Segment AC is the angle bisector of The figure is not to scale.


Which of the following additional statements would allow us to prove that

The equation shows the parallel line.

The graph is simply a structured representation of the data. It aids in our comprehension of the data. The numerical information gathered through observation is referred to as data.

In a line graph, the information or data is represented as a series of markers, or dots, and is then connected to one another by a straight line.

Given:

y = -x-1......................(1)

y = -x + 2...................(2)

Solving equation (1) and (2) we get

-x -1 = -x +2

0 = 3

Now, if compare the given equation then the equation gives the relation of Parallel lines.

Thus, the equation do not represent the same line.

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In 2020, Ramiro paid $4,537.22 for Social Security tax and $1,061.70 for Medicare tax

What is Percentage?

Percentage is a way of expressing a number as a fraction of 100. It represents a proportion or rate out of 100, and is often used to compare values or to express a change or growth.

Solution:

To find how much Ramiro paid for Social Security and Medicare taxes in 2020, we can follow these steps:

1. Calculate the amount of Ramiro's income that is subject to Social Security tax. In 2020, Social Security tax was only applied to the first $137,700 of income. Since Ramiro's income of $73,210 is less than $137,700, all of his income is subject to Social Security tax.

2. Calculate the amount of Social Security tax that Ramiro paid. Since Social Security tax was 6.2% of income in 2020, Ramiro paid:

3. Social Security tax = 0.062 x $73,210 = $4,537.22

1. Calculate the amount of Medicare tax that Ramiro paid. Medicare tax was 1.45% of all income, with no income limit. Therefore, Ramiro paid:

2. Medicare tax = 0.0145 x $73,210 = $1,061.70

Therefore, in 2020, Ramiro paid $4,537.22 for Social Security tax and $1,061.70 for Medicare tax, for a total of $5,598.92 in Social Security and Medicare taxes.

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On solving the provided question we can say that the equations are  y = 3x - 6 and y = -2x + 8

A mathematical equatiοn is a fοrmula that joins two statements and uses the equal symbol (=) to indicate equality. A mathematical statement that establishes the equality of twο mathematical expressions is known as an equation in algebra. Fοr instance, in the equatiοn 3x + 5 = 14, the equal sign places the variables 3x + 5 and 14 apart. The relatiοnship between the twο sentences οn either side of a letter is described by a mathematical formula. Often, there is οnly one variable, which alsο serves as the symbοl, fοr instance, 2x – 4 = 2.

the equations are

y = 3x-6

y = -2x+8

3x - 6 = -2x+8

5x -6 = 8

5x = 14

x = 14/5

Now solve for y:

y = 3(14/5) - 6

y = 42/5 - 6

y=42/5 - 30/5

y = 12/5

The position 12/5 is where these two lines cοnverge. The triangle created by these two lines and the x-axis has a height equal to this.

So that we can identify the triangle's base, let's lοcate the roots of these equations (where they contact the x-axis).

Put a 0 in both equations.

(I) 0 = 3x - 6  

6 = 3x

x = 2  

Set the second equation equal to 0.

(II)  y = -2x+8

2x = 8

x = 8/2

x = 4

The triangle has a base between the numbers (2, 0) and (4, 0), giving it a length of two units.

The triangle has a height of 12/5 units.

Area of a Triangle:

A = 1/2bh

A = (1/2) · (2) · (12/5)

A = 12/5

The region between the x-axis that is enclosed by the lines y = 3x - 6 and y = -2x + 8 has a 12/5 unit area.

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The correct value of the expression is,

⇒ (2²)³ - (8 - 4)² × 4 = 0

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The expression is,

⇒ (2²)³ - (8 - 4)² × 4

Now, We can solve as;

⇒ (2²)³ - (8 - 4)² × 4

⇒ (4)³ - (4)² × 4

⇒ 4³ - 4³

⇒ 64 - 64

⇒ 0

Thus, We get;

⇒ (2²)³ - (8 - 4)² × 4 = 0

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The number of cups of mix that is needed to be used will be 12.8 cups.

Any value assigned to a variable that results in equal outcomes, i.e., tends to equalize the Left Hand Side (LHS) and Right Hand Side (RHS) of the formula equal, is a solution to a formula. To solve a problem, you must find the formula's workable answer.

For every 2 cups of mix in a lemonade recipe, there should be 3 cups of water. Lemonade made with this recipe makes 5 cups.

Let 'W' be the amount of water in gallons and 'M' be the amount of mix in gallons.

