1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
777dan777 [17]
3 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]3 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)

You might be interested in
HEY YOU! STOP YOUR SCROLLING AND HELP ME OUT?! PLEASE?!
rusak2 [61]

t=2 should be your answer!

7 0
3 years ago
Read 2 more answers
Which rule explains why these triangles are congruent?
Vinil7 [7]
AAS

(20 characters minimum)
8 0
2 years ago
It appears that people who are mildly obese are less active than leaner people. One study looked at the average number of minute
hoa [83]

Answer:

Obese people

Lower = \mu - 2\sigma = 373- 2(67) = 239

Upper = \mu + 2\sigma = 373+ 2(67) = 507

Lean People

Lower = \mu - 2\sigma = 526- 2(107) = 312

Upper = \mu + 2\sigma = 526+ 2(107) = 740

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".  

The empirical rule, also referred to as the three-sigma rule or 68-95-99.7 rule, is a statistical rule which states that for a normal distribution, "almost all data falls within three standard deviations (denoted by σ) of the mean (denoted by µ). Broken down, the empirical rule shows that 68% falls within the first standard deviation (µ ± σ), 95% within the first two standard deviations (µ ± 2σ), and 99.7% within the first three standard deviations (µ ± 3σ)".

Solution to the problem

Obese people

Let X the random variable that represent the minutes of a population (obese people), and for this case we know the distribution for X is given by:

X \sim N(373,67)  

Where \mu=373 and \sigma=67

On this case we know that 95% of the data values are within two deviation from the mean using the 68-95-99.7 rule so then we can find the limits liek this:

Lower = \mu - 2\sigma = 373- 2(67) = 239

Upper = \mu + 2\sigma = 373+ 2(67) = 507

Lean People

Let X the random variable that represent the minutes of a population (lean people), and for this case we know the distribution for X is given by:

X \sim N(526,107)  

Where \mu=526 and \sigma=107

On this case we know that 95% of the data values are within two deviation from the mean using the 68-95-99.7 rule so then we can find the limits liek this:

Lower = \mu - 2\sigma = 526- 2(107) = 312

Upper = \mu + 2\sigma = 526+ 2(107) = 740

The interval for the lean people is significantly higher than the interval for the obese people.

5 0
2 years ago
What is the lcd of: 8/9x 2/3x=1/9x 45?
spayn [35]
LCD would be 18

8/9 = 16/18
2/3 = 12/18
1/9 = 2/18
5 0
3 years ago
On a coordinate plane, triangle A B C is shifted 4 units to the right and 2 units up to form triangle A prime B prime C prime. I
zheka24 [161]

Answer:

(x, y) ⟶ (x + 4, y + 2)  

Step-by-step explanation:

If you shift a point four units to the right, x ⟶ x + 4.

If you shift it up two units, y ⟶ y + 2.

If you combine the two shifts into one transformation, the rule becomes

(x, y) ⟶ (x + 4, y + 2)

3 0
3 years ago
Other questions:
  • 4y-x=6 solve the equation for x
    6·1 answer
  • You just got a free ticket for a boat ride, and you can bring along 2 friends! Unfortunately, you have 6 friends who want to com
    5·1 answer
  • What is the complete factorization of the quadratic expression 4×^2+8×-60
    12·1 answer
  • Zoe's pizza cost $12.99 she gave a tip of $2.00
    10·2 answers
  • Which of these numbers 3 4 5 6 7 8 makes the inequity true?20>4b
    5·1 answer
  • Which data display shows the number of observations? Check all that apply.
    15·2 answers
  • Which statement is true about the solution to the two equations? (1 point)
    10·2 answers
  • PLEASE HELP. An arithmetic sequence can be
    15·1 answer
  • (HELP ASAP) A bag contains lettered tiles. The theoretical probability of choosing a vowel is 30%. The bag contains 42 consonant
    9·2 answers
  • 3x+2y=5 What is x/y intercept
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!