Quadrilateral ABCD has vertices A(2,4), B(5, 4), C(8, 1), and D(5, 1). Graph the image of quadrilateral ABCD after a dilation centered at D with a scale factor of
followed by a reflection in the line x = 1.

So, any positive value of x is 3for this triangle. correct answer is (A)

A triangle is a three-sided polygon that is formed by connecting three straight lines or line segments. It is a basic geometric shape that is commonly studied in mathematics, geometry, and trigonometry. Triangles have a wide range of properties and characteristics that are important in various fields of study, including their angles, sides, and area. Triangles can be classified based on their angles (as acute, right, or obtuse triangles) or based on their sides (as equilateral, isosceles, or scalene triangles). The study of triangles is fundamental in many areas of mathematics and physics and is also important in practical applications such as engineering, architecture, and surveying.

by the question.

PC =7 and PQ= 14

PB = 9 and PR = 6X

Thel's theorem

[tex]PC/PQ =PB/PR\\7/14 = 9/6X\\42X = 126\\ X = 126/42\\ X= 3[/tex]

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a) [tex]$\sum\limits_{n=1}^{\infty} 5\left(\frac{3}{4}\right)^{n-1}$[/tex] series has sum of 20.

What is sum?

In mathematics, the sum of a series is the result obtained by adding together all the terms in a sequence of numbers.

The series that has a sum of 20 is [tex]$\sum\limits_{n=1}^{\infty} 5\left(\frac{3}{4}\right)^{n-1}$[/tex].

To see why, we can use the formula for the sum of an infinite geometric series:

[tex]S = \frac{a}{(1-r)}[/tex]

where S is the sum of the series, a is the first term, and r is the common ratio.

In this case, the first term is:

[tex]a = 5(\frac{3}{4} )^0 = 5[/tex]

And the common ratio is:

[tex]r = \frac{3}{4}[/tex]

So, the formula becomes:

[tex]S = \frac{5}{(1-\frac{3}{4} )}[/tex]

Simplifying the denominator, we get:

[tex]S = \frac{5}{\frac{1}{4}}[/tex]

Multiplying by the reciprocal, we get:

S = 20

Therefore, the sum of the series is 20, which means that the series [tex]$\sum\limits_{n=1}^{\infty} 5\left(\frac{3}{4}\right)^{n-1}$[/tex]

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Step-by-step explanation:

The 84 represents 80% of your grade and the 100 is 20 percent :

84 * 80%   + 100 * 20% =

84 (.8) + 100(.2) = 87.2 %

Drag the following expressions accordingly to complete the proof:

1/sinx· cos x)/ (sinx/cosx  + cosx/sinx) = cos²x

(cos x/sinx)/ ([sin²x/[sinx·cosx] + cos²x/[sinx·cosx]) = cos²x

(cos x/sinx)/ ([sin²x+cos²x] / sinx·cosx) = cos²x

(cos x/sinx)/ ( 1 / sinx·cosx) = cos²x

(cos x/sinx) · (sinx·cosx) = cos²x

Given: (csc x cos x)/ (tan x + cot x) = cos²x

We want to prove the trigonometric identity.

We have:

(csc x· cos x)/ (tan x + cot x) = cos²x

Recall the following trig. expressions and substitute for them:

csc x = 1/sinx

tan x = sinx/cosx

cot x = cosx/sinx

(1/sinx· cos x)/ (sinx/cosx  + cosx/sinx) = cos²x

(cos x/sinx)/ ([sin²x/[sinx·cosx] + cos²x/[sinx·cosx]) = cos²x

(cos x/sinx)/ ([sin²x+cos²x] / sinx·cosx) = cos²x

Recall sin²x+cos²x = 1. Subsitiute for it to get:

(cos x/sinx)/ ( 1 / sinx·cosx) = cos²x

(cos x/sinx) · (sinx·cosx) = cos²x

cosx  · cos x = cos²x

cos²x = cos²x

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Evaluating the function f(x) = [x - 1] at different values of x, f(-1.30)=-3, f(-3)=-4, f(2.3)=1, f(4)=3, and f(7.1)=6

Given the function f(x) = [[x - 1]], we are asked to evaluate f at several values of x.

For x=-1.30, we have:

[tex]$f(-1.30) = [[-1.30 - 1]] = [[-2.30]] = -3$[/tex]

For x=-3, we have:

[tex]f(-3) = [[-3 - 1]] = [[-4]] = -4[/tex]

For x=2.3, we have:

[tex]$f(2.3) = [[2.3 - 1]] = [[1.3]] = 1$[/tex]

For x=4, we have:

[tex]$f(4) = [[4 - 1]] = [[3]] = 3$[/tex]

For x=7.1, we have:

[tex]$f(7.1) = [[7.1 - 1]] = [[6.1]] = 6$[/tex]

Therefore, f(-1.30)=-3, f(-3)=-4, f(2.3)=1, f(4)=3, and f(7.1)=6

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Using equations,

A: y=-x²+6x-5

y=3

3=-x²+6x-5

y=0

B: (x-2) (x-4) =0

C: x-2=0 OR x-4=0

D: x=2 OR x=4

An equation is a mathematical statement that contains the symbol "equal to" between two expressions with identical values. as in 3x + 5 = 15, for example. There are many different types of equations, including linear, quadratic, cubic, etc.

Y=-x²+6x-5

Y=3

Using substitution:

3 = - x²+6x- 5

x²- 6x+8 = 0

Now factor your equation:

x²- 6x+8 = 0

⇒ x² -2x - 4x + 8 = 0

⇒ x (x-2) -4(x-2) = 0

⇒ (x- 2) (x-4) =0

Identify the x-values of the solutions:

x-2=0 or x-4 =0

x=2 or x=4

Identify the solution to the system:

x=2       y=3 and

x=4       y=3

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The correct statements regarding local extrema are:

The point at which the function's highest or minimum value is reached in some open interval containing the point is known as the local extremum (or relative extremum) of the function.

The correct statements regarding local extrema are:

Thus, the correct options are explained above.

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Also, we can contrast many indices and select the most pertinent and reliable one for our individual requirements.

A percentage, which is denoted by the number 100, is a proportion, fraction, or piece of a whole. The Roman phrase per centum, which meaning "by the 100" or "per one hundred," is where the term "percent" originates. A numerical value and the percentage symbol (%) can be used to express percentages.

When deciding whether to believe an index, it's crucial to grasp it because it gives the data being provided context. A statistical measure known as an index reflects changes in a certain set of data across time, across several regions, or among various populations. However, the techniques, calculations, or underlying assumptions used by various indices might vary, which may have an impact on their validity and dependability.

An index, for instance, can be based on a tiny sample size, use biassed data sources, or employ an antiquated methodology that doesn't adequately reflect contemporary trends or circumstances. In certain situations, the index might not accurately represent the phenomenon being assessed, which could result in inaccurate judgements or decisions.

Hence, by comprehending the underlying information, methods, and constraints of an index, we may more accurately evaluate its validity and trustworthiness and make defensible choices according to the data it offers. Also, by contrasting many indices, we can select the one that best suits our unique requirements and is the most reliable.

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Answer:

25

Step-by-step explanation:

To find the value of the expression, all you have to do is plug 9 in for w and plug 8 in for x.

When you plug the numbers in, your equation should look like 9(9)-7(8)

Then you just simplify the expression and get your answer of 25

[tex]9(9)-7(8)\\81-56\\25[/tex]

Approximately 106.79 mg of Tylenol remain in Courtney's body after 4 hours.

What is the capacity of taking medication?

When someone takes medication, it is important to understand how long the medication remains in their system. This can help ensure that the medication is effective and prevent unwanted side effects. In this case, Courtney has taken 250mg of Tylenol to relieve a headache. We are asked to find out how much of the Tylenol remains in her body after 4 hours.

To answer this question, we can use the formula A=250(.73)ⁿ, where A represents the amount of Tylenol remaining in the body after n hours. The value 250 represents the initial amount of Tylenol Courtney took, and 0.73 represents the percentage of Tylenol that is eliminated from the body per hour.

When we substitute n=4 into the formula, we get A= 250(.73)⁴. This means that after 4 hours, approximately 106.79 mg of Tylenol remain in Courtney's body. This calculation assumes that Courtney has not taken any additional Tylenol during this time period.

It is worth noting that individual factors such as age, weight, and metabolism can affect how long a medication remains in someone's system. Additionally, taking medications with other substances, such as alcohol or other medications, can also impact the body's ability to eliminate the medication. Therefore, it is always important to follow the advice of a medical professional and carefully read medication labels and instructions.

A = 250(.73)ⁿ

A = 250(.73)⁴ (substituting n=4)

A ≈ 106.79

In conclusion, we can calculate that after 4 hours, approximately 106.79 mg of Tylenol remains in Courtney's body. It is important to remember that medication elimination can vary based on individual factors, and it is always best to consult a healthcare professional if you have any concerns about medication use or potential side effects.

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[tex]\Large\textbf{Please give complete questions}[/tex]

The given expression can be written in scientific notation as 1.8 x 10² To obtain this, we first divide 2,520,000 by 14,000 to get 180. Then, we express this as 1.8 x 10² by moving the decimal point two places to the left and adding an exponent of 2.

For expressing very big or very small numbers in scientific notation, the number is written as the product of a number between 1 and 10 and a power of 10

To convert a number to scientific notation, first express it in the form a x 10^b, where a is a number between 1 and 10, and b is an integer.

Then, move the decimal point in a to obtain a number between 1 and 10, and add an exponent to 10 that corresponds to the number of places you moved the decimal point.

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Answer: 16

Step-by-step explanation: Solve the parentheses inside first, which should be (3 + 5) (3 - 1). Solve the inside which the answer would be (8) (2). Multiply after (2x8) to get the answer 16

hope it helps!!

Answer:

Step-by-step explanation:

this is a good aswer

Answer:

d = 523.8 miles

Step-by-step explanation:

law of cosines

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Step-by-step explanation:

The drawing attached represents the question. We create a triangle with the distances from each pair of cities, and we call the distance from B to C by 'd'.

First, we need to find the angle BAC:

55° + BAC + 7° = 90°

BAC = 28°

Then, we can use the law of cosines to find the value of d:

d^2 = 470^2 + 890^2 - 2*470*890*cos(BAC)

d^2 = 470^2 + 890^2 - 2*470*890*0.8829

d^2 = 274365.86

d = 523.8 miles

The balance based on the.data given in the table is shown below.

Balance from day 1 to 10 = 11000

Balance from day 11 to 21= 8000

Balance from day 21 to 30- 5500

Balance on day 31 7500

Balance from day 1 to 10= 11000

Balance from day 11 to 21= 8000 Balance from day 21 to 30 5500

Balance on day 31- 7500

The average daily balance of the credit card for the month of december is:

Average daily balance The ratio of total balance from each day in cycle to the total number of days in cycle.

Total balance from each day in cycle=

(11000 x 10)+(8000 × 10)+(5500 x 10) + (7500 x 1) = 104000

Average daily balance=104000 / 31

= 8145

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Answer:

Step-by-step explanation:

Let's start by setting up two variables to represent the number of pounds of type A and type B coffee used in the blend. Let:

x be the number of pounds of type A coffee used

3x be the number of pounds of type B coffee used (since there were three times as many pounds of type B used as type A)

The total cost of the blend is given as $796.00, so we can set up an equation based on the cost of each type of coffee and their respective amounts:

5.95x + 4.65(3x) = 796

Simplifying and solving for x, we get:

5.95x + 13.95x = 796

19.90x = 796

x = 40

Therefore, 40 pounds of type A coffee were used in the blend. To find the number of pounds of type B coffee, we can substitute x = 40 into our expression for the number of pounds of type B:

3x = 3(40) = 120

Therefore, 120 pounds of type B coffee were used in the blend.

Answer: $105,000

Step-by-step explanation:

$140,000-25%deposit =$105,000

Answer:

  z = 0.80

Step-by-step explanation:

You want the value of z such that p(-z < X < z) = 0.5762 for a normal distribution.

The area outside the region of interest will be split evenly between the two tails. That is, the lower tail will hold (1 -0.5762)/2 = 0.2119 of the area of the distribution. The required value of z will be the magnitude of the Inverse CDF function for this value.

The attached calculator shows the required value of z is about 0.80.

Multiply equation 2 by 3. Then subtract the result from equation 1.

Explanation:

The 2nd equation given to us is -2x+y = 8

Triple both sides to get -6x+3y = 24

This means the original system

[tex]\begin{cases}2x-3y = 12\\-2x+y = 8\end{cases}[/tex]

is equivalent to

[tex]\begin{cases}2x-3y = 12\\-6x+3y = 24\end{cases}[/tex]

If we were to add the equations, then the y terms would cancel out because -3y+3y = 0y = 0.

Subtracting the equations will not cancel out the y terms.

-3y minus 3y = -3y -3y = -6y

Therefore the portion saying "Then subtract the result from equation 1." in answer choice B is not correct. It should be "add the equations" or "add the result to equation 1" after tripling both sides of the 2nd equation.

Answer choices A and C say the same thing more or less. Adding the original equations straight down will cancel out the x terms. Therefore, choices A and C are valid approaches to using elimination. We can cross choices A and C off the list.

Step-by-step explanation:

138 = 10 log R

13.8 = log R       anti-log both sides of the equation

10^13.8 = R       Expand L side

6.3 x 10^13  = R

The measures of the numbered angles in the rhombus include the following:

In Mathematics and Geometry, a rhombus can be defined as a type of quadrilateral that is composed of four (4) equal sides and opposite interior angles that are congruent (equal). Additionally, a rhombus typically has two (2) diagonals that bisect each other at right angles (90 degrees).

This ultimately implies that, the opposite sides of a rhombus are parallel and the sum of all the four (4) interior angles is equal to 360 degrees.

m∠3 + 90° + 31° = 180°

m∠3 + 121° = 180°

m∠3 = 180° - 121°

m∠3 = 59°

m∠3 ≅ m∠6 ≅ m∠4 = 59°

Since opposite angles are equal, we have:

m∠1 ≅ m∠5 = 31°

Since the two (2) diagonals bisect each other at right angles (90 degrees), we have:

m∠2 = 90°

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Answer:

B

Step-by-step explanation:

This is known as the Collatz Conjecture, and it remains an unsolved problem in mathematics. Despite extensive computational evidence suggesting that the conjecture is true, a proof or counterexample has yet to be found.

The conjecture states that no matter what positive integer you start with, applying the "3n+1" rule (multiply by 3 and add 1 if n is odd) or "n/2" rule (divide by 2 if n is even) repeatedly will eventually lead to the sequence 4, 2, 1, and then it will loop endlessly: 4, 2, 1, 4, 2, 1, and so on.

While the conjecture has been checked for all starting values up to at least 10^20, no one has been able to prove that it holds true for all positive integers. It is possible that there exists a starting value that does not eventually fall into the 4, 2, 1 loop, but no such value has been found.

Answer:

Step-by-step explanation: Multiply all numbers and add all then divided by the lowest

Let x be the scale factor.

Then, the ratio of the areas of the two triangles is x².

We are given that the larger triangle has an area of 360 square meters and the smaller triangle has an area of 2.5 square meters. So we can set up the equation:

x²(2.5) = 360

Solving for x, we get:

x = sqrt(360/2.5)

x = sqrt(144)

x = 12

Therefore, the scale factor is 12:1. Answer: 12:1.

The rounded off answers for the area of the rectangles are as follows: 1) 24,000, 2) 42,000, 3) 31,200, 4) 31,200.

Rounding of a number is a mathematical process of approximating a given number to a specified level of accuracy or precision. Rounding is done to make numbers easier to work with or to communicate, especially when the number has many decimal places or digits.

The process of rounding involves changing a number to a nearby value that is easier to use or communicate, while still retaining its approximate value. The number is rounded to a certain number of decimal places or significant digits, depending on the required level of accuracy.

1. 5 x 4751 ≈ 5 x 4800 = 24,000.

To check the answer, we can estimate 4751 as 4800, and then multiply 5 by 4800 to get the approximate product of 24,000.

2. 7 x 6000 = 42,000.

To check the answer, we can simply multiply 7 by 6000 to get the product of 42,000.

3. 6 x 5214 ≈ 6 x 5200 = 31,200.

To check the answer, we can estimate 5214 as 5200, and then multiply 6 by 5200 to get the approximate product of 31,200.

4. 8 x 3867 ≈ 8 x 3900 = 31,200.

To check the answer, we can estimate 3867 as 3900, and then multiply 8 by 3900 to get the approximate product of 31,200.

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The following are the scaled off results for the rectangles' area:: 1) 24,000, 2) 42,000, 3) 31,200, 4) 31,200.

The mathematical process of approximating a given number to a predetermined degree of accuracy or precision is known as rounding. In particular when a number has numerous decimal points or digits, rounding is done to make numbers simpler to work with or communicate.

In order to make a number simpler to use or communicate, a number is rounded to a more manageable value while retaining its general meaning.

Depending on the necessary level of accuracy, the number is rounded to a particular number of significant digits or decimal places.

1. 5 x 4751 ≈ 5 x 4800 = 24,000.

To verify the result, we can convert 4751 to 4800, then increase 5 by 4800 to obtain a result that is roughly 20,000.

2. 7 x 6000 = 42,000.

We can quickly multiply 7 by 6000 to obtain the result of 42,000 to verify the solution.

3. 6 x 5214 ≈ 6 x 5200 = 31,200.

By converting 5214 to 5200 and multiplying that number by 6, we can approximate the solution to be 31,200.

4. 8 x 3867 ≈ 8 x 3900 = 31,200.

To verify the solution, we can convert 3867 to 3900 and multiply 8 by 3900 to obtain a result that is roughly 31,200.

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Answer:

x=-5, y=-2

Step-by-step explanation:

2x+4y=-18                (1)

5x-10y=-5                 (2)

apply 5×(1)+2×(2)

10x+20y=-90      (3)

10x-20y=-10   (4)

by adding (3) and (4)

20x=-100

x=-5

put the value of x in  (1)

we get 2×(-5)+4y=-18

⇒y=-2

After solving the given equations, the value of x and y are -5 and -2 respectively.

A mathematical equation is a formula that uses the equals sign to represent the equality of two expressions.

A mathematical statement that has an "equal to" symbol between two expressions with equal values is called an equation.

As in 3x + 5 Equals 15, for instance.

Equations come in a variety of forms, including linear, quadratic, cubic, and others.

So, we have the equations:

2x+4y=-18                (1)

5x-10y=-5                 (2)

Apply as follows: 5×(1)+2×(2)

10x+20y=-90      (3)

10x-20y=-10   (4)

After adding (3) and (4):

20x=-100

x=-5

Insert the value of x in  (1) as follows:

We obtain: 2×(-5)+4y=-18

⇒y=-2

Therefore, after solving the given equations, the value of x and y are -5 and -2 respectively.

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The area of the following shape is 76 units.

What is a hexagon?

A regular hexagon is a closed shape polygon which has six equal sides and six equal angles. In case of any regular polygon, all its sides and angles are equal.

The structure in the figure is hexagon in which two parallel lines are present.

These parallel lines are dividing this hexagon into three parts:

1. Rectangular part with length = 8 units and width = 7 units

2. Triangle of height 2 units.

3. Triangle of height 3 units.

We know,

1. Area of rectangle = L x B

  Area of rectangle = 8 x 7

  Area of rectangle = 56 units

2. Area of triangle 1 = 1/2 x base x height

   Area of triangle 1 = 1/2 x 2 x 8

   Area of triangle 1 = 8 units

3. Area of triangle 2 = 1/2 x base x height

   Area of triangle 2 = 1/2 x 3 x 8

   Area of triangle 2 = 12 units

So, area of hexagon = area of rectangle + Area of triangle 1 + area of triangle 2

Area of hexagon = 56 + 8 + 12

Area of hexagon = 76 units

Therefore, the area of the shape is 76 units.

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