According to the Rational Root Theorem, which number is a potential root of f(x) = 9x8 + 9x6 – 12x + 7?
2 answers:
Answer:
Seven-thirds
Step-by-step explanation:
The give equation is .
The leading coefficient is 9
The constant term is 7
According to the rational root theorem, the ratio of factors the constant terms to that of the coefficient of the leading term are all possible rational roots of the given polynomial.
Base on this theorem, or seven thirds is a potential root because the numeration is a factor of 7 and the denominator is a factor of 9.
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Answer:
1)
2)
3) The greatest age that Sue could be is 7.
4) The smaller of the two integers is 92.
5) Don needs to earn at least 244 points in the fourth game.
Step-by-step explanation:
1) An rectangle has 2 dimensions: width(w) and length(l)
The perimeter P is:
The problem states that the length of a rectangle is three times its width. So l = 3w and:
The perimeter of the rectangle is at most 112 cm. It means that the perimeter can be 112, so the equal sign enters the inequality. So
2)
The problem states that he earns $850 per week in sales. His earnings is modeled by the following equation:
, in which w is the number of weeks.
The problem also states that he spent $7500 to obtain his merchandise, and it costs him $300 per week for general expenses. So his expenses can be modeled by the following equation
, in which w is also the number of weeks.
He will make a profit when his earnings are bigger than his expenses, so: When they are equal, there is no profit, so the equal sign does not enter the inequality.
3)
I am going to call Jenny's age x and Sue's age y.
The problem states that Jenny is eight years older than twice her cousin Sue’s age. So
.
The sum of their ages is less than 32, so:
Sue's age has to be less than 8, so the greatest age that Sue could be is 7.
4)
The sum of two consecutive integers is at least 185.
There are two integers with sum of 185, so:
They are consecutive so:
Replacing in the sum equation:
The smaller of the two integers is 92.
5)
The average is the sum of all the scores divided by the number of games. So:
Don needs to earn at least 244 points in the fourth game.
Since the dice are fair and the rolling are independent, each single outcome has probability 1/15. Every time we choose
We have and
, because the dice are fair.
Now we use the assumption of independence to claim that
Now, we simply have to count in how many ways we can obtain every possible outcome for the sum. Consider the attached table: we can see that we can obtain:
- 2 in a unique way (1+1)
- 3 in two possible ways (1+2, 2+1)
- 4 in three possible ways
- 5 in three possible ways
- 6 in three possible ways
- 7 in two possible ways
- 8 in a unique way
This implies that the probabilities of the outcomes of are the number of possible ways divided by 15: we can obtain 2 and 8 with probability 1/15, 3 and 7 with probability 2/15, and 4, 5 and 6 with probabilities 3/15=1/5
