Mathematics High School

if a + b + c is equals to 270 then prove that sin a cos b sin c + cos a sin b sin c + sin a sin b cos c = cos a cos b cos c​

Answers

Answer 1

Answer:

[tex]Solution,\\a +b+c=270\\or, a +b = 270-c\\[/tex]

[tex]cos(a+b) = cos(270-c)~~~~~~~~~and~~~~~~~~~sin(a+b)=sin(270-c)\\or, cos(a+b) = -sinc,~sin(a+b) = -cosc\\Now,\\L.H.S. = sina.cosb.sinc +cosa.sinb.sinc + sina.sinb.cosc\\~~~~~~~~~~= sinc (sina.cosb+cosa.sinb)+sina.sinb.cosc\\~~~~~~~~~~=sinc[sin(a+b)]+sina.sinb.cosc\\~~~~~~~~~~=sinc.-cosc+sina.sinb.cosc\\~~~~~~~~~~=cosc(sina.sinb-sinc)\\~~~~~~~~~~=cosc[sina.sinb+cos(a+b)]\\~~~~~~~~~~=cosc[sina.sinb+cosa.cosb-sina.sinb]\\~~~~~~~~~~=cosc.cosa.cosb\\~~~~~~~~~~=cosa.cosb.cosc \\[/tex]

Hope I helped you!

Related Questions

Can someone plz help

Answers

Answer:

it should be 1/4

Step-by-step explanation:

Answer:

1/4 because it depends on how many times you flip it

explain why 1/12 + 1/2= 7/12

Answers

Answer:

1/12 + 1/2 = 1/12 + 6/12 - 1+6/12 = 7/12

Step-by-step explanation:

hope this makes sense

Step-by-step explanation:

1/2 of 12/12 is 6/12.

So, this means: 1/12 + 1/2 = 7/12

                                      is

                          1/12 + 6/12 = 7/12

SOMEONE HELP ME PLEASE ASAP AND SHOW THE WORK I WILL MAKE YOU BRAINLIEST AND GIVE YOU A GOOD RATE!!!!! SOMEONE HELP ASAPPPPPPPPPPPPPP!!!!!!!!!!!!!

Answers

Answer:

5x+10=30

Step-by-step explanation:

sorry, it does not have any works/steps in forming this equation.

Solving equation(if needed):

5x+10=30

5x=20

x=4

Answer: you can count by fives 5,10 15,20,25,30

Step-by-step explanation:

Write an inequality for the graph below.
'न
34
10
।। 12 13 14

Answers

Answer:

i like cheese wbu hahahahahaha

The temperature dropped 20 degrees from noon to midnight. The temperature at midnight was 24°F. Write and solve an equation to find the temperature at noon?

Answers

x - 20 = 24

Add 20 to both sides

x = 24 + 20 = 44

pls help me for brain list and a thanks and a 5 star review

Answers

3/4 + 2/4 = 6/4 or 3/2

Use the number line to add, second choice is simplified

Nancy has 1/3 of a cup of strawberries. She wants to share them with her 4 friends. How much will each of her friends get?

Answers

Each friend will get 1/12 cup of strawberries because 1/3 divided by 4 equals 1/12

You are making curtains for your little sister's dollhouse. There are 24 windows on the dollhouse and each
needs 3.75 inches of fabric for curtains. How much fabric will you need?
(please help I only have a couple of minutes)

Answers

is it 90? sorry if it’s wrong

Answer:

90 inches

Step-by-step explanation:

24 x 3.75 which is the same as 24 x 3 3/4 which is the same as

24 x 15/4 = 6 x 15 = 90

A . expression A
B . expression B
C . expression C
D . expression D

ill mark u brainliest if u answer !

Answers

Answer:

answer choice B.

Step-by-step explanation:

b hope this helps. :)


The equation y+ 3 = 5(x - 3) represents a linear function. What is the y intercept of the equation?

Answers

Answer:

-18

Step-by-step explanation:

If you're looking for the y-intercept for this equation this means that x = 0.

So substitute x as 0 in the equation and you'll get the following.

y + 3 = 5 (0 - 3)

y + 3 = -15

y = -18

Which of the following quantities are to the left of zero on a number line? Select three that apply.
A The opposite of 7
B The opposite of -9
С
3
D
-4
m

Answers

Answer:

A, D, and E

Step-by-step explanation:

because they are negative

Help with this plz ASAP

Answers

Answer: y=2x-4

Step-by-step explanation:

the answer to this equation is y= 2x -4

1 and 1/5y+3/10y-1/2y=1/3y+2/5

Answers

1/5y + 3/10y - 1/2y - 1/3y = 2/5
6/30y + 9/30y - 15/30y - 10/30y = 2/5
-10/30y = 2/5
y = 2/5 x (-30/10)
y = -6/5

Answer: y=12/20=0.6

Step-by-step explanation:

Rephrase the given equation

1 and 1/5y+3/10y-1/2y=1/3y+2/5

6/5y+3/10y-1/2y=1/3y+2/5

Find the GCF (greatest common factor) and multiply it on both sides

(6/5y+3/10y-1/2y)×30=(1/3y+2/5)×30

36y+9y-15y=10y+12

Add like terms together

30y=10y+12

Subtract 10y on both sides

30y-10y=10y+12-10y

20y=12

Divide 20 on both sides

20y/20=12/20

y=12/20=0.6

Hope this helps!!

Please let me know if you have any questions

Was hit with a hard one. Can someone explain this to me please?

Answers

Answer:

Step-by-step explanation:

4х +7
у+ 1
Зу — 11
12x – 1

Answers

i need to type and make this 20 characters long but here you go

Evaluate the exponential function
f(x) = 3x ; x = -2

Answers

Answer:

-6

Step-by-step explanation:

Plug (-2) in for X in the equation

3(-2)

-6

x + y = 5.90
2x + 4y = 16.80

Answers

What are you looking for ?
2+4y(5.90-y)=16.80

We move all terms to the left:

2+4y(5.90-y)-(16.80)=0

We add all the numbers together, and all the variables

4y(-1y+5.9)+2-(16.8)=0

We add all the numbers together, and all the variables

4y(-1y+5.9)-14.8=0

We multiply parentheses

-4y^2+23.6y-14.8=0

a = -4; b = 23.6; c = -14.8;
Δ = b2-4ac
Δ = 23.62-4·(-4)·(-14.8)
Δ = 320.16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
y1=−b−Δ√2ay2=−b+Δ√2a

y1=−b−Δ√2a=−(23.6)−320.16√2∗−4=−23.6−320.16√−8

y2=−b+Δ√2a=−(23.6)+320.16√2∗−4=−23.6+320.16√−8

Jack and beth are selling wrapping paper for a school fundraiser. Customers can buy rolls of plain wrapping paper and rolls of shiny wrapping paper. Jack sold 5 rolls of plain and 8 rolls of shiny for a total of $190. Beth sold of 5 rolls plain and 3 shiny for a total of $90. Find the cost of each roll of wrapping paper

Answers

Answer:

Cost of a roll of plain wrapping paper = $6

Cost of a roll of shiny wrapping paper = $20

Step-by-step explanation:

Let [tex]x[/tex] denotes cost of a roll of plain wrapping paper and [tex]y[/tex] denotes cost of roll of shiny wrapping paper.

Jack sold 5 rolls of plain and 8 rolls of shiny for a total of $190.

[tex]5x+8y=190\,\,\,(i)[/tex]

Beth sold of 5 rolls plain and 3 shiny for a total of $90.

[tex]5x+3y=90\,\,\,(ii)[/tex]

Subtract (ii) from (i).

[tex]8y-3y=190-90\\5y=100\\y=20[/tex]

Put [tex]y=20[/tex] in (ii)

[tex]5x+3(20)=90\\5x+60=90\\5x=90-60\\5x=30\\x=6[/tex]

Therefore,

Cost of a roll of plain wrapping paper = $6

Cost of a roll of shiny wrapping paper = $20

8th grade math! If you know the answer to this problem please interact(:

Answers

Answer:

the third one (-2,1)

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

so solving the first one we get

y=2x+5

and the second one we get

y=5x+10+1

y=5x+11

substiuting we get

2x+5=5x+11

3x=-6

x=-2

and y= 1

so it would be C

if my answer helps please mark as brainliest.

