Six less than two times a number is no more than 7

Mathematics

1 answer:

ziro4ka [17]3 years ago

3 0

Answer:

n <=6.5

Step-by-step explanation:

Six less than two times a number is no more than 7

2n-6 <=7

Add 6 to each side

2n-6+6 <=7+6

2n <=13

Divide by 2

2n/2 <=13/2

n <=6.5

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Use the Remainder Theorem to completely factor p(x) = x ^3 + 7x ^2 + 11x + 5.

tigry1 [53]

In order to use the remainder theorem, you need to have some idea what to divide by. The rational root theorem tells you rational roots will be from the list derived from the factors of the constant term, {±1, ±5}. When we compare coefficients of odd power terms to those of even power terms, we find their sums are equal, which means -1 is a root and (x +1) is a factor.

Dividing that from the cubic, we get a quotient of x² +6x +5 (and a remainder of zero). We recognize that 6 is the sum of the factors 1 and 5 of the constant term 5, so the factorization is

... = (x +1)(x +1)(x +5)

... = (x +1)²(x +5)

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The product of factors (x +a)(x +b) will be x² + (a+b)x + ab. That is, the factorization can be found by looking for factors of the constant term (ab) that add to give the coefficient of the linear term (a+b). The numbers found can be put directly into the binomial factors to make (x+a)(x+b).

When we have 1·5 = 5 and 1+5 = 6, we know the factorization of x²+6x+5 is (x+1)(x+5).

4 0

3 years ago

Read 2 more answers

X - y = 2<br><br> x + y = -3<br> Solve this using elimination<br> Quickly please!!!!

blagie [28]

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3 years ago

24/? = 8/9 What is the unknown ratio?

Murljashka [212]

24 divided by 8 is 3.

3 times 9 is 27 so your ratio would be

24/27 = 8/9

or 24: 27= 8:9

so your answer is 27

-Calypso, 8th, Algebra 1 Honers