Calculus

A photo would be nice...

The result is a straight line on an X/Y graph. It passes through the coordinate X=0, Y=1 and then through X=1, Y=4.

You can plot points on the line by substituting values for X and solving the equation for Y. For example:

At X=0... Y = 3*0 + 1 = 1
At X=1... Y = 3*1 + 1 = 4
At X=2... Y = 3*2 + 1 = 7
etc...

You do not have enough information to come up with an accurate answer. All wood does not weigh the same.

Only one.

2x - 12x = 220

-10x = 220

x= 220/-10

x = -22

3x + y - 8 = 0

-2x + by + 9 = 0

y = -3x + 8

by = 2x - 9

y = -3x + 8

y = (2/b)x - 9/b

Since the lines, represented by these equations, are perpendicular, their slopes are negative reciprocal of each other. So that 2/b must be equal to 1/3.

2/b = 1/3

b = 6

Multiply that by 1024.

(x + 5)(x + 2)

You can find the definition of the function, a statement about the function's values, and an inductive proof, in the Wikipedia article "Carmichael function", which I won't repeat here.

fist, you need to find what x is.

then, multiply it by 3.

then add by 5.

then your answer should be 77.

-or-

do 77-5

the divide it by3

that's your answer

FYI: that is 24

There is not really much to "solve". I suppose you mean 1.3 x 10-12. This is scientific notation, a convenient way to write very large or very small numbers. To change this into standard notation, move the decimal point in 1.3 12 positions to the left (adding digits if necessary). For a positive exponent, move the decimal point to the right. Thus, 1.3 x 10-12 = 0.0000000000013. However, it is better to learn about scientific notation, and just keep such large or small numbers in scientific notation, since that is much easier to read.

2(7)=3(7)

14=21

y=-2x-4

y=x+2

when equating the two equations

you get: 3x=-2 and get x=-2/3=-0.75 and y=1.25

Generally, function values are Y values, so..........

6X + 2Y = 24

subtract 6X from each side

2Y = - 6X + 24

divide both the integers on the right by 2

Y = - 3X + 12

-------------------------the function

If the Lotto is fair then it will not work. There is no way to forecast a truly random process: that is what random means. The numbers - or the processes that generate them - have no memory of what happened before. Each time is like the first time. So unless you believe in superstition, I would not waste my time trying to forecast the numbers.

But:

You should avoid "popular" patterns. This is not because the pattern is less likely but that if it does come up, the prize will be divided between a lot more people. So, for example, go for numbers above 31 (birth dates in the family are popular choices).

pH means -log10(H+concentration)

so pH of a H+ concentration 3.6x10-9 is:

pH = -log10(3.6x10-9)

≈ 8.4

the cells in your face are different from the others.

k = -3; factors are (9x + 3)(x - 1)

n(n-3)/2

3/2

You notice the first two items, 3bx + 3x factorizes into 3x(b+1). And the last two, by +y factorize into y(b+1) . So (b+1) is a common factor, so you can factorize these two into (b+1)(3x+y)

Reflex.

x=6

2x - 1 = 3x + 4

Subtract 2x from both sides: - 1 = x + 4

Subtract 4 from both sides: -5 = x

5x+3 = 3x+11

5x-3x = 11-3

2x = 8

x = 4

3.6 + x = 4.9 . . . . . . . . . . . . . . . . Original equation

3.6 - 3.6 + x = 4.9 - 3.6 . . . . . . . . . . . . Subtract 3.6 from each side

x = (4.9 - 3.6) . . . . . . . . . . . x is now isolated on one side

x = 1.3 . . . . . . . . . . . . . . . . Do basic subtraction; x is solved.

It's only true when x=5.