Find the slope with the given points: (-3, 12) (5, 7)
The slope of a graph is the difference in y divided by the difference in x. The difference in y is 12-7= 5. I does not matter with one you subtract first as long as you keep that pattern the same for the x values. For example, since we subtracted 7 from 12, we have to subtract 5 from -3. So -3-5= -8. The slope of this graph is -5/8. we can check this by drawing the line and checking if the y value decreases as the x increases and drawing a triangle to see "rise over run".
Use the Binomial Theorem to complete the expansion of (y+z)^3
The answer is y^3 + 3zy^2 + 3yz^2 + z^3 The Binomial theorem is meant to save you time. I start by focusing on just the variables and the powers they are raised to. If you look at just the y, you will see that it progresses in the equation from y^3 to y^2 to y^1 and y^0. Z goes in the opposite direction, z^0 to z^1 to z^2 to z^3. To explain the coefficients I will expand this. (y+z)^3 = (y+z)(y+z)(y+z) FOIL the first two groups... (y^2+2yz+z^2) multiply it by the remaining (y+z) y^3+2y^2z+yz^2 + zy^2 +2yz^2 + z^3 then combine like variables... y^3+ 3zy^2 + 3yz^2 + z^3
Fill in the missing numbers in the following Arithmetic Sequence... 72, 65, 58, __, 44....
The missing number is 51. An arithmetic sequence is a sequence of numbers such that the difference between the consecutive terms is constant. Start by subtracting 65 from 72. the difference is 7. See if that is true for 65 - 58, we see that the difference is still 7. So subtract 7 from 58. This is how we arrive at 51.