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harina [27]
3 years ago
14

What is true about the complex number -5 - 5i? A. The modulus is 5√2. B. It lies in quadrant 3. C. The modulus is 5. D. It lies

in quadrant 2.
Mathematics
1 answer:
vladimir1956 [14]3 years ago
8 0

Answer:

A. The modulus is 5√2.

B. It lies in quadrant 3

Step-by-step explanation:

Given a complex value z = x = iy

The modulus is expressed as;

|z| = √x²+y²

Given the complex number z = -5 - 5i

|z| = √(-5)²+(-5)²

|z| = √25+25

|z| = √50

|z| = √25 * √2

|z| = 5√2

For the argument;

theta = arctan(-5/-5)

theta = arctan 1

theta = 45degrees

since tan is positive in the third quadrant, hence it lies in quadrant 3

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Use the Pythagorean Theorem to find the length of the hypotenuse in the triangle below.
AfilCa [17]

Answer:

41

Step-by-step explanation:

The Pythagorean Theorem:

x^2+y^2=z^2

where x and y are two legs, and z is the hypotenuse

Plugging this in, we have

40^2 + 9^2 = 1681\\\sqrt{1681}=41

8 0
3 years ago
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The water in a swimming pool increased from 4.5 to 6 feet.What is the percent in the water level rounded to the nearest tenth of
GalinKa [24]

(6) / (4.5) = 4 / 3  =  1.333...

The level increased by 33-1/3 % .

The old level was  75%  of the new level.

The amount of water in the pool also had to
increase  33-1/3 % .  If you didn't have that
much water to put in the pool, you couldn't
change the surface level from  4.5ft  to  6ft .

8 0
4 years ago
Fiona loves pizza. She ate of a pizza for dinner one night. She ordered another pizza the
kvv77 [185]

\stackrel{1st~night}{\cfrac{5}{6}}+\stackrel{\textit{2nd night}}{\cfrac{1}{3} }\implies \cfrac{(1)5~~ +~~(2)1}{\underset{\textit{using this LCD}}{6}}\implies \cfrac{7}{6}\implies 1\frac{1}{6}

4 0
3 years ago
1.Which answer below represents the
Oksana_A [137]
I think B because you would have to divide by 5 to get y by itself.

5 0
3 years ago
94. Birth Rate of Unmarried Women In the United States, the birth rate B of unmarried women (births per 1000 unmarried women) fo
OLga [1]

Using concepts of quadratic equation, we have that:

a) The age of unmarried women with the highest birth rate 29 years.

b) The highest birth rate of unmarried women is of 65 births per 1000 unmarried women.

c) B(40) = 25.43, which means that the birth rate of unmarried women of age 40 is of 25.43 births per 1000 unmarried women.

The birth-rate for women of age a is given by:

B(a) = -0.33a^2 + 19.17a - 213.37

Which is a quadratic equation with coefficients a = -0.33, b = 19.17, c = -213.37

Item a:

The age with the highest value is the a-value for the vertex, which is:

a_V = -\frac{b}{2a} = -\frac{19.17}{2(-0.33)} = 29

The age of unmarried women with the highest birth rate 29 years.

Item b:

The rate is B(29), which is:

B(29) = -0.33(29)^2 + 19.17(29) - 213.37 = 65

The highest birth rate of unmarried women is of 65 births per 1000 unmarried women.

Item c:

B(40) = -0.33(40)^2 + 19.17(40) - 213.37 = 25.43

B(40) = 25.43, which means that the birth rate of unmarried women of age 40 is of 25.43 births per 1000 unmarried women.

A similar problem is given at brainly.com/question/24626341

4 0
3 years ago
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