What is the value of x?

A. 68°
B. 62°
C. 112°
D. 124

The expression f - 2g evaluates to -60, considering f = 4 and g = 32. The answer is not listed in the given multiple-choice options, suggesting a potential error in the question or options.

The expression to evaluate is f - 2g. With the given values for f and g, f = 4 and g = 32, we can substitute these into the expression. The calculation will be:

Therefore, the value of f - 2g is -60. This answer is not given in the multiple choice options, indicating a possible discrepancy between the question and the provided options. The correct evaluation should be confirmed.

Answer:  -2 is the correct answer

Explanation:

This is the graph for greatest integer function  by looking at the graph we can clearly conclude that  f at zero is giving the value -2

Greatest integer function gives the value that is less than or equal to the value taken inside the function

For example if we have 2.09  and is operating under greatest integer function the value comes out to be 2  because it will convert the decimal value in integer

denoted as [2.09]=2

The linear  expression 30 + 12h represents Michael's lawn care service charges, where '30' is the fixed fee and '12h' is the variable fee depending on the hours worked.

Michael's lawn care service uses an equation to calculate the charges for his customers: 30 + 12h dollars, where h represents the number of hours spent working on a lawn. In this expression, the number 30 represents a fixed fee, likely covering base expenses such as equipment, transportation, or administrative costs. The term 12h represents the variable fee, where 12 is the hourly rate in dollars Michael charges for his labor, and h is the number of hours he works on the lawn.

Thus, to determine the total cost to a customer, one would multiply the number of hours Michael works (h) by his hourly rate (12) and then add the fixed fee (30). For instance, if Michael works 5 hours on a lawn, the total cost would be calculated as follows: 30 + 12(5) = 30 + 60 = 90 dollars.

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Answer: The expression shows the number of dollars he will have saved by the end of the year is given by [tex]35(7)+40(5)=\$445[/tex]

Step-by-step explanation:

Since we have given that

Amount he saved per month over the first 7 months = $35

Amount he saved per month over the next 5 months = $40

So, total saving by the end of the year is given by

[tex]35\times 7+40\times 5\\\\=\$245+\$200\\\\=\$445[/tex]

Hence, the expression shows the number of dollars he will have saved by the end of the year is given by

[tex]35(7)+40(5)=\$445[/tex]

Answer:

33.56 miles per hour.

Step-by-step explanation:

First we will see how many meters the hummingbird can travel in an hour (in meters)

it can travel up to 15 meters per second, but we know that one hour has 3600 seconds ( because an hour has 60 minutes of 60 seconds each one ( 60 x 60 = 3600)

So the hummingbird can travel 3600 x 15 = 54,000 meters in one hour.

Now, we know that 1 mile = 1609 meters, so in order to convert the 54,000 meters in miles per hour we're going to use a rule of three.

1 mile ----------- 1609 meters

x miles ---------- 54,000 meters

x miles = 54,000/1,609 = 33.56

Therefore, the hummingbird speed is 33.56 miles per hour.

The measure of m∠D is 10 degrees

In line geometry, vertical angles are always equal.

Given the following vertical angles

m∠C=−2x+90 and m∠D=x−30

Since m∠C= m∠, hence;

-2x + 90 = x - 30

-2x - x = -30 - 90

-3x = -120

x = 40

Get the measure of m∠D

m∠D = x - 30

m∠D = 40 - 30

m∠D = 10degree

Hence the measure of m∠D is 10 degrees

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Lenny used the Associative property of addition to show that rearranging the grouping of numbers being added does not change the outcome of the equation.

While solving an equation, Lenny used the Associative property of addition which guarantees that the second equation (2x + (1+5) = 9) is equivalent to the first ((2x + 1) + 5 = 9). This property states that the grouping of numbers being added does not change the sum, as shown:

(A + B) + C = A + (B + C).

In the context of the provided equations, Lenny grouped the 1 and 5 together without changing the sum, illustrating that it doesn't matter how the numbers are grouped in addition.

Answer:

The correct answer is A) 15, 19, 26, 51, 18, 21

Step-by-step explanation:

So let me start by explaining what an outlier is: An outlier is any data that falls outside of the given points, The reason the answer is A) is because 51 is included in the points, While most of the points in A) Are anywhere from 15-26 51 is an outlier because its outside of that standard range. The other ones don't have an outlier.

The data set that contains one outlier is,

{15, 19, 26, 51, 18, 21}.

The correct option is A.

Sets are groups of well-defined objects or components in mathematics. A set is denoted by a capital letter, and the cardinal number of a set is enclosed in a curly bracket to indicate how many members there are in a finite set.

Given:

We have data set:

15, 19, 26, 51, 18, 21

22, 33, 31, 20, 28, 19

18, 20, 16, 22, 28, 26

27, 21, 31, 18, 21, 29

From the given choices,

the first data set has an outlier 51.

Because it is nowhere from the range of the data set.

Therefore, the set is {15, 19, 26, 51, 18, 21}.

To learn more about the set;

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A linear system in three variables has infinitely many solutions when the equations are dependent on each other and represent the same line or plane. To determine if a system has infinitely many solutions, we can solve the system and check if any of the equations can be derived from the others or if they represent the same line or plane.

