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3 years ago

8

Use greatest common factor and the distributive property to write equivalent expressions in factored form. 2 +8

1 answer:

ziro4ka [17]3 years ago

6 0

Answer:

2(x+4y)

Step-by-step explanation:

The greatest common factor would be 2. So 2/2 is 1 and then 8/2 is 4. Now if we plug back the variables, you should get 1x and 4y. To put it in distributive property, just put the greatest common factor outside and the variables inside. inside. That's your answer! Hope this helped and have a great dayyyyy!!!!

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3 years ago

The planet Mercury orbits around the sun at 29.74 miles per second. How many miles will mercury travel in 1 minute?

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3 years ago

f p(x) and q(x) are arbitrary polynomials of degreeat most 2, then the mapping< p,q >= p(-2)q(-2)+ p(0)q(0)+ p(2)q(2)defin

Natasha2012 [34]

We're given an inner product defined by

$\langle p,q\rangle=p(-2)q(-2)+p(0)q(0)+p(2)q(2)$

That is, we multiply the values of $p(x)$ and $q(x)$ at $x=-2,0,2$ and add those products together.

$p(x)=2x^2+6x+1$

$q(x)=3x^2-5x-6$

The inner product is

$\langle p,q\rangle=-3\cdot16+1\cdot(-6)+21\cdot(-4)=-138$

To find the norms $\|p\|$ and $\|q\|$ , recall that the dot product of a vector with itself is equal to the square of that vector's norm:

$\langle p,p\rangle=\|p\|^2$

So we have

$\|p\|=\sqrt{\langle p,p\rangle}=\sqrt{(-3)^2+1^2+21^2}=\sqrt{451}$

$\|q\|=\sqrt{\langle q,q\rangle}=\sqrt{16^2+(-6)^2+(-4)^2}=2\sqrt{77}$

Finally, the angle $\theta$ between $p$ and $q$ can be found using the relation

$\langle p,q\rangle=\|p\|\|q\|\cos\theta$

$\implies\cos\theta=\dfrac{-138}{22\sqrt{287}}\implies\theta\approx1.95\,\mathrm{rad}\approx111.73^\circ$

4 0

3 years ago