Figure ABCD is reflected across the x-axis.

What are the coordinates of A' , B' , C' , and D'

The value of the angle U in the triangle is 92.10 degrees.

The angle U in the triangle can be found using cosine rule as follows:

Let's use cosine formula to find the angle U

c² = a² + b² - 2ab cos C

Hence,

Therefore,

a = 58.8

b = 38.4

c = 71.4

Hence,

71.4²  = 58.8² +  38.4² - 2(58.8)(38.4) cos U

5097.96 = 3457.44 + 1474.56 - 4515.84 cos U

5097.96 - 4932 =  - 4515.84 cos U

165.96 = - 4515.84 cos U

divide both sides by - 4515.84

cos U = 165.96 / - 4515.84

cos U = - 0.03675063775

U = cos⁻¹ - 0.03675063775

U = 92.1032274244

Therefore,

U = 92.10 degrees

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to find 7/8 of 3.5, we multiplied 7/8 and 3.5 together to get 49/16, which we then converted to a mixed number in the simplest form, giving us the answer of 3 1/16.

To find 7/8 of 3.5, we can simply multiply 7/8 and 3.5 together.

7/8 x 3.5 = (7/8) x (7/2) = 49/16

So, the answer is 49/16. However, we need to write the answer as a mixed number in the simplest form.

To convert an improper fraction to a mixed number, we need to divide the numerator by the denominator. In this case, 49 divided by 16 is 3 with a remainder of 1.

So, the mixed number is 3 1/16.

To simplify the mixed number, we need to check if we can reduce the fraction part (1/16) further. 1 is not divisible by any number other than 1 itself, so it is already in its simplest form.

Therefore, the final answer is 3 1/16.

In summary, to find 7/8 of 3.5, we multiplied 7/8 and 3.5 together to get 49/16, which we then converted to a mixed number in the simplest form, giving us the answer of 3 1/16.

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Answer:

Of the given options, "an engine" is the most reasonable abstraction for a car.

An engine is a fundamental component of a car that powers its movement, and it is present in almost all cars. The number of miles driven and the driving car color are characteristics of a specific car rather than abstractions of a car itself. For example, a car can still be considered a car even if it has not been driven any miles yet or if it has no color at all.

Therefore, an engine is a more reasonable abstraction for a car as it captures an essential feature of a car that is present in all cars.

The solution is, D. Driving, a reasonable abstraction for a car includes. Driving is an action or behavior associated with a car, as it involves operating or using the car to travel from one place to another. It is an essential aspect of the car's purpose and function.

Here, we have,

we know that,

An engine is a machine designed to convert fuel into mechanical energy that can be used to power other machines or devices. In the context of automobiles, an engine is the primary source of power that drives the vehicle. It typically operates by burning fuel in a combustion chamber to generate high-pressure gases that drive a piston, which in turn rotates a crankshaft that ultimately powers the car's wheels.

Car color and number of miles driven are characteristics or properties of a car, while an engine is a component that helps to power the car. Driving, on the other hand, is an action or behavior associated with a car, as it refers to the act of operating or using the car to travel from one place to another.

Therefore, driving is a reasonable abstraction for a car, as it captures an essential aspect of the car's purpose and function.

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The sum of the matrices A and C from the list of options is the matrix B

Given the following matrices

Matrix A

| 0  6  2 |

| 1  5  -2 |

Matrix C

| -2  5  3 |

| -1  -7  3|

To find the sum of matrices A and C, we add the corresponding elements in each matrix:

So, we have: A + C

| 0 - 2  6 + 5  2 + 3 |

| 1 - 1    5 - 7  -2 + 3|

Evaluate the sum

| -2  11  5 |

| 0   -2  1 |

This represents option B

Therefore, the sum of matrices A and C is (B)

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Complete question

What is the sum of A+C?

Matrix A

| 0  6  2 |

| 1  5  -2 |

Matrix C

| -2  5  3 |

| -1  -7  3|

In the given triangle, the value of x = 5.

What is a triangle's definition?

A triangle is a geometrical shape that is defined as a polygon with three sides and three angles. It is a closed figure with three line segments as its sides, and these sides intersect at three points, which are called vertices. When we add all the angles of a triangle then the result will always be 180°.

Now,

As we know the property of a triangle that

sum of all angles of triangle=180°

given angles are (9x-1)°, 74° and 62°

then,

        9x-1+74+62=180°

9x+135=180

9x=45

x=5

Hence,

           the value of x is 5.

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The set of integers is a Pythagorean triple are option (A) 10, 24, 25 and (D) 6, 8, 10

A Pythagorean triple is a set of three positive integers a, b, and c, such that a^2 + b^2 = c^2, which represents the sides of a right triangle.

Let's check each set of integers

A. 10^2 + 24^2 = 100 + 576 = 676 = 25^2. Therefore, (10, 24, 25) is a Pythagorean triple.

B. 9^2 + 12^2 = 81 + 144 = 225 = 15^2. Therefore, (9, 12, 15) is a Pythagorean triple. However, the set given is (9, 12, 21), which is not a Pythagorean triple.

C. 8^2 + 15^2 = 64 + 225 = 289 = 17^2. Therefore, (8, 15, 17) is a Pythagorean triple. However, the set given is (8, 15, 23), which is not a Pythagorean triple.

D. 6^2 + 8^2 = 36 + 64 = 100 = 10^2. Therefore, the set of integers (6, 8, 10) is a Pythagorean triple.

Therefore, the correct options are (A) 10, 24, 25 and (D) 6, 8, 10

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The given question is incomplete, the complete question is:

Which set of integers is a Pythagorean triple?

A.

10, 24, 25

B.

9, 12, 21

C.

8, 15, 23

D.

6, 8, 10

The graph for the linear equation y=24x, will be a straight line having coordinate (1,24) i.e. B.

What is a linear equation, exactly?

A linear equation is a first-degree algebraic equation in which each term is either a constant or the product of a constant and a single variable (degree 1). A linear equation is stated as y = mx + b, where y is the dependent variable, x is the independent variable, m is the line's slope, and b= y-intercept .

A linear equation's graph is a straight line. The line's slope decides how steep it is, and the y-intercept indicates where the line crosses the y-axis. Linear equations are used to model relationships between variables that are directly proportional to each other, such as distance and time, or cost and quantity.

Now,

Given equation is y=24x

then for  x,    y is

              1,    24

              2,   48

              3,    72

              4,     96

Hence, the graph will be as represented in option 2.

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fv(40,20) ≈ (f(40.1,20) - f(40,20))/0.1 , ft(40,20) ≈ (f(40,20.05) - f(40,20))/0.05 are the required functional estimations of a given representations.

However, we can estimate the partial derivatives with respect to x (fv) and y (ft) at the point (40,20) using the definition of partial derivatives:

fv = ∂f/∂x ≈ (f(40+h,20) - f(40,20))/h

where h is a small increment in the x direction. Similarly,

ft = ∂f/∂y ≈ (f(40,20+k) - f(40,20))/k

where k is a small increment in the y direction.

To estimate fv(40,20) and ft(40,20), we need to choose small values of h and k and evaluate the function at the corresponding points. Let's say h = 0.1 and k = 0.05:

fv(40,20) ≈ (f(40.1,20) - f(40,20))/0.1

ft(40,20) ≈ (f(40,20.05) - f(40,20))/0.05

We can then use these estimates to approximate the value of f(40.1,20.05) using the first-order Taylor approximation:

f(40.1,20.05) ≈ f(40,20) + fv(40,20)0.1 + ft(40,20)0.05

Note that this is an approximation and may not be very accurate if the function is highly nonlinear or has discontinuities. However, it can give us a rough idea of the value of f(40,20) and how it changes with small variations in x and y.

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The value of x in the given triangle is 1.82 cm using the angle bisector theorem.

A triangle is a polygon with three edges and three vertices. It belongs to the basic geometric shapes. A triangle with the parts A, B, and C is referred to as triangle ABC. Any three points that are not collinear in Euclidean geometry result in a separate triangle and a distinct plane. A triangle is a type of polygon with three sides; the triangle's apex is the point where the two longest sides meet. Two sides are brought together at an angle.

What is angle bisector theorem?

The ratios of the two segments that a line that bisects the opposing angle splits a triangle's side into are the subject of the angle bisector theorem in mathematics. It contrasts their proportionate lengths with the other two triangle sides' proportional lengths.

In the given triangle,

5/6=x/4-x

20-5x=6x

20=11x

x=20/11= 1.82 cm

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The company's total income, expenditure and profit is given respectively as follows:

a.) £180

b.) £146

C.) £34

To calculate the profit of the company the formula such as given below is used.

Profit = total income - total expenditure

The total income = 25+20+35+100 = £180

The total expenditure = 110+20+6+10 = £146

Profit = 180-146 = £34

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Answer:

23 but not

Step-by-step explanation:

In the question given, The inequality will be h₂< h₁<h₃. Thus, Daniel is tallest.

In Mathematics, Inequality defines the relationship between two values that are not equal. When two values are not equal, we use “not equal sign (≠)”. But if there is a comparison between two values, whether it is less than or greater than, different inequalities are used. For example 5<7 , 8>4.

The following problem is to model an inequality situation.

Given that ,

Najid is taller than Emily and shorter than Daniel.

 Let, height of Najid is h₁

         height of Emily is h₂

  and height of Daniel is h₃

By the condition h₁>h₂ and h₁< h₃

Combining both the statement we have the inequality

              h₂< h₁<h₃

From this inequality we have the person having h₃ height is tallest.

Hence, Daniel is tallest.

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Aldo and Leola would put 9 fiction books and 18 nonfiction books on each of the 7 bookshelves, for a total of 189 books on the shelves. They would then put the remaining 7 books on Ms. Krebs's desk.

To represent the problem as an equation, we first need to define some variables. Let's let "f" represent the number of fiction books, and "n" represent the number of nonfiction books. We know from the problem that there are 2 times as many nonfiction books as fiction books, so we can write:

n = 2f

We also know that they put the same number of books on each of the 7 bookshelves and put as many as they can on each shelf. Let's call this number "s". We can then write an equation for the total number of books that can fit on the bookshelves:

7s = f + n

Since n = 2f, we can substitute 2f for n in the equation:

7s = f + 2f

Simplifying, we get:

7s = 3f

Finally, we know that any remaining books are put on Ms. Krebs's desk. Let's call this number "r". We can write an equation for the total number of books:

f + n = 7s + r

Substituting 2f for n, we get:

f + 2f = 7s + r

Simplifying, we get:

3f = 7s + r

Now we can solve for "f":

3f = 7s + r

f = (7s + r) / 3

We don't have enough information to solve for "s" or "r", but we can use this equation to find the number of fiction books. For example, if we know that there are a total of 70 books, we can write:

f + n = 70

f + 2f = 70

3f = 70

f = 23.33

Since we can't have a fractional number of books, we would round down to the nearest whole number and get:

f = 23

We could then use the equation f = (7s + r) / 3 to find the number of books on each shelf, assuming there are no books left over:

23 = (7s + 0) / 3

69 = 7s

s = 9.86

Since we can't have a fractional number of books on a shelf, we would round down to the nearest whole number and get:

s = 9

So Aldo and Leola would put 9 fiction books and 18 nonfiction books on each of the 7 bookshelves, for a total of 189 books on the shelves. They would then put the remaining 7 books on Ms. Krebs's desk.

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Answer:

x = 26.

Step-by-step explanation:

Given: 2x + 3x + 50 = 180

First, write it down:

2x + 3x + 50 = 180

Then, collect like terms:

2x + 3x = 180 - 50

Then calculate:

5x = 130  (Divide both sides by 5)

x = 26

Answer:

The shape of each cut surface is a rectangle. The dimensions of the first cut surface are 8 inches by 10 inches, and the dimensions of the second cut surface are 10 inches by 20 inches.

The area of the first cut surface is 8 inches x 10 inches = 80 square inches. The area of the second cut surface is 10 inches x 20 inches = 200 square inches.

To find the total area Jenny needs to paint, we need to add the area of the first cut surface to the area of the second cut surface.

Total area = Area of first cut surface + Area of second cut surface

Total area = 80 square inches + 200 square inches

Total area = 280 square inches

Therefore, Jenny needs to paint a total area of 280 square inches.

He needs an additional $0.23 to buy the football with the coupon after the discount coupon.

A discount is a reduction in the price of a product or service. It is often used as a marketing tool to attract customers and increase sales. Discounts can be expressed as a percentage or a dollar amount.

