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3 years ago

Which two numbers on the number line have a absolute value of 1?

Mathematics

2 answers:

const2013 [10]3 years ago

6 0

The one and the negative one

jolli1 [7]3 years ago

4 0

-1 and 1 is the answer to your problem

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If alpha and beta are the zeroes of the polynomial 6x2+x-2 find the value og alpha/beta + beta/alpha

castortr0y [4]

$6x^2+x-2=6x^2+4x-3x-2=2x(3x+2)-1(3x+2)\\\\=(3x+2)(2x-1)\\\\3x+2=0\to x=-\frac{2}{3}\\\\2x-1=0\to x=\frac{1}{2}\\\\\alpha=-\frac{2}{3};\ \beta=\frac{1}{2}\\\\\frac{\alpha}{\beta}+\frac{\beta}{\alpha}=\frac{-\frac{2}{3}}{\frac{1}{2}}+\frac{\frac{1}{2}}{-\frac{2}{3}}=-\frac{2}{3}\cdot\frac{2}{1}-\frac{1}{2}\cdot\frac{3}{2}=-\frac{4}{3}-\frac{3}{4}\\\\=-\frac{16}{12}-\frac{9}{12}=-\frac{25}{12}=-2\frac{1}{12}$

$use\ Vieta's\ formula:\\\\\frac{\alpha}{\beta}+\frac{\beta}{\alpha}=\frac{\alpha^2+\beta^2}{\alpha\beta}=\frac{\alpha^2+2\alpha\beta+\beta^2-2\alpha\beta}{\alpha\beta}=\frac{(\alpha+\beta)^2-2\alpha\beta}{\alpha\beta}=\frac{(\alpha+\beta)^2}{\alpha\beta}-2\\\\\alpha+\beta=\frac{-b}{a};\ \alpha\beta=\frac{c}{a}\\\\\frac{(\alpha+\beta)^2}{\alpha\beta}-2=\frac{\left(\frac{-b}{a}\right)^2}{\frac{c}{a}}-2=\frac{b^2}{a^2}\cdot\frac{a}{c}-2=\frac{b^2}{ac}-2$

$6x^2+x-2\\\\a=6;\ b=1;\ c=-2\\\\\frac{\alpha}{\beta}+\frac{\beta}{\alpha}=\frac{1^2}{6\cdot(-2)}-2=\frac{1}{-12}-2=-2\frac{1}{12}$

7 0

3 years ago

2^3a^7 times 2a^3 NEEE HELP

hichkok12 [17]

Step-by-step explanation:

explain step by step on photo, double check just in case

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3 years ago

Nathaniel participated in an 18-mile race. He ran 1 2 mile in 1 6 hour. If he ran the entire race at the same pace, how long, in

Softa [21]

Answer:

24 hours

Step-by-step explanation:

set up a ratio:

12 miles = 16 hours

------------- ------------

18 miles = x hours

cross multiply

12m * x = 16h * 18 m

solve for x

x=16h * 18m / 12m = 24 hours

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Mrs.Johnson just purchased a total of 12 books and magazines for her office. The total bill was $112. She spent $18 on magazines

SCORPION-xisa [38]

She bought 154 books

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What is the height, x, of the equilateral triangle shown?

lbvjy [14]

Answer:

I think it's either 10√3 or 10

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