The first coefficient is 2 and the last term is 6. They multiply to 2*6 = 12.
Now we must find two factors of 12 that add to 7 (the middle coefficient).
Through trial and error, you should find that:
3*4 = 12
3+4 = 7
So 3 and 4 are the numbers we're after. We'll split the 7m into 3m+4m and use the factor by grouping method as shown in the steps below.
2m^2 + 7m + 6
2m^2 + 3m + 4m + 6
(2m^2 + 3m) + (4m + 6)
m(2m + 3) + 2(2m + 3)
(m + 2)(2m + 3)
(2m + 3)(m + 2)
The order of the factors doesn't matter since something like 2*3 is the same as 3*2.
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Verifying the answer:
You can use technology like you did to check the answer, but here's one way to do it without a calculator.
(2m + 3)(m + 2)
n(m + 2) ...... let n = 2m+3
mn + 2n .... distribute
m( n ) + 2( n )
m(2m+3) + 2(2m+3) .... plug in n = 2m+3
m*2m + m*3 + 2*2m + 2*3 .... distribute
2m^2 + 3m + 4m + 6
2m^2 + 7m + 6
We arrive back at the original trinomial, so we have confirmed the answer.
Answer:
$3500 he can take off his income as a capital loss this year.
Step-by-step explanation:
Capital loss:
1. It is the loss realized when any investment's value gets decreased.
2. quantitatively it is the difference of price at which the invest is bought and price at which the investment is sold.
3. The condition for capital loss is that , selling price of investment should be less that buying price of same investment.
_________________________________________
Given
No. of shares bought = 500
cost of 1 share = $10
cost of 500 share = 500 *$10 = $5000
Thus, buying price of invest = $5000
Now price of share drops to $3 per share
thus total price of share now = 500*$3 = $1500
Thus, he sold his investment at $1500
capital loss incurred by him = $5000 - $1500 = $3500 (Answer)
The equation is 5+6*x=2-8*x...
and the answer is:
17
How I got this is you have to combine like terms...
you get:11*x=-6*x
17*x=x
than divide by x...
which than gives you 17...
Answer:
21 roads
Step-by-step explanation:
If each two cities are connected by a direct road, to find the number of roads we just need to solve a combination of 7 choose 2, that is, we need to find all pairs of two cities among the 7 cities:
Combination of 7 choose 2 = 7! / (5! * 2!) = 7*6/2 = 21
So there is a total of 21 roads on the island.
