Please help me to prove this!​

Please Help Me To Prove This!

Answers

Answer 1

Answer:  see proof below

Step-by-step explanation:

Given: A + B = C                → A = C - B

                                          → B = C - A

Use the Double Angle Identity:     cos 2A = 2 cos² A - 1

                                             → (cos 2A + 1)/2 = cos² A

Use Sum to Product Identity: cos A + cos B = 2 cos [(A + B)/2] · 2 cos [(A - B)/2]

Use Even/Odd Identity: cos (-A) = cos (A)

Proof LHS → RHS:

LHS:                     cos² A + cos² B + cos² C

[tex]\text{Double Angle:}\qquad \dfrac{\cos 2A+1}{2}+\dfrac{\cos 2B+1}{2}+\cos^2 C\\\\\\.\qquad \qquad \qquad =\dfrac{1}{2}\bigg(2+\cos 2A+\cos 2B\bigg)+\cos^2 C\\\\\\.\qquad \qquad \qquad =1+\dfrac{1}{2}\bigg(\cos 2A+\cos 2B\bigg)+\cos^2 C[/tex]

[tex]\text{Sum to Product:}\quad 1+\dfrac{1}{2}\bigg[2\cos \bigg(\dfrac{2A+2B}{2}\bigg)\cdot \cos \bigg(\dfrac{2A-2B}{2}\bigg)\bigg]+\cos^2 C\\\\\\.\qquad \qquad \qquad =1+\cos (A+B)\cdot \cos (A-B)+\cos^2 C[/tex]

[tex]\text{Given:}\qquad \qquad 1+\cos C\cdot \cos (A-B)+\cos^2C[/tex]

[tex]\text{Factor:}\qquad \qquad 1+\cos C[\cos (A-B)+\cos C][/tex]

[tex]\text{Sum to Product:}\quad 1+\cos C\bigg[2\cos \bigg(\dfrac{A-B+C}{2}\bigg)\cdot \cos \bigg(\dfrac{A-B-C}{2}\bigg)\bigg]\\\\\\.\qquad \qquad \qquad =1+2\cos C\cdot \cos \bigg(\dfrac{A+(C-B)}{2}\bigg)\cdot \cos \bigg(\dfrac{-B-(C-A)}{2}\bigg)[/tex]

[tex]\text{Given:}\qquad \qquad =1+2\cos C\cdot \cos \bigg(\dfrac{A+A}{2}\bigg)\cdot \cos \bigg(\dfrac{-B-B}{2}\bigg)\\\\\\.\qquad \qquad \qquad =1+2\cos C \cdot \cos A\cdot \cos (-B)[/tex]

[tex]\text{Even/Odd:}\qquad \qquad 1+2\cos C \cdot \cos A\cdot \cos B\\\\\\.\qquad \qquad \qquad \quad =1+2\cos A \cdot \cos B\cdot \cos C[/tex]

LHS = RHS: 1 + 2 cos A · cos B · cos C = 1 + 2 cos A · cos B · cos C   [tex]\checkmark[/tex]

Please Help Me To Prove This!
Please Help Me To Prove This!

Related Questions

Copy and fill in the charts.

Answers

Answer:

15% = 3/20 = 0.15

1.25 =125% =5/4

12 3/8 = 12.375 = 1237.5%

Step-by-step explanation:

15% to fraction , then decimal ;

[tex]15\% = \frac{15}{100} \\Cross\:cancel\:common\:factor ; 5\\\\15\div 5 = 3\\100\div 5 = 20\\\\= \frac{3}{20}\\\\\frac{3}{20} = 0.15[/tex]

1.25 to fraction , then percentage

[tex]1.25 = \frac{1.25}{1} \times \frac{100}{100} \\\\1.25\times 100 =125\\1\times 100 = 100\\\\= \frac{125}{100} \\= \frac{5}{4} \\\\1.25\times 100\\= 125\%[/tex]

12 3/8 to decimal then percentage

[tex]12\frac{3}{8} =\frac{99}{8} = 12.375\\\\12.375\times 100\\\\= 1237.5\%[/tex]

how to solve V1 T2 = V2 T1
V1 = 600mL T1 = 77.0 V2 = ? T2 = 86.0​

Answers

Answer:

V2 = 670.129

Step-by-step explanation:

V1T2 = V2T1

Let V2 = y

600 x 86.0 = y x 77.0

51600 = 77y

77y/77 = 51600/77

y = 670.129

since y= V2

V2 = 670.129


2w – y = 7w – 2, solve for w​

Answers

Answer:

-1/5y + 2/5

Step-by-step explanation:

add -7w to both sides

-5w-y=-2

Divide both sides by -5

w= -1/5y +2/5

helppp first to answerr will be marked as brainlist​

Answers

Answer:

A

Step-by-step explanation:

in the end of the sentence it mentions "in the future" so you need to make that verb future tense as well

I think the correct answer is A.

Explanation: It just makes the most sense to me. I dont really know how to explain it any better! Im sorry! I hope this helped!! :)

Find the value of x for which the lines p and q are parallel.

Answers

Answer:

Do you have a picture of the problem, please?

Step-by-step explanation:

Only then, can I edit this and provide an accurate answer! ;D

Answer:

x=7

Step-by-step explanation:

x=7

What’s the distance between (6,4) , (-5,-1) round to the nearest ten

Answers

Answer:

The answer is

12.1 units

Step-by-step explanation:

The distance between two points can be found by using the formula

[tex]d = \sqrt{ ({x1 - x2})^{2} + ({y1 - y2})^{2} } \\ [/tex]

where

(x1 , y1) and (x2 , y2) are the points

From the question the points are

(6,4) and (-5,-1)

The distance between them is

[tex]d = \sqrt{ ({6 + 5})^{2} + ( {4 + 1})^{2} } \\ = \sqrt{ {11}^{2} + {5}^{2} } \\ = \sqrt{121 + 25} \\ = \sqrt{146} \\ \: \: \: \: \: \: \: \: \: \: \: = 12.0830459[/tex]

We have the final answer as

12.1 units to the nearest tenth

Hope this helps

Midpoint (-10,9), (3,8)

Answers

Answer:

(-3.5 8.5)

Step-by-step explanation:

Midpoint Formula: ([tex]\frac{x2 + x1}{2}[/tex], [tex]\frac{y2 + y1}{2}[/tex])

What I did: -10 + 3 = 7, 7 / 2 = 3.5 x = 3.5 | 9 + 8 = 17, 17 / 2 = 8.5

Midpoint = (-3.5, 8.5)

A field in the shape of a square has an area of 8,100 square feet. How can you determine the length of one side of the field?

Answers

To determine the length of one side use the formula for the area of square. As a square is equal on all four sides, finding one length results in any of the four. Solve using the formula and you receive your answer of 90.

A = s²

8100 ft² = s² (set up formula)

√8100 ft² = s² ( get s alone by squaring both sides)

90 ft = s (answer)

We can conclude that the side of the given square with an area of 8100ft² is 90ft.

What is a square?A square is a regular quadrilateral in Euclidean geometry, which means that it has four equal sides and four equal angles. It can alternatively be explained as a rectangle with two neighboring sides that are of equal length. A square is a two-dimensional plane object in geometry that has four equal sides and four equal but 90-degree angles.

So, the area of the square is 8100ft².

Formula: s²So, we know that: 8100 = s²

Now, calculate for s as follows:

s² = 8100s = √8100s = 90ft

Therefore, we can conclude that the side of the given square with an area of 8100ft² is 90ft.

Know more about squares here:

https://brainly.com/question/28934226

#SPJ2

Joyce’s teacher asks her to write the sequence formed by the number of red squares in each picture for the first five pictures. What sequence should Joyce write?

Answers

Answer:

Joyce should write [tex]1,8,64,512,4096[/tex]

Step-by-step explanation:

Let's analyze the procedure of how the pictures are formed.

Her teacher said the images were created by taking a red square, dividing it into 9 smaller squares, and removing the center square.

For the first two images we can see and count that there is 1 red square in the first picture and 8 red squares in the second picture.

For the third image, there are 8 squares formed by 8 red squares each one.

