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Both √203 and √96 are irrational numbers since the numbers inside the roots are not perfect squares.

To determine whether a root is rational or irrational, we need to know if the number inside the square root is a perfect square or not. If it is not, then the root is irrational.

For √203, we can determine that 203 is not a perfect square, since the last digit is 3, which is not a perfect square. Therefore, √203 is an irrational number.

For √96, we can simplify the expression as follows:

√96 = √(16*6) = √16 * √6 = 4√6

Since 6 is not a perfect square, 4√6 is an irrational number.

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The solutions to the system of nonlinear equations are

x = 9 and x =[tex]3^2[/tex]= 9.

To determine the solution to the system of nonlinear equations:

f(x) = g(x)

We can substitute the given expressions for f(x) and g(x) and simplify:

log3(x) + 3 =[tex]log3(x^3) - 1[/tex]

Using the properties of logarithms, we can simplify this equation as follows:

log3(x) + 3 = 3*log3(x) - 1

4 = 2*log3(x)

2 = log3(x)

x =[tex]3^2[/tex]

Therefore, the solutions to the system of nonlinear equations are x = 9 and [tex]x = 3^2 = 9.[/tex]

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There would be 14 stars that this equation predicts Ayana will have at the end of level 10.

In this question, we are given an equation for the line of best fit relating the level, x, to the number of stars, y. The equation is y = (3/2)x - 1.

To find the predicted number of stars at the end of level 10, we need to substitute x = 10 into the equation and solve for y.

y = (3/2)x - 1

y = (3/2)(10) - 1

y = 15 - 1

y = 14

Therefore, the equation predicts that Ayana will have 14 stars at the end of level 10.

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The mathematical phrase 5 + 2 × 18 is an example of an arithmetic expression.

To solve this expression, follow the order of operations (PEMDAS/BODMAS):

1. Parentheses/Brackets (P/B)
2. Exponents/Orders (E/O)
3. Multiplication and Division (M/D)
4. Addition and Subtraction (A/S)

Your expression: 5 + 2 × 18

Step 1: No parentheses/brackets to solve.

Step 2: No exponents/orders to solve.

Step 3: Solve multiplication: 2 × 18 = 36

Step 4: Solve addition: 5 + 36 = 41

So, the value of the expression 5 + 2 × 18 is 41.

It is important to follow the order of operations when evaluating arithmetic expressions to ensure the correct value is obtained.

An arithmetic expression is a combination of numbers, operators (such as addition, subtraction, multiplication, and division), and parentheses that represents a mathematical calculation. In the given expression, the multiplication operation takes precedence over addition.

According to the order of operations (PEMDAS/BODMAS), multiplication is performed before addition. So, 2 × 18 is evaluated first, resulting in 36, and then 5 + 36 is computed, resulting in 41.

Therefore, the value of the expression is 41. Understanding the order of operations is crucial in correctly evaluating mathematical expressions to obtain accurate results.

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Answer:

Least Common Multiple (LCM) of 28,42,63 is 252 ∴ So the LCM of the given numbers is 2 x 3 x 7 x 2 x 1 x 3 = 252

Step-by-step explanation:

Answer:

252 is the answer

Step-by-step explanation:

find the multiples of all of them ( and make sure it is the least. )

28:

28, 56, 84, 112, 140, 168, 196, 224, 252, 280, 308

42:

42, 84, 126, 168, 210, 252, 294, 336

63:

63, 126, 189, 252, 315, 378

bolded + undurlined is the answer

you see that 252 is the answer

252 is the answer

Meena would have to pay a total of $57 for her family if she were to buy 3 snacks for everybody to share.

Meena would have to pay a total of $42 + 5xx for her family if she bought xx snacks for everybody to share.

To calculate the total money Meena would have to pay for her family, including movie tickets and snacks, we'll first look at the scenario with 3 snacks to share.

1. Calculate the cost of movie tickets: Meena + 2 kids = 3 tickets at $14 each.
  3 tickets * $14 = $42

2. Calculate the cost of 3 snacks at $5 each.
  3 snacks * $5 = $15

3. Add the cost of movie tickets and snacks.
  $42 + $15 = $57

Meena would have to pay a total of $57 for her family if she were to buy 3 snacks for everybody to share.

For the scenario where she buys xx snacks:

1. Calculate the cost of movie tickets (same as before):
  3 tickets * $14 = $42

2. Calculate the cost of xx snacks at $5 each.
  xx snacks * $5 = 5xx

3. Add the cost of movie tickets and snacks.
  $42 + 5xx = $42 + 5xx

Meena would have to pay a total of $42 + 5xx for her family if she bought xx snacks for everybody to share.

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The amount of popcorn the bigger box holds than the smaller box depends on the dimensions of the two containers, so it cannot be determined without additional information.

The difference in the amount of popcorn the two containers hold depends on the volume of each container. Let's assume the volume of Amanda's popcorn container is V1 and the volume of Mary's popcorn container is V2.

If we know the dimensions of both containers, we can calculate their volumes using the formula V = l × w × h, where l is the length, w is the width, and h is the height of the container. Then, we can find the difference in the volumes of the two containers by subtracting V1 from V2.

However, the question does not provide any information about the dimensions of the two containers, so we cannot determine the difference in their volumes. Therefore, the main answer is that the amount of popcorn the bigger box holds than the smaller box cannot be determined without additional information.

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Answer:

[tex]32 \div 4 = 8[/tex]

Answer: 32 divided by 4 =8

Step-by-step explanation:

Answer:

8.81

Step-by-step explanation:

Substitute x for 7 and then solve normally

{2(7)^2+7-8}/(7)+4

{(2x49)+7-8}/11

98+7-8/11

97/11

8.81

The area of the path surrounding a rectangular garden is 105 square feet

The area of path will be given by the relation -

Area of path = Outer area - inner area

Inner area = 20 × 12

Multiply the values

Inner area = 240 square feet

Outer area = (20 + 3) × (12 + 3)

Add the values inside parenthesis

Outer area = 23 × 15

Perform multiplication on Right Hand Side of the equation

Outer area = 345 square feet

Area of path = 345 - 240

Subtract the values

Area of path = 105 square feet

Hence, the area of rectangular path is 105 square feet.

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Maryam answered 26 questions correctly and got 4 questions wrong on the test with 30 questions.

To find how many questions Maryam got wrong, we need to first determine how many questions she got right. Since she scored 86.7%, we can multiply the total number of questions by the percentage to get the number of questions she answered correctly.

86.7% of 30 questions is (86.7/100) * 30 = 26.01 questions.

Since Maryam cannot have answered a fractional number of questions correctly, we round down to the nearest whole number. Thus, she answered 26 questions correctly.

To find out how many questions she got wrong, we can simply subtract the number of questions she got right from the total number of questions. Therefore, Maryam got 30 - 26 = 4 questions wrong.

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Answer:

Step-by-step explanation:

Since the length of the actual racecar is 19 feet, and the length of the model is represented by x, we can set up the following proportion:

Length (model) / Length (actual) = Width (model) / Width (actual)

This can be written as:

x / 19 ft = 1.4 in / 7 ft

To solve for x, we can cross-multiply and simplify:

x * 7 ft = 19 ft * 1.4 in

x = (19 ft * 1.4 in) / 7 ft

x = 3.8 in

Therefore, the length of the model is 3.8 inches.

To explain this solution in more detail, we can use proportionality concepts and unit conversions. The proportion relates the length and width of the actual racecar to the length and width of the model.

We set up the proportion with the length of the model as the unknown (x) and solve for it by cross-multiplying and simplifying. Since the width of the model and actual racecar are given in different units, we convert the width of the model from inches to feet before using the proportion.

The final answer is expressed in inches, which is the same unit as the width of the model.

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A triangular prism is a three-dimensional shape with two parallel triangular bases and three rectangular faces. In this case, the triangular bases have sides of 4 cm, 5 cm, and 5 cm, while the rectangular faces have a length of 10 cm and a height of 6 cm.

To find the volume of the prism, we can use the formula V = Bh, where B is the area of the base and h is the height. The area of a triangle can be found using the formula A = 1/2bh, where b is the base and h is the height.

So, for the triangular base of this prism, we have:

A = 1/2(4 cm)(3 cm) = 6 cm²

The height of the prism is 5 cm, so:

V = Bh = (6 cm²)(5 cm) = 30 cm³

Therefore, the volume of the prism is 30 cubic centimeters.

To find the surface area of the prism, we need to calculate the area of each face and add them up.

The two triangular faces each have an area of:

A = 1/2(4 cm)(5 cm) = 10 cm²

And the three rectangular faces each have an area of:

A = (10 cm)(6 cm) = 60 cm²

So, the total surface area is:

SA = 2(10 cm²) + 3(60 cm²) = 200 cm²

Therefore, the surface area of the prism is 200 square centimeters.

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Answer:

m= month 12k - 3500= 950 she needs to save for 2 in a half months to get her car

Step-by-step explanation:

The total of oranges left by the taylor is about 10 3/4 pounds

To solve this problem, we will start by using adding the weights of the navel oranges and temple oranges to discover the total weight of oranges Taylor has, that's:

Next, we are able to subtract the weight of the navel oranges she uses from the total weight of navel oranges to discover how a lot she has left, which is:

In the end, we can add the weight of the navel oranges left to the weight of the temple oranges to find the overall weight of oranges Taylor has left, which is:

Therefore, the total of oranges left by the taylor is about 10 3/4 pounds

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The equation of the dilated line in slope-intercept form is:
y' = 3x' - 3

To find the equation of the dilated line in slope-intercept form, we'll follow these steps:

1. Convert the original equation into slope-intercept form (y = mx + b).
2. Find the coordinates of the point after dilation.
3. Use the slope from the original equation and the new point to find the new equation.

Step 1: Convert the original equation into slope-intercept form:
15 + y = 3x
y = 3x - 15

Step 2: Find the coordinates of the point after dilation:
Dilation formula: (x', y') = (a(x - h) + h, a(y - k) + k)
Given point (h, k) = (3, -6) and scale factor a = 3

x' = 3(x - 3) + 3
y' = 3(y + 6) - 6

Step 3: Use the slope from the original equation (m = 3) and the new point (x', y') to find the new equation:
y' = 3x' + b

Substitute the expressions for x' and y' from step 2:
3(y + 6) - 6 = 3(3(x - 3) + 3) + b

Simplify the equation and solve for b:
3y + 18 - 6 = 9x - 27 + 9 + b
3y + 12 = 9x - 18 + b

Now, substitute the original point (3, -6) into the equation to find b:
-6 + 12 = 9(3) - 18 + b
6 = 27 - 18 + b
6 = 9 + b

b = -3

The equation of the dilated line in slope-intercept form is:
y' = 3x' - 3

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The length of BC is  5.25 units. when the rectangle has vertices located at the points: B is ( 2 2/3,3 1/2) and C is (2 2/3,-1 3/4).

We need to find the length of BC. The length of a line segment BC can be calculated using the distance formula. The formula to find the distance between two points (x1, y1) and (x2, y2) is given as :

d = √(x2−x1)²+(y2−y1)²

Given data:

A = (-1 1/4,3 1/2)

B = ( 2 2/3,3 1/2)

C = (2 2/3,-1 3/4)

D = (-1 1/4,-1 3/4)

We need to Convert the B and C mixed numbers to improper fractions, we get,

B = (2+2/3), (3 + 1/2)

= (8/3, 7/2)

C = (2+2/3) , (-1 + 3/4)

= (8/3, -7/4).

Substituting the B and C values into the distance formula, we get:

= √(8/3 − 8/3)² + ( −7/4 − 7/2 )²

​= √0 + ( − 21 / 4 )²

= √441/16​

[tex]= 21/4[/tex]

[tex]= 5.25[/tex]

Therefore, the length of BC is 5.25 units.

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The ∠BAE ≅ ∠DCF by SAS congruence of triangles. The solution has been obtained by using the congruence of triangles.

What is congruence of triangles?

If all three corresponding sides and all three corresponding angles of two triangles have the same size, the triangles are said to be congruent. These triangles can be moved, flipped, twisted, and turned to achieve the same result. They are parallel to one another when moved.

We are given the following:

AB ≅ CD

AD || BC

BG ≅ HD

∠CGE ≅ ∠AHF

AE ≅ FC

Now,

EF ≅ EF as it is the common side

Since, AD || BC so,

∠BCA ≅ ∠CAD as they are alternate interior angles

From this we get that triangle BAC ≅ triangle ACD.

So, the ∠BAE ≅ ∠DCF.

Hence, the ∠BAE ≅ ∠DCF by SAS congruence of triangles.

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The coordinates of the translated triangle A'B'C' are: A'(-1, -1), B'(4, 0), and C'(0, -2).

To find the coordinates of the vertices of the translated figure, we simply apply the given translation rule to each vertex of the original triangle.

For vertex A(-3, 3):
(x, y) --> (x+2, y-4)
(-3, 3) --> (-3+2, 3-4)
(-1, -1)

So, the translated coordinates of vertex A are (-1, -1).

For vertex B(2, 4):
(x, y) --> (x+2, y-4)
(2, 4) --> (2+2, 4-4)
(4, 0)

So, the translated coordinates of vertex B are (4, 0).

For vertex C(-2, 2):
(x, y) --> (x+2, y-4)
(-2, 2) --> (-2+2, 2-4)
(0, -2)

So, the translated coordinates of vertex C are (0, -2).

Therefore, the vertices of the translated triangle are A'(-1, -1), B'(4, 0), and C'(0, -2).

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The correct statement regarding the solution to the system of equations is given as follows:

There is one unique solution (−5, 9).

The slope-intercept representation of a linear function is given by the equation shown as follows:

y = mx + b

The coefficients m and b have the meaning presented as follows:

For the first line, the points are given as follows:

(-10, 10) and (0,8).

Hence the equation is:

y = -0.2x + 8.

For the second line, the points are given as follows:

(-8, 12) and (0,4).

Hence the equation is:

y = -x + 4.

Then the x-coordinate of the solution is obtained as follows:

-0.2x + 8 = -x + 4

0.8x = -4

x = -5.

The y-coordinate is given as follows:

y = -(-5) + 4 = 9.

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The exponential function that models the total population p after t years is p = 3,500 x 1.025^t.

To write an exponential function that models the total population of the town after t years, we need to use the formula:

p = p0 x  (1 + r)^t

where p0 is the initial population, r is the annual growth rate as a decimal (so in this case, 2.5% = 0.025), and t is the number of years.

In this case, we know that the initial population is 3,500, and the annual growth rate is 2.5%, or 0.025. So we can substitute these values into the formula to get:

p = 3,500 x (1 + 0.025)^t

Simplifying this expression gives:

p = 3,500 x 1.025^t

So the exponential function that models the total population p after t years is:

p(t) = 3,500 x 1.025^t

Note that the function is exponential because the population grows at a constant percentage rate each year, which means that the growth itself is increasing over time.

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The art studio can offer a maximum of 8 painting classes and 5 pottery classes per week, while still meeting the time constraint and earning at least $1000 per week.

To find the maximum number of classes the art studio can offer per week, we need to set up an equation based on the time constraint.

Let's assume that the studio offers x painting classes and y pottery classes per week. Since each painting class is 1 hour long and each pottery class is 1.5 hours long, the total time spent on classes can be represented by the equation:

1x + 1.5y ≤ 40

This equation states that the total number of hours spent on painting classes (1x) plus the total number of hours spent on pottery classes (1.5y) must be less than or equal to 40 hours per week.

To find the minimum revenue the art studio can earn per week, we can set up another equation based on the cost of each class and the minimum revenue requirement.

Let's assume that each painting or pottery class costs $35. Then the total revenue earned per week can be represented by the equation:

35x + 35y ≥ 1000

This equation states that the total revenue earned from painting classes (35x) plus the total revenue earned from pottery classes (35y) must be greater than or equal to $1000 per week.

Now we have two equations:

1x + 1.5y ≤ 40

35x + 35y ≥ 1000

We can use these equations to find the maximum number of classes the art studio can offer per week.

To do this, we can graph the two equations on the same coordinate plane and find the point where they intersect.

When we do this, we get the point (x, y) = (8, 16/3).

This means that the art studio can offer a maximum of 8 painting classes and 16/3 (or approximately 5.33) pottery classes per week, while still meeting the time constraint and earning at least $1000 per week.

Note that since the studio can only offer one class at a time, they would need to round down the number of pottery classes to 5 in order to offer a whole number of classes per week.

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The difference (pre-debate minus post-debate) in the sample proportions of likely voters who said they would vote for this candidate was approximately 0.025.

We are given a confidence interval of (-0.014, 0.064) for the true difference in proportions of likely voters who would vote for the political candidate before and after the debate. This means that we can be 95% confident that the true difference in proportions falls within this interval.

To find the difference in sample proportions, we need to subtract the pre-debate proportion from the post-debate proportion. Let's call the pre-debate proportion "p1" and the post-debate proportion "p2".

We are not given the sample proportions directly, but we can use the midpoint of the confidence interval as an estimate for the true difference in proportions. The midpoint is (-0.014 + 0.064)/2 = 0.025.

So, we can estimate the difference in sample proportions as:

p2 - p1 = 0.025

This means that the post-debate proportion was 0.025 higher than the pre-debate proportion, on average. Note that we don't know the actual values of p1 and p2, just their difference.

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a4 = 2

It is given that,

[tex]a_{1} = 5[/tex], and

[tex]a_{n} = (a_{n-1}) - 1[/tex]

Therefore, it can be said,

[tex]a_{2} = a_{1} - 1\\a_{3} = a_{2} - 1\\a_{4} = a_{3} - 1\\[/tex]

That is,

[tex]a_{2} = 5-1=4\\a_{3} = 4-1=3\\a_{4} = 3-1=2[/tex]

So, a4 = 2

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False because the statement "a 95 percent confidence interval estimate will have a margin of error.

A 95% confidence interval (CI) estimate is a range of values that is likely to contain the true population mean with 95% confidence. The margin of error for a confidence interval depends on the sample size, the variability of the data, and the desired level of confidence.

The general formula for the margin of error of a 95% confidence interval for the population mean is:

Margin of error = (z-value) x (standard deviation /√n)

where z-value is the number of standard deviations corresponding to the desired level of confidence (for a 95% CI, this value is 1.96), standard deviation is the standard deviation of the sample data, and n is the sample size.

The margin of error is usually expressed as a percentage of the sample mean, not the population mean. Moreover, the percentage of the margin of error is not fixed, but it varies depending on the data and the sample size.

Therefore, the statement "a 95 percent confidence interval estimate will have a margin of error that is approximately + or - 47.5 percent of the size of the population mean" is not correct.

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The inverse functions:

f'(2) = 4.

[tex]f^{-1}(x)[/tex] = sqrt(x - 4).

f'(s1(x)) = sqrt(x - 4).

(a) To find f'(2), we need to take the derivative of f(x) with respect to x and then substitute x = 2.
[tex]f(x) = x^2 + 4[/tex]
f'(x) = 2x
f'(2) = 2(2) = 4
Therefore, f'(2) = 4.
(b) To find the inverse function [tex]f^{-1}(x)[/tex], we need to first solve for x in terms of f(x) and then switch the roles of x and f(x).
[tex]f(x) = x^2 + 4[/tex]
[tex]x^2[/tex] = f(x) - 4
x = sqrt(f(x) - 4)
Switching x and f(x), we get:
[tex]f^{-1}(x)[/tex] = sqrt(x - 4)
Therefore, the inverse function is [tex]f^{-1}(x)[/tex] = sqrt(x - 4).
(c) To find the compound function f'(s1(x)),

we need to first find s1(x) and then take the derivative of f(x) with respect to s1(x) and then multiply by the derivative of s1(x) with respect to x.
s1(x) = sqrt(x - 4)
f(s1(x)) = (sqrt(x - 4)[tex])^2[/tex] + 4 = x
Taking the derivative of f(x) with respect to s1(x), we get:
f'(s1(x)) = 2s1(x)
Taking the derivative of s1(x) with respect to x, we get:
s1'(x) = 1/(2sqrt(x - 4))
Multiplying these two derivatives, we get:
f'(s1(x))s1'(x) = 2s1(x) * 1/(2sqrt(x - 4))
f'(s1(x))s1'(x) = sqrt(x - 4)
Therefore, the compound function is f'(s1(x)) = sqrt(x - 4).
(d) The given expression "derivative mets-() de 1-12" does not make sense and seems incomplete. Please provide more information or context so that I can help you with this part of the question.

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To find the coordinates of point B, we can use the section formula which states that the coordinates of the point that divides a segment with endpoints (x1, y1) and (x2, y2) in the ratio of m:n are given by:

((mx2 + nx1)/(m+n), (my2 + ny1)/(m+n))

The coordinates of point B are (4.25, 8.25), and the answer is (D).

Here, A (2, 6) and C (5, 9) are the endpoints of the segment, and we want to partition the segment in the ratio of 3:1. So, we have:

m:n = 3:1

m+n = 4

Solving for m and n, we get:

m = 3, n = 1

Now, substituting  values in the section formula, we get:

((35 + 12)/(3+1), (39 + 16)/(3+1)) = (4.25, 8.25)

Therefore, the coordinates of point B are (4.25, 8.25), and the answer is (D).

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Answer:

(4.25, 8.25)

Step-by-step explanation:

i took the quiz

f'(x) = -36/x²,  f'(-3) = -4,  f'(0) = Undefined , f'(6) = -1/6

The average rate of change of profit as x changes from 4-6 is 17.

Using the definition of the​ derivative, find f'(x). Then find f'(-3), f'(0), and f'(6) when the derivative exists. Given f(x) = 36/x. We need to find the derivative of f(x) to solve the problem.

To find the derivative of f(x), we use the quotient rule of differentiation.

(d/dx) (u/v) = [(v × du/dx) - (u × dv/dx)] / v²

The derivative of f(x) using the quotient rule is:

(d/dx)(36/x) = [(x × d/dx (36)) - (36 × d/dx(x))]/(x²)= [-36/x²]

So, f'(x) = -36/x²

Then we can find f'(-3), f'(0), and f'(6) when the derivative exists.

We know f'(x) exists if x ≠ 0.So, f'(-3) = -36/(-3)²= -4 f'(0) = Undefined (since x = 0) f'(6) = -36/6²= -1/6

Suppose that the total profit in hundreds of dollars from selling x items is given by P(x) = 2x² - 5x + 7. We need to find the average rate of change of profit as x changes from 4-6. We know that the average rate of change of a function f(x) over the interval [a, b] is: (f(b) - f(a)) / (b - a)Here, P(x) = 2x² - 5x + 7, a = 4, and b = 6.

So, the average rate of change of profit as x changes from 4-6 is:(P(6) - P(4)) / (6 - 4)=(2(6)² - 5(6) + 7 - 2(4)² + 5(4) - 7) / (6 - 4)= (72 - 30 - 8) / 2= 17

The average rate of change of profit as x changes from 4-6 is 17.

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The required height of the trapezoid is 4 ft.

In geometry, a quadrilateral with at least one pair of parallel sides is referred to as a trapezoid in American, Canadian, and British English. In Euclidean geometry, a trapezoid is inevitably a convex quadrilateral. The trapezoid's parallel sides are referred to as its bases.

Given data;

a= 3 ft, b = 7 ft, height = h, Area = 20 sq, ft

So,

Area = (a + b)h/2

20 = (3 + 7)h/2

20 = 10h/2

2 = h/2

h = 4 ft

Thus, required height of the trapezoid is 4 ft.

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The angle measures 43 degrees and its supplementary angle measures 180 - 43 = 137 degrees.

In geometry, the supplementary angle of an angle is the angle that, when added to the given angle, results in a sum of 180 degrees. In other words, two angles are supplementary if their sum is 180 degrees.

For example, if an angle measures 60 degrees, its supplementary angle would measure 120 degrees, since 60 degrees + 120 degrees = 180 degrees.

Let x be the measure of the angle in degrees.

By definition, the supplementary angle of x measures 180 - x degrees.

We are given that the angle measures 94 degrees less than its supplementary angle, so we can write:

x = (180 - x) - 94

Simplifying and solving for x, we get:

2x = 180 - 94

2x = 86

x = 43

Therefore, the angle measures 43 degrees and its supplementary angle measures 180 - 43 = 137 degrees.

To know more about supplementary angles visit:

brainly.com/question/18164299

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