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? Is it you or not Im confused

Thanks hectictar!

The question does not ask for the value of y. It is asking for the first equation solved for  y .

5x + y  =  31

Subtract  5x  from both sides of the equation to get

y  =  31 - 5x

This is the first equation solved for  y

From the sum formula for cosine:

cos(a + B) = cos a cos B  -  sin a sin B

Since  csc a  =  3 :

sin a  =  1/3

Since  sin a  =  1/3  and  cos²  a  =  1 - sin² a   :

cos²a  =  8/9       And since  a  is in quadrant II,

cos a  =  -√8 / 3

We can again use the Pythagorean identity and the fact that B is in quadrant II to get:

sin B  =  1/ √10

cos B  =  -3 / √10

And so...

cos(a + B) = (-√8 / 3)(-3 / √10)  -  (1/3)(1/ √10)

Plug this into a calculator or simpify it to get a final answer.....I don't have time to write a better explanation right now, but if you have any questions about this please ask!

The probability is 1/450.

Angle YZX = 42/2 + 70/2 = 56º

V (cone)   = ( pi ^ radius^2 * height )  / 3

104.67  = (3.14) * (radius)^2 *  4 / 3

Multiply both sides by 3  and divide both sides by 3.14

104.67 * 3  / 3.14   =  radius^2

The left side  evaluates  to  ≈  100

Taking the square root of both sides  gives that

10  =  radius

Double this value to find the diameter....

What is the number of square units in the area of a triangle whose sides measure 5, 6, and 6 units?

Height    h = sqrt(6² - 2.5²) = 5.454356057

Area      A = 2.5 * 5.454356057 = 13.63589014 units squared

There are 445 ways of placing the lamps.

The total of green marbles is 4 + 5/6(70 - 4)

GCD(174/5, 78/45, 679/10) = 1 / 30

I think this is more accurate:

(4, 5, 6, 7, 8, 9, 10, 10, 12, 13, 14, 14, 15, 16, 16, 18, 18, 20, 22, 24, 26)>>Total Sums =21

[6, 9, 12, 15, 18, 18, 24] = 7 Numbers divisible by 3

Probability is: 7 / 21 = 1 / 3

Primes[2, 3, 5, 7, 11, 13]

(5, 7, 8, 9, 10, 12, 13, 14, 15, 16, 16, 18, 18, 20, 24) >>Total Sums=  15

[9, 12, 15, 18, 18, 24]>>Total = 6 - numbers that are divisible by 3.

Probability is: 6 / 15 =2 / 5

The probability is 6/35.

Expanding along the third column, we find that most terms cancel, and we are left with a determinant of 1.

anyone?