For this question you will write a two-column proof of the first part of the Overlapping Angle Theorem. Use the proof for the Overlapping Segment Theorem as your model for this proof.
You must use the two-column format for this question. Write the proof in your journal and upload your answer. You will be awarded 5 points for the statements and 5 points for the reasons.
Given: m∠KER = m∠MEN
Prove: m∠1 = m∠3

Answer:

The answer is 8 1/2 if simplified if not simplified the answer is 8 3/6

Step-by-step explanation:

You are supposed ti and the whole number 5 and 3 and you multipy 2 to the denominator and the numorator to make it 2/6 + 1/6 which then you and the numorators 2 and 1 to get 3 and you leave the denominator alone. Hope this helps.

In the given formula we have variables:

If we have to solve it for P then it should be called 'Principal' or 'Loan amount'.

If we have to solve it for n then it should be called 'Number of payments' or 'Number of installments'.

Since n is the power of a number we need logarithm to solve it for n.

Answer:

"Principal (loan amount)"

"Term of the loan (in months)" or "Number of monthly payments"

Logarithms

Step-by-step explanation:

Monthly Payment Formula

\(M=\dfrac{Pr\left(1+r\right)^n}{\left(1+r\right)^n-1}\)

where:

If we solve for P, the name of the formula is "Principal (loan amount)".

If we solve for n, the name of the formula is "Term of the loan (in months)" or "Number of monthly payments".

When solving for n, we need to use logarithms:

\(\boxed{\begin{aligned}M&=\frac{Pr\left(1+r\right)^n}{\left(1+r\right)^n-1}\\\\M(\left(1+r\right)^n-1)&=Pr\left(1+r\right)^n\\\\\frac{\left(1+r\right)^n-1}{\left(1+r\right)^n}&=\frac{Pr}{M}\\\\1-\frac{1}{\left(r+1\right)^n}&=\frac{Pr}{M}\\\\\frac{1}{\left(r+1\right)^n}&=1-\frac{Pr}{M}\\\\\left(r+1\right)^{-n}&=1-\frac{Pr}{M}\\\\\ln \left(r+1\right)^{-n}&=\ln \left(1-\frac{Pr}{M}\right)\\\\-n\ln(r+1)&=\ln\left(1-\frac{Pr}{M}\right)\\\\n&=\frac{-\ln\left(1-\frac{Pr}{M}\right)}{\ln(r+1)}\end{aligned}}\)

The ordered pair that is the solution of the given system of inequalities is (2, -2)

A relationship between two expressions or values that are not equal to each other is called inequality.

Given is a system of inequalities, y < -x and 2x+y > 2, we need to determine solution set of the given system of inequalities,

The inequalities are,

y < -x....(i)

2x+y > 2

y < 2-2x...(ii)

To find the ordered pair, put y = -x in equation Eq(ii) and replace < by =

-x = 2 - 2x

x = 2

y = -2

Therefore, the ordered pair, is (2, -2) {look at the graph attached}

Hence, the ordered pair that is the solution of the given system of inequalities is (2, -2)

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The value of a(t) is -1 and b(t) is 55 + \(e^t\)

No, the given equation y' - y = 55 + \(e^t\) is not in the standard form of a first-order linear differential equation.

In the method for solving a first-order linear differential equation, an integrating factor is a function used to transform the equation into a form that can be easily solved.

For an equation in the standard form y' + a(t)y = b(t), the integrating factor is defined as:

μ(t) = e^∫a(t)dt

To solve the equation, you multiply both sides of the equation by the integrating factor μ(t) and then simplify. This multiplication helps to make the left side of the equation integrable and simplifies the process of finding the solution.

To put it in standard form, we need to rewrite it as y' + a(t)y = b(t).

Comparing the given equation with the standard form, we can identify:

a(t) = -1

b(t) = 55 + \(e^t\)

Therefore, The value of a(t) is -1 and b(t) is 55 + \(e^t\)

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Based on the given information and calculations, the decision regarding the null hypothesis is to reject it.

To determine whether the null hypothesis H0: π ≤ 0.70 can be rejected based on the sample of 100 observations with a sample proportion of p = 0.75, we can perform a one-sample proportion test.

