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9966 [12]
3 years ago
5

Got to turn my dreams to reality

Mathematics
1 answer:
OleMash [197]3 years ago
8 0

Answer:

Truly spoken

Step-by-step explanation:

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Factor completely x^8- 16.
Nataly_w [17]

Answer:

Step-by-step explanation:


So in this example we'll be using the difference of squares which essentially states that: (a-b)(a+b)=a^2-b^2 or another way to think of it would be: a-b=(\sqrt{a}-\sqrt{b})(\sqrt{a}+\sqrt{b}). So in this example you'll notice both terms are perfect squares. in fact x^n is a perfect square as long as n is even. This is because if it's even it can be split into two groups evenly for example, in this case we have x^8. so the square root is x^4 because you can split this up into (x * x * x * x) * (x * x * x * x) = x^8. Two groups with equal value multiplying to get x^8, that's what the square root is. So using these we can rewrite the equation as:

x^8-16 = (x^4-4)(x^4+4)

Now in this case you'll notice the degree is still even (it's 4) and the 4 is also a perfect square, and it's a difference of squares in one of the factors, so it can further be rewritten:

x^4-4 = (x^2-2)(x^2+2)

So completely factored form is: (x^2-2)(x^2+4)(x^4+4)

I'm assuming that's considered completely factored but you can technically factor it further. While the identity difference of squares technically only applies to difference of squares, it can also be used on the sum of squares, but you need to use imaginary numbers. Because x^2+4 = x^2-(-4). and in this case a=x^2 and b=-4. So rewriting it as the difference of squares becomes: x^4+4 = x^4 - (-4) = (x^2-\sqrt{-4})(x^2+\sqrt{-4}) = (x^2-2i)(x^2+2i) just something that might be useful in some cases.

7 0
2 years ago
Read 2 more answers
A normal distribution has a mean of 61 and a standard deviation of 15. What is the median?
vivado [14]

Answer:  median = 61

Reason:

A normal distribution is perfectly symmetric. Such distributions have mean = median = mode.

8 0
1 year ago
Students conducted a study of different sized containers and found that the box shown held 240 blocks. What is the empirical rat
N76 [4]

Answer:

  B.  2 blocks per cubic inch

Step-by-step explanation:

The volume in cubic inches is the product of the dimensions in inches. The ratio of blocks per cubic inch is found by dividing the number blocks by the number of cubic inches. (Effectively, "per" means "divided by".)

  (240 blocks)/((6 in)(4 in)(5 in)) = 240/120 blocks/in³ = 2 blocks/in³

4 0
3 years ago
Read 2 more answers
Plz help. I will award pts and brainliest to whoever gives me the answer. This question is worth 10 points in my class. please h
Papessa [141]

Answer:

x = -4

Step-by-step explanation:

6 0
3 years ago
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P: It's sunny.
lapo4ka [179]

Answer:

I think the answer is c

Step-by-step explanation:

please give me brainlist

5 0
3 years ago
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