The first thing to do is look at the left hand side and factorise it. To do this we use the reverse of FOIL. Then when the expression is factorised, we can solve for x.
1. First find the skeleton with just x's:
(2x )(x )
2. Next, find 2 numbers that mutiply to make 6, and these go at the end of the brackets. This could be 6 and 1 or 2 and 3, or -6 and -1 or -2 and -3.
Since there is a 7x term, the 2 numbers must add to 7 when one of them is multiplied by 2 - due to the 2x term (2x ).
so (2x 3)(x 2) or (2x 2)( 3)
3. Trial and error shows us that (2x + 3)(x + 2) is the right answer.
4. Now set each bracket respectively to 0 and solve for x. The solutions are x = -3/2 and x = -2.
And there we have the answers!
Answer:
Step-by-step explanation:
The fomula of a volume of a cylinder:
We have r = 12m and H = 9m. Substitute:
A) Total number of old plans = 3500 + 4700 = 8200
In the new month, the unlimited plans increased by 55%, which adds
0.55 • 3500 = 1925
unlimited plans, while the limited plans decreased by 25%, which subtracts
0.25 • 4700 = 1175
limited plans. Then
Total number of new plans = (3500 + 1925) + (4700 - 1175) = 8950
which corresponds to a percent change of
(8950 - 8200)/8200 ≈ 0.0915 = 9.15%
That is, percent change is given by
(new value - old value) / (old value)
B) The percent change is positive, so it's a percent increase.
Answer:
Below in bold.
Step-by-step explanation:
y = -4x2 + 8x - 13
Divide first 2 terms by -4:-
y = -4(x^2 - 2x) - 13
Convert to vertex form by completing the square:
y = -4[(x - 1)^2 - 1] - 13
y = -4(x - 1)^2 + 4 - 13
y = -4(x - 1)^2 - 9 <---------- Vertex form
y = a(x - j)^2 + k <---------- General form with vertex = (j, k).
So comparing, we see that the vertex is (1, -9).
First, subtract 63 from 75 to find out how much it decreased.
75 - 63 = 12
Divide 12 by 75.
12 / 75 = 0.16
In percents, that is 16%.
He spent 16% less this month.
Hope this helps!