Four movie tickets cost $26. How much do seven movie tickets cost?

Answer:

[tex]f^{-1}\,\circ \,g(5) = 10[/tex]

Step-by-step explanation:

Let [tex]f(x+7) = 3\cdot x -6[/tex] and [tex]g(2\cdot x +1) = x^{2}-1[/tex], we proceed to derive [tex]f(x)[/tex] and [tex]g(x)[/tex] by algebraic means:

(i)  [tex]f(x+7) = 3\cdot x -6[/tex]

1) [tex]f(x+7) = 3\cdot x -6[/tex] Given

2) [tex]f(x+7) = 3\cdot (x+0) - 6[/tex] Modulative property

3) [tex]f(x+7) = 3\cdot [(x+7) +(-7)]-6[/tex] Existence of additive inverse/Associative property

4) [tex]f(x+7) = 3\cdot (x+7) +3\cdot (-7)-6[/tex] Distributive property

5) [tex]f(x+7) = 3\cdot (x+7) -21-6[/tex]   [tex]a\cdot (-b) = -a\cdot b[/tex]

6) [tex]f(x+7) = 3\cdot (x+7) -27[/tex] Definition of subtraction

7) [tex]f(x) = 3\cdot x - 27[/tex] Composition of functions/Result

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

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

2) [tex]g(2\cdot x + 1) = (x\cdot 1)^{2}-1[/tex] Modulative property

3) [tex]g(2\cdot x +1) = [(2\cdot x)\cdot 2^{-1}]^{2}-1[/tex] Existence of additive inverse/Commutative and associative properties

4) [tex]g(2\cdot x +1) = (2\cdot x)^{2}\cdot 2^{-2}-1[/tex]   [tex]a^{c}\cdot b^{c}[/tex]/[tex](a^{b})^{c} = a^{b\cdot c}[/tex]

5) [tex]g(2\cdot x + 1) = \frac{(2\cdot x)^{2}}{4}-1[/tex] Definitions of division and power

6) [tex]g(2\cdot x + 1) = \frac{(2\cdot x + 0)^{2}}{4} -1[/tex] Modulative property

7) [tex]g(2\cdot x +1) = \frac{[(2\cdot x + 1)+(-1)]^{2}}{4} -1[/tex] Existence of additive inverse/Associative property

8) [tex]g(2\cdot x + 1) = \frac{(2\cdot x + 1)^{2}+2\cdot (2\cdot x + 1)\cdot (-1)+(-1)^{2}}{4} -1[/tex] Perfect square trinomial

9) [tex]g(2\cdot x + 1) = \frac{(2\cdot x + 1)^{2}}{4}+\frac{[2\cdot (-1)]\cdot (2\cdot x + 1)}{4} +\frac{(-1)^{2}}{4}-1[/tex] Addition of homogeneous fractions.

10) [tex]g(x) = \frac{x^{2}}{4}-\frac{2\cdot x}{4} + \frac{1}{4}-1[/tex] Composition of functions/[tex]a\cdot (-b) = -a\cdot b[/tex]

11) [tex]g(x) = \frac{x^{2}}{4}-\frac{x}{2}-\frac{3}{4}[/tex] Definitions of division and subtraction/Result

Now we find the inverse of [tex]f(x)[/tex]:

1) [tex]f = 3\cdot x - 27[/tex] Given

2) [tex]f + 27 = (3\cdot x - 27)+27[/tex] Compatibility with addition

3) [tex]f+ 27 = 3\cdot x +[27+(-27)][/tex] Definition of substraction/Commutative and associative properties

4) [tex]f+27 = 3\cdot x[/tex] Existence of additive inverse/Modulative property

5) [tex](f+27) \cdot 3^{-1} = (3\cdot 3^{-1})\cdot x[/tex] Compatibility with multiplication/Commutative and associative properties

6) [tex](f+27)\cdot 3^{-1} = x[/tex] Existence of multiplicative inverse/Modulative property

7) [tex]f^{-1} (x) = \frac{x+27}{3}[/tex] Symmetrical property/Notation/Result

Finally, we proceed to calculate [tex]f^{-1}\,\circ \, g (5)[/tex]:

1) [tex]f^{-1} (x) = \frac{x+27}{3}[/tex], [tex]g(x) = \frac{x^{2}}{4}-\frac{x}{2}-\frac{3}{4}[/tex]  Given

2) [tex]f^{-1}\,\circ\, g(x) = \frac{\frac{x^{2}}{4}-\frac{x}{2}-\frac{3}{4}+27}{3}[/tex] Composition of functions

3) [tex]f^{-1}\,\circ \,g(5) = 10[/tex] Result

Answer:

Length of one piece = 6 cm

Length of second piece = 16 cm

Step-by-step explanation:

Total Length of board = 22 cm

The board is divided into 2 pieces.

Let length of one piece = l

Length of second piece = 2l + 4

We need to find length of both pieces.

We can write the equation:

Total length = Length of one piece + Length od second piece

Putting values and finding length

[tex]22 = l+(2l+4)\\22=l+2l+4\\22=3l+4\\3l=22-4\\3l=18\\l=\frac{18}{3}\\l=6[/tex]

So, we get l= 6

Length of one piece = l =6 cm

Length of second piece = 2l + 4 = 2(6)+4 = 12+4 = 16 cm

Therefore,

Length of one piece = 6 cm

Length of second piece = 16 cm

Answer:

The answer is $2.99

Step-by-step explanation:

8.97/3=2.99

Answer:

the answer is 2.99

Step-by-step explanation:

because

8.97 divided by 3 = 2.99

Answer:

The bigger the number the more obtuse it is and the smaller the number is the more acute is

Step-by-step explanation:

Answer:

[tex]x^3+x^2+x+1=\left(x+1\right)\left(x^2+1\right)[/tex]  

Step-by-step explanation:

Given the expression

[tex]x^3+x^2+x+1[/tex]

Factorized by grouping

[tex]x^3+x^2+x+1=\left(x^3+x^2\right)+\left(x+1\right)[/tex]

Factor out x² from x³+ x²:  x²(x+1)

                        [tex]=\left(x+1\right)+x^2\left(x+1\right)[/tex]

                        [tex]=\left(x+1\right)+x^2\left(x+1\right)[/tex]

Factor common term x+1

                         [tex]=\left(x+1\right)\left(x^2+1\right)[/tex]

Therefore, we conclude that:

[tex]x^3+x^2+x+1=\left(x+1\right)\left(x^2+1\right)[/tex]                  

Answer:

22feet11111111111111dddddd

Answer:

Step-by-step explanation:

It is 3.75

Answer: 203.65

Step-by-step explanation:

subtract those checks from his starting balance

or,3(1/2 +1)=3/2

or,3/2+3=3/2

or,(3+6)/2=3/2

or,9/2=3/2

The numbers having an even number of factors are 8 and 15.

A factor is a number that completely divides another number. To put it another way, if adding two whole numbers results in a product, then the numbers we are adding are factors of the product because the product is divisible by them.

The given numbers are 8, 9, 15, 16, and 25.

Factors of 8 are 1, 2, 4, and 8.

Factors of 9 are 1, 3, 9.

Factors of 15 are 1, 3, 5, 15.

Factors of 16are 1, 2, 4, 8, 16.

Factors of 15 are 1, 5, 25.

Of which 1 and the number itself are improper factors.

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Answer:

no, It isnt

Step-by-step explanation:

Answer:

90 minutes or an hour and a half

Step-by-step explanation:

You need to find out how many minutes it takes her to run one mile, to do that you devide 54 by 6 and you get 9 minutes. Then you multiply the number of minutes per mile, 9, by 10 and you get 90 minutes.

cost of 8 books = 520 AED

we can do this using direct proportion

8/520 , 10/x

(cross multiply

= 8x = 520 x 10

= 8 x 5200

x = 5200/8

x =  650 AED

therfore,

cost of 10 books is 650.

Answer:

9 4/5

Step-by-step explanation:

Answer:

The value of a is 120.

Step-by-step explanation:

Given function;

f(x) = x⁴ - 62x² + ax + 9

find the derivative of the function;

f'(x) = 4x³ - 124x + a

The function (f) attains its maximum value on the interval [0, 2], at x = 1.

f'(1) = 0

0 = 4(1)³ - 124(1) + a

0 = 4 - 124 + a

0 = -120 + a

120 = a

Thus, the value of a is 120.

Step-by-step explanation:

40=1.6d-3.2

43,2=1.6d

27=d

Answer:

it's the fourth one i did that assignment aswell

Answer:

6600

Step-by-step explanation:

0.0575*80000=4600

4600+minimum salary which is 2000=6600

(can I get brainliest please)

Answer:

8:12

Step-by-step explanation:

8/2=4

4 times 3 = 12

Answer:

80

Step-by-step explanation:

1:4 = 20:80

We are multiplying 20 by 1 to get 20 grams of coconuts. Also, we are multiplying 4 by 20 to get 80 grams of sugar. Therefore, you will need 80 grams of sugar if you use 20 grams of coconut. By the way, I suggest you review ratios if you are having difficulties with it.

Answer:

3 and 1/2

Step-by-step explanation:

Mixed numbers are numbers with one whole number and a fraction.

Answer:

3 1/2

Step-by-step explanation:

well 3.5 in fraction form is 3 1/2.

the 5 is the 1/2 because 5/10 is half of 10 an 5/10 is equivalent to 1/2 sooo

3 1/2

Answer:

x  =  450 m

y =  900 m

P (min)  = 1800 m

Step-by-step explanation:

Let´s call   "x"  and  "y" de sides of the rectangular garden, y is the side parallel to the river ( that is it will be fenced only one )

Then:

2*x + y = P        ( perimeter of the area)

And   x * y  = 405000 m²

y = 405000/ x

And P as a function of x is:

P(x) = 2*x +  405000/x

Tacking derivatives relative to x on both sides of the equation.

P´(x)  = 2  - 405000/x²

P´(x) =  0      2*x²  - 405000 = 0

x²  = 202500

x = 450 m

And y =  405000 / 450

y = 900 m

And

P(min) = 2*450 + 900

P(min) = 1800 m

We know P is minimm at x =450 snce the second derivative of P

P´´(x) = 405000*2*x / x⁴   is always positive

Answer:

7,000

Step-by-step explanation:

Answer:

7000

Step-by-step explanation:

the hundreds is 5 so the 6 is turned into a 7 and the rest become 0, 5 or more let it soar, 4 or less let it rest or something

Answer:

20%

Step-by-step explanation:

The percentage of the concentration can be calculated by dividing the amount of solute by the total amount of the solution. In this case the solute would be the 20g of medication while the total solution amount is 100ml. Therefore, we divide these two values like so...

20 / 100 = 0.20

This is the percentage in decimal form, we can now multiply it by 100 to get the percentage value (which in this scenario is simply reversing the previous division)

0.20 * 100 = 20%

Answer:

15 / 17

Step-by-step explanation:

slope = (y2 - y1) / (x2 - x1)

  = (-9 + 24) / (8 + 9)

  = 15 / 17

Answer:

did you find the answer ??

The required height of the wall where the ladder meets the wall is 12 m.

Given that,
A ladder that has a length of 13 m leans against a wall with the base of the ladder 5 m away from the bottom of the wall. Use this information to find how high above the ground the ladder meets the wall is to be determined.

In a right-angled triangle, its side, such as hypotenuse, perpendicular and base is Pythagorean triplets.

Here,
Let the height be h,
Applying Pythagoras' theorem,
h = √[13²-5²]
h = √169-25
h = √144
h = 12

Thus, the required height of the wall where the ladder meets the wall is 12 m.

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Answer:

1

Step-by-step explanation:

13x-12=7x-6

Answer:

correct answer is d....

Answer:

d (22)^40 +(-7)^40 its very easy

Answer: 20.25

Step-by-step explanation: All you need to do is multiply 45 by 45%. 45% can be represented by 0.45, 45/100, or just 45%. You answer should be 20.25. Hope this helps!

45 percent of 45 is 20.25.

To calculate 45% of 45, we can multiply 45 by the decimal representation of 45%.

45% can be written as 0.45 (since percent means "per hundred" or "out of 100").

45 × 0.45 = 20.25

Therefore, 45% of 45 is 20.25.

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