In mathematics, a polynomial is an algebraic expression containing more than two terms. When the polynomial could not be reduced to a lower degree, it is classified as a prime polynomial. Just like whole numbers, a prime polynomial cannot be broken down into factors except 1 and by the number itself. Take for example, the polynomial x² + 5x + 6. It can be reduces to its factors x=-2 and -3. That would be expressed to x² + 5x + 6 = (x+2)(x+3). But if the polynomial is, say, x² + 5x + 7, there is no roots that are whole numbers. Therefore, it can't be reduced into factored groups because it is a prime polynomial.
Answer: x = -3
Step-by-step explanation:
2x + 7x = 9x
9x + 3 -24
- 3
9x = -27
divide by 9
-3 = x
One approach is to express
8x2y
so that the numerator and denominator are expressed with the same base. Since 2 and 8 are both powers of 2, substituting 23 for 8 in the numerator of 8x2y gives
(23)x2y
which can be rewritten
23x2y
Since the numerator and denominator of have a common base, this expression can be rewritten as 2(3x−y). In the question, it states that 3x−y=12, so one can substitute 12 for the exponent, 3x−y, which means that
8x2y=212
The final answer is A.
49. From 3 coin tosses, there are 8 possible outcomes:
... TTT, TTH, THT, THH, HTT, HTH, HHT, HHH
All but the first have at least one head, so 7/8 of the possibilities have at least one head. That's 87.5% (not among your choices).
Likewise, all but the last listed outcome have at least one tail. The problem is symmetrical that way when the coin is fair. 87.5% of outcomes have at least one tail.
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Perhaps you can tell I read your question as having two parts. If your question is the probability of getting at least one head AND at least one tail, you can see that condition includes 6 of the 8 outcomes, or 75%, matching selection d.
50. See for yourself: the calculator says 66.82%. Your best choice is selection d.
1. You could plug this into the calculator as either 70% of 156.33 or 0.7 × 156.33, but either way you know the discount is going to be $109.43
2. We got the discount, so all you have to do is subtract it from the original. 156.33 - 109.43 = $46.90 which is the sale price! I hope this helps
