Work our the size of angle x.

Answer: 240

Step-by-step explanation:

You would multiply each of the sides to get the final answer of 240 (:

Answer:

[tex]f^{-1}(x)= \frac{3}{2}(x+6)[/tex]

[tex]f(f^{-1}(x)) = f^{-1}(f(x))= x[/tex]

Step-by-step explanation:

Given

[tex]f(x) = \frac{2}{3}x - 6[/tex]

Required

Determine [tex]f^{-1}(x)[/tex]

[tex]f(x) = \frac{2}{3}x - 6[/tex]

Represent f(x) as y

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

Swap the positions of x and y

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

Add 6 to both sides

[tex]x+6=\frac{2}{3}y - 6+6[/tex]

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

Multiply both sides by 3

[tex]3(x+6)=\frac{2}{3}y * 3[/tex]

[tex]3(x+6)=2y[/tex]

Divide both sides by 2

[tex]\frac{3}{2}(x+6)=\frac{2y}{2}[/tex]

[tex]\frac{3}{2}(x+6)=y[/tex]

[tex]y= \frac{3}{2}(x+6)[/tex]

Replace y with [tex]f^{-1}(x)[/tex]

[tex]f^{-1}(x)= \frac{3}{2}(x+6)[/tex]

Justify the result:

First, we solve for [tex]f(f^{-1}(x))[/tex]

[tex]f(x) = \frac{2}{3}x - 6[/tex]

[tex]f(x) = \frac{2}{3}x - 6[/tex] becomes

[tex]f(f^{-1}(x)) = \frac{2}{3}x - 6[/tex]

Substitute [tex]\frac{3}{2}(x + 6)[/tex] for x

[tex]f(f^{-1}(x)) = \frac{2}{3}(\frac{3}{2}(x + 6)) - 6[/tex]

[tex]f(f^{-1}(x)) = \frac{2*3}{3*2}(x + 6)- 6[/tex]

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

[tex]f(f^{-1}(x)) = 1*(x + 6)- 6[/tex]

[tex]f(f^{-1}(x)) = x + 6- 6[/tex]

[tex]f(f^{-1}(x)) = x[/tex]

Next, we solve [tex]f^{-1}(f(x))[/tex]

[tex]f^{-1}(x)= \frac{3}{2}(x+6)[/tex]

[tex]f^{-1}(x)= \frac{3}{2}(x+6)[/tex] becomes

[tex]f^{-1}(f(x))= \frac{3}{2}(x+6)[/tex]

Substitute [tex]\frac{2}{3}x - 6[/tex] for x

[tex]f^{-1}(f(x))= \frac{3}{2}(\frac{2}{3}x) - 6+6[/tex]

[tex]f^{-1}(f(x))= \frac{3}{2}(\frac{2}{3}x)[/tex]

[tex]f^{-1}(f(x))= \frac{2*3}{3*2}x[/tex]

[tex]f^{-1}(f(x))= \frac{6}{6}x[/tex]

[tex]f^{-1}(f(x))= 1*x[/tex]

[tex]f^{-1}(f(x))= x[/tex]

Hence:

[tex]f(f^{-1}(x)) = f^{-1}(f(x))= x[/tex]

Answer:

1/2 or 50% probability

Step-by-step explanation:

There are just two players, player A and player B. Since it is between this two players, for player A to score first we would have:

AB where player A is the first player to score, we wouldn't have BA since player would not be the first here

Probability = number of favorable outcomes/total number of outcomes

Therefore probability of A being the first player = number of A/total number of players

=1/2 = 0.50

There is therefore a 50% chance of A being the first player

Answer:

b 15 gallons of fuel for $60.50

Step-by-step explanation:

because 1 gallon of fuel is for $4.299

and when you multiply 15×4.299 the answer is 64.485 which is greater than the offer you are getting it for.

Answer:

x = 14

Step-by-step explanation:

(6x - 12)° + (8x - 4)° = 180° (Supplementary angles)

6x - 12 + 8x - 4 = 180

Add like terms

14x - 16 = 180

14x = 180 + 16

14x = 196

x = 196/14

x = 14

Answer:

We conclude that the price is 3.5 times the number of board games.

Hence, option B is true.

Step-by-step explanation:

We know that when y varies directly with x, the equation is

y ∝ x

y = kx

k = y/x

where 'k' is called the proportionality constant.