First, let's define the significance level α = 0.05.

The decision rule for a one-sample proportion test is as follows:

If the test statistic falls in the rejection region, reject the null hypothesis.

If the test statistic does not fall in the rejection region, fail to reject the null hypothesis.

To determine the rejection region, we need to calculate the critical value.

The critical value corresponds to the value beyond which we reject the null hypothesis. Since H1: π > 0.70, we are conducting a right-tailed test.

Using a significance level of α = 0.05 and the normal distribution approximation for large sample sizes, we can calculate the critical value as:

Z_critical = Zα

where Zα is the Z-value corresponding to the upper α (0.05) percentile of the standard normal distribution.

Now, let's calculate the critical value using a standard normal distribution table or a statistical software. Zα = 1.645 (rounded to two decimal places).

Next, we can calculate the test statistic, which is the standard score for the observed sample proportion.

Z_test = (p - π) / sqrt(π(1 - π) / n)

where p is the sample proportion, π is the hypothesized population proportion, and n is the sample size.

Plugging in the values, we get:

Z_test = (0.75 - 0.70) / sqrt(0.70(1 - 0.70) / 100)

Finally, we compare the test statistic Z_test with the critical value Z_critical to make a decision.

If Z_test > Z_critical, we reject the null hypothesis.

If Z_test ≤ Z_critical, we fail to reject the null hypothesis.

Based on the calculated test statistic and the critical value, we can make a decision regarding the null hypothesis.

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Answer:

x=4, y=5

Step-by-step explanation:

\(x=2y-6\\ x-2y=-6\\\\y=3x-7\\y-3x=-7\\\\\\\\-3x+y=-7\\-3(2y-6)+y=-7\\-6y+18+y=-7\\-5y+18=-7\\-5y=-25\\y=5\\\\\\x=2y-6\\x=2(5)-6\\x=4\)

Answer:1280

Step-by-step explanation:

75% of something is 960 you can use trial and error to find the amount by just doing 75% of a number a little higher than what you got

The solution for the other variable, according to the stated statement, is\(X = 6^y\) and \(y = 21 * 2^X\)

Exponential numbers are represented by an, where an is multiplied by itself n times. An easy example is 8=2³=222. In exponential notation, an is known as the base, whereas n is known as the power, exponent, or index. Scientific notation is an example of an exponential number, with 10 usually typically serving as the base number.

Exponential functions are often employed in the biological sciences to describe the amount of a certain quantity over time, such as population size. Experiment data graphs are often created with time on the x-axis and amount on the y-axis.

a. y = log6(X)

\(6^y = X\)

\(X = 6^y\)

b. \(X = log2(y/21)\)

\(2^X = y/21\)

\(21 * 2^X = y\)

\(y = 21 * 2^X\)

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Answer:

$37046.05

Step-by-step explanation:

new mean wage = beginning mean wage x (105.125%)

                            = 35240 x 105.125%

                            = 37046.05

Answer:

$37,046.05

Step-by-step explanation:

New mean wage :

Answer:

5 is the answer

Step-by-step explanation:

because i said it was

Simultaneous equations can be solved by substitution, elimination, graphs and by matrices.

The values of x, y and z are:

The equations are given as:

\(\mathbf{-x - y -z = -8}\)

\(\mathbf{-4x + 4y +5z = 7}\)

\(\mathbf{2x +2z = 4}\)

Make z the subject in \(\mathbf{2x +2z = 4}\)

\(\mathbf{2z = 4 - 2x}\)

Divide by 2

\(\mathbf{z = 2 - x}\)

Substitute \(\mathbf{z = 2 - x}\) in \(\mathbf{-x - y -z = -8}\)

\(\mathbf{-x - y -z = -8}\)

\(\mathbf{-x - y - (2-x) = -8}\)

\(\mathbf{-x - y - 2+x = -8}\)

Cancel out common terms

\(\mathbf{- y - 2 = -8}\)

Add 2 to both sides

\(\mathbf{- y = -8+2}\)

\(\mathbf{- y = -6}\)

Divide by -1

\(\mathbf{y = 6}\)

