FGX is the inverse of f(x) what is the value of f(g(2))

Answer:

w = 24

Step-by-step explanation:

\(\frac{5w}{8}\) = 15

Multiply both sides by 8.

5w = 15 × 8

     = 120

Find w.

w = 120 ÷ 5

w = 24

Answer:

4 :)

Step-by-step explanation:

Answer: 4

Step-by-step explanation:

1. We want to have x by itself, so we can isolate it by moving -9 to the other side of the equation.

2. This leaves us with 2x=-1+9

3. This equals 2x=8

4. Now we want to completely leave x by itself, so since we know that it is being multiplied by 2, we have to move it to the other side.

5. This leaves us with x=8/2

6. Finally, 8/2=4.

7. x=4.

Answer:

x = 4

Step-by-step explanation:

So, the basic way that we solve a one variable equation is isolating the x variable on one side. We can see that we have a -9 on the left side, and a -1 on the right. Let's simplify this to isolate the x variable:

First, add 9 to both sides:

\(2x-9=-1\\+9.........+9\)

2x=8

Now, we can divide both sides by 2:

x = 4

Remember when doing these solving for x problems:

Whatever you do to one side, you have to do to the other

The value of x must be between -18 and -6. The solution has been obtained using Triangle inequality theorem.

What is Triangle inequality theorem?

The triangle inequality theorem explains how a triangle's three sides interact with one another. This theorem states that the sum of the lengths of any triangle's two sides is always greater than the length of the triangle's third side. In other words, the shortest distance between any two different points is always a straight line, according to this theorem.

We are given three sides of a triangle as 8, 6 and x+20

Using Triangle inequality theorem,

⇒8+6 > x+20

⇒14 > x+20

⇒-6 > x

Also,

⇒x+20+6 > 8

⇒x+26 > 8

⇒x > -18

Also,

⇒x+20+8 > 6

⇒x+28 > 6

⇒x > -22

From the above explanation it can be concluded that x is less than -6 but greater than -22 and -18.

This means that x must lie between -18 and -6.

Hence, the value of x must be between -18 and -6.

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SOLUTION:

We want to construct the augmented matrix for these equations;

We start by writing the equations with variables on the right and constants on the left; multiplying equation 1 by 3, we have;

Expanding equation 2 and collecting like terms, we have;

Expanding equation 3 and collecting like terms, we have;

Writing the 3 equations, we have;

Putting this in augmented matrix form we have;

Which is the final answer

Answer:

Please check the explanation.

Step-by-step explanation:

A number line is a horizontal line with negative values on the left-hand side of an arbitrary number 0 and positive values on the right-hand side of 0.

The location of point A on a number line = -24

The location of point C on a number line = 36

The distance between -24 and 36 can be simply calculated by counting the number of units between.

Starting from -24, we would need to move 24 units on the right side to reach the 0 and 36 units right to reach 36.

So, the total units will be: 24+36 = 60

A second simple method to calculate the distance between point A and point C is:

Distance between A and C = location of C - location of A

                                              = 36 - (-24)

                                              = 36+24

                                              = 60 units

Thus, the distance between A and C is 60 units.

Now, point B is located halfway between point A and point C.

Thus,

i.e.

The location of point B = The location of point C - 30

                                       = 36 - 30

                                       = 6

Thus, point B is located at 6.

Verification:

The location of point B = The location of point A + 30

                                       = -24 + 30

                                       = 6

Thus, point B is located at 6.

Thus, it is verified that point B, halfway between point A and point C.

Hence,

'6' is the value of point B halfway between point A and point C.

The formula to calculate the geometric mean of two numbers is the square root of their product.

So in this case, the geometric mean can be calculated as follows:

Geometric Mean = √(8 * 12) = √96 = 10

The growth factors for the population of Chattanooga in the past two years have a geometric mean of 10.

The geometric mean is a measure of central tendency that is used to describe the average growth rate of a set of numbers. It is especially useful when working with data that represents exponential growth or decay, such as population growth or the rate of return on an investment. Unlike the arithmetic mean, the geometric mean takes into account both the size and the direction of growth. This makes it a better measure of central tendency for data that is not symmetrically distributed.

In the case of population growth, the geometric mean can be used to determine the average annual growth rate over a given period of time. For example, if the population of a city grows by 8% in one year and then by 12% the following year, the average annual growth rate over the two years can be estimated using the geometric mean.

It is important to note that the geometric mean is always smaller than the arithmetic mean for the same set of numbers, and it can be a better representation of the underlying growth trend in some cases.

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Hey Mate!!

Your answer will be below.

Step-by-step explanation:

The answer is C. Because, There's vertical asymptotes at 1 and -1. Vertical asymptotes are present where the x on the denominator is equal to 0. So, Both the values are 1 and -1 set are equal to the 0 in the denominator, So, They're both horizontal asymptotes. Good Luck!

Step-by-step explanation:

post the whole q for understanding the question

Answer:

D. 0.00003471

Step-by-step explanation:

Greg can invite 7 friends for lunch, according to the given question.

What do you mean by  inequalities?

An inequality in mathematics is a relation that compares two numbers or other mathematical expressions in an unequal way. The majority of the time, size comparisons between two numbers on the number line are made.

According to the question,

We have the given information:

The cost of a burger is $4.50. The cost of a soda is $.75.

And he has $40.

Now, we need to find no. of friends, he can invite for lunch,

Total cost of lunch for one friend:

4.50+0.75 =5.25

Then $40 divide into $5.25,

40/5.25=7.619

Therefore, greg can invite 7 friends for lunch.

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From the given information provided, by using sample variance formula, there are 6 scores in the sample.

Sample variance is a measure of the variability or spread of a set of data points in a sample. It is calculated as the sum of squared deviations from the sample mean, divided by the sample size minus one.

We can use the formula for the sample variance to relate the sample size (n), sum of squares (SS), and sample variance (s^2):

s² = SS / (n - 1)

Substituting the given values, we get:

4 = 20 / (n - 1)

Multiplying both sides by (n - 1), we get:

4(n - 1) = 20

Simplifying, we get:

4n - 4 = 20

4n = 24

n = 6

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Answer:

yes

Step-by-step explanation:

Answer:

x = 3.05 and y = -0.615

Step-by-step explanation:

The given equations are :

3x-3y = 11 ...(1)

3x + 10y = 3 ...(2)

Subtract equation (2) from (1).

3x-3y-(3x + 10y) = 11-3

-3y-10y = 8

-13y = 8

y = -0.615

Put the value of y in equation (1).

3x-3(-0.615) = 11

3x = 11 -1.845

3x = 9.155

x = 3.05

Hence, the values of x and y are 3.05 and -0.615.

The estimated cost savings for the homeowner in a year if she replaces refrigerator A with refrigerator B would be $72.

To calculate the cost savings, we first need to calculate the annual electricity cost for refrigerator A, which is 500 watts/hour * 12 hours/day * 365 days/year = 2,190,000 watt-hours/year or 2190 kWh/year. Multiplying this by the cost per kWh of $0.12 gives us an annual electricity cost of $262.80.

For refrigerator B, which uses 50% less energy per year, the annual electricity cost would be 2190 kWh/year * 0.5 * $0.12/kWh = $131.40. Therefore, the estimated cost savings for the homeowner in a year would be $262.80 - $131.40 = $131.40. However, the cost savings over the lifespan of the refrigerator will depend on its lifespan, replacement cost, and future changes in energy prices.

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a. The absolute change in city employees who ride the bus to work is 2%.

b. The relative change in city employees who ride the bus to work is approximately 11%.

c. The relative change in city employees who ride the bus to work is approximately 11%.

d. The relative change of around 11% indicates an increase in the proportion of city employees riding the bus to work compared to last year.

a. The absolute change in city employees who ride the bus to work can be calculated as the difference between this year's percentage (20%) and last year's percentage (18%):

Absolute change = 20% - 18% = 2%

b. The absolute change of 2% indicates that the number of city employees riding the bus to work has increased by 2 percentage points compared to last year.

c. The relative change in city employees who ride the bus to work can be calculated as the absolute change divided by the previous year's percentage, multiplied by 100:

Relative change = (Absolute change / Previous year's percentage) * 100

Relative change = (2% / 18%) * 100 ≈ 11%

d. The relative change of approximately 11% implies that the proportion of city employees riding the bus to work has increased by around 11% compared to last year.

