What is the linear function equation that best fits the data set?

yˆ=2x−2

yˆ=x−2

yˆ=4x−2

yˆ=4x−11

Final answer:

The expression to verify that g(x) is the inverse of f(x) is to check if f(g(x)) = x and g(f(x)) = x. When we calculate both expressions for the given functions, they both simplify to x, which confirms that g(x) is the inverse of f(x).

Explanation:

To verify that g(x) is the inverse of f(x), we need to show that composing f with g yields the identity function. In other words, f(g(x)) should equal x, and vice versa, g(f(x)) should also equal x. For the given functions, f(x) = 5x - 25 and g(x) = 1/5x + 5, let's compute f(g(x)) and g(f(x)).

To find f(g(x)), we substitute g(x) into f(x):

f(g(x)) = f(1/5x + 5) = 5(1/5x + 5) - 25 = x + 25 - 25 = x

Next, to find g(f(x)), we substitute f(x) into g(x):

g(f(x)) = g(5x - 25) = 1/5(5x - 25) + 5 = x - 5 + 5 = x

Since both f(g(x)) and g(f(x)) equal x, we can conclude that g(x) is indeed the inverse of f(x).

Answer:

2,008,747,295,829,492‬

Step-by-step explanation:

2008747295829492= 1000 + 2008747295828492

Answer:

Part 1) The lateral area is [tex]LA=791.7\ ft^{2}[/tex]

Part 2) The surface area is  [tex]SA=1,244.1\ ft^{2}[/tex]

[tex]LA=791.7\ ft^{2}[/tex], [tex]SA=1,244.1\ ft^{2}[/tex]

Step-by-step explanation:

step 1

Find the lateral area of the cone

we know that

The lateral area of the cone is equal to

[tex]LA=\pi rl[/tex]

we have

[tex]r=12\ ft[/tex]

[tex]l=21\ ft[/tex]

substitute

[tex]LA=(3.1416)(12)(21)=791.7\ ft^{2}[/tex]

step 2

Find the surface area of the cone

we know that

The surface  area of the cone is equal to

[tex]SA=\pi r^{2}+LA[/tex]

we have

[tex]r=12\ ft[/tex]

[tex]LA=791.7\ ft^{2}[/tex]

substitute

[tex]SA=(3.1416)(12)^{2}+791.7=1,244.1\ ft^{2}[/tex]

Answer:

8 units

Step-by-step explanation:

Calculate the distance (d) using the distance formula

d = √ (x₂ - x₁ )² + (y₂ - y₁ )²

with (x₁, y₁ ) = (- 1, - 5) and (x₂, y₂ ) = (- 9, - 5)

d = [tex]\sqrt{(-9+1)^2+(-5+5)^2}[/tex]

  = [tex]\sqrt{(-8)^2+0^2}[/tex]

  = [tex]\sqrt{64}[/tex]

  = 8 units

Answer:

Corresponding angles theorem.

Step-by-step explanation:

The corresponding angles theorem states that corresponding angles are congruent.

Pretty much means that every other angle is congruent if two lines are parallel and a line traverses them.

Answer: angle 2 and angle 6 are both corresponding angles

Step-by-step explanation:

If the two angles are matching corners, they are corresponding to one another. Hope this helps and have a good day:)

Answer:

{1,2,3,7}

Step-by-step explanation:

The range of a relation is the set of y-values of the ordered pairs.

The given relation is:

ƒ={(5, 1),(6, 2),(7, 3),(8, 1),(9, 7)},

The set of y-values of the given ordered pairs are;

{1,2,3,7}

Therefore the range of y is {1,2,3,7}

Answer:

{[tex]1, 2, 3, 7[/tex]}

Step-by-step explanation:

Imagine fucntions as little machines that turn one number into another. The numbers that enter are called domain and the numbers that go out are called range. In this excercise we are given the couples of numbers that go in and out of the machine. Like this:

[tex](NumberIn,NumberOut)[/tex]

So the range of this function will be all the number going out of the function

(NumberOut) and this are:

{[tex]1, 2, 3, 7[/tex]}

Answer:

The diameter of the rug is [tex]4\ ft[/tex]

Step-by-step explanation:

we know that

The circumference of a circle (circular rug) is equal to

[tex]C=\pi D[/tex]

where

D is the diameter of the circle

In this problem we have

[tex]C=12.56\ ft[/tex]

substitute in the formula and solve for D

[tex]12.56=(3.14)D[/tex]

[tex]D=12.56/(3.14)=4\ ft[/tex]

The solution of the expression (a-b)²/{(1/a)-(1/b)} is ab² - a²b.

Factorization in mathematics is the process of dividing a large number into smaller ones that, when multiplied together, give you the original number. Factorization is the process of dividing a number into its components or divisors.

Given:

An expression,

(a-b)²/{(1/a)-(1/b)}.

Simplifying,

(a-b)²/{(1/a)-(1/b)},

= (a-b)²/{(b-a)/ab},

= -(a-b)² (ab)/(a-b)

= -(a-b)(ab)

= ab² - a²b.

Therefore,  ab² - a²b is the solution.

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Final answer:

The expression (a-b)²/(1/a-1/b) simplifies by first finding a common denominator, then multiplying to remove the fraction, resulting in the simplified form -ab(a-b).

Explanation:

To simplify the expression (a-b)²/(1/a-1/b), we can start by finding a common denominator for the terms in the denominator 1/a and 1/b. The common denominator is a × b, so we rewrite the expression as:

((a-b)²) / ((b - a) / (ab))

Now, we can simplify by multiplying both the numerator and the denominator by ab to eliminate the fraction in the denominator:

(a-b)² × (ab) / (b - a)

Note that (a - b) is equal to -(b - a), so:

(a-b)² × (ab) / -(a - b)

Because (a - b)² is (a - b) × (a - b), one (a - b) in the numerator cancels with the (a - b) in the denominator, leaving us with:

-(a - b) × (ab)

Which simplifies to:

-ab(a - b)

Answer: I'm pretty sure its 1562

Answer:

The sum of 22 terms of given AP = 1562

Step-by-step explanation:

Formula:-

Sum of n terms of AP,

Sₙ= (n/2)[2a + (n - 1)d]

To find the sum of 22 terms

Here. a = 8, d = 6 and n = 22

Sₙ= (n/2)[2a + (n - 1)d]

S₂₂ = (22/2)[2*8 + (22 - 1)*6]

  = 11[16 + 126] = 11 * 142 = 1562

The sampling method used in this case is Self-Selected Sampling (C) and it has bias because those who respond to the survey may overrepresent the number of readers in the community.

The sampling method used in this case is Self-Selected Sampling (C). The magazine invites readers to complete and mail in a survey, therefore the readers themselves choose whether or not to participate. There is no random selection involved in this sampling method.

The sampling method used in this case does have bias. (D) Yes, because the people who respond to the survey may overrepresent the number of readers in the community.

This is because only those who choose to respond will be included in the sample, and those who are more interested in the magazine or have strong opinions about reading may be more likely to respond.

Final answer:

The sampling method used in this situation is Convenience Sampling, and it does have bias because it may underrepresent the number of readers in the community.

Explanation:

The sampling method used in this situation is Convenience Sampling. This is because the magazine invites readers to complete and mail in a survey based on their convenience, rather than using a random or systematic method to select the sample.

The sampling method used in this situation does have bias. The correct answer is B. Yes, because the people who respond to the survey may underrepresent the number of readers in the community. This is because the sample is based on self-selection, meaning that only those who choose to respond to the survey are included. This can result in a biased sample that may not accurately represent the entire community's reading habits.

For this case we have that the equation of the line of the slope-intersection form is given by:

[tex]y = mx + b[/tex]

Where:

m: It's the slope

b: It is the cutoff point with the y axis

We have as data that:

[tex]m = \frac {1} {4}\\b = - \frac {3} {4}[/tex]

Substituting:

[tex]y = \frac {1} {4} x- \frac {3} {4}[/tex]

Answer:

[tex]y = \frac {1} {4} x- \frac {3} {4}[/tex]

Explanation:

15. x = 148°, z = 32°

In a parallelogram, adjacent angles are supplementary, so must add to 180°. That also means opposite angles are congruent.

___

17. x = 8, y = -3

The diagonals bisect each other, so ...

2x -4 = 12

x = (12 +4)/2 = 8

and ...

y +10 = 7

y = 7 -10 = -3

__

21. The diagonals of a parallelogram bisect each other, so their point of intersection is their midpoint. The midpoint of WY can be computed as ...

P = (W+Y)/2 = ((-3, 5) +(3, 1))/2 = (0, 6)/2 = (0, 3)

The diagonals intersect at (0, 3).

Answer:

29

Step-by-step explanation:

the rule PEMDAS means first use the parentheses, (  ,  )

so order of operation, first you do parentheses, 20/4=5 then 5-5=0

so that is the parentheses now take core of stuff outside of parentheses and    29 x 1=29

P= parentheses

E = Exponents

M= multiply

D = divide

A= addition

S= subtract

also know as order of operation!

hope this helps. please mark brainliest! have a good day

The value of expression 29 • 1 + 2(20 ÷ 4 – 5)= 29

The order of operations is a rule that tells the correct sequence of steps for evaluating a math expression. We can remember the order using PEMDAS: Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right).

To solve the given expression we will use:

The PEMDAS rule means

P= Parentheses

E = Exponents

M= multiply

D = divide

A= addition

S= subtract

first we do parentheses,

29 • 1 + 2(20 ÷ 4 – 5)= 29.1+2(5-5)

                                  = 29.1+2(0)

                                  = 29.1+0

                                 =29

Thus,  29 • 1 + 2(20 ÷ 4 – 5)  =29

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ANSWER

[tex]a_{34} = 8[/tex]

EXPLANATION

The given matrix is a 4 by 4 matrix.

The entry in the intersection of the first third row and the fourth column is denoted

[tex]a_{34}[/tex]

This entry is 8.

Check the attachment for how we got the 8.

Therefore

[tex]a_{34} = 8[/tex]

Answer:

He can make 52 canvases and will have 10 remaining staples

Step-by-step explanation:

1258/24=52 10/24

Answer:

52 canvases can be prepared and 10 staples will be remaining

Step-by-step explanation:

Sweet t has number of staples to create art canvases = 1258

Each canvas requires number of staples = 24

Let n canvases can be prepared by these staples.

Number of staples used in n canvases = 24n

The expression representing this process will be

24n = 1258

n = [tex]\frac{1258}{24}[/tex]

  = 52.42 canvases

Staples used to prepare 52 canvases = 52 × 24

= 1248

Remaining staples = 1258 - 1248

= 10 staples

Therefore, 52 canvases can be prepared and 10 staples will be remaining.

Answer:

11/12

Step-by-step explanation:

1/4+2/3

1/4×3/3+2/3×4/4

3/12+8/12

Final answer:

Tipping a fortune teller involves giving them a gratuity as a gesture of appreciation for their service.

Explanation:

When you tip a fortune teller, you are giving them a gratuity or extra money as a gesture of appreciation for their service. Tipping is a common practice in various service industries, including fortune-telling. It is a way to show gratitude for the insights or entertainment provided by the fortune teller.

ANSWER

The range is

{-1,0,1,3,4,5}

EXPLANATION

The relation is given to us as an ordered pair.

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

We list the set of all the values in ascending order without any repetition.

We then obtain the range as:

{-1,0,1,3,4,5}

Answer:

Each team recieved $312

Step-by-step explanation:

You will take $5145 - 777 = 4368 which is the balance

4368 of the balance  ÷ 14 teams =312

each team received  $312

After paying the expenses of $777 from the fund-raising total of $5145, $4368 was left. When this amount was divided evenly amongst 14 soccer teams, each team received $312.

To solve the problem, we first need to subtract the expenses from the total fund-raising amount. This gives us $5145 - $777 = $4368.

After the expenses are taken into consideration, the remaining money is divided evenly among the 14 soccer teams. This is calculated by taking the remaining money and dividing it by the number of teams, $4368 ÷ 14 = $312.

So, each team will receive $312 after all the expenses are paid.

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Answer : x^1/2 y -1/3/x^/4 cdot y^1/2= y^1/3

Step-by-step explanation: Hope this helps !!!

Plz give me 5 star & thanks! :}

Answer:

option A

(1.5,1.2)

Step-by-step explanation:

Given in the question two equations

Equation 1

y = √x

Equation 2

y = x²- 1

Equate both equations

√x = x²- 1

We can see from the graph that both meets when x =  1.5 and y = 1.2

we can plug the options given one by one to see which points satisfy

one thing we know is that x ≠ any negative value since

y = √x and square root of negative value is not possible

so option b and c are rejected

  option A

√1.5 = y = 1.2

1.5²- 1 = y = 1.2

[tex]\boxed{R_{4}=20\Omega}[/tex]

If resistors are in series, so the current  [tex]I[/tex] is the same in all of them. In this problem we have four resistors. So, we can get a relationship between the Equivalent resistance  of series combination and the four resistors as follows:

[tex]R_{eq}=R_{1}+R_{2}+R_{3}+R_{4}[/tex]

[tex]R_{eq}[/tex] is the total resistance [tex]50\Omega[/tex]. Moreover:

[tex]R_{1}=5\Omega \\ R_{2}=10\Omega \\ R_{3}=15\Omega[/tex]

Therefore:

[tex]50=5+10+15+R_{4} \\ \\ R_{4}=50-(5+10+15) \\ \\ R_{4}=50-30 \\ \\ \boxed{R_{4}=20\Omega}[/tex]

Answer:

(6x + 5)(7x² - 6)

Step-by-step explanation:

Factor the first/second and third/fourth term

42x³ + 35x² - 36x - 30

= 7x²(6x + 5) - 6(6x + 5) ← factor out (6x + 5) from each term

= (6x + 5)(7x² - 6)

Answer:

(6x+5)(7x2−6)

Step-by-step explanation:

Factor 42x3+35x2−36x−30

42x3+35x2−36x−30

=(6x+5)(7x2−6)

Answer:

Yep! an open dot is <

A closed dot means ≤

Hope this helps! :)

If you don't mind please mark as brainliest! :)

Answer:

9.9 x 10.1 x 10.0

Step-by-step explanation:

9.9 x 10.1 x 10.0 = 999.9 ft3

This the closest to the true known value.

Other answers mat be more precise, but not as accurate.

Accuracy is how close a measured value is to the actual or true value.

Cheers

Answer:

A)

Step-by-step explanation:

Here are the choices:

A) 9.9 x 10.1 x 10.0

B) 9.91 x 10.11 x 10.00

C) 9.911 x 10.112 x 10.002

D) 9.9113 x 10.1125 x 10.0028

Here are the volumes produced by each choice of measures.

A) 999.9

B) 1001.9

C) 1002.4

D) 1002.56

Answer: A) since the volume os colsest to the real volume.

Answer:

pictures 1, 2, 4, and 6

Step-by-step explanation:

Okay so in this question it says to solve f(7). This means to plug in the 7 every where you see an x, so that it looks like this: [tex]\frac{3}{7+2} -\sqrt{7-3}[/tex]Then you'll solve it like a normal equation.

Hope this helped! Let me know if there is anything I need to clarify or explain more in depth!

Answer:

- 1.67

Step-by-step explanation:

To evaluate f(7) substitute x = 7 into the expression

f(7) = [tex]\frac{3}{7+2}[/tex] - [tex]\sqrt{7-3}[/tex]

     = [tex]\frac{3}{9}[/tex] - [tex]\sqrt{4}[/tex]

     = [tex]\frac{1}{3}[/tex] - 2

     = [tex]\frac{1}{3}[/tex] - [tex]\frac{6}{3}[/tex]

     = - [tex]\frac{5}{3}[/tex] ≈ - 1.67

Point c.

You can graph the two points in a calculator to find out the answer OR you can identify the lines using the y-intercept aka b in the y=mx+b format.

Y=x - 3 has a y-intercept of -3, so look for the line where it goes through -3 on the y axis. (do the same for the other except when the y-intercept is 1)

From this, you can identify the lines and just find where they intersect.

Answer:

CCCCCCCCCCCCCC

Step-by-step explanation:

Answer:

$11.00

Explanation:

$60 given - $49 order = $11 change

Answer:

It's 11 because 60-49 equals 11.

Step-by-step explanation:

Answer:

Im pretty sure he got 24

Step-by-step explanation:

Because if you divide 12.30 by .50 you get 24.6 and the 6 could mean sales tax and other stuff