Find value of x. Round to the nearest tenth

A graph of the triangle after a 90 degrees counterclockwise rotation about the origin is shown in the image attached below.

In Geometry, the rotation of a point 90° about the center (origin) in a counterclockwise (anticlockwise) direction would produce a point that has these coordinates (-y, x).

By applying a rotation of 90° counterclockwise to the vertices for D, the coordinates of the vertices of the image point D' are as follows:

(x, y)                               →            (-y, x)

Ordered pair A  = (-3, 4) → Ordered pair A' = (-4, -3)

Ordered pair B  = (-5, -1) → Ordered pair B' = (1, -5).

Ordered pair C  = (-1, 2) → Ordered pair C' = (-2, -1).

In this exercise, we would use an online graphing calculator to plot the vertices of triangle A'B'C' as shown in the graph attached below.

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As per the question Sales revenue is $198,000 (from the sale of inventory)

Sales revenue, which is sometimes referred to as revenue from sales or just sales, is the entire sum of money that a business makes from the selling of goods or services to clients. It is one of the main revenue streams for the majority of businesses and is frequently used as a key performance indicator (KPI) to gauge a business's success.

Calculating sales income involves multiplying the quantity sold by the cost per unit. As an illustration, if a business sells 1,000 pieces of a product at $100 each, its sales revenue would be $100,000 ($100 x 1,000).

Sales revenue is a crucial indicator for businesses to monitor since it indicates how much demand there is for a company's goods or services.

According to question:

Cost of goods sold = $110,000 (the cost of the inventory that was sold)

Gross margin = Sales revenue - Cost of goods sold = $198,000 - $110,000 = $88,000

Expenses = Cost of goods sold + Operating expenses = $110,000 + $36,000 = $146,000

Operating income = Gross margin - Operating expenses = $88,000 - $36,000 = $52,000

Non-Operating Items = Gain on sale of land = $80,000 (the difference between the selling price and the original cost of the land)

Net income = Operating income + Non-Operating Items = $52,000 + $80,000 = $132,000

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The label covers approximately 4,800 square centimetres of the wheel of cheese.

What is the lateral surface area of a cylinder?

The lateral surface area of a cylinder can be found using the formula:

L = 2πrh

where L is the lateral surface area, r is the radius of the cylinder, and h is the height of the cylinder.

In this case, we need to find the lateral surface area of the wheel of cheese, so we can use the given radius of 30 centimetres and height of 20 centimeters to calculate:

L = 2 x (22/7) x 30 x 20

L = 4,800 square centimetres

This is the total surface area of the cylindrical-shaped wheel of cheese. However, the label does not cover the circular top and bottom, so we need to subtract their areas from the total surface area to find the area covered by the label.

The area of a circle can be found using the formula:

A = πr²

where A is the area of the circle, and r is the radius of the circle.

In this case, we have two circles (top and bottom), so the total area of the circles that are not covered by the label is:

2 x (22/7) x 30²

= 56,400/7 square centimeters

Subtracting this from the total surface area, we get:

4,800 - 56,400/7

= 33,600/7 square centimeters

= 4,800 square centimeters (rounded to the nearest whole number)

Therefore, the label covers approximately 4,800 square centimeters of the wheel of cheese.

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Answer:

Step-by-step explanation:

Here is a step-by-step explanation of the independence of the pair of events of choosing a number between 1000 and 5000 and flipping a coin:

Understanding the definition of independent events: Independent events are events that have no influence on each other. The outcome of one event does not affect the outcome of the other.

Event 1: Choose a number between 1000 and 5000: This event involves randomly selecting a number within the specified range.

Event 2: Flip a coin: This event involves flipping a coin and observing whether it lands on heads or tails.

Check for influence: To determine whether the events are independent, we need to check if the outcome of one event affects the outcome of the other. In this case, the outcome of the coin flip has no effect on the number you choose, and your choice of number has no effect on the outcome of the coin flip.

Conclusion: Since the outcome of one event does not affect the outcome of the other, the pair of events of choosing a number between 1000 and 5000 and flipping a coin are considered independent.

So, the pair of events of choosing a number between 1000 and 5000 and flipping a coin are independent events.

Hi there, here's your answer:

Given the question:

[tex](5^{-4})^{2}[/tex]

We know that a number [tex]x[/tex] raised to the power of a negative integer [tex]-y[/tex] is evaluates as [tex]\frac{1}{x^{y} }[/tex]

Hence, on evaluating this expression we get:

[tex](\frac{1}{5^{4} })^{2}[/tex] = [tex](\frac{1}{625} )^2 = \frac{1}{390625}[/tex]

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Answer:

D

Step-by-step explanation:

3x² - 10x - 8

consider the factors of the product of the coefficient of the x² term and the constant term which sum to give the coefficient of the x- term.

product = 3 × - 8 = - 24 and sum = - 10

the factors are - 12 and + 2

use these factors to split the x- term

3x² - 12x + 2x - 8 ( factor the first/second and third/fourth terms )

= 3x(x - 4) + 2(x - 4) ← factor out (x - 4) from each term

= (x - 4)(3x + 2)

Answer:

6.25 x h = 50.000

Step-by-step explanation:

Answer:

8 headbands.

Step-by-step explanation:

Winnie needs to sell AT LEAST 8 headbands. 50 divided by 6.25 is 8. Remember that the phrase "at least" is represented by a greater-than-or-equal-to symbol.

Answer:

57

Step-by-step explanation:

To find the ratio of the area of Alaska to the area of Rhode Island, we need to divide the area of Alaska by the area of Rhode Island.

The area of Rhode Island is 1000 square miles and the area of Alaska is 5.7 x 10^5 square miles.

So, the ratio is: 5.7 x 10^5 / 1000 = 57

Therefore, Alaska's area is 57 times the area of Rhode Island.

5.7 x 10^5 divided by 1000 = 57.

Carrie is slicing sticker sheets to fit four present bags. There will be an equal quantity of stickers in each bag.

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Answer:

5/6

Step-by-step explanation:

The required proof has been below that ΔJKL ≅ ΔLMN due to the SAS postulate.

Similar Triangles are defined as two triangles with the same shape, equal pair of corresponding angles, and the same ratio of the corresponding sides.

The triangles are given in the question, as shown.

As per the given figure, we have

JK = LM

∠LJK ≅ ∠NLM (same side inner angles)

Since L is the midpoint of JN. (Definition of midpoint)

Then JL ≅ LN

Now, for triangles ΔJKL and ΔLMN

JK ≅ LM (sides)

∠LJK ≅ ∠NLM (angle)

JL ≅ LN (sides)

By SAS postulate, ΔJKL ≅ ΔLMN.

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Note that the complete steps of the Flow Chart Proof is given as follows:

1) RS = TS, QR = UT [Given]

2) QR + RS = QR + RS [Reflexive Property of Equality]

3) QR + RS = RS + UT  [Substitution Property of Equality]

4) QR + RS = QS, TS + UT = US [Segment Addition Postulate]

5) QS = US [Substitution Property of Equality]

6) Line Segment QS is congruent to  Line segment US [Definition of Congruent Segments].

A flow chart proof is a type of proof that uses symbols and diagrams to show the logical flow of a proof.

It is a visual way of representing a mathematical argument that can be helpful for organizing and presenting complex ideas in a clear and concise manner.

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Answer:

Mrs. Morris drove a total of 1989 miles in June. This can be calculated by adding 873 miles (the amount she drove in May) to 1116 miles (the amount she drove more in June). Therefore, 873 + 1116 = 1989 miles.

The copy machine make 44 copies per minute.

The unitary method is the method of solving a problem by the first value of a single unit and than finding the value of single unit by multiplying. Unitary method is a technique by which we can find the value of a single unit from the value of multiple data and also the value of more than one unit from the value of single unit. This is a method that we use for most of the calculations in mathematics;

We are given that Time copy machine take= 4min 15sec

Number of copies=187

Now, 1min=60sec

4min=240sec

Total time=240+15 =255sec

Therefore, 255sec=187copies

60sec= 187 x 60/255

=44

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The kite is flying approximately 76.118 feet high.

What is ratio ?

Ratio can be defined as the given value divided by the total value.

We can use trigonometry to solve this problem.

Let's call the height of the kite h. Then, we have a right triangle, with one angle equal to 80 degrees and the adjacent side equal to 77 feet. We can use the sine function to find the height of the kite:

sin(80) = h/77

So, h = 77 * sin(80).

Using a scientific calculator or a trigonometry table, we can find the value of sin(80) to be approximately 0.98

Therefore, the height of the kite is:

h = 77 * 0.98 = 76.11

Hence, The kite is flying approximately 76.118 feet high.

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Answer: The composite function (g f)(x) is found by first applying the function f to x and then applying the function g to the result. In other words, (g f)(x) = g(f(x)).

So, for the given functions g(x) = x - 5 and f(x) = -x - 1, the composite function is:

(g f)(x) = g(-x - 1) = (-x - 1) - 5 = -x - 6

Evaluating the composite function at x = 7, we get:

(g f)(7) = -7 - 6 = -13

Step-by-step explanation:

Answer:

YOU L HAHA

Step-by-step explanation:

LOS ER

Answer:

4.52 %

Step-by-step explanation:

the percentage increase in height is calculated as

[tex]\frac{increase}{original}[/tex] × 100%

increase in height = 1.62 - 1.55 = 0.07 ,

then

% increase = [tex]\frac{0.07}{1.55}[/tex] × 100% = 0.045.. × 100% ≈ 4.52% ( to 2 decimal places )

Explanation:

Let's replace y with 0 and solve for x.

-x+6y = 2

-x+6*0 = 2

-x + 0 = 2

-x = 2

x = -2

We have x = -2 pair up with y = 0 to get the ordered pair (x,y) = (-2,0)

This is the x intercept of the graph. It's where the line crosses the x axis. You can use a tool like Desmos or GeoGebra to confirm.

Since we have infinitely many numbers to replace x or y with, we have infinitely many solution points on this line.

Each point is of the form (-2+6k, k) where k is any real number.  If k = 0, then it leads to (-2,0) found earlier.

The amount invested in the account that earns 7% interest is $6,000 and the amount invested in the account that earns 8% interest is $14,000.

The system of equations that represent the information in the question is:

a + b = 20,000 equation 1

0.07a + 0.08b = 1540 equation 2

Where:

a = amount invested in the account that earns 7% interest

b = amount invested in the account that earns 8% interest

The elimination method would be used to solve the equations.

Multiply equation 1 by 0.07

0.07a + 0.07b = 1,400 equation 3

Subtract equation 3 from equation 2

0.01b = 140

Divide both sides of the equation by 0.01

b = 140/ 0.01

b = 14,000

Substitute for b in equation 1:

a + 14,000 = 20,000

a = 20,000 - 14,000

a = 6,000

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The distance from point A to point B measures is 1,269.9 feet.

Trigonometric ratios for a right angled triangle are from the perspective of a particular non-right angle.

In a right angled triangle, two such angles are there which are not right angled(not of 90 degrees).

The slant side is called hypotenuse.

From the considered angle, the side opposite to it is called perpendicular, and the remaining side will be called base.

From that angle (suppose its measure is θ),

[tex]\sin(\theta) = \dfrac{\text{Length of perpendicular}}{\text{Length of Hypotenuse}}\\\cos(\theta) = \dfrac{\text{Length of Base }}{\text{Length of Hypotenuse}}\\\\\tan(\theta) = \dfrac{\text{Length of perpendicular}}{\text{Length of base}}\\\\\cot(\theta) = \dfrac{\text{Length of base}}{\text{Length of perpendicular}}\\\\\sec(\theta) = \dfrac{\text{Length of Hypotenuse}}{\text{Length of base}}\\\\\csc(\theta) = \dfrac{\text{Length of Hypotenuse}}{\text{Length of perpendicular}}\\[/tex]

Given;

The horizontal distance= 1196ft

Angle of elevation to the lighthouse’s=13°

Angle of elevation from point B =3 °

Now,

Distance from A to B = D;

D = Horizontal distance from B to LH - Horizontal distance from A to LH

Distance from A to B = 2237.9 feet - 968 feet ≈ 1269.9 feet;

Therefore, by the trigonometric ratios the distance from point A to point B, D will be 1,269.9feet;

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The support vector of the input dsolve('Dy = -3*y') is "dsolve(diff(y,t) == -3*y)".

A symbol is a mathematical object that represents a mathematical entity, such as a number, a variable, or a function. In mathematical software, symbols are used to represent variables, which can be used in mathematical expressions to perform computations.

In the past, character vectors or strings were used to represent symbols in certain mathematical software programs.

In the future release of this software, support for character vectors or strings will be removed. Instead, the program will require users to use the "syms" function to declare variables as symbols.

As an example of how this might be used in practice, consider the differential equation

=> "dy/dt = -3y".

In the past, this equation might have been entered into a mathematical software program using a character vector or string to represent the variable "y".

However, in the future release of this software, the user will need to use the "syms" function to declare "y" as a symbol. The equation would then be entered using the "diff" function, like this:

=> "dsolve(diff(y,t) == -3*y)".

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The total area of the quilt is: 112.5 square inches

The six-sided figure is given, and we can deduce the following parameters from the question:

The shape is made of a triangle and a rectangle

The side lengths derived from the question are:

The triangle on top:

base: 5 inches and height: 5.18 inches

The rectangle at the bottom:

Base: 16 inches with a height of 7.5 inches

So, we have the total area of the figure to be

Area of figure = 1/2 * 5 * 6 + 13 * 7.5

Area of figure = 112.5

Based on the parameters, the total area is 112.5 square inches

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a) The fraction of the stickers that Kate gave to her 6 friends was 1/2.

b) The fraction of Kate's stickers that each friend received from the 1/2 of stickers was 1/12.

The fraction is the portion or part of a whole.

Fractions can be proper, improper, and complex fractions, depending on the relative value of the numerator and the denominator.

The total number of stickers that Kate possesses = 1/1

The fraction Kate kept for herself = 2/5

The remaining portion of Kate's stickers = 3/5 (1 - 2/5)

The fraction Kate gave to her 6 friends to share equally = 5/6 of 3/5 = 1/2

The fraction of Kate's stickers that each friend received = 1/2 ÷ 6 = 1/12

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Answer:

C. No real factors

Step-by-step explanation:

Not factorable

The elements of the set A are given as follows:

A = {January, February, March, April, May, June, July, August, September, October, November, December}.

The set A in the context of this problem is defined as follows:

A = {x | x is a month of the year.}

Hence the set A is composed by 12 elements, which are all the months of an year, as follows:

A = {January, February, March, April, May, June, July, August, September, October, November, December}.

The problem asks for all the elements of the set A, given as follows:

A = {x | x is a month of the year.}

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The range of set 1 is 11. The range of set 2 is  208

The wider range of set 2, set 2 contains a wider spread of the given data.

The range of the data is defined as the difference between the maximum value of data and the minimum value of the data.

The set is given in the question, as follows:

Set 1: 1, 4, 6, 8, 10, 12

The maximum value = 12

The minimum value = 1

The range of the set 1 = maximum value - minimum value

Substitute the values in the above formula,

The range of the  set 1  = 12 - 1

Apply the subtraction operation to get the answer

The range of the set 1 = 11

Set 2: 230, 24, 33, 22, 41

Now, the range of the  set 2  = 230 - 22 = 208

Data set 1 has a range of 11, whereas data set 2 has a range of 208.

Therefore, the wider range of set 2, set 2 contains a wider dispersion of data.

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Answer:

1.8 quintillion or 1,800,000,000,000,000,000

Step-by-step explanation:

Answer:

N?A

Step-by-step explanation:

Answer:

Step-by-step explanation:

For part a:

Mean: Use the AVERAGE function to find the mean of the "Number" column.

Median: Use the MEDIAN function to find the median of the "Number" column.

Mode: There is no built-in function to find the mode in Excel, but you can use a combination of the IF, COUNTIF, and MAX functions to find the most frequently occurring value.

Maximum: Use the MAX function to find the maximum value in the "Number" column.

Minimum: Use the MIN function to find the minimum value in the "Number" column.

For part b:

Mean: Use the AVERAGE function to find the mean of the "Percent" column.

Median: Use the MEDIAN function to find the median of the "Percent" column.

Mode: There is no built-in function to find the mode in Excel, but you can use a combination of the IF, COUNTIF, and MAX functions to find the most frequently occurring value.

Maximum: Use the MAX function to find the maximum value in the "Percent" column.

Minimum: Use the MIN function to find the minimum value in the "Percent" column.

For part c:

The statistics on children whose parents do not have secure employment provide important insights into the state of the economy. In this case, the mean and median of the number of children in each state seem to be around 450,000. The mode cannot be determined since there are no repeated values in the "Number" column. The maximum number of children is 678,000 in Ohio, while the minimum number is 141,000 in Iowa.

Comparing the states, Indiana has a slightly higher mean and median percent of children whose parents do not have secure employment at 27%, compared to the other surrounding states which range from 20% to 31%. However, there is no clear state with the best or worst data as the range of the percent values is not too wide.

In terms of comparison, the number of children may provide a more comprehensive understanding of the extent of the problem, as it gives a clearer picture of the actual number of children affected. However, the percentage provides a more relative comparison between the states, allowing for easier comparison and a clearer understanding of the proportion of children affected in each state.