Then the equations are given as,

W / M = 3 / 2            ...1

W + M = 2               ...2

From equations 1 and 2, then we have

(3/2)M + M = 2

(5/2)M = 2

M = 4/5

M = 0.80 gallons

We know that in one gallon, there are 16 cups. Then we have

M = 0.80 x 16

M = 12.8 cups

The number of cups of mix that is needed to be used will be 12.8 cups.

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When x = 6 and y = 8, the expression that s given as x^2+y^2/10 is calculated by substituting the given values and it is equal to 42.4.

The expression to evaluate is: x^2 + y^2/10.

To evaluate this expression when x = 6 and y = 8, we substitute these values into the expression and then perform the arithmetic operations according to the order of operations (PEMDAS).

PEMDAS stands for Parentheses, Exponents, Multiplication and Division (performed left to right), and Addition and Subtraction (performed left to right). The order of operations ensures that we always evaluate expressions in a consistent and unambiguous manner.

So, we have:

x^2 + y^2/10 = 6^2 + 8^2/10

= 36 + 64/10

= 36 + 6.4

= 42.4

Therefore, when x = 6 and y = 8, the value of the expression x^2 + y^2/10 is 42.4.

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The ordered pairs that are solution to the system are (15, -1) (0,4) (10, 30) (5, 5) (1, 10)​

From the question, we have the following parameters that can be used in our computation:

2x + 3y>10

y≥ -3x + 2

Represent properly

2x + 3y > 10

y ≥ -3x + 2

Next, we make a plot of the system to determine the solution

The shaded area in the plot represent the solution to the inequality

In this case, the coordinates in the shaded area are

(15, -1) (0,4) (10, 30) (5, 5) (1, 10)​

None of the options represent the shaded area (see attachment)

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The length of CF is given as 45 cm

Since AE is the altitude of the parallelogram ABCD, it is perpendicular to the base DC. Similarly, CF is the altitude of the triangle ACD, and it is perpendicular to the base AD.

Let's use the properties of parallelograms and triangles to solve for the area and length of CF.

Since ABCD is a parallelogram, we know that opposite sides are parallel and equal in length. Therefore, BC = AD = 6 cm.

To find the area of the parallelogram, we can use the formula:

ar(ABCD) = base × height

We can choose any base and height, as long as they form a right angle. Since we know AE is the altitude of the parallelogram, we can use it as the height. Let's choose base AB, which is perpendicular to AE. Therefore,

ar(ABCD) = AB × AE = 12 cm × 7.5 cm = 90 cm²

So, the area of the parallelogram ABCD is 90 cm².

Now, let's find the length of CF. Since CF is the altitude of the triangle ACD, we can use the formula for the area of a triangle:

ar(ACD) = 1/2 × base × height

where the base is AD and the height is CF. We know the area of the triangle ACD is half the area of the parallelogram ABCD, which is 90/2 = 45 cm². Therefore,

45 cm² = 1/2 × 6 cm × CF

Simplifying this equation, we get:

CF = (45 cm² × 2) / (6 cm) = 15 cm

So, the length of CF is 15 cm.

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Answer:

$500 gain

Step-by-step explanation:

Sonu spent $2500 on the fridge itself, and he also spent an additional $300 on the repairs. He spent a total of $2800. He sold the fridge for $3300.

To find the loss or gain, we can subtract 2800 from 3300 to see how much total profit he made.

3300-2800=500

Sonu made a $500 gain.

Answer:

$500 gain

Step-by-step explanation:

mark me please

The equivalent expression to 50(1 + 0.15) is (b) 50(1.15)

From the question, we have the following parameters that can be used in our computation:

50(1 + 0.15)

When the expression in bracket is simplified,

We have the following representation

50(1.15)

The above expression is in option (b)

Hence, the equivalent expression is (b)

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The final count of integers between 3 and 89 that cannot be written as the sum of exactly two elements of the set is 39.

To determine the number of integers between 3 and 89 that cannot be written as the sum of exactly two elements of the set {1, 2, 3, 5, 8, 13, 21, 34, 55}, we can use a process of elimination.

First, we can list all the possible sums of two distinct elements of the set. This gives us a total of 28 sums.

Next, we can identify all the integers between 3 and 89 that can be expressed as the sum of two distinct elements of the set. We can do this by checking each integer between 3 and 89 to see if it can be written as a sum of two elements of the set. If an integer can be written as a sum of two elements of the set, we can cross it off the list.

