A triangle has coordinates A(5,10) B(15,20) and C(25,30). The triangle is dilated by a scale factor of 1/5. What are the coordinates of vertices of the image?

Yes, its true that the questionnaire is very carefully constructed by an individual to provide the measurement instrument.  

A questionnaire is a studies device which includes a sequence of questions for the motive of amassing facts from respondents. Questionnaires may be concept of as a form of written interview. A questionnaire is a listing of questions or gadgets used to collect facts from respondents approximately their attitudes, experiences, or opinions.

Questionnaires may be used to acquire quantitative and/or qualitative facts. Questionnaires are generally utilized in marketplace studies in addition to withinside the social and fitness sciences. Questionnaires are typically taken into consideration to be excessive in reliability. This is due to the fact it's miles feasible to invite a uniform set of questions. Any troubles withinside the layout of the survey may be ironed out after a pilot study. The greater closed questions used, the greater dependable the studies.

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From the information given in the question, we can initially fill up some boxes in the table.

There are 380 sweatshirts to sell. This total goes in the right-bottom corner of the table:

Of all the sweatshirts, 210 had no hood. That number goes at the end of the row 'No Hood' as follows:

We also know 180 sweatshirts were green. This number goes at the bottom of the column 'Green' as shown below:

Of the sweatshirts that were purple, 70 had a hood. This number goes in the cell that intercepts 'Purple' and 'Hood':

With the information given so far, we can fill up the rest of the table by addition and subtraction.

For example, the last column for Hood should be 380 - 210 = 170

The last row on the second column for Purple should have 380 - 180 = 200

The Green and Hood cell should have 170 - 70 = 100

The Green and No Hood cell should have 180 - 100 = 80

Finally, the cell Purple and No Hood can be calculated in several ways and it should result in the same number for all of them: 200 - 70 = 130

The final table is:

The equation for traveling x miles in the cab can be written as:

Cost = $0.60 + $0.14 * x. The cab charges $0.88 for a ride of 2 miles. And the cab charges $1.72 for a trip of 8 miles.

a. The equation for traveling x miles in the cab can be written as:

Cost = $0.60 + $0.14 * x

b. To find the number of miles for a cab ride that costs $0.88, we can set up the equation:

$0.88 = $0.60 + $0.14 * x

Subtracting $0.60 from both sides, we get:

$0.88 - $0.60 = $0.14 * x

$0.28 = $0.14 * x

Dividing both sides by $0.14, we find:

x = $0.28 / $0.14

x = 2 miles

Therefore, the cab charges $0.88 for a ride of 2 miles.

c. To calculate the cost of a trip of 8 miles, we can substitute x = 8 into the equation:

Cost = $0.60 + $0.14 * 8

Cost = $0.60 + $1.12

Cost = $1.72

Therefore, the cab charges $1.72 for a trip of 8 miles.

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The student covers a total distance of 22.05 kilometers in a week's time, walking between the park and the house each day.

To find the total distance covered by the student in a week's time, we need to calculate the distance covered in one round trip (from the house to the park and back) and then multiply it by the number of round trips in a week.

Given that the difference between the park and house is 1 kilometer and 575 meters, we can convert it to a total distance of 1.575 kilometers.

In a round trip, the student covers twice the distance between the park and the house, which is 1.575 kilometers * 2 = 3.15 kilometers.

Now, we need to determine how many round trips the student makes in a week. Let's assume the student makes one round trip each day.

Since there are 7 days in a week, the total distance covered by the student in a week's time is 3.15 kilometers * 7 = 22.05 kilometers.

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Answer: The first 3 options

Step-by-step explanation:

You have to make sure that the given variable would be able to equal -5. The  \(\geq\) sign in the second and third answer show that the variable could be equivalent to -5.

Answer:

g > -7, f ≤ -5 and g ≥ -5

Step-by-step explanation:

the < and > symbols mean less than and greater than respectively, but not including. Therefore -5 cannot be a valid solution if the range is (for example) g > -5. However, ≤ and ≥ mean less/greater than or equal to, so -5 would be a valid solution for g ≥ -5 (for example).

