Find the midpoint of the segment with the following endpoints.
(9,9) and (1,-1)

Answer:  see proof below

Step-by-step explanation:

Use the following Identities in the proof.

Sum & Difference Identities:

[tex]\cot (A+B)=\dfrac{\cot A\cdot \cot B-1}{\cot B+\cot A}\qquad \qquad \tan(A-B)=\dfrac{\tan A-\tan B}{1+\tan A\cdot \tan B}[/tex]

Half Angle Identities:

[tex]\cot \bigg(\dfrac{A}{2}\bigg)=\dfrac{1+\cos A}{\sin A}\qquad \qquad \qquad \tan\bigg(\dfrac{A}{2}\bigg)=\dfrac{1-\cos A}{\sin A}[/tex]

Unit Circle:

[tex]\cot \bigg(\dfrac{\pi}{4}\bigg)=1\qquad \qquad \qquad \qquad \tan\bigg(\dfrac{\pi}{4}\bigg)=1[/tex]

Proof LHS → RHS:

[tex]\text{LHS:}\qquad \qquad \qquad \qquad \cot\bigg(\dfrac{\pi}{4}+\dfrac{\theta}{2}\bigg)-\tan\bigg(\dfrac{\theta}{2}-\dfrac{\pi}{4}\bigg)[/tex]

[tex]\text{Sum and Difference:}\qquad \dfrac{\cot (\frac{\pi}{4})\cdot \cot (\frac{\theta}{2})-1}{\cot (\frac{\theta}{2})+\cot (\frac{\pi}{4})}-\dfrac{\tan (\frac{\theta}{2})-\tan (\frac{\pi}{4})}{1+\tan (\frac{\theta}{2})\cdot \tan(\frac{\pi}{4})}[/tex]

[tex]\text{Unit Circle:}\qquad \qquad \dfrac{\cot (\frac{\theta}{2})-1}{\cot (\frac{\theta}{2})+1}-\dfrac{\tan (\frac{\theta}{2})-1}{\tan (\frac{\theta}{2})+1}[/tex]

[tex]\text{Half Angle:}\qquad \quad \dfrac{\frac{1+\cos \theta}{\sin \theta}-1}{\frac{1+\cos \theta}{\sin \theta}+1}-\dfrac{\frac{1-\cos \theta}{\sin \theta}-1}{\frac{1-\cos \theta}{\sin \theta}+1}[/tex]

                        [tex]=\dfrac{\frac{1+\cos \theta}{\sin \theta}-\frac{\sin \theta}{\sin \theta}}{\frac{1+\cos \theta}{\sin \theta}+\frac{\sin \theta}{\sin \theta}}-\dfrac{\frac{1-\cos \theta}{\sin \theta}-\frac{\sin \theta}{\sin \theta}}{\frac{1-\cos \theta}{\sin \theta}+\frac{\sin \theta}{\sin \theta}}[/tex]

                        [tex]=\dfrac{1+\cos \theta -\sin \theta}{(1+\cos \theta)+\sin \theta}-\dfrac{1-\cos \theta -\sin \theta}{(1-\cos \theta)+\sin \theta}[/tex]

[tex]\text{Simplify:}\\ \dfrac{1+\cos \theta -\sin \theta}{(1+\cos \theta)+\sin \theta}\bigg(\dfrac{(1-\cos \theta)+\sin \theta}{1-\cos \theta)+\sin \theta}\bigg)-\dfrac{1-\cos \theta -\sin \theta}{(1-\cos \theta)+\sin \theta}\bigg(\dfrac{1+\cos \theta)+\sin \theta}{1+\cos \theta)+\sin \theta}\bigg)[/tex]

[tex]=\dfrac{2\sin \theta \cdot \cos \theta}{2\sin \theta(1+\sin \theta)}-\dfrac{-2\sin \theta \cdot \cos \theta}{2\sin \theta (1+\sin \theta)}[/tex]

[tex]=\dfrac{4\sin \theta \cdot \cos \theta}{2\sin \theta(1+\sin \theta)}[/tex]

[tex]=\dfrac{2\cos \theta}{1+\sin \theta}[/tex]

LHS = RHS [tex]\checkmark[/tex]

Answer:

8 mil.

