Problem 13
If we want to multiply (x^3-3x^2+2x) with (x^3-2x^2+x), then we can set up a diagram shown below. The terms are along the outside. The stuff inside is the result of multiplying each pair of outer terms.
- Example: x^3 times x^3 = x^6 in the top left corner
- Another example: 2x times x = 2x^2 in the bottom right corner.
This is known as the box method to keep track of all the terms multiplied.
Once the table is filled out, we add up each term inside the boxes. Combine like terms if possible. Notice that I color-coded the like terms (eg: the x^3 terms are in green boxes).
The final answer is x^6 - 5x^5 + 9x^4 - 7x^3 + 2x^2
To check if distances can be a triangle add the smaller two distances together. If the sum is larger (not equal to) than the longest distance then it is a possible side. For example, 2,2,4 or 1,2,5cannot be a triangle, 2,3, 4 can be a triangle because 2+3 is greater than 4.
Slope is rise/run
to find it we do (y1-y2)/(x1-x2)
y1 means the 1st y and y2 means the second y
in (x,y) form
y1=4
y2=4
x1=10
x2=7
(4-4)/(10-7)=0/3=0
slope is 0
Answer:
Step-by-step explanation:
curved surface area is 2πrh, so 2*π*7*15.
7*15*2=210.
210*π=659.734
a = 4, b = -21, c = -18
to keep from getting "mixed up", evaluate the discriminant first ...
b<sup>2</sup> - 4ac = (-21)<sup>2</sup> - 4(4)(-18) = 729
sqrt(729) = 27
x = (21 +/- 27)/8
x = -3/4, x = 6
since the discriminant is a perfect square, the original quadratic will factor ...
4x<sup>2</sup> - 21x - 18 = 0
(4x + 3)(x - 6) = 0
x = -3/4, x = 6
