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3 years ago

48x2 + 48xy2 + 12y4 =

Mathematics

2 answers:

drek231 [11]3 years ago

8 0

Step by step solution :

Step 1 :

Equation at the end of step 1 :

((48•(x2))+(48x•(y2)))+(22•3y4)

Step 2 :

Equation at the end of step 2 :

((48 • (x2)) + (24•3xy2)) + (22•3y4)

Step 3 :

Equation at the end of step 3 :

((24•3x2) + (24•3xy2)) + (22•3y4)

Step 4 :

Step 5 :

Pulling out like terms : 5.1

Pull out like factors :

48x2 + 48xy2 + 12y4 = 12 • (4x2 + 4xy2 + y4)

Trying to factor a multi variable polynomial :

5.2 Factoring 4x2 + 4xy2 + y4

Try to factor this multi-variable trinomial using trial and error

Found a factorization : (2x + y2)•(2x + y2)

Detecting a perfect square :

5.3 4x2 +4xy2 +y4 is a perfect square

It factors into (2x+y2)•(2x+y2)

which is another way of writing (2x+y2)2

How to recognize a perfect square trinomial:

• It has three terms

• Two of its terms are perfect squares themselves

• The remaining term is twice the product of the square roots of the other two terms

Final result :

12 • (2x + y2)2

Hope this helps!

stich3 [128]3 years ago

5 0

12y4+48xy2+48x2 that is the answer simplified

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Answer:

The actual SAT score is 2024.

The equivalent ACT score is 29.49.

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the z-score of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

SAT score that is in the 95th percentile

Scores on the SAT test are normally distributed with a mean of 1511 and a standard deviation of 312, which means that $\mu = 1511, \sigma = 312$

95th percentile is X when Z has a pvalue of 0.95, so X when Z = 1.645. The score is:

$Z = \frac{X - \mu}{\sigma}$

$1.645 = \frac{X - 1511}{312}$

$X - 1511 = 1.645*312$

$X = 2024$

The actual SAT score is 2024.

Equivalent ACT score:

The equivalent ACT score is the 95th percentile of ACT scores.

Scores on the ACT test are normally distributed with a mean of 21.1 and a standard deviation of 5.1, which means that $\mu = 21.1, \sigma = 5.1$ . So

$Z = \frac{X - \mu}{\sigma}$

$1.645 = \frac{X - 21.1}{5.1}$

$X - 21.1 = 1.645*5.1$

$X = 29.49$

The equivalent ACT score is 29.49.

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2 years ago

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Final answer:

Since absolute values determine the distance between the number and the value whether the value is positive or negative. As distance is always positive.

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Step-by-step explanation:

Step 1

It is said that |a| is always nonnegative even though even though |a|=-a for negative values of a.

Step 2

This is because by the definition of an absolute value, any real number inside an absolute value symbol || will always be positive.

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x^2 -2x +5

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