For quadratics, these formulas are used mainly for factoring.
Your equation can be written as ...
... 2(x² +2x -3) = 0
You factor this by looking for factors of -3 (c=x1·x2) that add to give +2 (b=-(x1+x2)). These are {-1, +3}, so the factorization is ...
... 2(x -1)(x +3) = 0
The roots are then 1 and -3, which sum to -b = -2.
(You will note that the numbers used in the binomial factors are the opposites of the roots x1 and x2 in the Viete's Formulas. That is how we can look for them to sum to "b", rather than "-b".)
Answer:
36 candy bars. (32 if sold in packs)
Step-by-step explanation:
We know that eight candy bars cost 6 dollars, and we purchased $27 dollars worth of them.
Therefore, we can use 27/6 = 4.5 to see how many packs/sets of candy bars we purchased. Since there are 8 in a pack/set, we do 8x4.5 = 36 to see we can purchase 36 candy bars. However, if you can only buy them in packs of 8, then you can only purchased 4 packs/32 bars since 6x5 = 30 and we only have 27 dollars.
Answer: x=36
Step-by-step explanation:
The total measurement for a 4 sided figure is 360°. You subtract 216 from 360 to get 144. Since x is going to get multiplied by 2 on both sides divide 144 by 2 to get 72. You then divide that by 2 again to relieve the answer of x being 36.
Answer: No, the ordered pair (2,5) is not a viable solution
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Explanation:
(2,5) means that b = 2 and h = 5
I'm assuming each ordered pair is of the form (b,h) where b comes first, since b is before h in the alphabet.
So if b = 2 and h = 5, then we can replace each letter with those numbers to get the following:
5b + 3h = 45
5*2 + 3h = 45 ..... b replaced with 2
5*2 + 3*5 = 45 ..... h replaced with 5
10 + 15 = 45
25 = 45
We don't get the same number on both sides, so (b,h) = (2,5) is not a solution.
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Put another way:
If b = 2 and h = 5, this means you bought 2 burgers and 5 hot dogs
1 burger = $5
2 burgers = 2*5 = $10
1 hot dog = $3
5 hot dogs = 5*3 = $15
total amount spent = $10 + $15 = $25
total amount spent = $25
This does not match up with the $45 total spent that we're given. So this is another way to see we don't have a solution.
The ratio simplified would be 9:8:6
