Ruben and his friends are celebrating Ruben's birthday at Adventure Zone, which has trampolines, mini golf, laser tag, and an arcade. Ruben's mom gives 18 arcade tokens to each kid at the party. In all, she gives out 144 tokens.
Use an equation to find the number of kids at Ruben's party.

Step-by-step explanation:

since g(f(x)) = x g (f (x) )= x, f - 1 (x) = 5x3 + 43 f - 1 (x) = 5 x 3 + 4 3

The inverse of the given function [tex]f(x) = 3(x-4)^{2} +5[/tex] is [tex]f^{-1} (x) = \sqrt{\frac{x-5}{3} } +4[/tex].

An inverse function or an anti function is defined as a function, which can reverse into another function. In simple words, if any function “f” takes x to y then, the inverse of “f” will take y to x. If the function is denoted by ‘f’ or ‘F’, then the inverse function is denoted by [tex]f^{-1}[/tex] or [tex]F^{-1}[/tex].

According to the given equation.

We have a function.

[tex]f(x) = 3(x-4)^{2} +5[/tex]

The above function can be written as

[tex]y = 3(x-4)^{2} +5[/tex]

Write the above function for x.

[tex]\implies y -5 = 3(x-4)^{2}[/tex]

[tex]\implies \frac{y-5}{3} = (x-4)^{2}[/tex]

[tex]\implies \sqrt{\frac{y-5}{3} } =x-4[/tex]

[tex]\implies \sqrt{\frac{y-5}{3} } +4=x[/tex]

[tex]0r\ x = \sqrt{\frac{y-5}{3}}+4[/tex]

Replace [tex]x[/tex] by [tex]f^{-1}(x)[/tex] and [tex]y[/tex] by [tex]x[/tex].

We get

[tex]f^{-1} (x) = \sqrt{\frac{x-5}{3} } +4[/tex]

Hence, the inverse of the given function [tex]f(x) = 3(x-4)^{2} +5[/tex] is [tex]f^{-1} (x) = \sqrt{\frac{x-5}{3} } +4[/tex].

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Answer:

16 × .15 and 16 × 15/100

Step-by-step explanation:

...

Answer:

2x+y = 3

Step-by-step explanation:

Let's take y=-2x+b through the point (1,1), so we get b is equal to 3. So this is y=-2x+3, so 2x+y=3

Answer:

1

Step-by-step explanation:

It is the only one that makes sense!

(Apologies since this super late; I hope future students will find this helpful)

Answer:

An angle measures 90º if and only if the angle is right.

Step-by-step explanation:

See the image below :)

Answer:

Step-by-step explanation:

2 tables and 3 chairs is $705

Let t stand for table and c stand for chair

3c + 2t = 705

We are told that the table costs $40 more than the chair, so t = c + 40

Now we can insert this into the equation

3c + 2(c + 40) = 705

The next step is to distribute the 2

3c + 2c + 80 = 705

Then combine like terms

5c + 80 = 705

To get the variable by itself, you have to subtract the 80 from both sides.

5c = 705 - 80

5c = 625

This means that 5 chairs costs $625.

Divided both sides by 5 to isolate the variable

c = 625/5

c = 125

Great, now you know the cost of one chair, $125!

The question is asking how much a table costs, and we know that a table costs $40 more than a chair.

A table costs $125 + $40

A table costs $165

Hope this helps! =)

Answer:

1.4 acres of grass can be planted.

Step-by-step explanation:

He has 9.24 pounds of seeds.

If one acre of grass needs 6.6 pounds of seeds we can divide 9.24 pounds by 6.6 pounds to find how many acres of grass he can plant.

9.24 lbs × [tex]\frac{1acre}{6.6 lbs}[/tex] = 1.4 acres

Answer:

You subtract because you're taking away money when you're withdrawing.

Answer:

Because withdrawal means taking out money from a total amount of money. That is we take away.

Answer:

B

Step-by-step explanation:

Answer:

$7.78

Step-by-step explanation:

140/18 = 7.78

9514 1404 393

Answer:

  7 mpg

Step-by-step explanation:

The equation shown on the graph tells you the unit rate is 7. (The unit rate is the coefficient of x.)

The truck travels 7 miles per gallon of gas.

Answer: y = .15x + 1250

y = weekly salary

x = sales

Step-by-step explanation:

Answer:

8.9

Step-by-step explanation:

7.1/8.9=Qn/11.1

QN = 8.9

{ Parallel lines divide in proportion to their segments }

The solution is 8.9

The length of the side of the triangle PNO is QN = 8.9

What are similar triangles?

If two triangles' corresponding angles are congruent and their corresponding sides are proportional, they are said to be similar triangles. In other words, similar triangles have the same shape but may or may not be the same size. The triangles are congruent if their corresponding sides are also of identical length.

