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I expect you posted this one too.

Why do you need help quick?

Should your question have more importance to the answerers than the other questions?

Why would that be?

They are all 3-4-5 triangles. Through pythagorean theorem \(CB=20\) . Through similar triangles, \(EB=5\) so \(x = 25 - 5 = \boxed{20}\)

And we are done!

Luann has a platter made out of a square, with semicircles of diameter 10 inches on each edge, as shown. What is the side length of the smallest square that can contain the platter, in inches?

This falls out really easily if you just expand it out and add like terms.

\([(q+4)(p+3)]-[(q+2)(p+1)]=44\\ etc\)

Maybe there is a quicker way to do this but here goes.

\(a\equiv (3^{2n}+4)^{-1}\pmod{9}\\ a\cdot (3^{2n}+4)\equiv 1\pmod{9}\\ a\cdot (3^{2n}+4)=9M+1\qquad \text{where M is an integer}\\ a\cdot (9^n+4)=9M+1\\ a\cdot 9^n+4a=9M+1\\ 4a-1=9M-a\cdot 9^n\\ 4a-1=9(M-a\cdot 9^{n-1})\\ 4a-1=9N \qquad \text{Where N is an integer}\\ \text{By inspection (or euclidean equation) }a=-2\;\;works\\ -2\pmod{9}\equiv 7\pmod{9}\\ a=7+9P  \qquad \text{Where P is an integer}\\ \text{So if } a \text{ is divided by 9 the remainder will be 7}\)

You can check all the numbers from 1 to 8 but this is the only one of those that works.  

LaTex:

a\equiv (3^{2n}+4)^{-1}\pmod{9}\\
a\cdot (3^{2n}+4)\equiv 1\pmod{9}\\
a\cdot (3^{2n}+4)=9M+1\qquad \text{where M is an integer}\\
a\cdot (9^n+4)=9M+1\\
a\cdot 9^n+4a=9M+1\\
4a-1=9M-a\cdot 9^n\\
4a-1=9(M-a\cdot 9^{n-1})\\
4a-1=9N \qquad \text{Where N is an integer}\\
\text{By inspection (or euclidean equation) }a=-2\;\;works\\
-2\pmod{9}\equiv 7\pmod{9}\\

a=7+9P  \qquad \text{Where P is an integer}\\
\text{So if a is divided by 9 the remainder will be 7}

If SR = 20 and XY = 7, find PQ.

Jon Jon, you fat-fingered the last digit ... should be 562 not 563. 

The prime factors of 20190 are 2*3*5*673

Now 3*673 = 2019, so this is a, say. 

b and c must be multiples of this, so b  2*2019 = 4038 and c = 5*2019 = 10095

The three numbers are:  2019, 4038 and 10095

I'll leave you to add them up.

A quarter-circle with radius 5 is drawn. A circle is drawn inside the sector, which is tangent to the sides of the sector, as shown. Find the radius of the inscribed circle.

One side of the square is 100 so the area of the square is 10,000. 

The radius of a circle is 50 so the area of the whole circle would be (3.1416)(50²) is 7,854 

but you don't count the whole circle because part of the square overlaps a fourth of it 

So the area of the remaining three-fourths of the circle is 5,890.5 

There are four of these "partial" circles so their total area is (4)(5,890.5) is 23,562  

Add the area of the square plus the four partial circles 10,000 + 23,562  =  33,562   

_.

The correct answer is D.  Erase that smallest arrow that points almost straight up and it will be obvious.  Look up "opposite angles" for more info.

_.

1/462 I'll give explan. If wanted

Expand the L side

40 - 50 i - 16i + 20 i^2         + -15 + 20 i\

20 -66i               - 15 + 20i

5 - 46i

I got it! Thanks!

(also choosing what first doesn't matter, i just learned that :o)

It's a:33,563squre units. 

481 8894396960 69AA754B04 65492A9763 262A56B896 7010000000 0000000000 0000000000

In 58! in base 12 has 27 zeros.

No matter what the value of n is, a^(-1) mod 9 = 7

a=1; b=1;d=(b+4)*(a+3)-(b+2)*(a+1) ; if(d==44, goto4, goto5);printa, b; a++;if(a<100, goto2, 0);a=1;b++;if(b<100, goto2, discard=0; 

p       q

16     1
15     2
14     3
13     4
12     5
11     6
10     7
9      8
8     9
7    10
6    11
5    12
4    13
3    14
2    15
1    16

thank you!

a + b + c  =  19(97)

a + n  =  b - n     --->     2n  =  b - a     --->     a  =  b - 2n

b - n  =  c/n     --->     n(b - n)  =  c     

Substituting:     a + b + c  =  19(97)     --->     (b - 2n) + (b) + ( n(b - n ) )  =  19(97)

       --->                                                                          2b - 2n + bn - n²  =  19(97)

                                                                                      2b + bn - 2n - n²  =  19(97)

                                                                                    b(2 + n) - n(2 + n)  =  19(97)

                                                                                            (b - n)(2 + n)  =  19(97)

Using the hint  19(97), let's try:       2 + n  =  19     and     b - n  =  97

--->                                                        n  =  17      and     b - 17  =  97     --->     b  =  114

a  =  b - 2n     --->     a  =  114 - 2(17)  =  80

c  =  n(b - n)  =  17(114 - 17)  =  1649

a + b + c  =  80 + 114 + 1649  =  1843     and     19(97)  =  1843

how did you solve this?

@ Guest, not exactaly. Maybe you made a mistake in expanding.

We know that (x+1)(x-1) is x^2-1, because of difference of squares. (x^2-1)(x^2+1) is difference of squares, yet again, so this is x^4-1.

I'm not sure if you count constants as expressions or not. If so, then it is 0, if not, then it is 1. 

When adding two polynomials with different degrees, you usally take the degree of the polynomial that has a higher degree. That should help you find the degree of f(x)+g(x).

Hint: which is greater, 3 or 4? So, which one do you use?

:)