True. A vector in space can be described by specifying its magnitude and its direction angles. The magnitude of a vector represents its length or size, while the direction angles determine the orientation of the vector with respect to a reference axis system.

In three-dimensional space, a vector can be decomposed into its components along the x, y, and z axes. By using trigonometric functions, the direction angles of the vector can be determined. The direction angles are typically measured with respect to the positive x-axis, the positive y-axis, and the positive z-axis.

Once the magnitude and direction angles of a vector are known, the vector can be fully described. This description allows for precise calculations and analysis of vector quantities, such as displacement, velocity, and force, in various physical and mathematical contexts.

It's worth noting that there are alternative ways to describe vectors, such as using Cartesian coordinates or unit vectors. However, specifying the magnitude and direction angles provides a convenient and comprehensive representation of a vector in space.

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The element (4, 2) refers to the value in the 4th row and 2nd column of the inverse matrix. In this case, the element is 3/5.

To find the inverse of the matrix:

\(| 1 3 4 |\)

\(| 0 2 6 |\)

\(| 0 3 1 |\)

We can use the formula for the inverse of a 3x3 matrix:

Let A be the given matrix, and let A^-1 be its inverse.

A⁻¹ = (1/det(A)) * adj(A)

where det(A) is the determinant of A and adj(A) is the adjugate of A.

Step 1: Calculate the determinant of A

det(A) = 1*(21 - 36) - 3*(01 - 36) + 4*(03 - 26)

= 1*(-16) - 3*(-18) + 4*(-12)

= -16 + 54 - 48

= -10

Step 2: Calculate the adjugate of A

The adjugate of a matrix is the transpose of its cofactor matrix.

The cofactor matrix of A is:

\(| 2 -18 -12 |\)

\(| -6 -4 6 |\)

\(| 12 \ 6 -2 |\)

Taking the transpose of the cofactor matrix gives us the adjugate of A:

\(| 2 -18 -12 |\)

\(| -6 -4 6 |\)

\(| 12 \ 6 -2 |\)

Step 3: Calculate A^-1

A⁻¹ = (1/det(A)) * adj(A)

= (1/-10) *

\(| 2 -18 -12 |\)

\(| -6 -4 6 |\)

\(| 12 \ 6 -2 |\)

Simplifying the scalar multiplication:

A⁻¹ =

\(| -1/5 \3/5\ -6/5 |\)

\(| 9/5\ 2/5\ -3/5 |\)

\(| 6/5 \-3/5 \1/5 |\)

Therefore, the inverse of the given matrix is:

\(| -1/5 \3/5\ -6/5 |\)

\(| 9/5\ 2/5\ -3/5 |\)

\(| 6/5 \-3/5 \1/5 |\)

To identify the value of element (4, 2) in the inverse matrix:

The element (4, 2) refers to the value in the 4th row and 2nd column of the inverse matrix. In this case, the element is 3/5.

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Using the given data, the number of suspects is; 7

The union of two sets A and B is the set of all those elements which are either in A or in B, and which is denoted as A ∪ B.

However, the intersection of two sets A and B is defined as the set of all elements which are common. The intersection of these two sets is denoted by A ∩ B.

Now, we are told that;

Total number of people in the office = 30 people

Number of people wearing a white button down shirts = 22

Number of people wearing black pants = 16

Number of people wearing a multicolored tie = 7

Thus, by definition of intersection of sets, if the suspect was wearing black pants, a white button-down shirt, and a multicolored tie, then;

The number of suspects =  A ∩ B ∩ C = 7 people

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16

Hope this helps! :D

Answer:

\(\Large \boxed{\sf 12.6}\)

Step-by-step explanation:

The diameter of the base is 8 so radius is 8/2 = 4

Use Pythagorean Theorem to find hypotenuse of the right triangle

\(\displaystyle c=\sqrt{4^2+12^2} =12.6\)

Answer:

No.

Step-by-Step Explanation:

When two lines are parallel, they might or might not be equal. It is not necessary that they should be equal.

See the triangle below in which two lines are parallel to each other.

Simplifying the expression gives 0 = 6

An algebraic expression is defined as an expression made up of variables and constants, with algebraic operations like addition, subtraction, and division.

Given the expression;

1/2 (x + 4) = 1/2x + 1

\(\frac{1}{2(x + 4)} = \frac{1}{2(x+ 1)}\)

cross multiply

2(x + 1) = 2(x+ 4)

Expand the bracket

2x + 2= 2x + 8

collect like terms

2x - 2x = 8 - 2

0 = 6

Thus, simplifying the expression gives 0 = 6

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The inverse Laplace transform of ℒ^-1 8s - 16 (s^2 + s)(s^2 + 1) is:

\(-4(e^-t - 1) - 4e^(-t) sin(t) - 4cos(t)\)

To find the inverse Laplace transform of ℒ−1 8s − 16 (s2 s)(s2 1), we can first simplify the expression:

\(8s - 16 (s^2 + 1)(s^2 + s)= 8s - 16 (s^4 + s^3 + s^2 + s)= -16s^4 - 16s^3 + 8s^2 - 16s\)

We can then use partial fraction decomposition to write this expression as a sum of simpler fractions:

\(-16s^4 - 16s^3 + 8s^2 - 16s = (-4s^2 + 4s - 4)/(s + 1) + (-4s^2 - 8s)/(s^2 + 1) + (-4s)/(s^2 + 1)\)

To find the inverse Laplace transform of each term, we can use theorem

\(L^-1 (-4s^2 + 4s - 4)/(s + 1) = -4L^-1 (s + 1) + 4ℒ^-1 1 = -4(e^-t - 1)\\L^-1 (-4s^2 - 8s)/(s^2 + 1) = -4L^-1 (s + 2i)/(s^2 + 1) = -4e^(-t) sin(t)\\ℒ^-1 (-4s)/(s^2 + 1) = -4ℒ^-1 (s/(s^2 + 1)) = -4cos(t)\)
Therefore, the inverse Laplace transform of ℒ^-1 8s - 16 (s^2 + s)(s^2 + 1) is:

\(-4(e^-t - 1) - 4e^(-t) sin(t) - 4cos(t)\)

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a. The function of a post-test in ANOVA is to determine if any statistically significant group differences have occurred.

After conducting an ANOVA, if the F test indicates that there is a significant difference between groups, a post-hoc test (also known as a post-test) can be conducted to determine which specific groups differ significantly from each other. The post-test helps to identify the groups that are driving the significant difference found in the ANOVA, and provides additional information beyond just the overall significance of the F test.

Different types of post-tests can be used, depending on the nature of the research question and the design of the study. Examples of post-tests include Tukey's Honestly Significant Difference (HSD), Bonferroni correction, and Scheffe's test. The goal of a post-test is to control the familywise error rate (the probability of making at least one type I error across all the comparisons) while maintaining statistical power.

Therefore, the correct option is a. Determine if any statistically significant group differences have occurred. Option b is partially correct, as post-tests do describe the groups that have reliable differences between group means, but the main function is to determine if these differences are statistically significant. Option c is incorrect, as the critical value for the F test (or chi-square) is set during the ANOVA test, not the post-test.

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The distribution function of M, FM(-), is given by FM(x) = x, 0 ≤ x ≤ 1.

The probability density function of M is\(fM(x) = n * x^(^n^-^1^)\), 0 ≤ x ≤ 1.

In order to understand the distribution function of M, we need to consider the probability that M is less than or equal to a given value x. Since each Xi is uniformly distributed over (0,1), the probability that Xi is less than or equal to x is x.

For M to be less than or equal to x, all of the random variables Xi must be less than or equal to x. Since these variables are independent, their joint probability is the product of their individual probabilities. Therefore, the probability that M is less than or equal to x can be expressed as the product of n x's: P(M ≤ x) = x * x * ... * x = \(x^n\).

The distribution function FM(x) is defined as the probability that M is less than or equal to x. Therefore, FM(x) = P(M ≤ x) = \(x^n\).

To find the probability density function (PDF) of M, we differentiate the distribution function FM(x) with respect to x. Taking the derivative of \(x^n\)with respect to x gives us \(n * x^(^n^-^1^)\). Since the range of M is (0,1), the PDF is defined only within this range.

The distribution function of M is FM(x) = x, 0 ≤ x ≤ 1, and the probability density function of M is \(fM(x) = n * x^(^n^-^1^)\), 0 ≤ x ≤ 1.

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The first derivative of G(r) is (3/2).
The second derivative of G(r) is (-3/4)/√(r³).

To find the first derivative of G(r), we use the power rule of differentiation:

G'(r) = (1/2)r(-1/2) + 5(1/2)r(-1/2)

Simplifying, we get:

G'(r) = (1/2)(1 + 5)√(r)/√(r)

G'(r) = (3/2)√(r)/√(r)

G'(r) = (3/2)

To find the second derivative, we differentiate G'(r) using the power rule again:

G''(r) = (-1/4)r(-3/2) + 5(-1/4)r(-3/2)

Simplifying, we get:

G''(r) = (-3/4)r(-3/2)

G''(r) = (-3/4)/√(r^3)

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Answer:

\(6\pi\), 6pi

Step-by-step explanation:

The area of the full circle would be \(\pi *4^{2}\), which is \(16\pi\)

A full circle is 360 degrees. Since we are only taking a part of that, 135, we would put it in a fraction. \(\frac{135}{360}\)

Last, multiply 16pi and 135/360 since we are taking a part of 16pi.

\(16\pi *\frac{135}{360}\)

\(\frac{2160\pi}{360}\)

\(6\pi\)

Answer:

Step-by-step explanation:

Dont do it. Just take the detention

If the sample is not truly representative, the conclusion may not accurately reflect the actual average age of all the students at the college.

Based on the given information, it can be concluded that the average age of all the students at City College is likely around 20. However, it's important to note that this conclusion is only valid if the sample of 90 students is representative of the entire student population at City College. If the sample is not truly representative, the conclusion may not accurately reflect the actual average age of all the students at the college.

The average age in a sample of 90 students at City College is 20. However, based on this sample alone, it cannot be conclusively determined that the average age of all the students at City College is also 20. This is because the sample may not be fully representative of the entire student population. More information or a larger sample would be needed to make a more accurate conclusion about the average age of all students at City College.

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If the sample of 90 students is representative of the entire student population at City College, then we can conclude that the average age of all students is approximately 20 years old.

Based on the given information, the average age in a sample of 90 students at City College is 20.

To determine if this sample can be used to conclude the average age of all students at City College, we need to consider these terms:
Sample:

A subset of a population, which in this case is the group of 90 students at City College.
Population:

The entire group of students at City College that we want to make a conclusion about.
Average (Mean) Age:

The sum of ages divided by the total number of students, in this case, 20 years.
Representativeness:

How well the sample reflects the characteristics of the entire population.
If the sample of 90 students is representative of the entire student population at City College, then we can conclude that the average age of all students is approximately 20 years old.

However, if the sample is not representative, the conclusion may not be accurate.

To make a more accurate conclusion, it is important to ensure that the sample is representative by using a larger sample size or random sampling methods.

