(A) Prove that the opposite sides of the rectangle are congruent.
Use Distance Formula: v(x2 - x1)^2 + (y2 - y1)^2

(B) Prove the diagonals of your rectangle are congruent.

(C) Using the slopes for each side, prove there are 4 right angles on the rectangle.

**Please Show All Work**

So for the maximum area, the values of the width and length of the  rectangle will  be  2.121.

Since we know that the formula for the area of a rectangle is:

A = XY, where x and y are the width and length

since we are given the are, y=√(9-x²), so

A = √(9-x²)

taking the derivative on both sides and considering it to be zero, we get

A' = (x/√(9-x²)(-2x) + √(9-x²) = 0, after multiplying by √(9-x²)

A' = -x² + 9 -x² = 0

=>-2x² =-9

=>x² = 9/2

=> x = 3/√2

so x=2.121 so the for y = √(9-(2.121)^2) =  √(9-4.498) = 2.121

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A rectangle is bounded by a  semicircle y = radical 9 − x^2 and the x-axis. What length and width should the rectangle be to maximize the area

The inequality x - 4 ≥ 8 represents the sentence "  the sum of a number and -4 is at least 8" and the solution of the inequality is the value of variable x is x ≥ 12.

Inequality is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are not equal.

Let's assume that the number would be x

The sum of a number and -4 is at least 8

According to the given question, translate the phrase into an algebraic form :

x - 4 ≥ 8

Add 4 both sides of the above inequality,

x - 4 + 4 ≥ 8 + 4

x ≥ 12

Therefore, the inequality x - 4 ≥ 8 represents the sentence "  the sum of a number and -4 is at least 8" and the solution of the inequality is the value of variable x is x ≥ 12.

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Answer:

Part B:16.5

Step-by-step explanation:

Answer

b

Step-by-step explanation:

In this case we are multiplying the numbers and dividing them.

Fist we got to work with are numbers given the equation.

Given:

[tex]1, 5[/tex]

Therefore, the equation is:

[tex]75 / 3\\5x3[/tex]

Therefore, the correct answers are 1 = 25, 5 = 125 and 3 = 75

The polynomial function over the complex numbers is,

(x + 1i) ( x - 1i) (x+ 7) ( x + 2).

What is factoring a polynomial?

Factorization of polynomials, also known as polynomial factorization, is a mathematical and computer algebraic technique that combines irreducible factors with coefficients in the same domain to produce a polynomial with coefficients in a given field or in integers.

Consider, the given polynomial

f(x) = x^4 + 9x^3 + 15x^2 + 9x + 14

We can use a factoring "trick" here....write this as

x^4 +  9x^3 + 14x^2  + x^2  + 9x  + 14 = 0    factor by grouping

x^2 ( x^2 + 9x + 14)  +  1 ( x^2 + 9x + 14) = 0

(x^2 + 1) (x^2 + 9x + 14) = 0

(x^2 + 1) (x^2 + 9x + 14) = 0

⇒ (x^2 + 1) = 0,  (x^2 + 9x + 14) = 0

x^2 = -1,          x^2 + 7x + 2x + 14 = 0

x = ±i ,              x(x + 7) + 2(x + 7) = 0

x = ±i ,              (x + 7)(x + 2) = 0

⇒ (x + i)(x - i)(x + 7)(x - 7) = 0

(x + 1i) ( x - 1i) (x+ 7) ( x + 2) = 0

Hence, the polynomial function over the complex numbers is,

(x + 1i) ( x - 1i) (x+ 7) ( x + 2).

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Answer:

3

Step-by-step explanation:

75/15=

             __3_________

   15    /   75

          -    75

     ---------------------------------

                   0

Have a great day

There are 65, 19-bit sequences of 0s and 1s that start with a 0 and end with a 0 that exist.

Any subsequent 0 in the sequence must come exactly two or three spots down from the previous one.

We begin at point 1 and finish at position 19 in this instance.

That is, we advance along the line a whole of 18 positions.