The discounted price is the price of a product or service after a discount has been applied. The discount is usually expressed as a percentage or a dollar amount and is subtracted from the original price.

In the given question,

The discount Justin can get is 12% of the original price, which is:

0.12 x 22.99 = 2.76

So the discounted price of the football is:

22.99 - 2.76 = 20.23

Since Justin has exactly $20, he doesn't have enough money to buy the football with the coupon. He needs:

20.23 - 20 = 0.23

So he needs an additional $0.23 to buy the football with the coupon.

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If the objective function coefficient for variable 1 decreases by 20, the solution will shift in the direction of the decrease in the objective function coefficient. It means that the optimal solution that was obtained previously will no longer remain optimal, and the new optimal solution will be found with the new objective function coefficient.

In linear programming, the objective function determines the maximum or minimum value that can be attained in the solution, subject to the constraints. The constraints in the problem can be either equalities or inequalities, which limit the range of values that the decision variables can take on.

The change in the objective function coefficient will change the direction of the optimal solution, and it may affect the feasibility of the solution. It means that some constraints may no longer be satisfied, or some variables may become infeasible.

In such cases, it will be necessary to revise the constraints or the variables to ensure the feasibility of the solution.

The solution can also be affected if the constraints of the problem change. The new constraints may limit the range of values that the variables can take on, or they may add new variables to the problem. These changes can affect the feasibility of the solution, and it may require the problem to be solved again to obtain the new optimal solution.


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Answer:

Area: 81*pi

Circumference: 18*pi

Step-by-step explanation:

Area: 9^2= 81

So it would be 81*pi

Circumference: 9*2= 18

So it would be 18*pi

If you want the full area then it's 81*pi= 254.34

If you want the full circumference it's 18*pi= 56.55

Answer:Hence, Nathan rode 2 miles

Step-by-step explanation:ask if you need any questions

Men will have completed oil changes in hours Therefore, Will and Gabriel will each have done 12 oil changes after 4 hours.

Hours is a unit of time measurement. It is used to measure a specific amount of time and is usually denoted by the symbol “h”. There are 24 hours in a day, 60 minutes in an hour and 60 seconds in a minute. Hours are used to measure both short and long periods of time. Commonly, hours are used to measure the length of a workday, the length of a school day, or the length of a movie. Hours are also used to measure how long a person has been alive, how long an event has been going on, or how long an item has been in use.

Let W be the total number of oil changes Will has completed, and G be the total number of oil changes Gabriel has completed.

System of equations:

W = 8 + 2t

G = 3t

Since they will be tied at some point during the day, W = G.

Substituting W into G's equation:

8 + 2t = 3t

Solving for t:

2t = 8

t = 4

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Answer:

f(x) = (x + 5)² + 3

Step-by-step explanation:

f(x) = x² + 10x + 28

to complete the square

add/subtract ( half the coefficient of the x- term )² to x² + 10x

f(x) = x² + 2(5)x + 25 - 25 + 28

     = (x + 5)² + 3 ← in vertex form

The standard error for the sample proportion of 150 teachers in an inner-city school district is found to be 0.037.

The formula for the calculation of the standard error of a sample proportion is below,

SE = √((p × (1 - p)) / n)

Here,

SE is the standard error of the sample proportion

p is the sample proportion (in decimal form)

n is the sample size

In the mentioned case, the sample proportion is 0.72 (since 72% of 150 is 108), and the sample size is 150. Substituting these values into the formula, we will be getting,

SE = √((0.72 × (1 - 0.72)) / 150)

SE = √((0.2052) / 150)

SE = √(0.001367)

SE = 0.037

Therefore, the standard error of the sample proportion is 0.037.

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A sample size of at least 61 should be taken to obtain a margin of error of 0.04 for the estimation of a population proportion at a 95% confidence level.

Given data:

To determine the sample size required for estimating a population proportion with a given margin of error at a 95% confidence level, you can use the following formula:

[tex]n=\frac{Z^2 \cdot p(1-p)}{E^2}[/tex]

n is the required sample size.

Z is the Z-score corresponding to the desired confidence level. For a 95% confidence level, the Z-score is approximately 1.96.

p is an estimate of the population proportion (since you don't have prior data, you can use p =0.5  for maximum variability, which results in the largest sample size requirement).

E is the desired margin of error, which is 0.04 in this case.

Substitute the values into the formula:

[tex]n=\frac{1.96^2*0.5^2}{0.04^2}[/tex]

The value of n = 60.26

Since the sample size is a whole number, n = 61

Hence, a sample size of at least 61 should be taken for the estimation of a population proportion at a 95% confidence level.

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So there are 200 different ways a doctor can prescribe the asthma drug to a patient, taking into account the various options for form, manufacturer, and strength.

This illustrates the importance of carefully considering all the available options and selecting the most appropriate prescription for each patient's unique needs.The number of different ways a doctor can prescribe the asthma drug to a patient depends on the number of options available for each of the three factors: form, manufacturer, and strength.

For each of the three factors, there are 10 different options. Therefore, the total number of different ways the doctor can prescribe the drug is the product of the number of options for each factor:

10 options for form x 10 options for manufacturer x 2 options for strength (regular or extra) = 200 total options.

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Using expressions,

4a. x= 0 is not possible.

4b. x= 1 is not possible.

5a. (9x-5)(9x+5)

5b. (x-3)(2x+1)

6. 1/(3x-7)

7a. x = (-5,∞)

7b. x = (∞,2]

7c. x = (-3,7]

A mathematical expression is a phrase that has a minimum of two numbers or variables and at least one mathematical operation.

Let's examine the writing of expressions.

The other number is x, and a number is 6 greater than half of it.

As a mathematical expression, this proposition is denoted by the expression x/2 + 6.

Here the values of x has to be such that the denominator is not equal to zero.

So, x cannot be zero and x cannot be 1 as these two values in the respective questions will make the denominator zero.

a. 81x²-25

= 81x² + 45x-45x-25

=9x(9x+5)-5(9x+5)

= (9x-5)(9x+5)

b. 2x²-5x-3

= 2x² + x - 6x -3

= x(2x+1)-3(2x+1)

=(x-3)(2x+1)

Next, the intervals for x are as follows:

x = (-5,∞)

x = (∞,2]

x = (-3,7]

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Hence, the value of  variable in the given expression x is 8

An angle is formed when two straight lines  meet at a common endpoint.

∠1 = 7x - 4

∠2 = 3x + 28

A secant line that crosses two parallel lines produces these angles. After that, these angles were congruent, which means that their measures are equal.

Then, equaling  both given expressions and solving for x,  we get:

Step1: subtract 3x both sides

7x - 4 = 3x + 28

Step2: add 4 both sides

7x - 3x - 4 = 28

Step2: simplify like terms

7x - 3x = 28 + 4  

Step3: divide by 4 both sides

4x = 32  

x = 32/4

x = 8

Hence, the value of x is 8.

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The linear function rule to model the cost y for any number of samples x is (y = x + 2.25) and this can be determined by forming the linear equation.

An international food festival charges for admission and for each sample of food.

Admission and 6 samples cost $8.25.

Admission and 8 samples cost $10.25.

The following steps can be used in order to determine the linear function rule to model the cost y for any number of samples x:

Step 1 - The linear equation is formed in order to determine the linear function.

Step 2 - The linear equation that represents the situation "admission and 6 samples cost $8.25" is:

8.25 - 6c = d   --- (1)

Step 3 - The linear equation that represents the situation "admission and 8 samples cost $10.25" is:

10.25 = 8c + d    --- (2)

Step 4 - Substitute the value of 'd' in equation (2).

10.25 = 8c + 8.25 - 6c

2 = 2c

c = 1

Step 5 - Substitute the value of 'c' in the equation (1).

d = 8.25 - 6

d = 2.25

Step 6 - So, the linear function rule to model the cost y for any number of samples x is:

y = x + 2.25.

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The amount of the mark up is $66 and the selling price is $286.

The amount by which a product's cost is raised to determine its selling price is known as the markup percentage. Usually, it is represented as a percentage of the item's price. Markup percentage is determined by the following equation:

Markup percentage = (Selling price - Cost price) / Cost price x 100%

Given that, the mark up is 30%.

Thus,

Mark up = 0.3 x $220 = $66

The selling price is:

Selling price = $220 + $66 = $286

Hence, the amount of the mark up is $66 and the selling price is $286.

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