Simplify the expression:
(6y + 10) - (2y + 3)
show work if u can

Answers

Answer:

4y + 7

Step-by-step explanation:

(6y + 10) - (2y + 3)

6y - 2y = 4y

10 - 3 = 7

4y + 7

What is the volume of this figure?

Answers

Answer:

875 ft^3

Step-by-step explanation:

Pick them apart starting at the bottom. The formul used is V=lwh

Starting at the bottom we have we have a sqare of 5 ft = 5ft^3= V = 125 ft^3

Then we have a rectangular prism: 5 x 5 x 20 = V = 500 ft^3

Third we have 5 x 5 x 10 = V = 250 ft3

125+500+250 = 875 ft^3

can you help me solve the linear equation algebraically y=-x-3. y=-2x-8​

Answers

Answer:

I can't it's to hard try studying

Answer:
x=-5
y=2

Explanation:
Since both of these equations are equal to y, they have to be equal to each other. Set them equal to each other like this: -x-3= -2x-8. Multiply everything by negative 1 to get rid of the negative signs. The equation will look like this: x+3= 2x+8. Than subtract the x from both sides. Than subtract 8 from both sides. That should get you to x=-5. Than plug in -5 into the x value for one of the linear equations. It will get you 2 for the y.

FIRST CORRECT ANSWER GETS BRANLIEST !!!!!!!!

Answers

Answer:

4 - 1 = 3

10 - 6 = 4

Step-by-step explanation:

Mia's dog, Chulo, weighs 13.8 pounds. How many ounces does her dog weigh?

Answers

Answer:

220.8 ounces

Chulo weighs 220.8 ounces

AYO PLEASE HELP ILL GOVE YOU BRAINLIEST

Answers

it's a i think, hope this helps

7(x-2)=28 Can somebody help me and show the steps?

Answers

Since the 7 is in front of the parentheses you must multiply it by everything inside the parentheses. 7 times X is 7X and 7 times -2 is -14. Then you need to make the X be by itself on one side, to do that you have to add 14 to -14 to make it disappear, and also add 14 to the other side, to 28. Then you divide both sides by 7 to make X be by itself.

7(x-2)=28
7X-14=28
7x=42
X=6

Find the surface area of the figure shown. The surface area of the figure is
5.1 ft
4 ft
2 ft
8.2 ft

Answers

I think it’s the total , 19.3

can anyone solve this?

Answers

It would be 76 degrees because it’s a vertical angle

The trend line passes through (10,9) and (35,0). Write an equation for the trend line.

Answers

Answer: Solution :  

Step 1 :

Make a scatter plot of Lily’s running data.

Step 2 :

To draw a trend line, use a straight edge to draw a line that has about the same number of points above and below it. Ignore any outliers.

Step 3 :  

Find the slope of the trend line.

The line passes through points (2, 20) and (4.5, 45).

Use the slope formula.  

m  =  (y2 - y1) / (x2 - x1)

Substitute x1, = 2, y1 = 20, x2 = 4,  and y2 = 45.

m  =  (45 - 20) / (4.5 - 2)

m  =  25 / 2.5

m  =  10

Step 4 :  

Find the y-intercept of the trend line.

Slope-intercept form equation of a line :  

y  =  mx + b

Plug y = 20, m = 10 and x = 2.  

20  =  10 · 2 + b

20  =  20 + b

Subtract 20 from both sides.  

0  =  b

Step 5 :  

Use your slope and y-intercept values to write the equation.

Slope-intercept form equation of a line :  

y  =  10x + 0

So, the equation for the trend line is

y  =  10x

Example 2 :

David records the number of chapters and the total number of pages for several books as given below.  

No. of chapters

3

4

5

8

10

11

15

17

19

No. of pages

20

44

50

95

90

130

125

170

160

Step-by-step explanation:

solve the equation t8/t2 = _____

Answers

Answer:

[tex]t^{6}[/tex]

Step-by-step explanation:

I am going to assume exponents for this question.

[tex]\frac{t^{8}}{t^{2}}[/tex]

When dividing exponents with the same base, it is simply subtraction, so 8 - 2 = 6 which produces the answer.

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