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2 years ago

What are the factors of x^2-8x-20

Mathematics

1 answer:

kipiarov [429]2 years ago

6 0

Answer:

(x+2)(x−10)

Step-by-step explanation:

x^2-8x-20

Factoring means something like this:

(x+_)(x+_)

Add together to get -8

Multiply together to get -20

think of the two numbers

Try 2 and -10:

2+-10 = -8

2*-10 = -20

Fill in the blanks of with 2 and -10 to get

(x+_)(x+_) = (x+2)(x−10)

I hope it's right!

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Two equivalent decimals for 2.50

Ad libitum [116K]

2.5 is an equivalent decimal because you can add infinity zeros after the last number in a decimal and it will still be the same.

&

2.500 would be an equivalent decimal because you can add infinity zeros after the last number in a decimal and it will still be the same.

2.5, 2.500, 2.5000, 2.50000, etc..

5 0

3 years ago

Find the maximum and minimum values attained by f(x, y, z) = 5xyz on the unit ball x2 + y2 + z2 ≤ 1.

Allushta [10]

Check for critical points within the unit ball by solving for when the first-order partial derivatives vanish:
$f_x=5yz=0\implies y=0\text{ or }z=0$
$f_y=5xz=0\implies x=0\text{ or }z=0$
$f_z=5xy=0\implies x=0\text{ or }y=0$

Taken together, we find that (0, 0, 0) appears to be the only critical point on $f$ within the ball. At this point, we have $f(0,0,0)=0$ .

Now let's use the method of Lagrange multipliers to look for critical points on the boundary. We have the Lagrangian

$L(x,y,z,\lambda)=5xyz+\lambda(x^2+y^2+z^2-1)$

with partial derivatives (set to 0)

$L_x=5yz+2\lambda x=0$
$L_y=5xz+2\lambda y=0$
$L_z=5xy+2\lambda z=0$
$L_\lambda=x^2+y^2+z^2-1=0$

We then observe that

$xL_x+yL_y+zL_z=0\implies15xyz+2\lambda=0\implies\lambda=-\dfrac{15xyz}2$

So, ignoring the critical point we've already found at (0, 0, 0),

$5yz+2\left(-\dfrac{15xyz}2\right)x=0\implies5yz(1-3x^2)=0\implies x=\pm\dfrac1{\sqrt3}$
$5xz+2\left(-\dfrac{15xyz}2\right)y=0\implies5xz(1-3y^2)=0\implies y=\pm\dfrac1{\sqrt3}$
$5xy+2\left(-\dfrac{15xyz}2\right)z=0\implies5xy(1-3z^2)=0\implies z=\pm\dfrac1{\sqrt3}$

So ultimately, we have 9 critical points - 1 at the origin (0, 0, 0), and 8 at the various combinations of $\left(\pm\dfrac1{\sqrt3},\pm\dfrac1{\sqrt3},\pm\dfrac1{\sqrt3}\right)$ , at which points we get a value of either of $\pm\dfrac5{\sqrt3}$ , with the maximum being the positive value and the minimum being the negative one.

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3 years ago

Don has an album that holds 900 hockey cards. Each page of the album holds 9 hockey cards. If 68% of the album is empty, how m

nikitadnepr [17]

Since there are 9 hockey cards per page and it holds 900 hockey cards you can multiply 9 by 68 to get the total of 612 hockey cards. Then take 900 and subtract 612 from it and you should get 288 hockey cards in the album. Then divide that number by 9 to get the total number of pages filled 288/9=32 pages filled

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2 years ago

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Help me please i need answers for my sisters homework

frozen [14]

Eleven Million Seven Hundred and Sixty Thousand Eight Hundred and Twenty-five.

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3 years ago

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Andrea is told that the means of two groups in a study were statistically significant. She knows the means and standard deviatio

salantis [7]

Answer:

Cohen's D

Step-by-step explanation:

Cohen's D is a statistic that measures effect size. It shows standardised difference between 2 means.

Effect size is defined as how large the effect of a something is or its magnitude.

Cohen's D works effectively when the sample is >50 (that is for large samples). However a correction factor can be used to make results from small samples more accurate

The formular for Cohen's D is:

D = (mean1 - mean2) ÷ (√({standard deviation1}^2 + {standard deviation 2}^2)/2)

This is the most appropriate method in the given scenario

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3 years ago