In order to achieve 18, we must add all series consecutive 2s and 3s.

There are numerous methods for doing this:

Case 1: There is just one possible arrangement for nine 2s.

Case 2: Two 3s with six 2s - thus ⁸C₂ ways = 28 ways

Case 3: Four 3s with three 2s - thus ⁷C₄ ways = 35 ways

Case 4: Six 3s - Only 1 way to arrange.

Thus, the number of arrangements = 1 + 28 + 35 + 1 = 65 .

Therefore ,the total possible number of the sequence that cane be made is 65 .

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Using simple mathematical operations, we can conclude that there are 250 sheets in a stack.

A mathematical function known as an operation converts zero or more input values into a precisely defined output value.

The quantity of operands affects the operation's arity.

The order of operations refers to the rules that govern how to solve an expression with several operations.

Parentheses, Exponents, Multiplication, Division, Addition, and Subtraction are all referred to as PEMDAS (from left to right).

So, the number of sheets in the stack is represented by n.

According to the information provided, a stack of tissue paper is roughly 2.5 inches high.

The thickness of each sheet is roughly 0.01 inches. Determine the number of sheets in the stack, please.

N sheets' thickness would be.

We'll now compare the thickness of n sheets to the thickness of the stack as follows:

0.01n = 2.5

Now, solve for n as follows:

0.01n/0.01 = 2.5/0.01

n = 250

Therefore, using simple mathematical operations, we can conclude that there are 250 sheets in a stack.

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It will cost his parents $187.5 to invite 15 friends to his party because it cost $12.5 to invite just one.

The unitary approach involves calculating the value of a single unit, from which we may calculate the values of the necessary number of units. A single or distinct unit is referred to by the word unitary. Therefore, the goal of this strategy is to establish values in reference to a single unit. The unitary technique, for instance, may be used to calculate how many kilometers a car would go on one litre of gas if it travels 44 km on two litres of fuel.

Here,

For inviting 20 friends, The cost of party was $250.

So for 1 friend,

=250/20

=$12.5

Now he wish to invite 15 friends,

=12.5*15

=$187.5

The cost of inviting 15 friends to his party will cost $187.5 to his parents as cost of inviting 1 friend was $12.5.

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The expression 0.3d = 0.95 could be used to find the number of dimes he has.

A mathematical expression is made up of terms (constants and variables) separated by mathematical operators. A mathematical equation is used to equate two expressions. Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.

We have joe who has dime and nickels in his piggy bank totaling $1.45 the number of nickels. He has is 5 more than twice the number of dimes [d].

We can write the the number of nickels as -

[n] = 2d + 5

0.1d + 0.1(2d + 5) = 1.45

0.1d + 0.2d + 0.5 = 1.45

0.3d = 0.95

Therefore, the expression 0.3d = 0.95 could be used to find the number of dimes he has.

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Answer: 7/12

Step-by-step explanation: First, flip the 4/3 to its reciprocal and change it to multiplication. Then, you can simplify the 9 and 3 to 3 and 1. After that, multiply straight across. Hope this helps! :)

Answer:

1. 7/9 ÷ 4/3 As a fraction) 21/36

2. 7/9 ÷ 4/3=21/36 as a simplified fraction) 7/12

3. 7/9 ÷ 4/3 As a decimal) 0.583

4. 7/9 ÷ 4/3 As a percentage) 58.3%

Let's see how it's done!

7/9 ÷ 4/3:

7/9 ÷ 4/3 (Invert or flip the second fraction and multiply across)

7/9 x 3/4 = 21/36

How to simplify 21/36

21/36 ÷ 3 (Divide the numerator "the top part of the fraction" and the denominator "the bottom part of the fraction" by 3. This will equal 7/12

How to turn 21/36 into a decimal

21 divided by 36 = 0.5833333333333333...

Round to the nearest thousandth: 0.583

How to turn 0.583 into a percent

Move the decimal point 2 places to the left, drop the zero(s)

and add the percent sign! 58.3%

These are all the same answer but in different forms and how to do them!

Hope it helps!

Step-by-step explanation:

so, if I understand correctly :

angle A = 22°

angle B = 53°

angle D = 38°

remember : the sum of all 3 angles in every triangle is always 180°.

so,

180 = 22 + 53 + AEB

angle AEB = 180 - 22 - 53 = 105°

per the attributes of crossing lines the angles between them are the same on both sides of any of the lines (just left-right mirrored).

so, CB and AD are crossing lines, therefore

angle AEB = angle CED = 105°

and then

180 = 105 + 38 + C

angle C = 180 - 105 - 38 = 37°

Answer:

24%

Step-by-step explanation:

Walmart has 152/200 employees, simplify that to a number over 100, you get 76/100. 100-76=24

Answer:

Step-by-step explanation:

152/200 = .76

100-76 = 24

=24%

Therefore, the percentage the amount of workers decrease is by 24%.

Please do tell if this helps!

The volume of the cylinder is 10,099.09 inches³.

Here we have to find the volume of the cylinder.

Given data:

Circumference = 46 inches

height(h) = 5 foot = 12 × 5 = 60 inches

Circumference = 2πr

46 = 2 ×π × r

r = 23/π

The formula for the volume of the cylinder = πr²h

Volume = π( 23/π)² 60

               = 529× 60 / π

               = 10,099.09 inches³

Therefore the volume is 10,099.09 inches³.

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The period of the solar system's orbit is 2.05 x 108 years.

What is the time period?

A period is a number that in algebraic geometry can be expressed as the integral of an algebraic function over an algebraic domain. Periods form a ring because their sums and products always remain in the same period.

Don Zagier and Maxim Kontsevich presented some theories and gave a survey of the eras. Periods also appear when computing the integrals that result from Feynman diagrams, and extensive work has been done to understand the relationships.

Solution Explained:

Given,

Radius of the solar system, r=25000 light year

Speed v=230 km/s

Calculate time period by

T = 2πr / v

T = 2πr X (25000 X 3 X 10^8 X 365 X 24 X 60 X 6) / (230 X 10^3)

  = 6.46 X 10^15 X (1 year / 365 X 24 X 60 X 60)
  = 2.05 X 10^8 years

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Answer:

Step-by-step explanation: find a point and find another point

y=1x+1/2

The given function is neither continuous nor differentiable at x = 1.

Given the piecewise function defined below, the function is not continuous at x = 1 because the left-hand limit is not equal to the right-hand limit. Specifically, the left-hand limit of f(x) as x approaches 1 is 3, while the right-hand limit of f(x) as x approaches 1 is 4. Furthermore, the function is not differentiable at x = 1 because the derivative does not exist at this point. This is because the derivative of the function is discontinuous at x = 1, with a derivative of 0 for x < 1 and a derivative of 1 for x > 1.

Therefore, the function f(x) is not continuous or differentiable at x = 1.

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Answer: y = 1.75x - 1

Step-by-step explanation: The slope of the line is 1.75

For the factorial study, Dr Rhodes can use the statement  b) effect of variable A depends on variable B

In a factorial study, two intervention comparisons are undertaken side by side. As a result, in addition to behavioral treatment or standard medical care, individuals may be randomly randomized to receive either aspirin or a placebo. In factorial designs, three different sorts of outcomes are pertinent: main effects, interaction effects, and simple effects.

The primary effect is the impact of one independent variable on the dependent variable, averaged over the values of the other independent variable. Dr Rhodes can forecast the relationship between independent variables A and B using the assumption that the effect of variable A depends on variable B.

Complete question

Dr. Rhodes notices an interaction in his factorial study. In describing this, which statement might he use to explain the link between Independent Variable A and Independent Variable B in predicting the dependent variable? TRUE OR FALSE

Variable A cancels out Variable B.

The effect of Variable A depends on Variable B.

The effect of Variable A is confused by Variable B.

Variable A mainly affects Variable B.

The effect of Variable A is mediated by Variable B.

The effect of Variable A depends on Variable B.

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Answer:

565.9

Step-by-step explanation:

There were 13 notepads, each of which cost $1.05 when the bookstore reduced the price of various notepads from $2.00 to $1.00.

Given that,

The bookstore reduced the price of various notepads from $2.00 to $1.00 while maintaining the price. The whole lot was sold. The selling of the pads generated a total profit of $29.45.

We have to find what number of notepads were sold and how much did each notepad cost.

We know that,

One approach to solving this issue is to divide $29.45 by each of the values from $1.01 to $1.99. That is the price for each notepad if one of them fits evenly with no leftovers. The number of pads is the quotient (result of division). The number has to be placed evenly because we cannot use half of the pad (leave no remainder).

Although we can check each of them, I realized that $29.45 ends in a 5 and is therefore divisible by 5, so I chose to check 1.05 as a potential price and it entered evenly. 13 is the quotient.

Therefore, There were 13 notepads, each of which cost $1.05 when the bookstore reduced the price of various notepads from $2.00 to $1.00.

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The monthly payment amount a woman has to pay for the car is $462.91.

Here we have to find the monthly payment amount.

The cost of car = $23,800

Down payment = $3,500

Rate(r) = 4.5%

time(t) = 4 years

Periodic interest(i) = 0.045/12

Formula to calculate monthly payment:

A = P i( 1 + i[tex])^{n}[/tex] / ( 1 + i[tex])^{n}[/tex] - 1

Loan amount = 23800 - 3500

                      = $ 20300

A = 20300 ( 0.045 /12 ( 1 + 0.045/12[tex])^{48}[/tex])/ (1 + 0.045/12[tex])^{48}[/tex] - 1

  = 20300× 0.004488 / 0.196814

  = 462.91

Therefore the monthly payment is $462.91.

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The curve with parametric equations x = [tex]e^{- t}[/tex] + t, y = [tex]e^t[/tex] − t, − 2 ≤ t ≤ 2 can be plotted on a graph. The arrow shows the direction where t increases in the interval (-2,2).

The length of a curve of the provided parametric equations is indicated by the arrow pointing in the direction wherein the curve is traced given data.

Think about the equations for the parameterized curve in the x-y plane.

x = x( t )

y = y( t )

where the argument is t. The graph of the curve is created by charting the series of points as the variable t changes (x,y).

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The question is -

Select the curve generated by the parametric equations. Indicate with an arrow the direction in which the curve is traced as t increases. x = [tex]e^{- t}[/tex] + t , y = [tex]e^t[/tex] − t , − 2 ≤ t ≤ 2

Answer:

What is the value of √m = ∓ 17

The value of √m = ∓ 17 is undefined.

Answer:

x=2/3

Step-by-step explanation:

3x - 1 = 1

   + 1   + 1

---------------

3x = 2

÷3    ÷3

------------------

x=2/3

-----------------------

using subtraction and division properties of equality, you can simplify the expression to solve it. you can use other properties of equality for different equations as well, but for this one you only need subtraction and division. :)

What is the unit rate for 20 pounds for $4.00? Which answer is correct?

(1): 5 pounds/$1.00

(2): 4 pounds/$1.00

(3): 1 pound/$4.00

(4): 1 pound/$5.00

A 90​% confidence interval about μ if the sample​ size, n, is 25 is (111.6, 118.4), a 90​% confidence interval about μ if the sample​ size, n, is 20 is (111.1, 118.9), a 80​% confidence interval about μ if the sample​ size, n, is 25 is (112.4, 117.6) and we need population to be normal. So we can not make intervals.

In the given question,

Sample​ mean, x​, is found to be 115.

Sample standard​ deviation, s, is found to be 10.

(a) We have to construct a 90​% confidence interval about μ if the sample​ size, n, is 25.

We need to build a 90% confidence interval. So p=0.90.

t-score for confidence interval is given by the excel code is

t=1.7109

Using these values, the margin of error is

ME = 1.7109× 10/√25

ME = 3.4

So confidence interval is

CI = (115-3.4, 115+3.4)

CI = (111.6, 118.4)

(b) We have to construct a 90​% confidence interval about μ if the sample​ size, n, is 20.

We need to build a 90% confidence interval. So p=0.90.

t-score for confidence interval is given by the excel code is

t=1.7291

Using these values, the margin of error is

ME = 1.7291× 10/√20

ME = 3.9

So confidence interval is

CI = (115-3.9, 115+3.9)

CI = (111.1, 118.9)

(c) We have to construct a 80​% confidence interval about μ if the sample​ size, n, is 25.

We need to build a 80% confidence interval. So p=0.80.

t-score for confidence interval is given by the excel code is

t=1.3178

Using these values, the margin of error is

ME = 1.3178× 10/√25

ME = 2.6

So confidence interval is

CI = (115-2.6, 115+2.6)

CI = (112.4, 117.6)

​(d) Now we have to check, could we have computed the confidence intervals in parts​ (a)-(c) if the population had not been normally​ distributed.

To use t-distribution, the population has to be normal.Otherwise we need a sample size of at least 30. Here sample size is less than 30.

So we need population to be normal. So we can not make intervals.

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The right question is:

A simple random sample of size n is drawn from a population that is normally distributed. The sample​ mean, x​, is found to be 115​, and the sample standard​ deviation, s, is found to be 10.

(a) Construct a 90​% confidence interval about μ if the sample​ size, n, is 25.

​(b) Construct an 90​% confidence interval about μ if the sample​ size, n, is 20.

​(c) Construct an 80​% confidence interval about μ if the sample​ size, n, is 25.

​(d) Could we have computed the confidence intervals in parts​ (a)-(c) if the population had not been normally​ distributed.

The domain and range of the function C(t) based on the context of the problem is

The range is calculated from minima and maxima, this will be achieved using derivative

C(t) = -5t² + 10t

C'(t) = 0 = -10t + 10

t = 1

substituting t = 1

C(t) = -5(1)² + 10t = 5

so at point (1, 5) it is either minima or maxima,

The second derivative test will help to confirm if point (1, 5) is minima or maxima

C'(t) = -10t + 10

C''(t) = -10

a negative value means it is a maxima

Hence the highest value of the concentration C(t) is 5 mg/L and this is at t = 1

The concentration cannot be less than zero or negative hence the lowest concentration is 0. and the range is 0 to 5

0 ≤ C ≤ 2

The time cannot be below zero so the lowest time will be zero

The domain is controlled by the input values. considering the least concentration of the drug which will be at C = 0

C(t) = -5t² + 10t

0 = -5t(t - 2)

-5t = 0

t = 0

t - 2 = 0

t = 2

The roots of the quadratic equation gives the domain to be 0 to 2

0 ≤ t ≤ 2

The graph is attached

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The required range of the given function g(x) = -1/2 |x-6| + 1 will be g(x) ≤ 1 or in internal notation form as (-∞, 1]. which is the correct answer would be an option (A).

The function is given in the question below as:

g(x) = -1/2 |x-6| + 1

We have to determine the range of the given function.

As per the given question, we have

⇒ g(x) = -1/2 |x-6| + 1

The range of an absolute function of the form:-

c|ax+b|+k is :f (x) ≤ k

In this case k = 1

⇒ g(x) ≤ 1

[tex]\mathrm{Range\:of\:}-\frac{1}{2}\left|x-6\right|+1:\quad \begin{bmatrix}\mathrm{Solution:}\:&\:f\left(x\right)\le \:1\:\\ \:\mathrm{Interval\:Notation:}&\:(-\infty \:,\:1]\end{bmatrix}[/tex]

Therefore, the required range of the given function will be g(x) ≤ 1 or in internal notation form as (-∞, 1].

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