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Hello Guest!

These formulas were derived with the help of the addition theorems.

\(sin\ C+sin\ D=\color{blue}2sin\ \frac{C+D}{2}cos\ \frac{C-D}{2}\\ sin\ 3\theta=\color{blue}3sin\ \theta-4sin^3\theta \)

   !

-5-3(6x-8)=-5x+19

Distribute the -3:

-5-18x+24=-5x+19

Combining like terms on the LHS:

-18x+19=-5x+19

13x=0

x=0

V = π a^2 h  [Volume of a cylinder]
(for a circular right cylinder with center at the origin, height h, radius a)

This is very arbitrary !!

Suppose the diameter of the box==50 inches

Then the height of the box==108 - 50 ==58 inches

50 / 2 ==25 inches - the radius of the box.

V = π a^2 h ==Pi x 25^2 x 58==113,882.73 - cubic inches - volume of the box for this assumption.

Note: You can assign x and y to the 2 dimensions used in this example.

Supplementary angles are pairs of angles whose measures sum to 180 degrees.

Let the angle ==A

Its supplementary angle ==180 - A

A - [180 - A] ==178

A - 180 + A ==178

2A ==178 + 180==358

A ==358 / 2 ==179

Its supplementary angle==180 - 179 ==1

So, the 2 angle are: 179 and 1 degrees.

The 1 degree angle is:179 - 1 ==178 degrees LESS than its supplementary angle of 179.

Why do you have difficulty with a simple question such as this?

What does the average of 36 hours for 6 people mean?

It means:  36  x  6 ==216 hours - total hours of the 6 people.

But you know the exact hours of 5 of them. So:

216 - 30 - 32 - 38 - 36 - 30 ==50 hours worked by the 6th person!!

14 pennies and 8 nickles 

Let the number of days ==D

[77.48D  +  (.10 x 250) ]==460, solve for D

77.48D  +  25 ==460

77.48D ==460 - 25

77.48D ==435

D ==435 / 77.48

D ==5.614 days ==~5.5 days - assuming he drives the 250 miles in 5.5 days, which will cost him $451.14

Note: If it must be a "whole number" of days, then use 5 days.

Your are supposed to read their minds!! I think "7 times" should read "6 times"! I believe it was posted recently as 6 times:

[n + (n+ 1) +(n + 2) + (n + 3) +(n + 4) + (n + 5) + (n + 6)]==6(n + 6), solve for n

7n + 21 ==6n + 36

7n - 6n ==36 - 21

n ==15 - the smallest integer

Pearl writes down seven consecutive integers and adds them up.

The sum of the integers is equal to 7 times the largest of the seven integers.

What is the smallest integer that Pearl wrote down?

7x+1+2+3+4+5+6 = 7(x+6)

This question makes no sense.

How about presenting your question to the best of your ability.  Or are you just too lazy?

Find the value of x.

Hello Guest!

The sum of the interior angles of a triangle is 180°.

\(x = 180^{\circ}-90^{\circ}-(180^{\circ}-121^{\circ})\\ \color{blue}x=31^{\circ}\)

  !

me and brother

m-5=b+5

b-14=2(m+14)

solve simultaneously

This question has been posed twice.

See the answer from the other (later) submission.

Plot the left hand side against x, then plot the right hand side against x and see where they intersect.  You can do this on the online Desmos graphing calculator.

For, f(x) to be onto, codomain should be exactly equal to range.

Hello, i tried to prove the following trigonometric problem from a textbook but i think the equation doesn't hold. Can anyone confirm it?

So the domain of the angle is 3π/2 < x < 2π , and the equation is:

sqrt((1+cos(x))/(1-cos(x)))+sqrt((1-cos(x))/(1+cos(x))) = -2cot(x)

First I need to work out your backets.  Some spacing woud have been nice.

sqrt (  [1+cos(x)]    /  [1-cos(x)] )      +   sqrt(  [1-cos(x)]  / [1+cos(x)] ) = -2cot(x)

\(\sqrt\frac{1+cos(x)}{1-cos(x)}+\sqrt{\frac{1-cos(x)}{1+cos(x)}} = -2cot(x)\)

Is this what you are asking us to try and prove?

Here are the 2 graphs, you can see that they are not the same.  Not even in the given domain.

The triangles are similar.

If we look at the 102-degree angle in the middle, we can subtract it from 180(a straight line) and divide it in half which gives us (180-102)/2=39. 

The other two angles in the left triangle(90 and 51), sum up to 180 when added with 39. The other triangle is the same since the interior angles of a triangle are 180 degrees and we know two angles(39 and 90).

We now know that those two triangles have 3 exact angles, so they must be similar.

1  x  3  x  5  x  7 ==105 ways to spell "ARCH"

It's wrong.

Correct rhs is -2/sin(x).

\(-7 = f(2)\)

  \(-7 = f(5-3)\)

\(\color{brown}\boxed{(5, -7)}\)

1. (a,b) = (5,-12)

2. (a,b) = (-3,10)

3. (a,b) = (-1,9/2)

Recall that: \((a-b)(a+b)=a^2-b^2\) for any a and b. (Difference between two squares).

So, rearrange the given question:

\((1-3i)(1+3i)(1-i)(1+i)\)

So, using the above formula:

\((1^2-(3i)^2)(1^2-(i)^2)=(1-9i^2)(1-i^2) \\ \text{But, } i^2=-1 \hspace{0.4cm} \text{ so:} \\ (1+9)(1+1)=10(2)=20\) 

I hope this helps!

You have not proof read the question either.   A group of  howmany canditades?  A number is missing.