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Step-by-step explanation:

Área of a circle is given as

\(\pi \times {r}^{2} \)

Therefore you can substitute the values as follows:

\(3.14 \times {6}^{2} = 113.09733552923\)

Answer not rounded to any decimal place and used of 3.14 as said in the instruction

The area is:

Explanation:

To find the circle's area, use the formula \(\sf{A=\pi r^2}\).

where:

A = area;

π = 3.14 (pi);

r = radius

Diagram:

\(\setlength{\unitlength}{1cm}\begin{picture}(0,0)\thicklines\qbezier(2.3,0)(2.121,2.121)(0,2.3)\qbezier(-2.3,0)(-2.121,2.121)(0,2.3)\qbezier(-2.3,0)(-2.121,-2.121)(0,-2.3)\qbezier(2.3,0)(2.121,-2.121)(-0,-2.3)\put(0,0){\line(1,0){2.3}}\put(0.5,0.3){\bf\large 6\ in}\end{picture}\)

Plug in the data:

\(\sf{A=3.14\times6^2}\)

\(\sf{A=3.14\times36}\)

\(\sf{A=113.04\:in^2}\)

The centroidal moments of inertia can be calculated by determining the moments of inertia for each component and applying the parallel axis theorem.



To determine the centroidal moments of inertia for the given built-up steel beam, we need to calculate the individual moments of inertia for each component and then use the parallel axis theorem to find the total centroidal moments of inertia.

First, we calculate the moment of inertia for the W18x97 wide flange beam using its properties. The moment of inertia for a wide flange beam can be found in engineering handbooks or online databases.Next, we calculate the moment of inertia for the vertical plate. Since it is centered on the web of the wide flange, its centroid coincides with the centroid of the wide flange.Similarly, we calculate the moment of inertia for the horizontal plate. Since it is also centered on the web, its centroid coincides with the centroid of the wide flange.

Finally, we use the parallel axis theorem to find the total centroidal moments of inertia. The parallel axis theorem states that the moment of inertia about any axis parallel to an axis through the centroid is equal to the sum of the moment of inertia about the centroidal axis and the product of the area and the square of the distance between the two axes.In this case, the total centroidal moments of inertia will be the sum of the moment of inertiainertia of the wide flange beam, the vertical plate, and the horizontal plate.

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Answer:

y = - \(\frac{5}{2}\) x - 2

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

with (x₁, y₁ ) = (- 2, 3) and (x₂, y₂ ) = (0, - 2) ← 2 points on the line

m = \(\frac{-2-3}{0-(-2)}\) = \(\frac{-5}{0+2}\) = - \(\frac{5}{2}\)

the line crosses the y- axis at (0, - 2 ) ⇒ c = - 2

y = - \(\frac{5}{2}\) x - 2 ← equation of line

Answer: 19.8x - 11.1y

Step-by-step explanation: you’re welcome:)

Again lol

Answer:

C) 99 + 3x

Step-by-step explanation:

Since it's always going to cost 99, it'll stay like that since it's a constant

Since it's 3 PER person, that means 3 will have a variable: 3x

Using the t-distribution, it is found that the data does not provide convincing evidence that the mean number is greater when the coupons were addressed to a female.

At the null hypothesis, it is tested if there is no difference, that is, the mean is of 0, hence:

\(H_0: \mu = 0\)

At the alternative hypothesis, it is tested if the mean number is greater for females, that is, the mean is greater than 0, hence:

\(H_1: \mu > 0\)

The test statistic is given by:

\(t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}\)

The parameters are:

In this problem, the parameters are given as follows:

\(\overline{x} = 1.5, \mu = 0, s = 4.75, n = 50\).

Hence, the test statistic is given by:

\(t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}\)

\(t = \frac{1.5 - 0}{\frac{4.75}{\sqrt{50}}}\)

t = 2.23

Considering a right-tailed test, as we are testing if the mean is greater than a value, with a significance level of 0.01 and 50 - 1 = 49 df, the critical value is given by \(t^{\ast} = 2.4\).

Since the test statistic is less than the critical value for the right-tailed test, the data does not provide convincing evidence that the mean number is greater when the coupons were addressed to a female.

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The dot plot represents the number of experiments ranging from 5 to 30 in increments of 5. The data set shows a distribution with the following dot counts: 1 dot for 5, 5 dots for 10, 3 dots for 15, 2 dots for 20, 3 dots for 25, and 6 dots for 30. To determine the center and spread of the data, we find that the center is located between 15 and 20, and the spread ranges from 5 to 30.

In the dot plot, the center of the data set can be estimated by identifying the middle value or values. As there are 20 data points in total, the median will fall between the 10th and 11th values when arranged in ascending order. Considering the dot counts for each value, we find that the 10th value (15) has 3 dots and the 11th value (20) has 2 dots. Therefore, the center lies between these two values. Since the increment is 5, we can conclude that the center is between 15 and 20.

Regarding the spread of the data, it refers to the range of values covered by the data set. In this case, the range is determined by the smallest and largest values. The smallest value is 5 (represented by 1 dot), and the largest value is 30 (represented by 6 dots). Hence, the spread of the data spans from 5 to 30.

To summarize, the center of the data set lies between 15 and 20, while the spread of the data ranges from 5 to 30.

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The question is incomplete, so this is a general answer

The solution is : the probability, to the nearest 10th of a percent, that both marbles drawn will be green will be 0.053.

Here, we have,

n(r) = 7

n(b) = 8

n ( g) = 5

Total number of marbles = 20

The probability that both marbles drawn will be green will be

The probability of the first being green = 5/20 and the probability that the second marble is green = 4/19.

We will multiply the two together , we have

5/20 x 4/19

= 20/380

= 0.05263157895

Therefore : the probability, to the nearest 10th of a percent, that both marbles drawn will be green will be 0.053

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Answer:

21

Step-by-step explanation:

1/2*30+6 = 15+6 = 21

Hope I helped

Therefore, Guy would be willing to pay approximately $5,989.00 today for this investment based on the expected cash flows and the interest rate. The correct option is C) $5,989.00.

The formula for present value of a series of cash flows is given by:

\(PV = C1/(1+r)^1 + C2/(1+r)^2 + C3/(1+r)^3 + ... + Cn/(1+r)^n\)

Where:

PV is the present value,

C1, C2, C3, ..., Cn are the cash flows at different time periods,

r is the interest rate, and

n is the number of time periods.

In this case, the cash flows are $2,000, $1,500, $3,000, and $400, occurring at the end of year 1, year 2, year 3, and year 4, respectively. The interest rate (r) is 6%.

Substituting these values into the formula, we have:

\(PV = 2,000/(1+0.06)^1 + 1,500/(1+0.06)^2 + 3,000/(1+0.06)^3 + 400/(1+0.06)^4\)

Simplifying the expression:

\(PV ≈ 2,000/1.06 + 1,500/1.06^2 + 3,000/1.06^3 + 400/1.06^4\)

Using a calculator, we find that PV ≈ $5,989.00.

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Answer:

Area = 370 m²

Cost to paint = £105

Step-by-step explanation:

Area of the wall of a cinema hall = Area of a trapezoid (1)+ Area of a rectangle (2) + Area of a trapezoid (3)

Area of a trapezoid = \(\frac{1}{2}(b_1+b_2)h\)

where \(b_1\) and \(b_2\) are the parallel sides and h is the distance between these sides.

Area of trapezoid (1) = \(\frac{1}{2}(11+12)\times 6\)

                                  = 69 m²

Area of the rectangle (2) = Length × Width

                                         = 12 × 15

                                         = 180 m²

Area of the trapezoid (3) = \(\frac{1}{2}(12+10)\times 11\)

                                         = 121 m²

Now area of the wall = 69 + 180 + 121

                                   = 370 m²

One tin covers the area = 25 m²

Number of tins required to paint the wall = \(\frac{\text{Total area}}{\text{Area covered by one tin}}\)

= \(\frac{370}{25}\)

= 14.8

Therefore, number of tins to be purchased = 15

Cost to paint the complete wall = 15 × £7

                                                       = £105

Answer:

the answer to this question is 2 1/3x - 2 2/3

Step-by-step explanation:

i know this is correct because i took the k12 test also im sorry its a day late but i hope this helps you out! good luck

Answer:

2 1/3x - 2 2/3

Step-by-step explanation: