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lora16 [44]
3 years ago
8

What is the slope of the line?

Mathematics
1 answer:
koban [17]3 years ago
5 0
4/3 USE THE FORMULA TO GET YOUR ANSWER
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A

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What kind of quadrilaterals is this?
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Read 2 more answers
Report Error Suppose $P(x)$ is a polynomial of smallest possible degree such that: $\bullet$ $P(x)$ has rational coefficients $\
motikmotik

Answer:

We want a polynomial of smallest degree with rational coefficients with zeros in \sqrt{7}, 1 - \sqrt{6} and -3. The last root gives us the factor (x+3). Hence, our polynomial is

P(x) =(x+3)q(x)

where q is a polynomial with rational coefficients and roots \sqrt{7} and 1 - \sqrt{6}. The root \sqrt{7} gives us a factor x-\sqrt{7}, but in order to obtain rational coefficients we must consider the factor x^2-7.

An analogue idea works with 1 - \sqrt{6}. For convenience write  x - 1 + \sqrt{6} = ( x - 1) + \sqrt{6}. This gives the factor (x-1)^2-6. Hence,

P(x) = (x+3)(x^2-7)((x-1)^2-6)=x^5+x^4-18x^3-22x^2+77x+105

Notice that P(-1)=24. So, in order to satisfy the last condition we divide by 3 the whole polynomial, without altering its roots. Finally, the wanted polynomial is

P(x) =(1/3)x^5+(1/3)x^4-6x^3-(22/3)x^2+(77/3)x+35

Step-by-step explanation:

We must have present that any polynomial it's determined by its roots up to a constant factor. But here we have irrational ones, in order to eliminate the irrational coefficients that a factor of the type x-\sqrt7 will introduce in the expression, we need to multiply by its conjugate x+\sqrt7. Hence, we will obtain x^2-7 that have rational coefficients. Finally, the last condition is given with the intention to fix the constant factor. Usually it is enough to evaluate in the point and obtain the necessary factor.

4 0
2 years ago
Estimate the unit rate is 12 pair of socks sale for $5.79
lesantik [10]
About $0.48
you can make an equation
12/5.79 = 1/x
8 0
3 years ago
Emma went to a salon to get her hair cut. The price of the haircut is $65. She wants to leave a 20% tip. What is the total amoun
Alina [70]

Answer:

$78

Step-by-step explanation:

$65 x 1.20 = $78

or

$65 x 0.20 = $13

$65 + $13 = $78

8 0
3 years ago
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