the value of x is 63°. Let's replace the x value in the first equation.

[tex]x+y = 90\\63 + y = 90\\y = 90 - 63\\y = 27[/tex]

Thus, the value of y is 27°.

Therefore, the correct option is the option says x = 63°, y = 27°.

I hope I've helped. :D

Enjoy your studies. \o/

Answer:

160 liters

Step-by-step explanation:

"a confectioner mixes forty liters of 60%":

Equation: 40 * .60

ow plug it in

0.60*40 + 0.10x = 0.20(40+x)

"how much of the 10% syrup should she use?":

.10x

"...to make a 20% sugar syrup.":

0.20(40+x)

Now that I have split the question into equations, let's put them together:

0.60*40 + 0.10x = 0.20(40+x)

Solve:

60*40 + 10x = 20*40 + 20x

10x = 40*40

x = 160 liters (amt of 10% solution needed)

Hope this helps :)

160 liters of 10% syrup is needed to make the mixture.

An equation is an expression used to show the relationship between two or more variables and numbers.

Let x represent the amount of 10% syrup. Hence:

(60% of 40) + (x of 10%) = (x + 40) of 20%

0.6 * 40 + x * 0.1 = (x + 40) * 0.2

24 + 0.1x = 0.2x + 8

x = 160 liters

160 liters of 10% syrup is needed to make the mixture.

Find out more on Equation at: https://brainly.com/question/13763238

Answer:

2p+3q

Step-by-step explanation:

3p+7q-p-4q

2p+3q

hope it is helpful

Step-by-step explanation:

b is the equal ratios just divide 22 and 14 with 2 you gonna get you answer easily

Answer:

a) 4/6 is not equivalent to 8/6.

b) 11/7 is equivalent to 22/14

c) 8/7 is not equivalent to 16/12

d) 1/3 is not equivalent to 3/2

Step-by-step explanation:

a) 4/2             8/2

   -----        :  ---------        

   6/2             6/2

= 2/3 is not equal to 4/3, therfore they are not equivalent ratios.

b) 11 * 2

   --------           =  22/14

    7*2    

= Therefore, 11/7 is equivalent to 22/14.

c) 8*2

 --------         =           16/14

   7*2

= Therefore, they are not equivalent ratios.

c 1*3                                3/9, Therefore, they are not equivalent ratios...

 ------                =

 3*3

                  I hope this helps !!!

             Please mark it as Brainliest!!!

Answer:

teacher - apple = 2

grapes - students = 29

grapes - total = 33

oranges - teachers = 1

students - total = 75

teachers - total = 7

total - total = 82

Answer:

Son's age = 24 years

Man's age = 48 years

Step-by-step explanation:

Let's take the age of son as x

Man's age = 2x

Twelve years ago,

Son's age= x-12

Man's age= 2x-12

Man is three times as old as his son so,

[tex] \frac{2x - 12}{x - 12 } = \frac{3}{1} [/tex]

Solving for x,

2x-12(1) = x-12(3)

2x-12 = 3x-36

2x-3x = -36+12

-x = - 24

x = 24

So if we substitute the values we get,

Son's age = 24 years

Man's age = 48 years

Hope you understand :)

Step-by-step explanation:

[tex] \underline{ \underline{ \text{Solution}}} : [/tex]

Let the present age of father be ' x ' years and that of the son be ' y ' years. From the first condition ,

From the second condition ,

Substituting the value of x from equation ( i ) in equation ( ii ) :

[tex] \sf{2y - 12 = 3(y - 12)}[/tex]

Solve for y ( age of the son ) :

⟿ [tex] \sf{2y - 12 = 3y - 36}[/tex]

⟿ [tex] \sf{2y - 3y = - 36 + 12}[/tex]

⟿ [tex] \sf{ - y = - 24}[/tex]

⟿ [tex] \sf{y = 24}[/tex]

Now , Substituting the value of y in equation ( i ) , we get :

[tex] \sf{x = 2 \times 24}[/tex]

⟿ [tex] \sf{x = 48}[/tex]

So, the present age of the father is 48 years and that of the son is 24 years.

Hope I helped ! ツ

Have a wonderful day / night ♡

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Answer:

Hi hope you have a wonderful and blessed day!!!!

Step-by-step explanation:

Answer:

Hi have a wonder full day!!!!!!!!!!!!!!!!!!!!!!!!

Step-by-step explanation:

Answer:

A. 5x+y+3

Step-by-step explanation:

to combine like terms you get the numbers that have the same variable. you will combine 2x and 3x and to combine them you add them 2x+3x and it equals 5x. you will do the same for the numbers left... -2y and 3y = 1y or y and 3 is left so we dont do nothing and after you do that you will put it in an equation variables go first and you order them in alphabetical order so 5x will go first then y and lastly the 3

Answer:

division property of equality

Step-by-step explanation:

Consider the equation and its solution.

In the first step, 8 is distributed inside the parenthesis. So distributive property is used.

In the second step, 16 is added on both sides. So addition property is used.

In the last step , 8 is divided on both sides. So, division property of equality is used.

Step-by-step explanation:

Answer:

division property of equality

Step-by-step explanation:

because you divide 8 and 80 to have the x alone leaving you with x=10

Answer:

Step-by-step explanation:

milă (terestră) = 1.609,344 m = 1.760 yards = 63.360 inches (țoli)

1 „milă romană” (mille passus) = 1.000 (passus) (1 pasus = doi pași, pas dublu) circa. 1.470 - 1.490 m

The question is incomplete. Here is the complete question.

A family needs to build a fence around their rectangular home and square pool, depicted below. A rectangle labeled home has its right side (2 + 5x) yards and its bottom side labeled (3 + 10x)yards. The square, labeled pool, is smaller than the rectangle. One of its side is labeled (2x)yards. The total amount of fencing they need can be written as x + 10. If x = 5:

The family needs _____ yards of fencing for their home.

The family needs _____ yards of fencing for their pool.

Answer: 160 yards

               40 yards

Step-by-step explanation: Perimeter is the sum of every side of a polygon.

Rectangle and Square are quadrilateral, i.e., have 4 sides each, but in a rectangle, the 2 parallel sides are equal, while in a square, 4 sides are equal.

To determine the amount of yards to fence a rectangle home:

P = 2l + 2w

where

l is length (in this case, bottom side)

w is width (right side)

P is perimeter

P = 2(2 + 5x) + 2(3 + 10x)

P = 4 + 10x + 6 + 20x

P = 10 + 30x

As x = 5:

P = 10 + 30(5)

P = 160

The family will need 160 yards of fencing for their home.

For the square pool:

P = 4s

with s representing a side of the square

P = 4(2x)

P = 8x

As x = 5:

P = 8(5)

P = 40

The family needs 40 yards of fencing for their pool.

Answer:

38, 160, 40

Step-by-step explanation:

Answer:

below explained

Step-by-step explanation:

Answer:

The correct answer is x = -92/9 or x = -10.2

Step-by-step explanation:

(The error is that the student didn't multiply 8 inside the parenthesis )

Steps to show work:

3/4x + 8 = 1/3

9x + 96 = 4 ➙ 9x = 4 - 96

9x = -92

x = -10.2 or -92/9

Answer to 32:

You need to find a common denominator and then multiply both sides of the equation by that number. You can do practically anything you want one side of the equation, as long as you do it to the other side as well.

-----

Hope this helped :)

Step-by-step explanation:

(m - 2)x + y = 2

y = -(m - 2)x + 2

8 = -(m - 2)(2) + 2

6 = -(m - 2)(2)

3 = -(m - 2)

-3 = m - 2

-1 = m

mx + 2y = k

2y = -mx + k

[tex]y = - \frac{1}{2} mx + \frac{k}{2} \\ y = \frac{1}{2} x + \frac{k}{2} \\ 8 = \frac{1}{2} (2) + \frac{k}{2} \\ 7 = \frac{k}{2} \\ 14 = k[/tex]

Answer:

The answer tot he question provided is 25.