The number of red squares is 8 x 8 = 64

We can write the sequence as

1 , 8 , 64 ⇒ 1 , 8 , [tex]8^{2}[/tex]

For the fourth picture we can do the same reasoning and figure out that there are 8 x 8 x 8 = 512 red squares in the fourth image.

The sequence so far is

1 , 8 , 64 , 512 ⇒ 1 , 8 , [tex]8^{2}[/tex] , [tex]8^{3}[/tex]

We can generalize the sequence and write that the sequence is :

[tex]8^{n}[/tex] with [tex]n[/tex] ∈ IN ⇒ The first five numbers will be

[tex]8^{0},8^{1},8^{2},8^{3},8^{4}[/tex] = [tex]1,8,64,512,4096[/tex]

working together Alberto and Amanda can paint a fence in 4.12 hours. had she done it alone it would have taken Amanda 10 hours. find how long it would take Alberto to do it alone. A) 6.75 B) 5.02 c) 7.54 D)7.01

Answers

Answer:

  D)  7.01

Step-by-step explanation:

The rates of doing work, in terms of jobs per hour, will add when the two painters are working together. If A represents Alberto's time to do the job alone, we have ...

  1/4.12 = 1/10 + 1/A

(Jobs per hour is the inverse of hours per job.)

  A = 1/(1/4.12 -1/10) ≈ 7.0068 ≈ 7.01

It takes Alberto 7.01 hours to do the job alone.

Diego says the constant of proportionality is 550 Andrew say is the constant of proportionality is 9 1/6 do you agree with either of them explain your reason

Answers

Answer:

The question is incomplete. The complete question is :

A plane traveling at a constant speed flew over Pittsburgh, Saint Louis, Albuquerque, and Phoenix on its way from New York to San Diego.

Complete the table as you answer the questions. Be prepared to explain your reasoning.

       segment                              time                     distance        speed

Pittsburgh to Saint Louis    1 hour                    550 miles  

Saint Louis to Albuquerque 1 hour 42 minutes  

Albuquerque to Phoenix                             330 miles  

Step-by-step explanation:

We can complete the table as :

  segment                              time                     distance        speed

Pittsburgh to Saint Louis    1 hour                   550 miles   550 miles/hour

Saint Louis to Albuquerque 1 hour 42 minutes    93.5 miles 550 miles/hour

Albuquerque to Phoenix   3/5 hour           330 miles 550 miles/hour

Since it is given in the question that the plane is flying in a constant speed from one place top another place.

So, it is maintaining the same speed to cover different distances for different time.

Thus the constant of proportionality is 550.

i dont know can someone help me​

Answers

Answer:

x = 11/4

Step-by-step explanation:

[tex]\frac{x+8}{4} = \frac{6x+5}{8}[/tex]

Step 1: Cross-multiply.

[tex](x+8)*(8)=(6x+5)*(4)[/tex]

[tex]8x+64=24x+20[/tex]

Step 2: Subtract 24x from both sides.

[tex]8x+64-24x=24x+20-4x[/tex]

[tex]-16x+64=20[/tex]

Step 3: Subtract 64 from both sides.

[tex]-16x+64-64=20-64[/tex]

[tex]-16x=-44[/tex]

Step 4: Divide both sides by -16.

[tex]\frac{-16x}{-16} = \frac{-44}{-16}[/tex]

[tex]x = \frac{11}{4}[/tex]

14=7(2x-4)
I have to solve this equation using two different methods and I don’t know how

Answers

Answer:

14=7(2x-4)

0r, 14/7 = 2x-4

or, 2= 2x-4

0r,2x= 6

or x=3

14=7(2x-4)

14=14x -28

14x=42

x=42/14=3

Method 1

Divide both sides by 7 first to get

14 = 7(2x-4)

14/7 = 7(2x-4)/7

2 = 2x-4

Then add 4 to both sides

2+4 = 2x-4+4

6 = 2x

2x = 6

Finally, divide both sides by 2

2x/2 = 6/2

x = 3

which is the final answer

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

Method 2

Distribute the 7 through to each term in the parenthesis

14 = 7(2x-4)

14 = 7*2x + 7*(-4)

14 = 14x - 28

Then we follow similar steps as done earlier. Add 28 to both sides

14+28 = 14x-28+28

42 = 14x

14x = 42

Then divide both sides by 14 to fully isolate x

14x/14 = 42/14

x = 3

Either way we get the same result. As to which method you pick (if you could only choose one), its up to you based on whichever you find easier.

