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1st digit    26 choices

2nd digit   26 choices

5 numbers can make  100 000  numbers   (00000 - 99 999)

26  *  26  * 100 000 = ....... 

Squares have sides of equal length.....

   diagonals create triangles with equal leg lengths  and a 90 degree angle

       true

What do you want to do with this equation?

Solve for y ?

y ( 5 + b ) = - 24

y = - 24/ (5+b)

Is there  a diagram that goes with this Q?      You have only 2 equations   but three unknowns (JP   MK  and y) ....so there could be infinite solutions for 'y'....    sorry !

\((f\cdot g)(x) = f(x) \cdot g(x) = 6x(x + 5) = 6x^2 + 30x\)

But if you meant \((f\circ g)(x)\):

\((f\circ g)(x) = f(g(x)) = 6 g(x) = 6(x + 5) = 6x + 30\)

Question: If a blue triangle is the base of a pyramid, then what is its height?

\(\left|difference\;\;of\;\;roots\right|=\left| [{-b + \sqrt{b^2-4ac} \over 2a}]-[{-b- \sqrt{b^2-4ac} \over 2a}]\right|\)

Can you take it from there jxc?

What happens if there is an odd number of ppl?

The missing side between the two triangles is √(5² - 2²) = √21. 

x = √((√21)² - 3²) = 2√3 ≈ 3.5

Plug g(x) into the x in f(x)

Parallel lines have the same slope so the only change would be the y intercept. It goes up and right one so to get to x=0 we add 2 so the y intercept is (0, -3) and the equation is y=x-3

Part of an aops problem... use the msg board... week 19 right?

This is an aops problem. Don't cheat on these. Use the msg board

25-4=21. Using Pythagorean x would be sqrt(21-9) = sqrt(11) -> about 3.3

Since each person forwards to email to 3 other people, the expression for the number of additional people who received it after $n$ rounds (including Elijah) is $3^0 + 3^1 + 3^2 + 3^3 + \dots + 3^n. $ We can rewrite this as $\boxed{\sum_{k=0}^n 3^n}.$

JNK is similar to JML, so the ratio of their sides will be the same. Let JL = x. Then,

 \(\frac{7}{6} = \frac{x}{36}\\x=42\)

Diagram:

This is the same as asking to permute the string \(333221\) in distinguishable ways. That would be equal to \(6!=6\cdot5\cdot4\cdot3\cdot2\), but we're overcounting by a factor of \(3! = 3\cdot2\) multiplied by \(2!=2\), so we need to divide that from the original 6!. That would be equal to \(\frac{6\cdot5\cdot4\cdot3\cdot2}{3\cdot2\cdot2} = \boxed{60}\)

The sum of the angles in a triangle is $180°, $ and we find that $$(180-106) + 45+ 31+ x = 180°.$$ We know this because vertical angles are equal, so the vertical angle to the angle of $x°$ is also equal to $x°.$ 

Now you can try to solve this equation yourself.

OR

If the scale factor of the area is 1:3

then the scale factor of the side length is 1:sqrt(3)

so

\(\frac{\sqrt3}{1}=\frac{12}{2x-16}\)

now solve it for yourself.

Here ya go:

Put g(x) into f(x) as 'x'

x^2 + 1

(x-3)^2  + 1

x^2 -6x +10

Let the number of Skittles of each color be a, b, c, d, and e. We have 12 skittles in total:

a + b + c + d + e = 12

Note that we also need at least one of each color, so we can substitute a' = a + 1, b' = b + 1, and so on, to ensure that each color has at least one Skittle.

a' + b' + c' + d' + e' = 7

This is an example of stars and bars, and the ways to choose is (7+5-1) choose (7-1) = 462.

write in vertex form first: y = a(x + 1)^2 + 7

The coefficient "a" is there because knowing the vertex isn't enough to determine the equation. We can plug in the point (0, 10):

10 = a + 7

a = 3

So, the equation is y = 3(x+1)^2 + 7.

sum of roots = -b/a = -10/2 = -5

product of roots = c/a = 5/2

(2a - 3)(4b - 6) = 8ab - 12a - 12b + 18

= 8(5/2) - 12(-5) + 18

= 98