Corresponding sides of similar triangles are in the same ratio. The ratio of area of similar triangles is the same as the ratio of the square of any pair of their corresponding sides

Given data ,

Let the first triangle be ΔPNO

Let the second triangle be ΔPQR

Now , ΔPNO ≅  ΔPQR

And , The corresponding sides of similar triangles are in the same ratio

So , substituting the values in the equation , we get

RO / PR = QN / PQ

On simplifying the equation , we get

7.1 / 8.9 = QN / 11.1

Multiplying both sides of the equation by 11.1 , we get

QN = ( 7.1 x 11.1 ) / 8.9

The value of QN will be

QN = 8.85

Rounding the value of QN to the nearest tenth , we get

QN = 8.9

Therefore , the value of QN is 8.9

Hence , The length of the side of the triangle PNO is QN = 8.9

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Answer:

Option 4)  y - 1 = -2(x - 0)

Step-by-step explanation:

Given the slope, m = -2, and the y-intercept, (0, 1):

Substitute these values into the following point-slope form:

y - y1 = m(x - x1)

y - 1 = -2(x - 0)  ← This is the point-slope form given the slope, m = -2, and the y-intercept, (0, 1).

Therefore, the correct answer is Option 4: y - 1 = -2(x - 0)

HI how was your day today

Answer:

4x-5y+45=0.

Step-by-step explanation:

1) formula is:

[tex]\frac{x-X_A}{X_B-X_A} =\frac{y-Y_A}{Y_B-Y_A};[/tex]

2) if point A is (0;9) and point B is (5;13), then:

[tex]\frac{x}{5} =\frac{y-9}{13-9}; \ => \frac{x}{5} =\frac{y-9}{4}; \ => \ 4x-5y+45=0.[/tex]

Answer:

A) [tex]x^{3} y^{4}[/tex]

B) [tex]-\frac{5x^{2} }{y}[/tex]

C) [tex]9m^{4}n^{4}[/tex]

D)[tex]\frac{1}{x^{3} }[/tex]

Step-by-step explanation:

Hope this helps.

Answer: the answer is P(HHlC') = 1/2

Step-by-step explanation:

Answer:

1. x=105

2. 12 cans for $4

3. 14

Step-by-step explanation:

1. 15/18 = x/126

126/18=7

x=15*7=105

2. 12 cans for $4.  36 for $11.50.  

36/3=12.  11.50/3=3.8333.  

12 cans for $4 is the better deal because it would be an equal deal if it was 36 for 12:00.  

3. Circumference = pi*d.  Circumference = 43.96.  pi=3.14.  3.14*x=43.96.  x=diameter.  x=14.  diameter = 14

--Explanation to 3.14*x=43.96:

3.14*x=43.96, = 3.14x=43.96

3.14x*100 =43.96*100

314x=4396

314x/314 = 4396/314

x=14

Answer:

The domain is the set of all the values of x .

The range is the set of all the values of y.

Domain:

{0,4,5,10}

Range:

{4,9,2}

Step-by-step explanation:

your answer is is from an algebra solver called mathwey but an a instead of  an e it solves everything i promise i use it all the time

Answer:

SSS~

RQP

Step-by-step explanation:

36/15 = 2.4

48/20 = 2.4

72/30 = 2.4

Triangles are similar by SSS~.

triangle JKL is similar to triangle RQP

Answer:

48

Step-by-step explanation:

First you would subtract 9 from 393 which is 384 then you would divide the 384 remaining student among the 8 busses which is 48.

Hope this helps.

Answer:

x • (x^3 - 3x^2y + 3xy^2 + 7y^3)

Step-by-step explanation:

(8x • (y^3)) +  x • (x - y)^3

2^3xy^3 +  x • (x - y)^3

Evaluate :  (x-y)^3   =   x^3-3x^2y+3xy^2-y^3

Pull out like factors :

x^4 - 3x^3y + 3x^2y^2 + 7xy^3  =

x • (x^3 - 3x^2y + 3xy^2 + 7y^3)

x^3 - 3x^2y + 3xy^2 + 7y^3 is not a perfect cube

Answer:

Step-by-step explanation:

If a quadratic function has only one zero, then it has multiplicity of two as it is a second degree polynomial and should have two roots. Since one root is a real number, the second root is also a real number being same as the first number.

The function could be:

We know the rule for single zero of quadratic equations

[tex]\\ \sf\longmapsto g(x)=(x-n)^2[/tex]

[tex]\\ \sf\longmapsto g(x)=(x-12)^2[/tex]

Done

Answer:

107r³

Step-by-step explanation:

Answer:

c. tetrahedron

Step-by-step explanation: