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morpeh [17]
3 years ago
14

What is the rational roots of 4x^3+9x^2-x+10=0

Mathematics
1 answer:
almond37 [142]3 years ago
3 0

9514 1404 393

Answer:

  ±1/4, ±1/2, ±1, ±5/4, ±2, ±5/2, ±5, ±10

Step-by-step explanation:

The <em>rational root theorem</em> tells you possible rational roots of this equation would be ...

  ±(divisor of 10)/(divisor of 4)

The divisors of 10 are 1, 2, 5, 10. The divisors of 4 are 1, 2, 4. Then the possible rational roots are ...

  ±1/4, ±1/2, ±1, ±5/4, ±2, ±5/2, ±5, ±10

_____

This particular cubic has one irrational real root near -2.689. It has no rational roots.

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Write an explicit formula for the sequence -13,-6,1,8
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Answer:

\large\boxed{a_n=7n-20}

Step-by-step explanation:

It's an arithmetic sequence.

-6-(-13)=-6+13=7\\1-(-6)=1+6=7\\8-1=7

The difference is constant.

The explicit formula of an arihmetic sequence:

a_n=a_1+(n-1)d

Substitute:

a_1=-13,\ d=7

a_n=-13+(n-1)(7)                <em>use distributive property</em>

a_n=-13+7n-7\\\\a_n=7n+(-13-7)\\\\a_n=7n-20

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3 years ago
How long is line UW?
Neko [114]

Answer: UW= 9√3

Step-by-step explanation:

This right triangle is a 30-60-90 triangle. This is a special triangle. Since this is a special triangle, the hypotenuse is 2x.

The hypotenuse is 18. We can figure out the length of x.

2x=18

x=9

Since we got 9, you would think it is the answer, but it's not. The length across the 60° angle is x√3. Now that we know the length across from 60°, we can plug in x.

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We can check our answer by using Pythagorean Theorem.

9²+(9√3)²=18²

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Since they are equal, we know we have the right answer.

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Answer:

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Step-by-step explanation:

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