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AfilCa [17]
3 years ago
13

c. Use the identity for the difference of two squares, , and the imaginary number i to create an identity for the sum of two squ

ares. Show that the identity is true.
Mathematics
1 answer:
mash [69]3 years ago
5 0
The identity for the difference of two squares is
a² - b² = (a + b)(a - b)

Note that by definition, i² = -1.
Then
a² - (bi)² = a² - i²b² = a² - (-1)b² = a² + b².

Also from the identity,
a² - (bi)² = (a + bi)(a - bi) = a² - abi + abi - i²b² = a² - (-1)*b² = a² + b²

Therefore
a² - (bi)² = a² + b²

This identity is true.

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Amanda surveyed 13 students in her class about their heights in inches. Her data are listed below: 58, 59, 55, 52, 57, 59, 62, 5
Aleonysh [2.5K]

Answer:

IQR is 4, median is 58.

Step-by-step explanation:

Enter these values in a list, hit stat > calc > 1-var stats. That gives you the 5 number summary. To get IQR, subtract Q3 from Q1.

3 0
3 years ago
Read 2 more answers
PLS help i rly need help ive posted with no help im rly confused
vesna_86 [32]
Asked and answered elsewhere.
brainly.com/question/8666894
8 0
3 years ago
Please help. thanks.
Free_Kalibri [48]
Hello!

You have to find the area of the prism and the pyramid

rectangular prism is lwh

Put in the values you know

15 * 5 * 7 = 525

For a prism you use

\frac{lwh}{3}

Put in the values you know

\frac{15 * 5 *13 }{3}

Multiply

975/3

Divide

325

Add the values you know

325 + 525 = 850

The answer is D)850cm^{3}

Hope this helps!
5 0
3 years ago
1. Suppose that 35% of all patients admitted to a hospital's intensive care unit (ICU) have high blood pressure, 42% have some s
Lelechka [254]

Answer:

a) 65%

b) 28.57%

Step-by-step explanation:

Suppose that 35% of all patients admitted to a hospital's

intensive care unit have high blood pressure, 42% have some sort of infection, and 12% have both problems. Probabilities estimated from the data in ICU Admissions. (10POINTS)

 (a)  Find the probability that a randomly chosen patient in this ICU has either high blood pressure or an infection.

 (b)  Find the probability that a patient admitted to the ICU has high blood pressure given that an infection is present.

Solution:

Let H represent the people with high blood pressure and I represent the people with infection.

P(H) = 35% = 0.35, P(I) = 42% = 0.42, P(H ∩ I) = 12% = 0.12

Those with only high blood pressure = P(H ∩ I') = P(H) - P(H ∩ I) = 0.35 - 0.12 =0.23

Those with only infection = P(H' ∩ I) = P(I) - P(H ∩ I) = 0.42 - 0.12 =0.30

a) probability that a  patient has either high blood pressure or an infection = P(H ∪ I)

P(H ∪ I) = P(H ∩ I') + P(H' ∩ I) + P(H ∩ I) = 0.23 + 0.3 + 0.12 = 0.65 = 65%

b) probability that a patient has high blood pressure given that an infection is present = P(H / I)

P(H / I) = P(H ∩ I) / P(I) = 0.12 / 0.42 = 0.2857 = 28.57%

4 0
2 years ago
Find the domain for the function f(x)=sqrt x^2-x+6
dybincka [34]

Answer:

The domain is {x : x ∈ R} or (-∞ , ∞)

Step-by-step explanation:

* Lets explain how to find the domain

- The domain of the function is the values of x which make the

  function defined

- The quantity under the square root must be ≥ 0 because there is

  no square root for negative value

* Lets solve the problem

∵ f(x) = √(x² - x + 6)

∴ The value of (x² - x + 6) must be greater than or equal zero because  

   there is no square root for negative value

- Graph the function to know which values of x make the quantity

  under the root is negative that means the values of x which make

  the graph under the x-axis

∵ The graph doesn't intersect the x-axis at any point

∵ All the graph is above the x-axis

∴ There is no value of x make f(x) < 0

∴ x can be any real number

∴ The domain of f(x) is all real numbers

∴ The domain is {x : x ∈ R} or (-∞ , ∞)

6 0
3 years ago
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