The basic idea with either method is that we follow PEMDAS in reverse to undo everything happening to x. This way we fully isolate it.

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

Checking the answer:

Plug x = 3 into the original equation. Simplify to get

14 = 7(2x-4)

14 = 7(2*3-4)

14 = 7(6-4)

14 = 7*2

14 = 14

This confirms the answer. As you can see, if we know the value of x, we use PEMDAS to simplify both sides. But if we don't know x, and want to find it, then we follow PEMDAS in reverse.

solve 2x^2 = x^4 +1 to find the value of x

Answers

Answer:

x= -1

x=1

Step-by-step explanation:

is it greater than or less than 4.29__4.3

Answers

Step-by-step explanation:

Think of 4.29 and 4.3 as 429 and 430.

Now which is greater, 429 or 430?

430, right? Then we convert them back to decimals.

4.29<4.3

Hope it helps!

Help me solve the following

Answers

Answer:

C. c = 8

Step-by-step explanation:

Step 1: Write equation

7 - 3c = -17

Step 2: Subtract 7 on both sides

-3c = -24

Step 3: Divide both sides by -3

c = 8

Answer:

C)8

7-3c=-17

-3c= -24

c=8

A recipe for orange water says, “Mix 3 teaspoons yellow water with 1 teaspoon red water.” For this recipe, we might say: “The ratio of teaspoons of yellow water to teaspoons of red water is 3:1.”

Answers

Answer:6:2

Step-by-step explanation:

Answer:

how many batches you need to know? If 2 batches the answer is 6:2 and if 4 batches it is 12:4

Solve the formula for m.

e = mc2

m =

Answers

Answer:

m = e/c^2

Step-by-step explanation:

Equation: e = mc^2

Isolate m: e/c^2 = mc^2/c^2

Cancel out: e/c^2 = m

2p-3 = 3p+2.



answer please!!!!​

Answers

Answer:

- 5

Step-by-step explanation:

Step 1:

2p - 3 = 3p + 2

Step 2:

2p = 3p + 2 + 3

Step 2:

2p = 3p + 5

Step 3:

- p = 5

Answer:

p = - 5

Hope This Helps :)

Answer:

-5

Step-by-step explanation:

2p - 3 = 3p + 2

combine the like terms

-3 -2 = 3p -2p

-5 = p


which value of x satisfies the equation 7/3 (x + 9/28) = 20?​

Answers

Answer:

x=8.25

Step-by-step explanation:

Divide both sides by 7/3

(x+9/28) = 8.57

Subtract 9/28 on both sides

x = 8.25

What’s the domain and range?

Answers

Answer:

the first component of ordered pair is domain and second component is range

Answer:

In its simplest form the domain is all the values that go into a function, and the range is all the values that come out

Ashley wants to pour 97.94 grams of salt into a container. So far, she has poured 39.1 grams. How much more salt should Ashley pour?​

Answers

58.84 grams. 97.94 - 39.1 = 58.84 grams of salt

the dots above are

4
16
56
PLEASE HURRY

Answers

Answer:

Equation 1

hope this helps

401 km 101 m – 34 km 153 m

Answers

Given :

An expression D = 401 km 101 m – 34 km 153 m.

To Find :

Value of D.

Solution :

We know, 1 km = 1000 m.

So, 401 km 101 m =( 401000 + 101 ) m = 401101 m.

Also, 34 km 153 m = ( 34000 + 153 ) m = 34153 m.

Now, D is given by :

D = 401101 - 34153 m

D = 366948 m

Now, D = 366948 m = 366 km 948 m.

Therefore, the difference is 366 km 948 m.

Hence, this is the required solution.

Can someone help me with this question? Thanks if you do!

Answers

Here’s the answer, hope this helps :)

PLEASE HELP MY BIRTHDAY WILL BE CANCELLED IF I DONT GET A GOOD GRADE ON THIS

Answers

Answer:

Option 4

Step-by-step explanation:

If the circle is filled in them it will be either ≤, ≥, ≈ .

One circle is open one is closed

please help very confused limited time!

Answers

slope-intercept form: y = mx + b

m = the slope and b = the y-intercept.

We know that the line passes through x-coordinate 1 and y-coordinate 1 and has a slope of 2

Let's plug our numbers into the slope-intercept form

1 = 2(1) + b

Simplify the right side

1 = 2 + b

Subtract 2 from both sides

-1 = b

The final answer: y = 2x - 1

the answer is A.) y=2x-1

substitute (1,1) in for y and x
1=2(1)+b
1=2+b
-1=b

3y + 2 ayuda necesito esto para hoy :(

Answers

Hey there!☺

[tex]Answer:\boxed{3y+2}[/tex]

[tex]Explanation:[/tex]

[tex]3y+2[/tex]

Since there are no like terms and it can't be factored the answer is:

[tex]3y+2[/tex]

Hope this helps!

(10 points)What is the sum of the first ten terms of the sequence 4,-12, 36, -144...

A. 59,050
B.-78,732
C.-59,048
D.118,096
If you could show work I would be grateful

Answers

Answer:

b

Step-by-step explanation:

The sum of the first ten terms of the sequence is -59,048. The correct option is C.-59,048

Here is the correct question:

What is the sum of the first ten terms of the sequence 4, -12, 36, -108...

From the question,

The given sequence is 4,-12, 36, -108...

This is a geometric progression since it has a common ratio.

The common ratio, r = -3

Recall that,

Given a geometric progression, the common ratio, r is given as

[tex]r = \frac{T_{2} }{T_{1}} = \frac{T_{3} }{T_{2}} =\frac{T_{4} }{T_{3}} = ...[/tex]

From the given sequence,

[tex]T_{1} = 4[/tex]

[tex]T_{2} = -12[/tex]

[tex]T_{3} = 36[/tex]

[tex]T_{4} = -108[/tex]

∴ [tex]r = \frac{-12 }{4} = \frac{36}{-12} =\frac{-108} {36} = -3[/tex]

Therefore, the sequence is a geometric progression with a common ratio of 3

Now, to determine the sum of the first ten terms of the sequence,

From the formula

[tex]S_{n} = \frac{a(1-r^{n}) }{1-r}[/tex]

Where [tex]S_{n}[/tex] is the sum of n terms

[tex]a[/tex] is the first term

[tex]r[/tex] is the common ratio

and [tex]n[/tex] is the number of terms in the series

From the question

[tex]a = 4[/tex]

[tex]r = -3[/tex]

and [tex]n = 10[/tex] (Since, we are to determine the sum of the first 10 terms)

Now, put the parameters into the formula

[tex]S_{n} = \frac{a(1-r^{n}) }{1-r}[/tex]

We get

[tex]S_{10} = \frac{4(1-(-3)^{10}) }{1-(-3)}[/tex]

[tex]S_{10} = \frac{4(1-59049) }{1+3}[/tex]

[tex]S_{10} = \frac{4(-59048) }{4}[/tex]

[tex]S_{10} = \frac{-236192 }{4}[/tex]

[tex]S_{10} = -59048[/tex]

Hence, the sum of the first ten terms of the sequence is -59,048. The correct option is C.-59,048

Learn more here: https://brainly.com/question/10315487

What is the answer for this? Ugh I hate study island!!

Answers

Answer:

[tex]\frac{7x}{8}-\frac{1}{40}[/tex]

Step-by-step explanation:

[tex](\frac{3x}{4}-\frac{5}{8})+(\frac{x}{8}+\frac{3}{5})[/tex]

By combining the like terms,

= [tex](\frac{3x}{4}+\frac{x}{8})+(\frac{3}{5}-\frac{5}{8})[/tex]

= [tex](\frac{6x}{8}+\frac{x}{8})+(\frac{3}{5}\times \frac{8}{8}-\frac{5}{8}\times \frac{5}{5} )[/tex]

= [tex]\frac{7x}{8}+(\frac{24}{40}-\frac{25}{40})[/tex]

= [tex]\frac{7x}{8}-\frac{1}{40}[/tex]

Therefore, by solving the given expression we find the answer as [tex]\frac{7x}{8}-\frac{1}{40}[/tex].

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