Given the definitions of f(x) and g(x) below, find the value of g(f(0))
f(x)= -x+9
g(x)=x^2 - 6x+9​

Answers

Answer 1

Answer:

The value of g(f(0)) is 36

Step-by-step explanation:

g(f(x)) is a composite function, where f(x) is the value of x in g(x), which means substitute x in g(x) by f(x)

Let us use this rule to solve our question

∵ f(x) = -x + 9

∵ g(x) = x² - 6x + 9

→ Substitute x in g by f

∵g(f(x)) = g(-x + 9)

∴ g(f(x)) = (-x + 9)² - 6(-x + 9) + 9

→ Let us simplify it

∵ (-x + 9)² = (-x)(-x) + (-x)(9) + (9)(-x) + (9)(9)

∴ (-x + 9)² = x² + -9x + -9x + 81

→ Add the like terms (-9x + -9x)

∴ (-x + 9)² = x² + -18x + 81

→ Remember (+)(-) = (-)

∴ (-x + 9)² = x² - 18x + 81

∵ - 6(-x + 9) = -6(-x) + (-6)(9)

∴ - 6(-x + 9) = 6x + -54

∴ - 6(-x + 9) = 6x - 54

→ Substitute them in g(f(x))

∴ g(f(x)) = x² - 18x + 81 + 6x - 54 + 9

→ Add the like terms

∴ g(f(x)) = x² + (-18x + 6x) + (81 -54 + 9)

∴ g(f(x)) = x² + (-12x) + (36)

∴ g(f(x)) = x² - 12x + 36

→ Now substitute x by 0

∴ g(f(0)) = (0)² - 12(0) + 36

∴ g(f(0)) = 0 - 0 + 36

g(f(0)) = 36

There is an easy way to find it quickly

Substitute x in f by 0

f(0) = -(0) + 9

f(0) = 9

Substitute x in g by 9

Find g(9)

g(9) = (9)² - 6(9) + 9

g(9) = 81 - 54 + 9

g(9) = 36


Related Questions

whoever answers first gets brainliest!!!!

Answers

Answer:

38%

Step-by-step explanation:

Answer:

C. 38%

Step-by-step explanation:

3 ÷ 8 = 0.375

Make it a percent

0.375 x 10 = 37.5

Since it isn't an option, round up. A good rounding rule is:  Four or less, let is rest. Five or more, let it soar.

Since this number ends in 5, round up.

37.5 is now 38

38%

Help A costume designer needs to make 12 costumes for the school play.Each costume requires 2 2/3 yards of fabric.How many yards of fabric does the costume designer need to make all costume

Answers

Answer:

32

Step-by-step explanation:

PLEASE MARK ME AS BRAINLIEST I REALLY WANT TO LEVEL UP

Hope this helps! :)

Have a blessed day and remember to keep smiling! :)

[tex][Hello,BrainlyUser][/tex]

Answer:

32 Yards

Step-by-step explanation:

Given;

Length of fabric required for each costume = 2 2/3

Total number of costumes to be made =12

Solve;

12 * 2 2/3

We can multiply mixed numbers by converting it to fractions.

⇒ 12 * 8/3

⇒ 32

Thus, you need 32 yards of fabric.

[CloudBreeze]

what is 1/6 as a decimal (This question is worth 15 points)

Answers

Answer:

0.17

Step-by-step explanation:

divide one by six and you will get 0.16666 and so on, depending on the question but it will be best if you put it in two decimal place, which us 0.17

Let R be the region in the first quadrant bounded by x2 − y2 = 16, the horizontal line y = 0, and the vertical line x = 5. What is the volume of the solid formed by revolving R about the x-axis?

Answers

Check the picture below.

so the region is the one bounded by a hyperbola and two straight lines, one of which is the x-axis, or namely y = 0, since the hyperbola has a vertex at x = 4, then our bounds are from 4 to 5.

[tex]x^2-y^2=16\implies x^2-16=y^2\implies \pm\sqrt{x^2-16}=y \\\\\\ \stackrel{I~Quadrant}{+\sqrt{x^2-16}=y}\qquad \qquad \implies \stackrel{\textit{using the disk method}~\hfill }{\displaystyle\int_{4}^{5}~\pi \left( \sqrt{x^2-16} \right)^2\cdot dx\implies \pi \int_{4}^{5}(x^2-16)dx} \\\\\\ \pi \left( \left. \cfrac{x^3}{3} \right]_{4}^{5} ~~ - ~~\left. 16x\cfrac{}{} \right]_{4}^{5}\right)\implies \pi \left[\cfrac{61}{3}~~ - ~~16 \right]\implies \cfrac{13\pi }{3}[/tex]

how do you find the center of a data set (statistic)

Answers

Step-by-step explanation:

The center of a data set is also called the middle. So, just arrange them in numerical order least to greatest and the middle number is your answer.

