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777dan777 [17]
2 years ago
8

%20-%20%20%7Bb%7D%5E%7B2%7D%20%29" id="TexFormula1" title="( \frac{1}{2} {a}^{2} + \frac{1}{2} ab - {b}^{2} )" alt="( \frac{1}{2} {a}^{2} + \frac{1}{2} ab - {b}^{2} )" align="absmiddle" class="latex-formula">
​
Mathematics
1 answer:
Zigmanuir [339]2 years ago
5 0

Answer:

\frac{1}{2} (a + 2b)(a - b)

Step-by-step explanation:

Assuming you require the expression to be factored

Given

\frac{1}{2} a² + \frac{1}{2} ab - b² ← factor out \frac{1}{2} from each term

= \frac{1}{2} (a² + ab - 2b²) ← factor the quadratic

Consider the factors of the coefficient of the b² term(- 2) which sum to give the coefficient of the ab- term (+ 1)

The factors are + 2 and - 1, since

2 × - 1 = - 2 and 2 - 1 = + 1, thus

a² + ab - 2b² = (a + 2b)(a - b) and

\frac{1}{2} a² + \frac{1}{2} ab - b² = \frac{1}{2}(a + 2b)(a - b)

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A college-entrance exam is designed so that scores are normally distributed with a mean of 500 and a standard deviation of 100.
yawa3891 [41]

Answer:

The probability is  0.003

Step-by-step explanation:

We know that the average \mu is:

\mu=500

The standard deviation \sigma is:

\sigma=100

The Z-score is:

Z=\frac{x-\mu}{\sigma}

We seek to find

P(x800)

For P(x>800) The Z-score is:

Z=\frac{x-\mu}{\sigma}

Z=\frac{800-500}{100}

Z=3

The score of Z = 3 means that 800 is 3 standard deviations from the mean. Then by the rule of the 8 parts of the normal curve, the area that satisfies the conficion of 3 deviations from the mean has percentage of 0.15%

So

P(x>800)=0.15\%

For P(x<200) The Z-score is:

Z=\frac{x-\mu}{\sigma}

Z=\frac{200-500}{100}

Z=-3

The score of Z = -3 means that 200 is 3 standard deviations from the mean. Then by the rule of the 8 parts of the normal curve, the area that satisfies the conficion of 3 deviations from the mean has percentage of 0.15%

So

P(x

Therefore

P(x800)=P(x800)

P(x800)=0.0015 + 0.0015

P(x800)=0.003

6 0
3 years ago
Which equation is the result of subtracting the second equation from the first?
rewona [7]

Answer:

the answer is

-x-8y=8

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Step-by-step explanation:

4x - 6y = 13 - (5x + 2y = 5)

or, 4x - 6y = 13

- 5x - 2y = -5

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

- x - 8y = 8

5 0
2 years ago
Quadrilateral PQRS is located at P (−4, 1), Q (−2, 3), R (1, 1), and S (−2, −2). Russell and Jamie have both classified PQRS dif
Usimov [2.4K]

Answer:

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Step-by-step explanation:

3 0
3 years ago
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nydimaria [60]

Answer:

19x I believe

Step-by-step explanation:

Added 10 and 9, left the x

8 0
3 years ago
Read 2 more answers
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masya89 [10]
Answer will be 1/17
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3 years ago
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