Someone please help me to prove this. ​

Someone Please Help Me To Prove This.

Answers

Answer 1

Answer:  see proof below

Step-by-step explanation:

Use the following Product to Sum Identities:

2 sin A · cos B = sin (A + B) + sin (A - B)

2 cos A · cos B = sin (A + B) + sin (A - B)

Given:  cos A + cos B = 1/2      and      sin A + sin B = 1/4  

Proof LHS → RHS

[tex]\text{LHS:}\qquad \qquad \qquad \tan\dfrac{A+B}{2}[/tex]

[tex]\text{Expand:}\qquad \qquad \dfrac{\sin\frac{(A+B)}{2}}{\cos\frac{(A+B)}{2}}[/tex]

[tex]\text{Multiplication:}\qquad \quad \dfrac{\sin\frac{(A+B)}{2}}{\cos\frac{(A+B)}{2}}\bigg(\dfrac{2\cos\frac{A-B}{2}}{2\cos \frac{A-B}{2}}\bigg)[/tex]

[tex]\text{Simplify:}\qquad \qquad \quad \dfrac{2\sin \frac{A+B}{2}\cdot \cos \frac{A-B}{2}}{2\cos \frac{A+B}{2}\cdot \cos \frac{A-B}{2}}[/tex]

[tex]\text{Product to Sum:}\qquad \dfrac{\sin A+\sin B}{\cos A+\cos B}[/tex]

[tex]\text{Given:}\qquad \qquad \qquad \quad \dfrac{\frac{1}{4}}{\frac{1}{2}}[/tex]

[tex]\text{Simplify:}\qquad \qquad \qquad \dfrac{1}{2}[/tex]

LHS = RHS:    1/2 = 1/2  [tex]\checkmark[/tex]

Someone Please Help Me To Prove This.

Related Questions

what quadrant would (0,4) be in

Answers

Answer:

Step-by-step explanation:

Answer:

the answer is

36(thirty six)

did I do this right also how should I finish it?

Answers

it depends on what your supposed to do i would finish it myself

what is 1xy+3x-(23y+3)

Answers

Answer:

[tex]xy+3x-23y-3[/tex]

Step-by-step explanation:

[tex]1xy+3x-(23y+3)\\[/tex]

Multiply ; 1× x =x

[tex]=xy+3x-\left(23y+3\right)\\[/tex]

Use - to open the bracket

[tex]-\left(23y+3\right):\quad -23y-3\\\\=xy+3x-23y-3[/tex]

After being treated with chemotherapy, the radius of the tumor decreased by 23%. What is the corresponding percentage decrease in the volume of the tumor

Answers

Answer:

The volume of the tumor experimented a decrease of 54.34 percent.

Step-by-step explanation:

Let suppose that tumor has an spherical geometry, whose volume ([tex]V[/tex]) is calculated by:

[tex]V = \frac{4\pi}{3}\cdot R^{3}[/tex]

Where [tex]R[/tex] is the radius of the tumor.

The percentage decrease in the volume of the tumor ([tex]\%V[/tex]) is expressed by:

[tex]\%V = \frac{\Delta V}{V_{o}} \times 100\,\%[/tex]

Where:

[tex]\Delta V[/tex] - Absolute decrease in the volume of the tumor.

[tex]V_{o}[/tex] - Initial volume of the tumor.

The absolute decrease in the volume of the tumor is:

[tex]\Delta V = V_{o}-V_{f}[/tex]

[tex]\Delta V = \frac{4\pi}{3}\cdot (R_{f}^{3}-R_{o}^{3})[/tex]

The percentage decrease is finally simplified:

[tex]\%V = \left[1-\left(\frac{R_{f}}{R_{o}}\right)^{3} \right]\times 100\,\%[/tex]

Given that [tex]R_{o} = R[/tex] and [tex]R_{f} = 0.77\cdot R[/tex], the percentage decrease in the volume of tumor is:

[tex]\%V = \left[1-\left(\frac{0.77\cdot R}{R}\right)^{3} \right]\times 100\,\%[/tex]

[tex]\%V = 54.34\,\%[/tex]

The volume of the tumor experimented a decrease of 54.34 percent.

Solve for x: −4x − 4 = −4(x + 2)

Answers

Answer:

Step-by-step explanation:

-4x - 4 = -4x - 8

=4 ≠ -8

no solution

undefined

Answer:

no solution

Step-by-step explanation:

-4x - 4 = -4(x + 2)

Distribute

-4x -4 = -4x -8

Add 4x to each side

-4x+4x - 4 = -4x+4x -8

-4 = -8

This is never true so there is no solution

Is 253/10 a rational or irrational

Answers

Answer:

irrational

Step-by-step explanation:

If 8b-9=b then 7b=?
Please answer if you can!
Also it’s NOT 1.5

Answers

Answer:

9 is your answer.

Step-by-step explanation:

Solve for b. Note the equal sign, what you do to one side, you do to the other. Do the opposite of PEMDAS.

First, add 9 to both sides:

8b - 9 (+9) = b (+9)

8b = b + 9

Next, subtract b from both sides:

8b (-b) = b (-b) + 9

8b - b = 9

7b = 9

Divide 7 from both sides:

(7b)/7 = (9)/7

b = 9/7

Plug in 9/7  for b in the equation given:

7(b) = 7(9/7) = 9

9 is your answer.

~

Jack's bank statement shows an account balance of $25 50 Which descubes the magnitude or size of the debt in dollars? $50 50 $25 50 SO 0-$25 50​

Answers

Answer:

it’s B. $25.50

The mean of four numbers is 70. When a fifth number is included, the mean of the five numbers is 80. What is the fifth number?

Answers

Answer: 120

=============================================

Explanation:

S = sum of the first four values

S/4 = 70 since we divide the sum by 4 to get the mean of the first four values

S = 280 is the result after multiplying both sides by 4

Let x be the fifth unknown value. Adding it onto S leads to S+x = 280+x. This represents the sum of all five values.

Dividing that sum 280+x over 5 leads to the new mean 80, which leads to...

----------

(280+x)/5 = 80

280+x = 5*80

x+280 = 400

x = 400-280

x = 120

The fifth number is 120

The fifth number is 120

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the four numbers be = a , b , c , d

Let the fifth number be = e

Now , the mean of 4 numbers is m = 70

So , the equation will be

( a + b + c + d ) / 4 = 70

Multiply by 4 on both sides , we get

a + b + c + d = 280   be equation (1)

Now , the mean of 5 numbers is m = 80

So , the equation will be

( a + b + c + d + e ) / 5 = 80

Multiply by 5 , we get

a + b + c + d + e = 400   be equation (2)

Substitute the value of equation (1) in equation (2) , we get

a + b + c + d + e = 400

280 + e = 400

Subtracting 280 on both sides , we get

e = 400 - 280

e = 120

Therefore , the value of e is 120

Hence , The fifth number is 120

To learn more about equations click :

https://brainly.com/question/10413253

#SPJ5

Find the value of X in this equation.

g=c+x​

Answers

Answer:

x=g-c

Explanation:

You want to get x by itself, so you need to subtract c on both sides. Then, you are left with x=g-c.
x=g-c that’s the value of this equation

passes through (-4, 11) and (2,8)

Answers

Are you looking for slope?

if u r the slope is -6/3

A slope of line will be "[tex]-\frac{1}{2}[/tex]".

Slope of line:

According to the question,

(-4, 11) = (X1, Y1)(2,8) = (X2, Y2)

We know,

Slope of line:

= [tex]\frac{Y2-Y1}{X2-X1}[/tex]

By substituting the values, we get

= [tex]\frac{8-11}{2-(-4)}[/tex]

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

= [tex]-\frac{1}{2}[/tex]

Thus the answer above is correct.

Find out more information about slope here:

https://brainly.com/question/3493733

0.3(10-5x)=31.5(8x+9)

Answers

Answer:

x = - 1.106

Step-by-step explanation:

0.3(10-5x)=31.5(8x+9)

Expand the terms in the bracket

That's

3 - 1.5x = 252x + 283.5

Subtract 3 from both sides

3-3 - 1.5x = 252x + 283.5 - 3

-1.5x = 252x + 280.5

Subtract 252x from both sides

That's

- 1.5x - 252x = 252x - 252x + 280.5

- 253.5x = 280.5

Divide both sides by -253.5

We have the final answer as

x = - 1.106

Hope this helps you

i need seven please help

Answers

Answer:

3n + 6

Step-by-step explanation:

7.

three times a number: 3n

six more than three times a number: 3n + 6

Simplify this equation 2x³y³/4y²

Answers

x3y/2.


Is the correct answer

Can you pls help me solve this?​

Answers

Answer:

x=−9

Step-by-step explanation:

i hope this helps you

Answer:

x=-9

Step-by-step explanation:

Subtracting 53 from both sides, you get -2/3x=6.

-9*2/3x=6

x=-9

0.15(y-0.2)=2-0.5(1-y)

The answer is -153/35 I just need to know how to get that

Answers

Answer:

[tex]y=-\dfrac{153}{35}[/tex].

Step-by-step explanation:

The given equation is

[tex]0.15(y-0.2)=2-0.5(1-y)[/tex]

Using distributive property, we get

[tex]0.15(y)+0.15(-0.2)=2-0.5(1)-0.5(-y)[/tex]

[tex]0.15y-0.03=2-0.5+0.5y[/tex]

[tex]0.15y-0.03=1.5+0.5y[/tex]

Isolate variable terms.

[tex]0.15y-0.5y=1.5+0.03[/tex]

[tex]-0.35y=1.53[/tex]

Divide both sides by -0.35.

[tex]y=\dfrac{1.53}{-0.35}[/tex]

[tex]y=-\dfrac{1.53}{0.35}\times \dfrac{100}{100}[/tex]

[tex]y=-\dfrac{153}{35}[/tex]

Therefore, [tex]y=-\dfrac{153}{35}[/tex].

Find the perimeter of each polygon created by the coordinates.
A(-2, 3), B(3, 1), C(-2, -1), D(-3, 1)

a) 16.7

b) 14

c) 15.2

Answers

i believe the answer is c

lX – 12.2l= 0.3 gives the minimum and maximum acceptable lengths of the wires in centimeters. What is the minimum acceptable length of a wire?​

Answers

Answer:  11.9 cm

Work Shown:

|x-12.2| = 0.3

x-12.2 = -0.3 or x-12.2 = 0.3

x = -0.3+12.2 or x = 0.3+12.2

x = 11.9 or x = 12.5

The min length is 11.9 cm and the max length is 12.5 cm

Subtracting 12.2 from either x value leads to a positive difference of 0.3 which is the margin of error.

I need help on this giving brainlist ASAP

Answers

Answer:

no solution

Step-by-step explanation:

|x| = -10

Absolute value means that it is positive or 0

It cannot be negative

There is no solution

Step-by-step explanation:

There is no solution

|A|

can be only 0 or positive number

can't be -

from the rule of Mathematics

The scale of a map is 1cm : 70km. What is the actual distance between two towns that are 3cm apart on the map

Answers

Answer:

210 km

Step-by-step explanation:

1cm : 70km

3 x 70 = 210

3cm : 210km

Hopefully this helps you :)

pls mark brainlest ;)

The surface area of the side of a right cylinder can be found by multiplying twice the number π by the radius times the height. If a circular cylinder has radius r and height h, write an expression that represents the surface area of its side.

Answers

Answer:

2[tex]\pi[/tex]rh

Step-by-step explanation:

A little easier way to see:

2 * [tex]\pi[/tex] * r * h

Solve the equation for W

Answers

Answer:

fourth option

Step-by-step explanation:

Given

[tex]\frac{2x-1}{y}[/tex] = [tex]\frac{w+2}{2z}[/tex] ( cross- multiply )

y(w + 2) = 2z(2x - 1) = 4xz - 2z ( divide both sides by y )

w + 2 = [tex]\frac{4xz-2z}{y}[/tex] ( subtract 2 from both sides )

w = [tex]\frac{4xz-2z}{y}[/tex] - 2

Solve for x.
y= 2x
y=20
Simplify your answer as much as possible.

Answers

Answer:

20=2x

20/2=x

X=10

Step-by-step explanation:

Answer:

x=10

Step-by-step explanation:

20 divided by 2 equals 10.

. Sonya buys four pairs of shoes on
sale for buy one, get one 50% off.
The sales tax is 6.5%. If the
original price for each pair of shoes
was $35, how much does Sonya
pay for the four pairs altogether?
A. $74.55
B. $105.00
C. $111.83
D. $149.10
________________

Answers

b because sonya ...........

Answer:

c

Step-by-step explanation:

35/2=17.5 *2= 35+35+35= 105

6.5% of 105 is 6.83, so 105+ 6.83= 111.83

what is the standerd form of number shown in this calculater display. 1.46e-6

Answers

Answer:

scientific notation

Step-by-step explanation:

This number is shown in scientific notation.

Answer:

0.00000146

Step-by-step explanation:

I took the test

HELP PLZ!!! A, B, C,or D.

Answers

Answer:

D

Step-by-step explanation:

Solve this system of equations and enter an ordered pair (x,y). y = x + 3 y = -x - 5

Answers

Answer:

(x,y). y = x + 3 y = -x - 5

Step-by-step explanation:

add it up cowgirl howdey with PHOTOT MATHS

Answer:

(-4,-1)

Step-by-step explanation:

I graphed the two lines using a graphing tool. When graphed, the lines intercept at (-4,-1). Therefore, (-4, -1) is the solution.

Please see the graph attached.  

Hope this helps.

Help meeeee !!!!!!!!!

Answers

Answer:

3n²+3n-60

Step-by-step explanation:

Area of rectangle= L*W

A=3(n-1)(n+2)

A=3(n²+n-2)

A=3n²+3n-6

54=3n²+3n-6

3n²+3n-6-54=0

3n²+3n-60=0

Answer:

3, 3, - 60

Step-by-step explanation:

Area = lw

Therefore 54=(3n-3)(n+2)

Expand and we get:

3n^2+6n-3n - 6=54

Combine terms and move 54 to left side:

3n^2+3n-60

Hope this helped!

If HJ = 7x27 find the value of x. 3x-5. x-1
•———————-•——•
H. I. J

Answers

Answer:8.6

Step-by-step explanation:

30. When asked his age, the algebra teacher said, "If you
square my age, then subtract 23 times my age, the
result is 50. How old is be?
F. 23
G. 25
H. 27
J. 46
K. 50

Answers

Answer:

25 years old

Step-by-step explanation:

Let the teacher's age be a.

Then:

a^2 - 23a = 50

In standard form, this quadratic is

x^2 - 23a - 50 = 0

Factoring this, we get (x - 25)(x + 2) = 0

So a is either 25 or a is -2.  Only a = 25 is relevant here.

The teacher is 25 years old (Answer G)

Other Questions
Give examples of two substances that look similar, but have different properties. If x=.5, what is the numerical value of 20x ? What were the effects of the Spanish Civil war. plzzzz Help!!!!!!A plumber charges $55 for a service call plus $40 for each hour he works. If the total bill for a job costs $215, write an equation to represent the situation. 40 + 55 = x + 215 215 = x + 40 + 55 215 = 40 + 55x 215 = 40x + 55 HELP I DONT KNOW WHICH CHOICE TO PICK What are five words that can be used to name proteins,lipids,carbohydrates and nucleus acids collectively A school choir needs to make T-shirts for its 75 members and has set aside some money in their budget to pay for them. The members of the choir decided to order from a printing company that charges $3 per shirt, plus a $50 fee for each color to be printed on the shirts. List several figures other than rectangles that tessellate the plane using translations on Tuesday, the Soto salad restaurant served 6 1/2 cups of Italian salad dressing. if the restaurant serves 1/2 cups of dressing with each salad, how many salads where ordered? How can fear bring out the best and the worst in people? There are 18 men on 2 baseball teams. 2/3 of them brought their sons to watch them play. How many brought their son? When was the Cherokee tribe established? Pls help ASAP (: Jacinta is very fast and ran 300 metres in 30 seconds. What is her speed in km/h? Which region of Oklahoma is home to Lake Eufaula? A. the Prairie Plains B. the Sandstone Hills C. the Red River Plains D. the Red Beds Plains 1.if you had to come up with a nonprofit, it would be called?2.the purpose of my nonprofit would be?3.the reason this would be my nonprofit is? Choose the nonmetallic elements from the list. Check all that apply. yttrium oxygen boron polonium argon gallium carbon The goal of the consumer in a market economy is to use his or her limited income to buy:________.A) The greatest number of goods and services possible.B) The goods and services that maximize profits for bussiness.C) The combination of goods and services which maximize their utility given a limited budget.D) Those goods and services with the lowest prices. How much discount is received on an item with a marked price of Rs 500 if the discount rate is 3%? * Rs 50 Rs 15 Rs 25 Rs 5 Which statement correctly describes hydrogen bonds? Which statement correctly describes hydrogen bonds? They hold together adjacent water molecules. They form when opposite charges repel each other. They happen only between water molecules. They form between the hydrogen atoms of different water molecules. QUESTION: lines 151-171 What do thesedetails suggest about thethreats the Danes face andthe personal qualities theyvalue?