I spent $4.80 on groceries and $1.20 on vegetables. What is the ratio of:
a. Cost of groceries to cost of vegetables;
b. Cost of vegetables to cost of groceries;
c. Cost of vegetables to total cost;
d. Cost of groceries to total cost?
Help me plz

Answers

C = 1.20 : 6
D = 4.80 : 6

The required ratio is given as a) 4/1 b) 1/4 c) 1/5 and d) 4/5.

Given that,
Spent $4.80 on groceries and $1.20 on vegetables.

What is the Ratio?

The ratio can be defined as the proportion of the fraction of one quantity towards others. e.g.- water in milk.

Total cost = 4.80 + 1.20
Total cost = $6.00

a. Cost of groceries to cost of vegetables;
Ratio = 4.80 / 1.20 = 4 / 1

b. Cost of vegetables to cost of groceries;
Ratio = 1.20 / 4.80 = 1 / 4

c. Cost of vegetables to total cost;
Ratio = 1.20 / 6 = 1 / 5

d. Cost of groceries to total cost
Ratio = 4.80 / 6 = 4 / 5

Thus, the required ratio is given as a) 4/1 b) 1/4 c) 1/5 and d) 4/5.

Learn more about ratios here:

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67+90(56768*4387)-78÷3456




help















talk to me please

Answers

Answer Is: 22413709506.977

Solve the system of linear equations in two variables by elimination or substitution.

4x+ 3y=2

2x-3y=1

Answers

Answer:

( [tex]\frac{1}{2}[/tex], 0 )

Step-by-step explanation:

Given the 2 equations

4x + 3y = 2 → (1)

2x - 3y = 1 → (2)

Adding (1) and (2) term by term will eliminate the y- term, that is

6x = 3 ( divide both sides by 6 )

x = [tex]\frac{3}{6}[/tex] = [tex]\frac{1}{2}[/tex]

Substitute x = [tex]\frac{1}{2}[/tex] into either of the 2 equations and evaluate for y

Substituting into (1)

4([tex]\frac{1}{2}[/tex] ) + 3y = 2

2 + 3y = 2 ( subtract 2 from both sides )

3y = 0 ⇒ y = 0

Solution is ( [tex]\frac{1}{2}[/tex], 0 )

Are the following equations perpendicular y=-1/3x+4 and y=1/3x+12?

Answers

Answer: No, they are not perpendicular

Explanation:

Compare each equation to the form y = mx+b

m = slope

The first equation has slope -1/3 and the second equation has slope 1/3

The slopes do not multiply to -1, so the lines aren't perpendicular.

The slopes aren't equal, so the line aren't parallel either.

Bob bought some new boots that cost $67.34. He paid 7.5% tax. How much did he pay at the cash register?
A. $3.20
B. $24.78
C. $72.39
D. $33.40

Answers

Answer:

72.39

Step-by-step explanation:

Cost of boots: 67.34

Tax: 7.5%

Amount of tax he payed: 67.34 * 7.5/100 = 5.05

Total Amount = 67.34 + 5.05 = 72.39

True or False. A function is increasing if its outputs get larger as the inputs
get larger.*

Answers

Answer:

True

Step-by-step explanation:

A function is increasing if its outputs get larger as the inputs is a "true statement" or the first option. If the inputs are getting larger for every input and the outputs are getting larger for every output, if you plot the data on a scatter plot or a coordinate plane of sorts you would see it take shape of a line that is moving from the left to the top right which means the function is indeed increasing when the outputs/inputs get larger.

Hope this helps.

HELP QUICK PLSSSSSSSSS

Answers

Answer:

I believe the answer is 198

Answer:

791.68135 cubic metres

Step-by-step explanation:

V=πr2h=π·62·7≈791.68135

Adnan pours out 18 servings of lemonade. Each serving contains 120 milliliters of lemonade.

How many liters of lemonade in all did Adnan pour out?