From the table,

For the point (2, 7)

k = y/x

  = 7/2

  = 3.5

For the point (4, 14)

k = y/x

   = 14 / 4

   = 7/2

    = 3.5

For the point (5, 17.50)

k  = y/x

   = 17.5 / 5

   = 3.5

For the point (9, 31.50)

k  = y/x

   = 31.50 / 9

   = 3.5

From the above calculations, we computed that the value of the proportionality constant remains the same.

Thus, the table of numbers represents a proportional relationship.

Therefore, the equation becomes

y = kx

The price of 2 board game

y = 3.5 (2)

  = 7

The price of 4 board game

y = 3.5 (4)

  = 14

Therefore, we conclude that the price is 3.5 times the number of board games.

Hence, option B is true.

Answer:

5/6

Step-by-step explanation:

Answer:

18.3% chance it will land on that particular side

Answer:

WHat did he say

Step-by-step explanation:

Answer:

Jessicas current elevation is -20 feet.

Step-by-step explanation:

Start and 40 on the number line and make a straight line to -20 on the number line with dots at 40 and -20 on the number line

Answer:

(40+ 19) – 38

Step-by-step explanation:

We need to find the expression for "thirty-eight less than the sum of forty and nineteen".

Sum of forty and nineteen = 40 + 19

38 less than the above is 40 + 19 - 38

Overall expression is :

(40 + 19) - 38

Hence, the correct option is (d) "(40+ 19) – 38".

Answer:

Answer: B San Francisco

Step-by-step explanation:

It can be read that Geneva is 12°C colder than Nikki's hometown. It can be seen in the table that Geneva is at -3°C.

This means that Nikki's hometown is 12°C hotter than Geneva, thus:

Temperature of Nikki's hometown = -3°C + 12°C = 9°C.

The only city with a temperature of 9°C is San Francisco.

Answer: B San Francisco

Answer: its C

Step-by-step explanation: Ive taken this question  dont know how but its C.

This data is Inaccurate Data

   Where are  

Divide first by 5:

Multiplye secondly by -2:

-2x - 2y = -200

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9514 1404 393

Answer:

  70°

Step-by-step explanation:

Angles 2 and 13 are alternate exterior angles, so are congruent. The value of x can be found by solving the equation that equates the expressions for the measures of these angles. Once x is found, the measure of angle 13 can be determined. The measure of angle 9 is the supplement of angle 13.

So, ...

  m∠2 = m∠13

  8x +14 = 10x -10

  24 = 2x  . . . . . . . .  add 10-2x

  12 = x

  m∠13 = 10x -10 = 10·12 -10 = 110

  m∠9 = 180° -110°

  m∠9 = 70°

Step-by-step explanation:

12/13 of a number = 24

13/13 of a number = 24 * (13/12) = 26

Hence the number is 26.

Answer:

26

Step-by-step explanation:

Let n be the number. Then:

12n/13=24

n=13/12 x 24

  =26 ..............

Answer:

possibly you could use kid per candy, number of trickery treaters or something

you could explain lets say over the holidays Miss. So and So's class's kids got an average of around 4-6 Christmas presents while Miss. Mary Sue's class had  kids with 2 presents and kids with 12, since the range between 2-12 is bigger it had a greater standard of deviation

(hopefully this helps and I am not overcomplicating or incorrecting the standard of deviation, good luck)

Answer:

117

Step-by-step explanation:

The formula for a triangle is base times hight divided by two. So, 13 x 18 = 234, and 234/2 = 117

Answer:

g = 6

Step-by-step explanation:

5.2g + 10 = 2.2g + 28 (Given)

3g + 10 = 28 (Subtracted 2.2g on both sides)

3g = 18 (Subtracted 10 on both sides)

g = 6 (Divided 3 on both sides)

To check to make sure you are correct, simply substitute your answer for g:

5.2(6) + 10 = 2.2(6) + 28

31.2 + 10 = 13.2 + 28

41.2 = 41.2

You'll know you're correct if they both equal the same. In this case, the solution works.

Sum of Interior Angles = (Number of Sides -2) • 180 degrees

Sum of Interior Angles =  29 * 180

Sum of Interior Angles =  5,220

The interior angle sum of 31-gon is A = 5220°

What is the sum of the interior angles of a polygon?

The sum of the interior angles of a polygon is given by the formula

Sum of Interior angles of a polygon with n sides is

nθ = 180 ( n - 2 )

where n is the number of sides

θ = angle in degrees

Given data ,

Let the interior angle sum of the polygon be = A

Now , the value of A is calculated by

The number of sides of the polygon n = 31

So , the interior angle sum of the 31-gon is given by the equation

Sum of Interior angles of a polygon with n sides is

nθ = 180 ( n - 2 )

where n is the number of sides , so

Substituting the values in the equation , we get

The value of nθ = 180 ( n - 2 )

The value of nθ = 180 ( 31 - 2 )

The value of nθ = 180 x 29

The value of nθ = 5220°

Therefore , the value of A is 5220°

Hence , The interior angle sum of 31-gon is A = 5220°

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To make 100 ml of 25% saline solution, Riley will need 50 ml = 12% saline mixture and 50 ml= 38% saline mixture.

Given,

We have 12% and 38% of saline mixtures.

We need to find the amount in ml from each saline mixture which would give us 100 ml of 25%.

What are the methods to solve a system of linear equations?

There are a number of methods but the most and easiest used method is the substitution method and the elimination method.

We can make two linear equations from the given statements.

Let x = amount from 12% saline mixture and y = amount from 38% saline mixture.

Now we need to make 100 ml of 25% saline.

so,

x + y = 100.

So we have two equations.

x + y = 100..............(1)

12% of x + 38% of y = 100 x 25%

0.12x + 0.38 = 25 ...............(2)

Using the substitution method we have,

x = 100 - y

Putting x = 100 - y in {2}

0.12 ( 100 - y ) + 0.38y

= 2512 - 0.12y + 0.38y

= 250.38y - 0.12y

= 25 - 120.26y = 13y

= 13 / 0.26y = 50.

Putting y = 50 in (1)

x + y = 100x

100 -50x = 50.

So Riley will need 50 ml = 12% saline mixture and 50ml = 38% saline mixture to make 100 ml of 25% saline solution.

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Answer:

Each fudge cookie has 80 calories.

Each lemon cream has 65 calories.

Step-by-step explanation:

We will let [tex]\ell[/tex] represent the calories in lemon creams and [tex]f[/tex] represent the calories in fudge cookies.

Two lemon creams and four fudge cookies together have 450 calories. So, we can write the following equation:

[tex]2\ell+4f=450[/tex]

And four lemon creams plus two fudge cookies together have 420 calories. So, we can write the following equation:

[tex]4\ell+2f=420[/tex]

We now have a system of equations. We can solve this by elimination.

For the first equation, we can multiply both sides by -2. This way, the [tex]\ell[/tex] will cancel when we add the two equations together.

So, the first equation becomes:

[tex]-4\ell-8f=-900[/tex]

Add this to the second equation. Hence:

[tex](-4\ell+4\ell)+(-8f+2f)=(-900+420)[/tex]

Simplify:

[tex]-6f=-480[/tex]

Divide both sides by -6. Hence:

[tex]f=80[/tex]

So, there are 80 calories in one cookie.

We can use the first equation again to find the amount of calories in one cream. We have:

[tex]2\ell+4f=450[/tex]

Substituting 80 for [tex]f[/tex] yields:

[tex]2\ell+320=450[/tex]

Then it follows that:

[tex]\ell=65[/tex]

So, there are 65 calories in each lemon cream.

Answer:

567

Step-by-step explanation:

Step-by-step explanation:

HCF of 60 and 84 = 6

So the required greatest number that divides 60 and 84 without leaving remainder is 6.

9514 1404 393

Answer:

  (x, y) = (10, 2)

Step-by-step explanation:

The upper angle marked with an expression in x and y is supplementary to the angle marked 70°. The lower angle marked with an expression in x and y is an alternate interior angle with respect to the one marked 70°, is equal to that. This gives the two equations in x and y:

  6x +10y +30 = 110

  4x +10y +10 = 70

Subtracting the second equation from the first gives ...

  2x +20 = 40

  x +10 = 20 . . . . . divide by 2

  x = 10 . . . . . . . . . subtract 10

Substituting into the second equation gives ...

  4(10) +10y +10 = 70

  4 + y + 1 = 7 . . . . . . . . divide by 10

  y = 2 . . . . . . . . . . . . . . subtract 5

The values of x and y are 10 and 2, respectively.

Answer:

9514 1404 393

Step-by-step explanation:

Answer:

i think the answer is -13

Step-by-step explanation:

b-6= -7-6

=-13

your correct answer is 13

I am sure it's correct... just go for it

Answer:yo it’s me leo remember me my acount got deleted

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

n = 8

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Equality Properties

Step-by-step explanation:

Step 1: Define

Set up the equation.

3n = n + 16

Step 2: Solve for n