Work out the size of angle x

Problem 1

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Explanation:

The notation (f o g)(x) means f( g(x) ). Here g(x) is the inner function.

So,

f(x) = x+1

f( g(x) ) = g(x) + 1 .... replace every x with g(x)

f( g(x) ) = 6x+1 ... plug in g(x) = 6x

(f o g)(x) = 6x+1

Now let's flip things around

g(x) = 6x

g( f(x) ) = 6*( f(x) ) .... replace every x with f(x)

g( f(x) ) = 6(x+1) .... plug in f(x) = x+1

g( f(x) ) = 6x+6

(g o f)(x) = 6x+6

This shows that (f o g)(x) = (g o f)(x)  is a false equation for the given f(x) and g(x) functions.

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Problem 2

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Explanation:

Let's say that g(x) produced a number that wasn't in the domain of f(x). This would mean that f( g(x) ) would be undefined.

For example, let

f(x) = 1/(x+2)

g(x) = -2

The g(x) function will always produce the output -2 regardless of what the input x is. Feeding that -2 output into f(x) leads to 1/(x+2) = 1/(-2+2) = 1/0 which is undefined.

So it's important that the outputs of g(x) line up with the domain of f(x). Outputs of g(x) must be valid inputs of f(x).

The given statement is false.

Composite function is a combination of two or more than two functions combined by mathematical operation of addition,subtraction,multiplication and division.Where output of one function is input to the other function.

According to the given question two functions are given f(x) and g(x) and and we have to compose in different order and see if they are same or not.

Given, f(x) = x + 1 and g(x) = 6x

So, (fog)(x) is, output of g(x) is the input of f(x) which is

f(6x) = (6x) + 1

f(6x) = 6x + 1.

Now, (gof)(x) is, output of f(x) is now input of g(x) which is

g(x+1) = 6(x+1)

g(x+1) = 6x + 6.

Thus we can see fog(x) ≠ gof(x).

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Answer:

Alex has twice as much money as Jennifer.

a = 2j

Jennifer has $6 less than Shannon.

j = s-6

j+6 = s

All together the three friends have $54.

a + j + s = 54

Replace a and s

2j + j + (j+6) = 54

4j = 54 - 6

4j = 48

j = 48/4

j = 12  

Jennifer has $12

Alex= 2*12 = $24

Shannon = 24+12+s = 54

= 36+s = 54

s = 18

Shannon has $18

Answer:

Steepest to most gentle: W, Z, U, Y

Step-by-step explanation:

Answer: WZUY

Step-by-step explanation: On Edgenuity!!!!!!!!!!!

Answer:

it is J

Step-by-step explanation:

Answer: 5

Step-by-step explanation:

The question is asking how many tenths are in one half. You need to divide one half by one tenth. To divide fractions you need to invert and multiply.

1/2 ÷ 1/10

Step 1: Invert and multiply

1/2 × 10/1 = 10/2

Step 2: Simplify

10/2 = 5

Answer:

Well from all the exams and assignments I've had, 100 points is the full grade so losing 100 points would mean you would fail with a 0

Answer: 77/12

Step-by-step explanation:

1) 11/12 * 7 = (11*7)/12 = 77/12

Answer:

Step-by-step explanation:

given that the initial time before pumping is 3:40 p.M.

after pumping the time reads 3:44, hence he use 4 min to fill his tank

time taken=4 min

also given is that had pumped 10.2 gallons

the capacity of tank= 10.2gallon

Then the average rate of pump is

average rate= capacity of tank/time taken

average rate= 10.2/4min

average rate=2.55gallons.min

Answer:

4 hours

Step-by-step explanation:

240/60=4

The rule that best describes the problem is time = 240/60.

A unitary method is a mathematical way of obtaining the value of a single unit and then deriving any no. of given units by multiplying it with the single unit.

Given, A motorist drives at a constant rate of 60 kph and his destination is 240 kilometers away from his starting point.

We know, Distance = time×speed.

time = distance/speed.

time = 240/60.

time = 4 hours.

speed×time = distance.

60t = 240.

60x = 240.  (x = t).

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Answer:

64

Step-by-step explanation:

f(x) = 4^x,

When x = 3,

=> f(3) = 4^3

= 4 * 4 * 4

= 64

Answer:

f(3) = 64

Step-by-step explanation:

To evaluate f(3), substitute x = 3 into f(x) , that is

f(3) = 4³ = 64

Answer:

The solution is x = 2 and x = 4

Step-by-step explanation:

Let us revise some rules in logarithmic function:

Let us solve the question

∵ [tex]log_{2}(x)+log_{2}(6-x)=3[/tex]

→ By using the first rule above

∴ [tex]log_{2}(x)(6-x)=3[/tex]

→ Multiply x by (6 - x)

∵ x(6 - x) = x(6) - x(x) = 6x - x²

∴ [tex]log_{2}(6x-x^{2})=3[/tex]

→ Change the logarithmic function to exponential function using

   the second rule above

∴ [tex]2^{3}=(6x-x^{2})[/tex]

∵ 2³ = 8

∴ 8 = 6x - x²

→ Add x² to both sides

∴ x² + 8 = 6x

→ Subtract 6x from both sides

∴ x² - 6x + 8 = 0

→ Factorize it into 2 brackets

∴ (x - 2)(x - 4) = 0

→ Equate each factor by 0 to find the values of x

∵ x - 2 = 0

→ Add 2 to both sides

∴ x = 2

∵ x - 4 = 0

→ Add 4 to both sides

∴ x = 4

∴ The values of x are 2 and 4

∴ The solution of the equation is x = 2 and x = 4

Answer:

30

Step-by-step explanation:

Answer:

Oh thats easy its $30

Step-by-step explanation:

so for 2 icecreams it costs $6

so if u divide them it would become 1 icecream for $3 so

10 times 3 will be $30

Answer:

The slope-intercept form is y=mx+b y = m x + b , where m is the slope and b is the y-intercept. Using the slope-intercept form, the slope is 3 .

Step-by-step explanation:

brainliest please

Answer:

AD is 12

Step-by-step explanation:

Answer:

AD=12

Step-by-step explanation:

AB=4

BD=8

AD=AB+BD

AD=4+8

AD=12

Hope this helps :)

Answer:

angles ABD and BAD

Answer:

angles ABD and BAD

Step-by-step explanation:

Answer:

see explanation

Step-by-step explanation:

Given

[tex]\frac{20}{\sqrt{2} }[/tex]

To rationalise the denominator multiply the numerator and denominator by [tex]\sqrt{2}[/tex], that is

[tex]\frac{20(\sqrt{2}) }{\sqrt{2}(\sqrt{2}) }[/tex]

= [tex]\frac{20\sqrt{2} }{2}[/tex]

= 10[tex]\sqrt{2}[/tex]

Answer:

75 grams

Step-by-step explanation:

1/2 cm = 25 grams

(1 1/2) /( 1/2) = 3 times as much

1 1/2 cm = 3 x 25 75 grams

Is that 2m=43 or m^2=43??

If 2m=43 then...

m=43/2

m=21.5

If m^2=43 then...

m=√43

Answer:m=21.5

Step-by-step explanation:

[tex] {x}^{2} - 6x - 7 = (x - 7)(x + 1) \\ [/tex]

[tex]width = (x - 7)[/tex]

So

[tex]length = (x + 1)[/tex]

Just it...

So we're done.

Thanks for watching buddy good luck.

♥️♥️♥️♥️♥️

Answer:

Regular price guests = 3300

Discount price guests = 1100

Step-by-step explanation:

Breakeven point is the point where total revenue and total cost are equal.

Now, we know total cost is $66,000 per month.

Now, we are told that the museum sells 75% of its tickets for the regular price of $14.

If the total number of tickets is x. It means the number of regular tickets guests is 75%x = 0.75x

We are told that variable cost per guest in each group is $2. This means that total revenue from regular tickets guest is;

14(0.75x) + 2(0.75x) = 12x

Now, the remaining tickets are discount tickets sold for $10.

It means number of discount tickets guests = 0.25x

Total revenue from discount tickets =

10(0.25x) + 2(0.25x) = 3x

Thus, at break even point, we have;

12x + 3x = 66000

15x = 66000

x = 66000/15

x = 4400

Thus;

Regular price guests = 0.75 × 4400 = 3300

Discount price guests = 0.25 × 4400 = 1100

Answer:

1/16

Step-by-step explanation:

I usually provide explanations, but I'm pretty sure you need an answer fast. Tell me if you need an explanation!

Answer:

1/16

Step-by-step explanation:

please mark me brainliest

Answer:

Find the difference between the two, divide by the years, and should get the percent of change

Step-by-step explanation:

The change in percentage is 69.89%.

Given that, a gym's membership in 2012 was $9,300.

Percentage is defined as a given part or amount in every hundred. It is a fraction with 100 as the denominator and is represented by the symbol "%".

The current membership is $2,800.

We know that, the percentage change = (New value - Original value)/Original value × 100

Now, the percentage change = (9300-2800)/9300 × 100

= 6500/9300 × 100

= 0.6989 × 100

= 69.89%

Therefore, the change in percentage is 69.89%.

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Answer:

D = (3.5,1)

Step-by-step explanation:

(-2.5,5) is given

you must do (x+6,y-4)

x y

(-2.5,5)

-2.5+6=3.5

x=3.5

5-4=1

y=1

(3.5,1)

Answer:

(3.5, 1)

Step-by-step explanation:

edg 2021

Answer:

yes

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

If 9 members paid on the first day, this means they did not pay on the third day

The remaining people (everyone but the 9) paid on the third day

Therefore we must subtract to find out how many members paid on the third day

22 - 9 = 13

Each of the 13 members paid $12.80 which means we must multiply

13 × 12.80 = 166.40

In total, the grocery store collected $166.40 on the third day of the month

Answer:

Yes.

Step-by-step explanation:

If the catetes are 5 and 12, then the hypotenuse is 13, and it is a special right triangle.

Answer:

y=3x^2+12x+13

a=3

b=12

c=13

Step-by-step explanation: