How do I simplify this into a radical?

The statement that must be true for the parallelogram is

Alternate internal angles are pairs of angles that lie on opposite sides of a transversal line intersecting two parallel lines. The angles are on the interior (between the two parallel lines) and are not adjacent to each other.

These angles are equal in measure (i.e., they are congruent), which means that if one angle has a certain degree of measure, the other angle will have the same degree of measure.

In the problem, the diagonal of the parallelogram is the transversal line and it is used to make the alternate internal angle theorem possible

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Option C : (-4, 6) are the coordinates of B'.

What are meant by coordinates?

Coordinates are two integers (Cartesian coordinates) or often a letter and a number that identify a particular place on a grid known as a coordinate plane. A coordinate plane has four quadrants and two axes: the horizontal x-axis and the vertical y-axis (vertical).

Given T(ABCD) = (A'B'C'D') and A = (6, -8) , A' = (-2, 4)

If B = (4, -6) then let B' = (x, y)

now, x - 4 = -2 - 6

x = 4 - 2 - 6 = -4

and y - (-6) = 4 - (-8)

y + 6 = 4 + 8

y = 6

Therefore, B' = (-4, 6)

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The slope and y - intercept are -1/3 and - 8 while the equation of line is

y = -1/3x - 8

Taking two points from the graph attached;

A = (-6, -6)

B = (0, -8)

We can find the slope of the line as;

slope (m) = y₂ - y₁ / x₂ - x₁

m = -8 - (-6) / 0 - (-6)

m = -8 + 6 / 6

m = -2 / 6

m = -1/3

Using the slope and any point, we can find the y - intercept of the graph. This can also be easily calculated by simply looking for where the graph crossing the y -axis.

This point is at -8 and the y - intercept is -8

The equation of the line will be written as y = -1/3x - 8

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Answer:

Step-by-step explanation:

Let me explain step by step:

Determine the common ratio: We see that each term is half the previous term, so the common ratio is 1/2.

Write the formula for the nth term: We can use the formula for an infinite geometric series to find the nth term:

a_n = a_1 * r^(n-1), where a_1 is the first term (60), r is the common ratio (1/2), and n is the term number.

Plug in the values: We want to find the 9th term, so we plug in the values into the formula:

a_9 = 60 * (1/2)^(9-1)

Calculate the expression: We can simplify the expression by using the exponent rule for powers of 1/2:

a_9 = 60 * (1/2)^8

Divide the result by 256: We can simplify the expression further by dividing both sides by 256:

a_9 = 60 * 1/256

a_9 = 60 / 256

Get the final answer: We divide 60 by 256 to get the final answer:

a_9 = 0.234375

So the 9th term of the sequence is approximately 0.234375.

a) The rate in this problem is 23 miles.

b) The unit fraction is associated with this rate is 23/1.

c) In 12 gallons the car will travel 276 miles.

Unit rate is the ratio of two different units, with denominator as 1.

Given:

A certain car gets 23 miles to the galloon open highway.

a) The rate in this problem is 23 miles

b) The unit fraction is associated with this rate is 23/1.

c) In 12 gallons the car will travel

23/ 1 = x/ 12

x= 23 . 12

x= 276 miles

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The number of boxes of donuts he can buy is 3.

An expression contains two variables or numbers with addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

A box of dozen donuts costs = $6.50

Amount taken = $25

The number of boxes of donuts he can buy.

= 25 ÷ 6.50

= 3.85

Thus,

The number of boxes of donuts he can buy is 3.

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This curve symbolizes the curve of indifference. Those combinations of quantities that the customer considers to be of equal value are connected by a curve on a graph whose axes reflect amounts of two commodities.

It dislikes all product combinations that offer the same level of enjoyment to the consumer. Because each combination provides the same level of enjoyment, the buyer Favours them all equally. The indifference curve therefore gets its name.

An indifference curve is a graphic representation of a collection of products that give consumers comparable levels of satisfaction, leading to their indifference. A consumer or person is indifferent between the two products at every point on the indifference curve because they provide the same kind of benefit.

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Answer:

To perform a dilation with a scale factor of 2 centered at the origin, we need to multiply each coordinate of the original points A and B by the scale factor of 2.

The coordinates of point A after dilation are:

A′(2 * 3, 2 * 7) = A′(6, 14)

Similarly, the coordinates of point B after dilation are:

B′(2 * 4, 2 * 9) = B′(8, 18)

So, the endpoints of the dilated line segment are A′(6, 14) and B′(8, 18).

Answer:

Width: [tex]9[/tex] Length: [tex]21.[/tex]

Step-by-step explanation:

Let's say [tex]l[/tex] is the length, and [tex]w[/tex] is the width. We can rewrite [tex]l[/tex] as [tex]2w + 3.[/tex] So  [tex]2(2w + 3) + 2w = 60,\\4w + 6 + 2w = 60,\\6w + 6 = 60,\\6w = 54,\\w = 9.\\[/tex]So the length of the rectangle is [tex]2 \cdot 9 + 3 = 21[/tex] and the width is [tex]9.[/tex]

Hope that helps!

What is a Right Angle Triangle?

A Right Angle Triangle is a triangle where one of the angles is equal to 90 degrees.

To calculate the values using SOHCAHTOA

 SOHCAHTOA calculate the angles and sides of the right triangle, using trigonometric function sine, cosine, and tangent. There are two triangles in which the adjacent and opposite changes based on which angle is in question, the hypotenuse always stays the same.

Where Sin A = Opposite/ Hypotenuse

            Cos A = Adjacent / Hypotenuse

   And  Tan A = Opposite / Adjacent

For question 1,

If Opposite = PR

Adjacent = PQ

Hypotenuse = QR

Sin A = 14/50

Cos A = 48/50

Tan A = 14/48

For question 2,

If Opposite = PQ

Adjacent = PR

Hypotenuse = QR

Sin A = 48/50

Cos A = 14/50

Tan A = 48/14

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Step-by-step explanation:

Your picture looks blurry however I think the graph passes through the points (0,0)(-1,0) and (3,0) so the equation becomes

[tex](x +1)(x - 3)x[/tex]

[tex] {x}^{3} - 2x {}^{2} - 3x + c[/tex]

Where C is the y intercept.

Since C is 0, our equation becomes

[tex] {x}^{3} - 2 {x}^{2} - 3x[/tex]

Answer:

  EF = 18

Step-by-step explanation:

Given similar triangles DEF and JHI, midpoints G and K of sides DE and HI, with sides marked GF=9, EF=x+8, KI=14, HI=3x-2, you want to know the length of EF.

Corresponding sides in similar triangles are proportional. This means ...

  EF/GF = HI/KI

  (x+8)/9 = (3x-2)/14 . . . . substitute given values

  14(x +8) = 9(3x -2) . . . . multiply by 14·9

  14x +112 = 27x -18 . . . . eliminate parentheses

  130 = 13x . . . . . . . . . . . add 18-14x

  10 = x . . . . . . . . . . . . . divide by 13

Now, we can find EF:

  EF = x+8 = 10 +8

  EF = 18

The numeric value of the exponential function at x = 19.5 is given as follows:

f(19.5) = 178.41.

The standard definition of an exponential function is given as follows:

y = ab^x.

In which:

Considering that f(4.5) = 25 and f(14) = 85, the two equations are given as follows:

Hence:

a = 25b^(-4.5).

Then the value of b is obtained as follows:

25b^(-4.5)b^(14) = 85.

b^(9.5) = 85/25

b = (85/25)^(1/9.5)

b = 1.14.

Then the value of a is obtained as follows:

a = 25 x (1.14)^(-4.5)

a = 13.86.

Then the function is defined as follows:

y = 13.86(1.14)^x.

At x = 19.5, the numeric value is given as follows:

y = 13.86(1.14)^19.5

y = 178.41.

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Answer: Decreased 40%

Step-by-step explanation:

Alright, we know they reduced $10.00 (25-15)

Now all we have to do is find the percentage, 10 is how much of 25?

10/25 =0.4

(to get 0.4 to a percentage multiply by 100)

The price was decreased by 40%

Answer:

The coordinates of the remaining vertices are (1, -1) and (3, 1).

Step-by-step explanation:

A square is a quadrilateral with with four sides of equal length. It has two sets of parallel sides and its interior angles are all right angles.  Therefore, each vertex shares its x-coordinate with one adjacent vertex, and its y-coordinate with the other adjacent vertex.

If AC with vertices A(1, 1) and C(3, -1) is the diagonal of a square, the coordinates of the remaining vertices will be:

Note that in order to solve the above, we had to assume a start date for the construction. Hence, by March 2022​, a total number of liters supplied is 3,380,000 liters.

To solve the problem, we need to know how many weekdays are in March 2022. March 2022 has 23 weekdays (31 days - 4 Saturdays - 4 Sundays).

Since the company has to supply a minimum of 12 water tankers and a maximum of 16 water tankers to the construction site on weekdays, we can assume an average of 14 water tankers per weekday. Therefore, the total number of water tankers to be supplied on weekdays in March 2022 would be:

14 water tankers/day x 23 weekdays = 322 water tankers

On Saturdays, the company has to supply a minimum of 4 water tankers. Since there are 4 Saturdays in March 2022, the total number of water tankers to be supplied on Saturdays in March 2022 would be:

4 water tankers/day x 4 Saturdays = 16 water tankers

Therefore, the total number of water tankers to be supplied in March 2022 would be:

322 water tankers (weekdays) + 16 water tankers (Saturdays) = 338 water tankers.

Assuming each water tanker carries a load of 10,000 liters, the total volume of water supplied to the construction site in March 2022 would be:

338 water tankers x 10,000 liters/tanker = 3,380,000 liters

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Full Question:

The company has to supply a minimum of 12 water tankers and a maximum of 16 water tankers to the construction site on weekdays except on Saturdays which is limited to the minimum of 4 water tankers a day. Assuming the start month for the construction was February 2022, Calculate the total number of water loads that were supplied to the project on the constitution site by the water tanker in March 2022​

The estimate of the number 7th grader who play in the school band will be 120.

It is important to note that an expression is simply used to show the relationship between the variables that are provided or the data given regarding an information. In this case, it is vital to note that they have at least two terms which have to be related by through an operator.

Some of the mathematical operations that are illustrated in this case include addition, subtraction, etc. The estimate of the number 7th grader who play in the school band will be:

= 60 / 200 × 400

= 120

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When there are 20 circles and 8 squares, the simplest ratio of squares to circles is equals to the 2/5.

We have some numbers of circles and squares. The number of circles = 20

The number of squares = 8

Ratio is number which expressed that how many times one number is contains other one. The symolically represention of ratio is "/" or " : ". If a and b are two numbers then "a/b or a : b " represents 'a' ratio 'b'. For example, if we consider eight apples and six mangoes in a bowl of fruit, then the ratio of apples to mangoes is equal eight to six, i.e., 8 : 6 or 4:3. Now, we have to determine the ratio of squares to circles. Comparing the square and circles with a and b then the ratio of squares to circles is 8 : 20 or 8/20. But we want simplfy form of ratio so,

simplfy it by dividing the upper and lower parts of ratio with the common factor of 8, 20 that is 4.

=>( 8/4)/(20/4)

=> 2/5

Hence, required ratio is 2/5.

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The  total manufacturing costs for each factory are to be the same is M = 3318.52.

Let's denote the number of pairs of jeans produced at the Medney factory as M, and the number of pairs of jeans produced at the Selbourne factory as S.

Total cost of production at the Medney factory = Total cost of production at the Selbourne factory

28000 + 30M = 35200 + 24S

Total number of pairs of jeans produced = 6000

M + S = 6000

We can solve for M and S by using substitution or elimination. Here, we will use substitution:

M + S = 6000 (from equation 2)

M = 6000 - S (subtracting S from both sides)

28000 + 30M = 35200 + 24S (from equation 1)

Substituting M = 6000 - S:

28000 + 30(6000 - S) = 35200 + 24S

180000 - 30S = 35200 + 24S

180000 = 54S + 35200

54S = 144800

S = 2681.48

So the number of pairs of jeans produced at the Selbourne factory is approximately 2681.48. To find the number of pairs of jeans produced at the Medney factory, we can substitute this value of S back into equation 2:

M + S = 6000

M + 2681.48 = 6000

M = 3318.52

So the number of pairs of jeans produced at the Medney factory is approximately 3318.52.

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Answer:32

Step-by-step explanation: 24 divided by .75=32

To get the cash flows from operating activities, we subtract this from the change in total cash, which is $0.01 billion, to get -$0.39 billion. Rounding to two decimal places, we get -$1.01 billion).

What is algebraic expression ?

An algebraic expression is a combination of variables, numbers, and mathematical operations, such as addition, subtraction, multiplication, and division. It can be used to represent a mathematical relationship or formula and can be simplified or evaluated using algebraic rules.

The change in total cash of Rectangle is $0.02 billion (3.59 - 0.59 - 4.18 = -0.98, which is rounded to -$1.00 billion, and then added to the beginning cash amount of $0.69 billion to get $0.69 - $1.00 = -$0.31 billion or -$0.31/100 = -$0.02 billion).

The ending cash amount of Circle is $0.72 billion (1.39 - 0.29 - 1.38 = -0.28, which is added to the beginning cash amount of $0.69 billion to get $0.41 billion or $0.41/100 = $0.72 billion).

The amount of cash flows from financing activities of Pentagon is -$0.55 billion (the change in total cash of $0.05 billion is the sum of the operating cash flows and investing cash flows, which is $0.08 billion + $0.62 billion = $0.70 billion. To get the cash flows from financing activities, we subtract this from the change in total cash, which is $0.05 billion, to get -$0.65 billion. Rounding to two decimal places, we get -$0.55 billion).

The amount of cash flows from investing activities of Square is -$0.40 billion (the change in total cash of $0.01 billion is the sum of the operating cash flows and financing cash flows, which is $0.59 billion + $0.41 billion = $1.00 billion. To get the cash flows from investing activities, we subtract this from the change in total cash, which is $0.01 billion, to get -$0.99 billion. Rounding to two decimal places, we get -$0.40 billion).

The amount of cash flows from operating activities of Hexagon is -$1.01 billion (the change in total cash of $0.01 billion is the sum of the investing cash flows and financing cash flows, which is -$1.40 billion + $1.02 billion = -$0.38 billion.

Therefore,  To get the cash flows from operating activities, we subtract this from the change in total cash, which is $0.01 billion, to get -$0.39 billion. Rounding to two decimal places, we get -$1.01 billion).

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An area of a rectangle is 32x¹²y⁹ square inches and the length is 8x⁴y³ therefore the expression which represents the width of the rectangle in inches is 4x⁸y⁶.

This is referred to as a quadrilateral with four right angles.

Area of rectangle = Length × width

Width = Area/ Length

       =   32x¹²y⁹  /  8x⁴y³

        = 4x⁸y⁶

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The mean number of hours the students spent listening to music is 31.25 hours.

In statistics, the mean is a measure of central tendency of a set of data. It is also referred to as the arithmetic mean and is calculated by adding up all the values in the data set and dividing by the total number of values.

Mean = (sum of all values) / (number of values)

For example, suppose we have the following set of data: 5, 7, 9, 11, 13. To find the mean, we add up all the values and divide by the total number of values, which is 5 in this case:

Mean = 9

Therefore, the mean of this data set is 9.

The mean is a commonly used measure of central tendency because it takes into account all the values in the data set and is sensitive to changes in the data. However, it can be affected by outliers or extreme values in the data set, which can skew the results.

We can find the mean number of hours spent listening to music using the formula:

mean = (sum of (midpoint of each class) * (frequency of each class)) / (sum of frequencies)

The midpoint of each class can be found by taking the average of the upper and lower class limits.

Using this formula, we get:

mean = ((1.25 + 3.75 + 6.25 + 8.75 + 11.25) * (22 + 15 + 3 + 3 + 1)) / (22 + 15 + 3 + 3 + 1)

mean = (31.25 * 44) / 44

mean = 31.25

Therefore, the mean number of hours the students spent listening to music is 31.25 hours.

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Answer:

y = 18 + b

Step-by-step explanation:

Add 18 to both sides

y = 18 + b

No one bank is not always better. Factors such as the fees and the charges in one bank may differentiate it from another bank.

No, one bank is not always better than another. The best bank for an individual depends on a variety of factors, including their financial needs and preferences, location, and the fees and charges associated with different banks.

For example, one bank may have lower fees for checking accounts but higher fees for ATM withdrawals or international transactions, while another bank may have higher fees for checking accounts but lower fees for other services.

Other factors that might affect which bank has the better fee structure include the type of account, the minimum balance required to avoid fees, and the level of customer service provided by the bank. Ultimately, the best bank is the one that meets an individual's financial needs at the lowest cost.

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