After eliminating all the integers that can be written as a sum of two elements of the set, we are left with the integers that cannot be expressed as such.

In summary, we can determine the number of integers between 3 and 89 that cannot be written as the sum of exactly two elements of the set by listing all possible sums, identifying the integers that can be expressed as such sums, and eliminating them from the list.

The remaining integers are those that cannot be expressed as the sum of exactly two elements of the set.

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All three cities have the same transformed sine wave, but with different amplitude, period, phase shift, and midline shift values.

A sine wave is a mathematical function that depicts an oscillation that is smooth and repeated. It exists in nature and is useful in many disciplines of research and engineering. It is also employed in a variety of electrical signals, including alternating current (AC).

In the given question,

City 1: Miami

f(x) = 0.48 sin(0.27(x-1.5)) + 0.77

The parent function f(x) = sin(x) has been transformed in several ways, such as the amplitude being changed from 1 to 0.48, the period being changed from 2π to 0.27π, the phase shift being changed from 0 to 1.5, and the midline being shifted up by 0.77. This means that the function is shifted up from the midline of the parent function.

City 2: Honolulu

f(x) = 0.24 sin(0.13(x+1.25)) + 0.86

The parent function f(x) = sin(x) has been transformed in several ways, such as the amplitude being changed from 1 to 0.24, the period being changed from 2π to 0.13π, the phase shift being changed from 0 to 1.25, the midline being shifted up by 0.86, meaning the function is shifted up from the midline of the parent function.

City 3: Austin

f(x) = 0.41 sin(0.21(x-1)) + 0.86

The parent function f(x) = sin(x) has been transformed in several ways, such as the amplitude being changed from 1 to 0.41, the period being changed from 2π to 0.21π, the phase shift being changed from 0 to 1, and the midline being shifted up by 0.86. This means that the function is shifted up from the midline of the parent function.

According to the data supplied, all three cities appear to have the same converted sine wave, but with distinct amplitude, period, phase shift, and midline shift values.

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After 5 hours of snow falling, Kaj would have 9.5 inches of snow on her lawn.

What is Algebraic expression ?

Algebraic expression can be defined as combination of variables and constants.

After 3 hours of snow falling, Kaj would have:

7 + 0.5(3) = 8.5 inches of snow on her lawn.

To find how much snow Kaj would have on her lawn after t hours of snow falling, we can use the following formula:

S = 7 + 0.5t

where S is the amount of snow on Kaj's lawn in inches and t is the time in hours since the beginning of the snowstorm.

For example, if we wanted to find how much snow Kaj would have on her lawn after 5 hours of snow falling, we could substitute t = 5 into the formula:

S = 7 + 0.5(5) = 9.5

Therefore, After 5 hours of snow falling, Kaj would have 9.5 inches of snow on her lawn.

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Answer:

600 calories

Step-by-step explanation:

The problem asks us to use the given trend line to find how many calories are burned after 40 minutes. The trend line is the slope of the graph that is given, so all that we have to do is find 40 minutes on the x axis, and then find the point on the slope in the given graph that has an x value of 40, and this point ends up being (40, 600). This means that in 40 minutes, 600 calories are burned.

the probability of getting a head on the next flip is estimated to be 0.81. The probability of getting two heads in a row would be the square of this probability, or 0.81 * 0.81 = 0.6561.

The probability of getting a head on any single flip of a fair coin is 1/2. However, based on the results of the previous 100 tosses, we can estimate the probability of getting a head on the next flip as the ratio of heads to total tosses, which is 81/100 or 0.81. So, the probability of getting a head on the next flip is estimated to be 0.81. The probability of getting two heads in a row would be the square of this probability, or 0.81 * 0.81 = 0.6561. The mathematical concept of probability quantifies the possibility that an event will occur. A number between 0 and 1, where 0 denotes an improbable event and 1 denotes a certain event, is used to express it. Events with intermediate probabilities (between 0 and 1) indicate a likelihood of occurrence that is between impossible and certain. The sum of the probabilities of all possible outcomes of an event must equal 1. Probability is used to make predictions and inform decision making in fields such as statistics, finance, and insurance.

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Complete Question

Suppose you toss a coin 100 times and get 81 heads and 19 tails. Based on these results, what is the probability that the next flip results in a head head?

Answer:

Step-by-step explanation:

The simplified expression after rationalizing the denominator are:

1)  (17 + √3)/13.

2) -3(2+√5)/5.

What is rationalizing the denominator?

To rationalize the denominator with two terms, find the conjugate of the denominator. Then multiply and divide the fraction by the conjugate of the denominator.

1).

a) The conjugate of the denominator is 4 + √3.

b) To rationalize the denominator, we need to multiply both the numerator and the denominator by the conjugate of the denominator:

(5/4 - √3) * (4 + √3) / (4 + √3) * (4 - √3)

Simplifying the numerator:

5(4) + 5(√3) - 4(√3) - 3 / 13

= (17 + √3)/13

Therefore, the simplified expression after rationalizing the denominator is (17 + √3)/13.

2).

a) The conjugate of the denominator is 1 - √2.

b) To rationalize the denominator, we need to multiply both the numerator and the denominator by the conjugate of the denominator:

2 / (1 - √2) * (1 + √2) / (1 + 2)

Simplifying the numerator:

2(1 + √2) / (-1 + 2)

= -2(1 + √2)

Therefore, the simplified expression after rationalizing the denominator is -2(1 + √2).

a) The conjugate of the denominator is 2 + √5.

b) To rationalize the denominator, we need to multiply both the numerator and the denominator by the conjugate of the denominator:

3 / (2 - √5) * (2 + √5) / (2 + √5)

Simplifying the numerator:

3(2 + √5) / (-5)

= -3(2+√5)/5.

Therefore, the simplified expression after rationalizing the denominator is -3(2+√5)/5.

Hence, the simplified expression after rationalizing the denominator are:

1)  (17 + √3)/13.

2) -3(2+√5)/5.

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Answer:

-2, 2

Step-by-step explanation:

trust me

The area of the trapezoid is given as 40 cm square

The formula for the trapezoid is given as

A = (a + b) / 2 * h

the question did not tell us the sides hence I have taken

a = 6

b = 10

h = 5 cm

such that we would have

6 + 10 / 2 * 5

8 * 5

= 40 cm square

Hence the area of the trapezoid is given as  40 cm square

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Answer:7

Step-by-step explanation:

let P(a)=27, like cold tea,

    P(b)=42, like hot tea,

  P(a∪b)=62,

using formula,

P(a∩b)=P(a)+P(b)-P(a∪b)

            =27+42-62

             =7

Rounding to the nearest whole number, the magazine will have 34638 subscribers in 10 years.

What is  whole number?

A whole number is a positive integer that doesn't include any fractional or decimal component. Whole numbers include positive integers such as 0, 1, 2, 3, 4, and so on. Whole numbers do not include fractional numbers or decimals, such as 0.5, 1.7, and so on. Whole numbers are used to count items or represent discrete quantities, such as the number of people in a room or the number of apples in a basket.

If the prediction that magazine subscriptions will drop by 10% each year is correct, then in 10 years the number of subscribers for a magazine with 98000 subscribers will be:

98000 * (1 - 0.10)^10 = 98000 * 0.3548 = 34638 subscribers

So, rounding to the nearest whole number, the magazine will have 34638 subscribers in 10 years.

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The table of values satisfies the linear equation y = −3x/4 − 6 is: C. table C.

In order to determine which ordered pairs are valid and true solutions based on the given linear equation, we would have to test the given ordered pairs by substituting their values into the linear equation as follows;

For ordered pair (-4, -9), we have:

y = −3x/4 − 6

-9 = −3(-4)/4 − 6

-9 = 3 − 6

-9 = -3 (False).

For ordered pair (-8, -12), we have:

y = −3x/4 − 6

-12 = −3(-8)/4 − 6

-12 = 8 − 6

-12 = 2 (False).

For ordered pair (-4, -3), we have:

y = −3x/4 − 6

-3 = −3(-4)/4 − 6

-3 = 3 − 6

-3 = -3 (True).

For ordered pair (0, -6), we have:

y = −3x/4 − 6

-6 = −3(0)/4 − 6

-6 = 0 − 6

-6 = -6 (True).

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Complete Question:

Which table of values satisfies the linear equation y = −3x/4 − 6?

Answer:

  n = 7

Step-by-step explanation:

You have a geometric sequence with first term 625 and common ratio 1/5, and you want to know the number of the term whose value is 1/25.

The general term of a geometric sequence is ...

  tn = t1·r^(n-1)

Using the given values, we can solve for n:

  1/25 = 625·(1/5)^(n-1)

  1/(5^2·5^4) = 1/5^(n-1) . . . . . . divide by 625; write as powers of 5

Comparing exponents of 5, we have ...

  6 = n -1

  7 = n

The value of n for which tn = 1/25 is 7.

__

Additional comment

The attachment shows the first 7 terms of the sequence.

<96141404393>

Answer: The number of blue marbles in the sample is 11, so the proportion of blue marbles in the sample is 11/20. If the sample is representative, we can use this proportion to estimate the proportion of blue marbles in the whole bag of 950 marbles. So, our estimate of the number of blue marbles in the whole bag is:

950 * (11/20) = 477.5

So, we can estimate that about 478 marbles out of 950 are blue.

Step-by-step explanation:

Ivan would expect to make $43.67 in profit if he had 50 customers.

From the question, we have the following parameters that can be used in our computation:

Expected Profit = 1.45 • Customers – 28.83.

If Ivan had 50 customers, using the least squares regression equation, the expected profit would be:

Expected Profit = 1.45 * 50 - 28.83

So, we have

Expected Profit = 72.5 - 28.83

Evaluate the difference

Expected Profit = 43.67

Hence, the expected profit is $43.67

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Complete question

Ivan has a lemonade stand. He keeps records of his daily profits and how many customers he had that day. The scatter plot shows his profits versus the number of customers for 25 days.

The least squares regression equation is:

Expected Profit = 1.45 * Customers - 28.83.

How much profit would Ivan expect to make if he had 50 customers?

The total cost of the fencing can be expressed as a function of x: C(x) = $24x.

Let's assume that the width of the soccer field is x feet. Then the length of the soccer field is 3x feet.

The east and west sides have a combined length of 3x feet, and the cost per foot of fencing is $6, so the total cost for the east and west sides is $6 * 3x = $18x.

The north and south sides have a combined length of 2x feet, and the cost per foot of fencing is $3, so the total cost for the north and south sides is $3 * 2x = $6x.

The total cost of the fencing is the sum of the cost of the east and west sides and the north and south sides: $18x + $6x = $24x.

So, the total cost of the fencing can be expressed as a function of x: C(x) = $24x.

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Answer:

[tex]104 ft^2[/tex]

Step-by-step explanation:

The answer is [tex]104 ft^2[/tex].

Divide the shape into 3 different rectangles. Now we have 2 rectangles that are 5 by 4.

The last rectangle is 16 by 4. (8-4 =4)

This is because 6+5+5=16.

Then you add up the area to get the whole figure.

The two smaller rectangles are 20 each or 40 altogether and the larger rectangle is 64.

When you add it up you get an area of [tex]104 ft^2[/tex]

The required equation models the cost of renting a moving truck for u-move-it based on the number of hours the truck is rented is C = 49 + 16(t - 1). Option A is correct.

The equation model is defined as the model of the given situation in the form of an equation using variables and constants.

Here,
To determine the equation model for the cost of renting a moving truck for u-move-it based on the number of hours the truck is rented we need to put values on (specific one ordered pair in the given equation) to determine the correct equaiton model,

So, for hours of rented is 1.
For A,

C = 49 + 16(1 - 1) = 49   [satisfy the eqation]

Similarly,
For b
C = 16t = 16   [not satisfied]

For C,
C = 49 + 16t = 65   [not satisfied]

For D,
C = 49 + 16(t + 1) = 81  [not satisfied]

Thus, the required equation models the cost of renting a moving truck for u-move-it based on the number of hours the truck is rented is C = 49 + 16(t - 1) . Option A is correct.

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Answer:

6 is not the solution.  7 is the solution.

Step-by-step explanation:

5(x -3) = x + 13  Substitute 6 for x

5(6 -3) = 6 + 13

5(3) = 19

15 ≠ 19

6 is not a solution because it results in a false statement.  The two sides do not equal each other.

5(x - 3) = x + 13   Distribute the 5

5x -15 = x + 13  Subtract x from both sides

5x - x - 15 = x - x + 13

4x - 15 = 13  Add 15 to both sides

4x - 15 + 15 = 15 + 13

4x = 28  Divide both sides by 4

x = 7

7 is the solution to the equaion.

The equation of the straight line would be -

y = 2x.

Given is that a straight line passes through the points (2, 4) and (3, 6).

We can write the slope as -

m = (6 - 4)/(3 - 2)

m = 2/1

m = 2

For the point (2, 4), we can write -

y = 2x + c

c = 4 - 4

c = 0

Therefore, the equation of the straight line would be -

y = 2x.

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