0.216 L

2.16 L

21.6 L

216 L

Answers

Since all the answers are in litres, it would be smart to convert what we have to litres as well.

Since there are 1000mL in a L, we divide our mL by 1000 to get L.

120 / 1000 = 0.120 L

Since there are 18 of these, multiply by 18.

0.120 x 18 = 2.16

Answer is 2.16 L

A sundae requires 333 ice-cream scoops and 444 strawberries, and a milkshake requires 222 ice-cream scoops and 666 strawberries. Ramses wants to make sundaes and milkshakes with at most 252525 ice-cream scoops and 373737 strawberries. Let SSS denote the number of sundaes he makes and MMM the number of milkshakes he makes.

Answers

Answer:

[tex]3x+2y\leq 25 \\4x+6y \leq 37[/tex]

Step-by-step explanation:

Sunday ice cream :

Ice cream scoops = 3

Strawberries = 4

Milkshake :

Ice cream scoops = 2

Strawberries = 6

Ramses wants to  make sundaes and milkshakes with at  most 25 ice-cream scoops  and 37 strawberries.

Let x be the no. sundaes and y be the no. of milkshakes

So, Equations are :

[tex]3x+2y\leq 25 \\4x+6y \leq 37[/tex]

Now we are supposed to graph the solution

[tex]3x+2y\leq 25[/tex] --- Blue

[tex]4x+6y \leq 37[/tex] --- Green

Refer the attached figure


When Amira goes bowling, her scores are normally distributed with a mean of 160
and a standard deviation of 13. What percentage of the games that Amira bowls does
she score less than 192, to the nearest tenth?

Answers

Using the normal distribution, it is found that she scores less than 192 in 99.3% of games.

Normal Probability Distribution

In a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

It measures how many standard deviations the measure is from the mean. After finding the z-score, we look at the z-score table and find the p-value associated with this z-score, which is the percentile of X.

In this problem, the mean and the standard deviation are given, respectively, by [tex]\mu = 160, \sigma = 13[/tex].

The proportion of games in which she scores less than 192 is the p-value of Z when X = 192, hence:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{192 - 160}{13}[/tex]

[tex]Z = 2.46[/tex]

[tex]Z = 2.46[/tex] has a p-value of 0.993.

Hence, she scores less than 192 in 99.3% of games.

More can be learned about the normal distribution at https://brainly.com/question/24663213

The area of a circle is 144pi m2. What is the diameter of the circle?
A. 6m
B. 12m
C. 24m
D. 144m

Answers

B.12

The answer is 12
The diameter of the circle is 12m which is B. 12m

If f(-4) for f(x)=-2x+7 is 15, then what is f^-1 (15)?

Answers

let's recall that for a function f(x) that has an inverse function f⁻¹(x), the domain of f(x) corresponds to the range of f⁻¹(x), what the heck does that all mean?

well, it means that for any coordinate pairs (a , b) in f(x), there's a corresponding pair of (b , a) on f⁻¹(x).

we know in this case that f(-4) = 15, or namely that f(x) has a pair of (-4 , 15), well, that means that f⁻¹(x) has a swapped pair of (15 , -4).

the above means that f⁻¹(15) = -4.

Please help me with this math problem!! Will give brainliest!! Please include a drawing in your answer. No links please!!

Answers

Answer:

Step-by-step explanation:

AC = 150  Feet

CB = 75 feet.

BD = 100 feet

You use the tangent here.

Tan(A) = opposite/ Adjacent

Opposite = BD = 100 feet

Adjacent = AB = AC + CB = 150 + 75 = 225  feet.

Tan(A) = 100 / 225

Tan(A) = 0.4444

A = Tan-1(0.4444)

A = 23.96 degrees, but the front row of trees cannot be more than 100 feet tall

help please ive been stuck on this for days ( the shapes need an answer )

Answers

Answer:

circle = 1/3

pls mark brainliest

i finished all of these but i wanted to make sure these were correct! i will be posting others and thank you for answering :)

Answers

Answer:

Step-by-step explanation:

Where are your answers?

if a certain cannon is fired from a height of 8.5 meters above the ground, at a certain angle, the height of the cannonball above the ground, h, in meters, at time, t, In seconds, is found by the function h(t)=-4.9t^2+27.5t+8.5 Find the time it takes for the cannonball to strike the ground.

Answers

Answer: 2.88 seconds

Step-by-step explanation:

we need to find t in the formula, when h(t) = 0, (meaning it hits the ground).