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Answer:

A scalene triangle is one whose sides are all a different length. So there is no way you can find the length of b when you are only given the length of a and the perimeter.

Step-by-step explanation:

hopes it help :)

Answer:

15

Step-by-step explanation:

5x3 = 15 It's Simple Hope it helps

The number of ways to arrange the letters is 423360.

We have,

COMBINATORICS

There are 13 letters in total, including 5 vowels (O, I, A) and 8 consonants (C, M, B, N, T, R, S).

Now,

Take out the vowels from the word.

We get,

_C_M_B_N_T_R_C_S_

We see that,

There are 7 spaces where we can put the vowels.

And there are 8 consonants.

So,

= \(^7C_5\) / 2! x 8!

We divide the combination by 2! because there are two vowels with repetition.

Now,

= \(^7C_5\) / 2! x 8!

= ((7 x 6)/2 x 2)x 8 x 7 x 6 x 5 x 4 x 3 x 2

= 7 x 3 x 4 x 7 x 6 x 5 x 4 x 3 x 2

= 423360

Thus,

The number of ways to arrange the letters is 423360.

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Answer:

39

Step-by-step explanation:

multiple 159 by 74% them subtract

Answer:

50 bags of sugar

Step-by-step explanation:

There are 1000 grams in 1 kilogram

We know each shelf can hold up to 30 kilograms and we know each bag of sugar weighs 600 grams.

We multiply 30 kilograms (kg) by 1000 to make it equal to grams so:

30 kg x 1000 = 30,000 grams

We should divide 30,000 by 600 to know how many bags each shelf can hold

30,000/600 = 50 bags of sugar

Answer:

25%

Step-by-step explanation:

when we count, we know that there are 8 possible outcomes as to where the spinner will land.

{the following will be assuming each section has an equal chance of being landed on; that the spinner is not weighted}

We know that two of these 8 possibilities are "A"

This means that A has a 2/8 chance of being landed on

we can simplify 2/8 to 1/4; because they are equivalent ratios/fractions

to calculate percentage, we can follow through with our equation of 1/4

[divide 1 by 4]

1 / 4 = 0.25

We multiply this number by 100 to find percentage,

0.25 × 100 = 25

meaning that A has a 25% chance of being spun

hope this helps!! have a lovely day :)

Answer:

25%

Step-by-step explanation:

2 / 8 = 0.25

0.25 = 25%

The respective functions f(x) obtained from the given derivatives and points are

35. f(x) = 2x² + x - 1.

36. f(x) = 3x - x² - 1.

37. f(x) = -x²/2 - x³/3 + 9/2.

38. f(x) = x³ + 3x² - 2x + 6.

39. f(x) = (1/4)x⁴ + 2/x + 2x - 19/4.

40. f(x) = 2x⁽¹/²⁾ + (1/2)x² + 1/2.

41. f(x) = -e⁽⁻ˣ⁾ + (1/2)x² + 5.

42. f(x) = 3ln|x| - 4x + 4.

To find the function f(x) based on the given derivative f'(x) and a particular point (a, b), we can integrate f'(x) with respect to x and then use the given point to determine the constant of integration.

Let's go through each exercise:

35. f'(x) = 4x + 1; (1, 2)

Integrating f'(x) gives:

f(x) = 2x² + x + C

Using the given point (1, 2), we can substitute x = 1 and y = 2 into the equation:

2 = 2(1)² + 1 + C

2 = 2 + 1 + C

C = -1

Therefore, f(x) = 2x² + x - 1.

36. f'(x) = 3 - 2x; (0, -1)

Integrating f'(x) gives:

f(x) = 3x - x² + C

Using the given point (0, -1), we can substitute x = 0 and y = -1 into the equation:

-1 = 0 + 0 + C

C = -1

Therefore, f(x) = 3x - x² - 1.

37. f'(x) = -x(x + 1); (-1, 5)

Integrating f'(x) gives:

f(x) = -x²/2 - x³/3 + C

Using the given point (-1, 5), we can substitute x = -1 and y = 5 into the equation:

5 = -(-1)²/2 - (-1)³/3 + C

5 = -1/2 + 1/3 + C

C = 27/6 = 9/2

Therefore, f(x) = -x²/2 - x³/3 + 9/2.