Step-by-step explanation:

Answer:

8 mil.

Step-by-step explanation:

Answer:

The diameter is approximately 8.9 cm

Step-by-step explanation:

The circumference is given by

C = pi *d

28 = pi *d

Divide each side by pi

28/pi = d

We can approximate pi by 3.14

28 /3.14 =d

8.917 = d

The diameter is approximately 8.9 cm

Answer:

n=7

Step-by-step explanation:

it told me I couldn't send this unless it was 20 words so that's why I'm typing this lol but the answer is 7

Answer:

slope = (11/2)

Step-by-step explanation:

slope= (x2-x1, y2-y1)

= (6-(-5)), (-5-(-7))

= (11,2)

Answer:

1, -1, 0, 101

Answer:

D

Step-by-step explanation:

We have the expression:

[tex](-2x+8.1y)-(-9x+5.3y)[/tex]

First, let's distribute the negative on the right. This gives us:

[tex]=(-2x+8.1y)+(9x-5.3y)[/tex]

Now, let's combine like terms:

[tex]=(-2x+9x)+(8.1y-5.3y)[/tex]

Add:

[tex]=(7x)+(8.1y-5.3y)[/tex]

Subtract:

[tex]=(7x)+(2.8y)[/tex]

Simplify:

[tex]=7x+2.8y[/tex]

So, our answer is D.

And we're done!

Answer:

d.  7x + 2.8y

Step-by-step explanation:

You have to combine like factors to solve.  Distribute before solving.

(-2x + 8.1y) - (-9x + 5.3y)

-2x + 8.1y + 9x - 5.3y

7x + 8.1y - 5.3y

7x + 2.8y

Answer:

x = 6

Step-by-step explanation:

Vertical angles are congruent, thus

∠ A = ∠ B , substitute values

3x - 9 = x + 3 ( subtract x from both sides )

2x - 9 = 3 ( add 9 to both sides )

2x = 12 ( divide both sides by 2 )

x = 6

Answer:

x = -3

Step-by-step explanation:

Step-by-step explanation:

A piecewise function is a function built from pieces of different functions over different intervals.

Step-by-step explanation:

A piecewise function is a function built from pieces of different functions over different intervals. For example, we can make a piecewise function f(x) where f(x) = -9 when -9 < x ≤ -5, f(x) = 6 when -5 < x ≤ -1, and f(x) = -7 when -1 <x ≤ 9.

Mark me as brainlist

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Explanation:

Let's see what happens when a = b

Let's pick something like a = 2, so b = 2.

|a-b| = |2-2| = |0| = 0

|a|-|b| = |2|-|2| = 2-2 = 0

Both result in 0.

We see that |a-b| = |a|-|b| is true for this example.

The given equation is either "sometimes true" or "always true"

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

Now let's pick something where a < b. Let a = 1 and b = 2

|a-b| = |1-2| = |-1| = 1

|a|-|b| = |1|-|2| = 1-2 = -1

We get different results, so |a-b| = |a|-|b| is not true for this example.

So this leads us to say the original equation is sometimes true.

[tex]|a-b| = |a| - |b|[/tex] if and only if [tex]a \ge 0\,\land\,b\ge 0[/tex]. That is, it is sometimes the same.

Absolute Value is a mathematic Form which represents either the Magnitude or the Distance respect to Origin of a given Real Number, whose is depicted below:

[tex]|x| = \left \{ {{x,\,x\ge 0} \atop {-x,\,x< 0}} \right.[/tex], for all [tex]x\in \mathbb{R}[/tex] (1)

In this question we must check if [tex]|a|-|b| = |a - b|[/tex]. Hence, we must check it for the following four cases:

(i) [tex]a \ge 0\,\land\,b\ge 0[/tex]

(ii) [tex]a\ge 0\,\land \,b < 0[/tex]

(iii) [tex]a < 0\,\land\,b<0[/tex]

(iv) [tex]a< 0\,\land b\,\ge 0[/tex]

Case I

1) [tex]|a| \ge 0[/tex], [tex]|b| \ge 0[/tex], [tex]|a-b| \ge 0[/tex] Definition of absolute value.

2) [tex]a \ge 0\,\land\,b\ge 0[/tex] Given.

3) [tex]a - b = a - b[/tex] Definition of absolute value/Reflexive Property

4) [tex]|a-b| = |a| - |b|[/tex] Result.

Case II

1) [tex]|a| \ge 0[/tex], [tex]|b| \ge 0[/tex], [tex]|a-b| \ge 0[/tex] Definition of absolute value.

2) [tex]a\ge 0\,\land \,b < 0[/tex] Given.

3) [tex]a - b =^{?} a - (-b)[/tex] Definition of absolute value.

4) [tex]a - b =^{?} a + b[/tex]    [tex]-(-x) = x[/tex]

5) [tex]-b =^{?} b[/tex] Compatibility with addition/Modulative property/Existence of additive inverse/Absurd found.

6) [tex]|a-b| \ne |a| - |b|[/tex] Reductio ad absurdum.

Case III

1) [tex]|a| \ge 0[/tex], [tex]|b| \ge 0[/tex], [tex]|a-b| \ge 0[/tex] Definition of absolute value.

2) [tex]a < 0\,\land\,b<0[/tex] Given.

3) [tex]a-b =^{?} -a-(-b)[/tex] Definition of absolute value.

4) [tex]a-b =^{?} -(a -b)[/tex]   [tex](-1)\cdot x = -x[/tex]/Distributive property/Absurd found.

5) [tex]|a-b| \ne |a| - |b|[/tex] Reductio ad absurdum.

Case IV

1) [tex]|a| \ge 0[/tex], [tex]|b| \ge 0[/tex], [tex]|a-b| \ge 0[/tex] Definition of absolute value.

2) [tex]a< 0\,\land b\,\ge 0[/tex] GIven.

3) [tex]a-b =^{?} -a - b[/tex]  Definition of absolute value.

4) [tex]a =^{?} -a[/tex] Compatibility with addition/Modulative property/Existence of additive inverse/Absurd found.

5) [tex]|a-b| \ne |a| - |b|[/tex] Reductio ad absurdum.

In a nutshell, [tex]|a-b| = |a| - |b|[/tex] if and only if [tex]a \ge 0\,\land\,b\ge 0[/tex]. That is, it is sometimes the same.

Please see this question related to Absolute Values: https://brainly.com/question/11220129

Answer:

A formal sanction is a reward or punishment given by a formal organization or regulatory agency, such as a school or government. An informal sanction is a spontaneous expression of approval or disapproval given by an individual or a group, such as a standing ovation or gossip.

An official institution or regulatory body, such as a school or the government, may impose a formal sanction as a reward or punishment. A spontaneous display of approval or disapproval from a person or group, such as a standing ovation or rumours, is known as an informal sanction.

Informal consequences are answers to behaviour that may help to dissuade nonconformity or promote adherence to a standard, standard, or regulation.

As a result, a sanction can be either positive or negative, encouraging or discouraging behaviour that adheres to accepted norms of what is proper, reasonable, or anticipated.

Thus, An official institution or regulatory body, such as a school or the government

For more details about  informal sanction, click here:

https://brainly.com/question/25523750

#SPJ6

Answer: Ix - 5I ≥ 5.

Step-by-step explanation:

We want the set:

[0, 10]

to be the solution of:

Ix - bI ≤ c

So we need to find the values of c and b.

The first step is to find the middle point in our segment.

We can do that by adding the extremes and dividing it by 2.

M = (10 + 0)/2 = 5

And we also want to find half of the difference between the extremes, this is:

D = (10 - 0)/2 = 5.

Now, this set will be the set of solutions of:

Ix - MI ≥ D

Then in our case, we have:

Ix - 5I ≥ 5.

so we have that b = 5, and c = 5.

Answer:

1

Step-by-step explanation:

9 - 4 x 2

4 x 2 = 8

9 - 8 = 1

Answer:

9/50 = 0.18

Step-by-step explanation:

The first cup has 10 paper clips, 3 of which are blue.

The second cup has 10 paper clips, 6 of which are orange.

So the probability is:

P = (3/10) (6/10)

P = 9/50

P = 0.18

Answer:

-5 because it is negative

Step-by-step explanation:

Answer:

$12

Step-by-step explanation:

divide 6 by 2 to show how much 1 pineapple cost which is 3

then time 4 by 3

Answer:

89.44

Step-by-step explanation:

using the Pythagorean Theorem: [tex]a^{2} +b^{2}=c^{2}[/tex]

[tex]80^{2} +b^{2} =120^{2} \\6400+b^{2} =14400\\b^{2} = 8000\\b = 40\sqrt{5}[/tex]

120 is the hypotenuse so it would be c in the equation.

To solve, I simplified and isolated the variable. I got the square root of 8000 simplified (but idk how to write that out lol)

This answer is closest to 89.44

*Hope this helped! Have a great day/ night wherever you are! : )*

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Work Shown:

5 & 5/8 = 5 + 5/8

-5 & 5/8 = -(5 & 5/8) = -(5 + 5/8) = -5 - 5/8

So,

( -5 & 5/8 ) + ( 3 & 1/2 )

( -5 - 5/8 ) + ( 3 + 4/8 )

( -5+3 ) + ( -5/8+4/8 )

-2 + (-1/8)

-(2 + 1/8)

-(2 & 1/8)

-2 & 1/8

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

Alternative Method

We could convert each mixed number to decimal form

-5 & 5/8 = -5-5/8 = -5.625

3 & 1/2 = 3+1/2 = 3.5

( -5 & 5/8 ) + ( 3 & 1/2 ) = -5.625+3.5 = -2.125

Then convert back to mixed number form

-2.125 = -2 & 125/1000

-2.125 = -2 & (1*125)/(8*125)

-2.125 = -2 & 1/8

Answer:C is you answer

Step-by-step explanation:

Answer:

im confused

Step-by-step explanation: i need help with this question

Answer:

-63

Step-by-step explanation:

Answer:

The answer in the simplest form would be 28/9 or 3 1/9

Step-by-step explanation:

Very simple you would divide the 56 and the 18 by 2 and you get 28/9.

or you could change it to a improper fraction in that case it would be 3 1/9

18 goes into 56 three times which gives us 54. 54 divided by 18 is 3. we should have 3 2/18 which simplifies to 3 1/9

Answer:

Step-by-step explanation:

Given

Perimeter = 2(l + w)

Substitute values in perimeter formula

Then, the value of width is

Area of rectangle

Area of circle

Shaded area

Answer:

126.14in²

Step-by-step explanation:

P = 2w + 2l

68 = 2(x + 2) + 2(20)

68 = 2x + 4 + 40

68 = 2x + 44

24 = 2x

12 = x

x + 2

12 + 2

14 (width)

14 * 20

280in² (area of rectangle)

A = πr²

A = π(7)²

A = 49π

A = 153.86 (area of circle)

280 - 153.86

126.14 (area of shaded region)

Best of Luck!

He needs 5 bottles of wood glue and 4 bottles of craft glue.

Answer:

-3

Step-by-step explanation:

I attached I picture of the work

just ignore the stuff at the very top

Step-by-step explanation:

To find the slope, we must know and memorize the following formula.

[tex]\frac{y2}{x2} -\frac{y1}{x1} =m[/tex]

Identified 2 points:

Substitute the 2 points into the formulas format.

Then, solve for our final answer.

[tex]\frac{6}{1} -\frac{9}{0} =\frac{-3}{1} =-3[/tex]

[tex]m=-3[/tex]

Answer:

Step-by-step explanation:

For instance, x = x/1. The reciprocal of a number is this fraction flipped upside down. In other words, the reciprocal has the original fraction's bottom number—or denominator—on top and the top number—or numerator—on the bottom. So the reciprocal of 6 is 1/6 because 6 = 6/1 and 1/6 is the inverse of 6/1.

Step-by-step explanation:

correct but what's the question

Answer:

true regular means that all sides are equal and congruent also means equal so the statement is true a regular hexagon would have 6 congruent sides

Answer:

7

Step-by-step explanation: