f (x) = x ^ 4-x ^ 3 + x ^ 2-x
For this case what we can do is graph the function and see the behavior of it.
We have then that the function grows upwards (see attached image)
It has two cutting points with the x axis in:
x = 0
x = 1
Therefore, the other roots of the polynomial are imaginary.
Answer: 2 x intercepts appear on the graph of this polynomial function
<span>Answer:
First step is to find out what your x values are. The length of the interval from 2 to 14 is 12. Divide it into six equal parts, which is 2. Then the x points for the left endpoints are: 2, 4, 6, 8, 10, 12 (and the last rectangle goes from 12 to 14), but you don't use 14 unless you are doing right endpoints or trapezoids or something.)
Next step is to find the areas of the rectangles. It is just the base times the height, and the height is the function value of the x value, since the rectangle sits on the x axis and extends vertically up or down to the graph of the function. In integrals an area below the axis is considered to contribute a negative quantity to the integral, so we will do the same for rectangles that extend below the x axis.
f(2) = 3 - (1/2) 2 = 3 - 1 = 2
f(4) = 3 - 4/2 = 1
f(6) = 3 - 6/2 = 0
f(8) = 3 - 8/2 = -1
f(10) = 3 - 10/2 = -2
f(12) = 3 - 12/2 = -3
That should be in a table. Next to it you write the area, multiplied by -1 if f(x) < 0 (I'm saying that because areas are always positive.)
That gives 4, 2, 0, -2, -4, -6 for the six rectangles. Add all that up and it mostly cancels but you get -6 for the final answer.
I have explained as I went along. You do not have to explain so much when you give the answer on a test or homework. Just the computations and not so many words.</span>
The question is find the total cost when the price is $89.75 and the tax is 7 1/4%
Total cost = price + tax
Tax = 7 1/4 % of price
Tax rate = [7 + 1/4] = 7.25 %
Tax = 7.25 % * price = 7.25 % * $89.75 = $[7.25/100] * 89.75 = $6.51
Total cost = $89.75 + $ 6.51 = $96.26
Vertical angles are always equal.
x = 130
That's your answer.
Have an awesome day! :)
Answer:
the reasoning states that "all the numbers begin with a 7 or an 8"
however this is not accurate as they can be in different placements
which can make a big difference in the total estimate.
for example:
the number could've been an 8, or an 80
they both begin with an 8
however have totally different values and could have messed up the total estimated number.
hope this helps :D