Substitute \(\mathbf{z = 2 - x}\mathbf{\ and\ y = 6}\) in \(\mathbf{-4x + 4y +5z = 7}\)

\(\mathbf{-4x + 4 \times 6 + 5 \times (2 - x) = 7}\)

\(\mathbf{-4x + 24 + 5 \times (2 - x) = 7}\)

Open brackets

\(\mathbf{-4x + 24 + 10 - 5x = 7}\)

Collect like terms

\(\mathbf{-4x - 5x =- 24 - 10 + 7}\)

\(\mathbf{-9x =-27}\)

Divide through by -9

\(\mathbf{x =3}\)

Recall that: \(\mathbf{z = 2 - x}\)

So, we have:

\(\mathbf{z = 2-3}\)

\(\mathbf{z = -1}\)

Hence, the results are:

\(\mathbf{x =3}\)

\(\mathbf{y = 6}\)

\(\mathbf{z = -1}\)

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Set up for the volume obtained by rotating about (i) x = 5Volume = ∫πy² dx between

\(0 and y = 8 for x ≥ 5Volume = π∫(5 + √(1 + 3y))² dy between y = 0 and y = 8= π∫(26 + 10√(1 + 3y) + 3y) dy= π\[\left( {26y + 10\int {\sqrt {1 + 3y} dy} + \frac{3}{2}\int {ydy} } \right)\].\)

Given the curves y =\(2x² - x³, x-axis (y = 0), x = 5 and y = 5\).(1) Find A and BA = x-coordinate of the point of intersection of the curves y = 2x² - x³ and x-axis (y = 0)\(0 = 2x² - x³0 = x² (2 - x)x = 0 or\) x = 2Hence A = 0 and B = 2.(2) Set up for the area. Enclosed area = ∫(y = 2x² - x³).

dy between x = 0 and x = 2= ∫(y = 2x² - x³)dy between y = 0 and y = 0 [Inverse limits of integration]= ∫(y = 2x² - x³)dy between x = 0 and x = 2y = \(2x² - x³ = > x³ - 2x² + y = 0\)

Using the quadratic formula, \[x = \frac{{2 \pm \sqrt {4 - 4( - 3y)} }}{2} = 1 \pm \sqrt {1 + 3y} \]

Using x = 1 + √(1 + 3y), y = 0,x = 1 - √(1 + 3y), y = 0.

limits of integration change from x = 0 and x = 2 to y = 0 and y = 8∫(y = 2x² - x³) dy between y = 0 and y = 8= ∫(y = 2x² - x³)dx

between x =\(1 - √3 and x = 1 + √3∫(y = 2x² - x³)dx = ∫(y = 2x² - x³)xdy/dx dx= ∫[(2x² - x³) * (dy/dx)]dx= ∫[(2x² - x³)(6x - 2x²)dx]= 2∫x²(3 - x)dx= 2(∫3x²dx - ∫x³dx)= 2(x³ - x⁴/4) between x = 1 - √3 and x = 1 + √3= 8(2 - √3)\)

\((ii) y = 5Volume = ∫πx² dy between x = 0 and x = 2Volume = π∫(2y/3)² dy between y = 0 and y = 5= π(4/9) ∫y² dy between y = 0 and y = 5= π(1000/27) cubic units(iii) x = -1Volume = ∫πy² dx between y = 0 and y = 8 for x ≤ -1.\).

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Answer:

120

Step-by-step explanation:

betwenn 360 & 600, 120 is the greatest common factor

Let's solve the problems and provide the answers with the correct number of significant figures:

(4.307 × 10^4) × (6.2 × 10^-3)

Multiplying the numbers:

(4.307 × 6.2) × (10^4 × 10^-3) = 26.6974 × 10^1

Since the result is in scientific notation, we multiply the decimal part by the power of 10:

26.6974 × 10^1 = 266.974

To express the answer with the correct number of significant figures, we consider the least number of significant figures in the original values, which is three significant figures in this case.

Therefore, the answer is 267 with three significant figures.

26.127 + 3.9 + 0.0324

Adding the numbers:

26.127 + 3.9 + 0.0324 = 30.0594

To express the answer with the correct number of significant figures, we consider the least number of decimal places in the original values, which is one decimal place in this case.

Therefore, the answer is 30.1 with one decimal place.

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...........................

Since sn = 1/2 - 1/(n + 2), as n → ∞, sn → 1/2. Therefore, the given series converges to 1/2.

The given series is Σn=3∞ 2/(n² - 1)n. We need to express sn as a telescoping sum. Let's start by finding a general formula for the nth term of the series, tn.

tn = 2/(n² - 1)n = 2/[(n - 1)(n + 1)]n.

The given expression can be written as:

Σn=3∞ 2/(n² - 1)n

= Σn=3∞ [1/ (n - 1) - 1/(n + 1)]

Multiplying numerator and denominator of the first term by (n + 1) and the second term by (n - 1), we get

Σn=3∞ [1/ (n - 1) - 1/(n + 1)]

= [1/2 - 1/4] + [1/3 - 1/5] + [1/4 - 1/6] + .......+ [1/n - 1/(n + 2)] + .......

Now, let's find a formula for the nth partial sum, sn.

s1 = [1/2 - 1/4]

s2 = [1/2 - 1/4] + [1/3 - 1/5]

s3 = [1/2 - 1/4] + [1/3 - 1/5] + [1/4 - 1/6]......

s2 = [1/2 - 1/4] + [1/3 - 1/5]

s3 = [1/2 - 1/4] + [1/3 - 1/5] + [1/4 - 1/6]....+ [1/n - 1/(n + 2)]

s3 - s2 = [1/4 - 1/6] + [1/5 - 1/7] + [1/6 - 1/8].....- [1/3 - 1/5]

s4 - s3 = [1/5 - 1/7] + [1/6 - 1/8] + [1/7 - 1/9].....- [1/4 - 1/6]

s4 - s1 = [1/3 - 1/5] + [1/4 - 1/6] + [1/5 - 1/7].....- [1/n - 1/(n + 2)]

It can be observed that, on simplifying sn, the terms get cancelled, leaving only the first and last terms. Hence, sn can be written as:sn = [1/2 - 1/(n + 2)]

Therefore, the given series is a telescoping series, which means that each term after a certain point cancels out with a previous term, leaving only the first and last terms.

Since sn = 1/2 - 1/(n + 2), as n → ∞, sn → 1/2. Therefore, the given series converges to 1/2.

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The provided test cases show the expected output of the Turing Machine for different inputs.

How to design turning machine?

To design a Turing Machine in JFLAP to compute the function f(x) = x (mod 5) represented in unary, follow the steps below:

Test cases:

Input: 1111

Output: 0010

Input: 11111111

Output: 0001

Input: 111111111111111111

Output: 0000

Input: 111111111111111111111111

Output: 0001

Input: 1111111111111111111111111111111111111111

Output: 0010

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A M function file 'tconvert.m', which can convert coordinates (x, y) into Polar from Cartesian coordinates. is:
"```matlab
function [theta, r] = tconvert(x, y)
```"

To create the M function file 'tconvert.m' that converts Cartesian coordinates (x, y) into Polar coordinates, follow these steps:

1. Open the MATLAB Editor or any text editor and create a new file named 'tconvert.m'.

2. In the file, start with the function declaration line: `function [theta, r] = tconvert(x, y)`.

3. Inside the function, write the conversion code using MATLAB's built-in functions:

  - Calculate the angle theta using `atan2(y, x)`, which returns the angle in radians.

  - Calculate the radius r using `sqrt(x^2 + y^2)`, which gives the distance from the origin.

4. End the function with the `end` keyword.

5. Save the file in a directory accessible by MATLAB.

The function 'tconvert' takes the Cartesian coordinates (x, y) as input and returns the corresponding Polar coordinates (theta, r). The angle theta represents the direction in radians, and the radius r represents the distance from the origin.

The function can be called from the MATLAB command window or from another script or function file.

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Complete question:

Write a M function file 'tconvert.m', which can convert from Cartesian coordinates (x,y) into Polar coordinates.

As similarity theorem, the value of x that will make the triangles similar by SSS similarity theorem is 77.

Similarity theorem:

In math, similarity theorem refers the line segment splits two sides of a triangle into proportional segments if and only if the segment is parallel to the triangle's third side.

Given,

Here we need to find the t value of will make the triangles similar by the similarity theorem.

For example, we are told that the 2 triangles are similar by SSS theorem.

Here we know that, SSS means Side - Side -Side and it is a congruence theorem which states that the 3 corresponding sides of two triangles have same ratio, then we can say that the two triangles are congruent by SSS theorem

Therefore, in the triangles ,applying the SSS postulate gives;

=> x/35 = 44/20

Then by applying the multiplication property of equality, let us multiply both sides by 35 to get;

=> x = (44 * 35)/20

When we simplify this one then we get,

=> x = 77

Therefore, the value of x is 77.

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Answer:

a. x = 82 degrees

b. All angles less than 90 degrees are 65 degrees and 33 degrees and 82 degrees in an acute triangle.

Step-by-step explanation:

A triangle has to equal to 180 degrees, add 65 and 33 together to get 98 degrees, subtract 180 from 98 to get 82 degrees.  Part B is self explanatory.

Answer:

59

Step-by-step explanation:

Answer:

I got you it

Step-by-step explanation:

B and have a good day

The solutions to the equation \(2/x - 1 = 16/(x^2 + 3x - 4) are x = 2 and x = (-1 ± √17) / 2.\)

To solve the equation \(2/x - 1 = 16/(x^2 + 3x - 4),\) we'll simplify and rearrange the equation to isolate the variable x. Here's the step-by-step solution:

1. Start with the given equation: 2/x - 1 = 16/(x^2 + 3x - 4)

2. Multiply both sides of the equation by x(x^2 + 3x - 4) to eliminate the denominators:

\(2(x^2 + 3x - 4) - x(x^2 + 3x - 4) = 16x\)

3. Simplify the equation:

\(2x^2 + 6x - 8 - x^3 - 3x^2 + 4x - 16x = 16x\)

4. Combine like terms:

  -x^3 - x^2 + 14x - 8 = 16x

5. Move all terms to one side of the equation:

\(-x^3 - x^2 - 2x - 8 = 0\)

6. Rearrange the equation in descending order:

  -x^3 - x^2 - 2x + 8 = 0

7. Try to find a factor of the equation. By trial and error, we find that x = 2 is a root of the equation.

8. Divide the equation by (x - 2):

\(-(x - 2)(x^2 + x - 4) = 0\)

9. Apply the zero product property:

  x - 2 = 0 or x^2 + x - 4 = 0

10. Solve each equation separately:

   x = 2

11. Solve the quadratic equation:

   For x^2 + x - 4 = 0, you can use the quadratic formula or factoring to solve it. The quadratic formula gives:

 \(x = (-1 ± √(1^2 - 4(1)(-4))) / (2(1)) x = (-1 ± √(1 + 16)) / 2 x = (-1 ± √17) / 2\)

Therefore, the solutions to the equation\(2/x - 1 = 16/(x^2 + 3x - 4) are x = 2 and x = (-1 ± √17) / 2.\)

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Answer:

$350 left lost 50$

Step-by-step explanation:

Answer:

Step-by-step explanation:

Hndnenenennjejejejekwkkwnwbfnfn

Answer:

????????????????????????????????

Step-by-step explanation:

The product of the rational expression shown above include the following: B. x² - 36/(x² - 9).

In Mathematics, a rational expression simply refers to a type of expression  which is expressed as a fraction. This ultimately implies that, a rational expression is composed of two (2) main parts and these include the following:

In this exercise, we would determine the product of the numerator for this rational expression and the product of the denominator for this rational expression as follows;

Product of numerator = (x + 6)(x - 6)

Product of numerator = x² + 6x - 6x - 36

Product of numerator = x² - 36

For the denominator, we have the following:

Product of denominator = (x + 3) × (x - 3)

Product of denominator = x² - 3x + 3x - 9

Product of denominator = x² - 9

Therefor, the product of the rational expression is given by x² - 36/(x² - 9).

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Answer:

131.95 in

Step-by-step explanation:

C=2πr

C=2π(21)

C= 131.95 in

Answer:

131.88

Step-by-step explanation:

42x π(3.14)=131.88