When a linear system in three variables has infinitely many solutions, it means that the three equations are dependent on each other and represent the same line or plane. This happens when the coefficients of the variables in the equations are proportional to each other. To determine if a system has infinitely many solutions, we can solve the system and check if any of the equations can be derived from the others or if they represent the same line or plane.

Let's take the system of equations given in the question:

We can start by solving equations (1) and (2) for y:

Simplifying equation (2), we get:

y = 2

Substituting y = 2 into equation (1), we have:

7(2) = 6x + 8

14 = 6x + 8

6x = 14 - 8

6x = 6

x = 1

Now, let's substitute the values of x and y into equation (3):

y + 7 = 3x

2 + 7 = 3(1)

9 = 3

This equation is not true. Therefore, the system of equations is inconsistent and does not have infinitely many solutions. The system does not represent the same line or plane.

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NMO = LMO = x+34

LMO = 1/2 of LMN

so 2(x+34) = 6x-28

2x+68 = 6x-28

2x +96 = 6x

96 = 4x

x =96/4 = 24

x = 24

 LMO = x+34 = 24+34 = 58

 since NMO = LMO, NMO = 58

s - 2 ≤ 7

  +2   +2

s ≤ 9

s ≤ 9

Answer:

The owner of a business sometimes withdraw assets other than cash because cash is more liquid and can be used in transactions easily, whereas the assets after a period of times becomes liable of depreciation.

The depreciation on assets decreases the amount of the assets based on the time and wear and tear of the tangible assets.

Therefore, to retain some liquid assets in hand the tangible or intangible assets are used first.

Hence, the businessman here did the right thing.

By solving a system of linear equations, the set fee for renting a bike is determined to be $6 and the hourly rate is $4.50. Hence, the cost to rent the bike for 3 hours is $19.50.

The question involves creating linear equations based on the given information to find the cost of renting a bike for a certain number of hours. We are told that renting a bike for 4 hours costs $24 and renting for 7 hours costs $37.50. We can express this situation with two equations, where x represents the set fee and y represents the hourly rate:

We solve this system of equations to find the values of x and y. Subtracting the first equation from the second gives us 3y = 13.5, hence y = 13.5 / 3 = $4.50 per hour. We can then substitute y back into the first equation: 4(4.50) + x = 24, which simplifies to 18 + x = 24, hence x = $6.

To rent the bike for 3 hours, the cost would be 3(4.50) + 6 = $13.50 + $6 = $19.50.

The response explains which statements are substantiated facts and why. It clarifies the concept by using examples from the question.

Substantiated facts are statements supported by evidence or proof. In the given examples:

Joel borrowed money at an interest rate of approximately 2.73%. This was determined by using the simple interest formula to calculate the interest paid over 6 years and then re-formulating to find the interest rate using the known principal amount and time period.

The subject of this question is simple interest which is a concept in Mathematics. The question is asking for the interest rate at which Joel borrowed money to purchase a vehicle. By knowing that Joel borrowed $18,000, repaid a total of $20,953.80 after 6 years, and by applying the simple interest formula I = PRT (where I is interest, P is principal amount, R is interest rate and T is time in years), we can find out the interest rate.

The first step is to calculate the simple interest itself, which can be found by subtracting the original principal amount from the total amount repaid. So, $20,953.80 - $18,000 = $2,953.80 is the interest paid over 6 years.

Then we rearrange the simple interest formula to solve for the rate: R = I / (PT). Substituting the known values, our equation is: R = $2,953.80 / ($18,000 * 6), which gives R = 0.027325, or approximately 2.73% when expressed as a percentage.

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A. calculate the average of the x-coordinates

C. divide 12 by 2

D. take the average of the endpoint

The equation that represents the function B(a) as the length of the side parallel to the base is B(a) = a/6 - 9, as per the area of a trapezoid.

If the length of two parallel sides of a trapezoid is 'a', 'b' and the height of that trapezoid is 'h', then the area of a trapezoid can be represented as

= [(a + b)h]/2

Given, the base of the trapezoid is 9 and the height of the trapezoid is 12.

Therefore, 'b' is the parallel side of the base.

The given function that represents the area of the trapezoid is:

A(b) = [12(b + 9)]/2

Let, A(b) = a.

Therefore, a =  [12(b + 9)]/2

⇒ 2a = 12(b + 9)

⇒ a = 6(b + 9)

⇒ a = 6b + 54

⇒ 6b = a - 54

⇒ b = (a - 54)/6

⇒ b = a/6 - 9

If we assume the length of the side parallel to the base 'b' = B(a), therefore, the equation will be:

B(a) = a/6 - 9

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Inga lives 2b + 3 miles from school, where b is the distance Brent lives from school in miles.

Therefore, the distance that Inga lives from school, in terms of b, is 2b + 3 miles.

The problem states that Inga lives 3 miles more than twice the distance that Brent lives from school. If the distance Brent lives from school is b miles, this can be expressed algebraically as 2*b (twice the distance of Brent) + 3 (the extra 3 miles that Inga lives). Therefore, the distance that Inga lives from school, in terms of b, is 2b + 3 miles.

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