0 = -4.9t² + 27.5t + 8.5

Using the quadratic formula:

x = (-b ± √b² - 4ac)/2a

x = (-27.5 ± √27.5² - 4(-4.9)(8.5))/2(27.5)

x = (-27.5 ± 30.38)/55

x = 2.88   OR     x = -57.88

Since time cannot be negative, we will stick with the positive answer, 2.88 seconds.

Hope this helped :)

I need this answer asap... quickest answer
gets marked brainiest and hella points
PLEASE HURRY!!!

Answers

Answer: $2,728.40

Step-by-step explanation:

The starting value is: $17,000

the rate of deprecation is: 12.25%

time = 14 years

Lets plug this into the interest formula:

Cost after 14 years = Principle(1 - r)^t

Cost after 14 years = 17,000(1 - 0.1225)^14

Cost after 14 years ≅$2,728.40

Deprecation happens pretty quickly!

F

a
If
F
=
48
when
a
=
3
find,
F
when
a
=
4

Answers

Answer:

F(4) = 36

Step-by-step explanation:

F = C/a, where C is a constant

Since 48 = C/3

C = 144

F(a) = 144/a

-----

F(3) = 144/3

F(3) = 48

----

F(4) = 144/4

F(4) = 36

Which number line shows the solutions to n > 3?

Answers

Answer:

The second one.

Step-by-step explanation:

The hollow dots represent > or < depending the direction of the arrow. The filled dots represent less than or equal to. So the second.

Answer: Your answer would be B

Step-by-step explanation: The open circle means it's not greater than or equal to! So therefore, answer is B! Let me know if I'm wrong. If not have a great day!

I need to know the answer to this and how to solve it .

Answers

Answer:

=> B.125

Step-by-step explanation:

=> 180°- 55°{ linear pair }

=> 125°

The measure of angle COE = 125

B. 125 that’s the answer to your question

Farmer MacDonald has 72 cows and pigs on his farm. The ratio of cows to pigs is 5 to 3. How many cows and how many pigs does he have?

Answers

Answer: 45 and 27

Step-by-step explanation:

A lil trick Is that u add 5+3=8  then 72/8 = 9

So then 5x9 and 3x9 because each ratio "unit" Is equal to 9 so ya

gl

Sylvia’s cat weighs 12 pounds Michele’s cat weights 9 pounds.
How many more ounces does Sylvia’s cat weigh than Michele’s cat?

Answers

Answer:

Sylvia's cat weighs 3 pounds more than Michelle's cat

Sylvia’s cat weighs 48 ounces more than Michele’s cat.

What is weight?

The downward force exerted by any object due to the effect of the earth's gravity is called weight.

Given that:-

Sylvia’s cat weighs 12 pounds Michele’s cat weighs 9 pounds.

The difference between the weight = 12 - 9 = 3 pound

1  pound = 16 ounces

3 pounds = 16 x 3 ounces = 48 ounces

Therefore Sylvia’s cat weighs 48 ounces more than Michele’s cat.

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5 times what equals 53

Answers

Answer:

The answer is 10.6

Step-by-step explanation:

Divide 53 by 5 :)

Answer:

10.6

Step-by-step explanation:

53/5=10.6

or 10.6 multiplied by 5 equals 53

y=-3x^2-24x-42 in vertex form

Answers

Answer:

Step-by-step explanation:

y = - 3x² - 24x - 42

y = - 3( x² + 8x + 14 )

y = - 3( x² + 2·4·x + 16 - 16 + 14 )

y = - 3[ ( x + 4 )² - 2 ]

y = - 3( x + 4 )² + 6

please help asap it will help very much

Answers

Answer:

180 cm²

Step-by-step explanation:

From inspection of the diagram, the surface area is made up of the area of 4 congruent triangles and the area of one square.

Area of a square = x² (where x is the length of one side)

⇒ area of the square = 6² = 36 cm²

Area of a triangle = 1/2 x base x height

⇒ area of one triangle = 1/2 x 6 x 12 = 36 cm²

Total surface area = 4 x area of one triangle + area of the square

                               = 4 x 36 + 36

                               = 144 + 36

                               = 180 cm²

Answer:

180 I was the first so could I have brainlyest

Step-by-step explanation:

we need the area of 4 triangles and one square triangle = base x height x 1/2     square = base x height         6 x 6 = 36 + (  6 x 12 / 2 x 4 = 144)  = 180

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