38. f'(x) = 3x² + 6x - 2; (0, 6)

Integrating f'(x) gives:

f(x) = x³ + 3x² - 2x + C

Using the given point (0, 6), we can substitute x = 0 and y = 6 into the equation:

6 = 0 + 0 - 0 + C

C = 6

Therefore, f(x) = x³ + 3x² - 2x + 6.

39. f'(x) = x³ - 2/x² + 2; (1, 3)

Integrating f'(x) gives:

f(x) = (1/4)x⁴ + 2/x + 2x + C

Using the given point (1, 3), we can substitute x = 1 and y = 3 into the equation:

3 = (1/4)(1)⁴ + 2/1 + 2(1) + C

3 = 1/4 + 2 + 2 + C

C = -19/4

Therefore, f(x) = (1/4)x⁴ + 2/x + 2x - 19/4.

40. f'(x) = x⁽⁻¹/²⁾ + x; (1, 2)

Integrating f'(x) gives:

f(x) = 2x⁽¹/²⁾ + (1/2)x² + C

Using the given point (1, 2), we can substitute x = 1 and

y = 2 into the equation:

2 = 2(1)⁽¹/²⁾ + (1/2)(1)² + C

2 = 2 + 1/2 + C

C = 1/2

Therefore, f(x) = 2x⁽¹/²⁾ + (1/2)x² + 1/2.

41. f'(x) = e⁽⁻ˣ⁾ + x; (0, 4)

Integrating f'(x) gives:

f(x) = -e⁽⁻ˣ⁾ + (1/2)x² + C

Using the given point (0, 4), we can substitute x = 0 and y = 4 into the equation:

4 = -e⁽⁻⁰⁾+ (1/2)(0)² + C

4 = -1 + 0 + C

C = 5

Therefore, f(x) = -e⁽⁻ˣ⁾ + (1/2)x² + 5.

42. f'(x) = 3/x - 4; (1, 0)

Integrating f'(x) gives:

f(x) = 3ln|x| - 4x + C

Using the given point (1, 0), we can substitute x = 1 and y = 0 into the equation:

0 = 3ln|1| - 4(1) + C

0 = 0 - 4 + C

C = 4

Therefore, f(x) = 3ln|x| - 4x + 4.

These are the respective functions f(x) obtained from the given derivatives and points.

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Answer:

24+p=t

Step-by-step explanation:

If he scored 24 points in the first half, and p in the next half, he scored a total of t points.

Therefore , the solution to the given problem of percentage comes out to be  total number of student  = 182 (approx).

In mathematics, a percentage is a number or ratios that is expressed as a portion of 100. Occasionally, the acronyms "pct.," "percent growth," & "pc" are also used. But it is commonly indicated by the percent sign, "%." The % amount has no dimensions. Percentages are essentially fractions when the denominator is 100. Use the percent sign (%) to indicate that a quantity is a percentage by placing it next to it.

Here,

Given :  22% of x is 40

thus,

To find the value of x , where x is the total number of students in that class.

=>  22/100* x = 40

=> x = 40 * 100 /22

=> x = 4000/22

=> x =181.81

So, x = 182 (approx)

Therefore , the solution to the given problem of percentage comes out to be   total number of student  = 182 (approx).

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To determine if the value for b (18 hours) lies within the solution set of the system of inequalities, we need to follow these steps:
Step 1: Identify the given inequalities in the system. Unfortunately, you did not provide the specific inequalities, so I will use a general example: a < b and b < c.
Step 2: Plug in the given value for b (18 hours) into the inequalities: a < 18 and 18 < c.
Step 3: Assess whether the value of 18 hours for b satisfies both inequalities. If both inequalities hold true, then the value of b lies within the solution set of the system of inequalities.
In the given example, if a is less than 18 and c is greater than 18, then the value of 18 hours for b would satisfy the system of inequalities, and Marcus would be able to pick up a weekly workload of 18 hours. To provide a definite answer, please provide the specific inequalities for the system in question.

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Answer:

Step-by-step explanation:

2590

Answer:

surface area= 6l²

= 6×12²

= 164cm²

hope it helps