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use a math calculator like mathway or symbolab. (answer is 111 I think)

y//x = 7/2.

By Lagrange Interpolation, p(8) = 5/28.

The perimeter of the rectangle is 242.

The answer is stated in the question !! There are 12 pairs as follows:

 x       y

  0     -5       
-3     -4
3      -4
-4    -3
4     -3
-5     0
5      0
-4    3
4     3
-3   4
3    4
0    5

By a very short computer code in C++.

The lengths of two sides of ABC are 15 and 20, and the triangle perimeter is 50. What is the third side of ABC?  

The perimeter of a triangle is the sum of the lengths of all three sides. 

You know the length of two sides; namely 15 and 20.  These two sides total 35.  

So the third side has to be 50 (the total perimeter) minus the other two sides.  

50 – 35 = 15 the length of the third side   

_.

How did you get that guest?

Hints:

What kind of triangle is BPC ?

What does that mean?

You can work out one angle easily enough so you can work out all of them.

sin 7A = cos 8A.

hint:

sin x = cos (90-x)

just expand it out the same as you would for  (6+7x)(3-4x)

Find the cost of a pencil and eraser if two pencils and three erasers cost 140 dollars, and fivepencils and four erasers cost 250 dollars.​ 

Let P stand for the cost of one pencil  

Let E stand for the cost of one eraser  

2P + 3E = 140  multiply both sides of the equation by 4 to get   8P + 12E = 560    (call this eq 3) 

5P + 4E = 250  multiple both sides of the equation by 3 to get 15P + 12E = 750    (call this eq 4) 

subtract eq 3 from eq 4 and you get  7P = 190

                                                             P = 190 / 7 = 27.14 dollars for one pencil  

plug the value of P back into one of the original equations  

(2 • 27.14) + 3E = 140   

        54.28 + 3E = 140  

                     3E = 140 – 54.28 = 85.72  

                       E = 85.72 / 3 = 28.57 dollars for one eraser     

Those are some pretty expensive writing instruments. 

Check answer.  Plug values into one of the original equations:  

(5 • 27.14) + (4 • 28.57)

      135.70 + 114.28                         =  249.98  

The original problem specified 250 .... 249.98 is close enough, owing to rounding values  

_.

159  167  235  333  Total =  4

9  +  7  +  5  +  3==24 sum of "z's"

The expression x^2 + 15x + 54 can be written as (x + a)(x + b), and the expression x^2 - 17x + 72 written as (x - b)(x - c), where a, b, and c are integers. What is the value of a+b+c?   

x² + 15x + 54 factors to (x + 6)(x + 9)      a = 6 and b = 9   

x² – 17x + 72 factors to (x – 9)(x – 8)                      b = 9 and c = 8   

so a + b + c  =  6 + 9 + 8  =  23   

_.

For each value of $x,$ there is a negative value of $x.$ So, the answer to this problem is $\boxed0$

$\frac9{\frac34}=\frac{36}3=\boxed{12}$

We can add the 3 numbers together:

$\frac{64}3+17\frac23+18\frac15=$

$21\frac13+17\frac23+18\frac15=$

$39+18\frac15=\boxed{57\frac15}$

A = 2/7 = 6/21

B = 3/4 = 6/8

A      =      B

21    :       8

- 84        +58

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

 3      :       2

21x - 84 = 3 parts

42x - 168 = 6 parts

8x + 58 = 2 parts

24x + 174 + 2 parts

42x - 168 = 24x + 174

 18x + 32

    x = 19

Total = 29 * 19 = 551

6(x+25) - 4x = 310

2x = 310 - 150 = 160

4x + 310

= 320 +310

= 630

Sorry, I misread the question !! I took the number of men & women ==310.

Men ==M

Women ==M + 310

1 - 5/6 ==1/6 of women remaining

1 - 3/4 ==1/4 of men remaining

1/6 * [M + 310] ==1/4M + 25, solve for M

M==320 - Number of men originally

310 + 320 ==630 - Number of women originally.

There were 310 more women than men at a musical theatre. After 5/6 of the women and 3/4 of the men had left, there were 25 more women than men remaining behind. How many women were there at the musical theatre at first?

Let the number of women ==W

The number og men ==310  -  W

[1/6W]  =  [1/4 *[310 - W]] +25

W==246 - Number of women originally

310  -  246 ==64 - Number of men originally.

Euclidean algorithm computes the GCD of 2 numbers, which you already have. What you want is called the "Extended Euclidean Algorithm" to  find x and y, which are called "Bezout's coefficients" !! This is along and involved procedure which can be found here: https://www.youtube.com/watch?v=6KmhCKxFWOs

The answer is: x==5  and  y== - 21