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KIM [24]
3 years ago
7

Which of the following expressions is the conjugate of a complex number with 2 as the real part and 3i as the imaginary part?

Mathematics
2 answers:
lbvjy [14]3 years ago
4 0
The complex number is represented as 2 + 3i. The conjugate of the complex number is the number with equal real part and imaginary part equal in magnitude but opposite in sign. Therefore, the correct answer is option B. The conjugate of the complex number is 2 − 3i.
luda_lava [24]3 years ago
4 0

Answer:

The conjugate of the complex number is 2 − 3i.

Step-by-step explanation:

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Two pools are leaking, after 15 minutes pool A has leaked 2/3 gallon, after 20 minutes pool B has leaked 2/3 gallon. Which pool
shepuryov [24]

Answer:

Pool A.

Step-by-step explanation:

This can be solved through ratios. You would write it as \frac{gallons}{minutes} So, \frac{2/3}{15} for the first one, and \frac{2/3}{20} for the second. You might want to use a calculator for that part, but you could also change the gallons to cups, which gives you a much better number of 10.515. So, \frac{10.515}{15} = 0.701, and \frac{10.515}{20} = 0.52575 So, pool A is at a faster rate. If you want it in gallons per minute, it's by 0.01 (with the 1 repeating) gallons per minute. By cups, it's 0.17525 cups per minute.

(The reason I did not do this by cross multiplying and dividing ratios is because it gives you the exact same answer if you are finding it per one, as I am here with per one minute. You can do it this way, it just wastes a bit of time.)

6 0
3 years ago
Garcia's Grill offers 77 side dishes, 55 types of steak, and 88 toppings. How many different smothered steak dinners can be made
svet-max [94.6K]

Answer:

Therefore the total number of ways that the customer can order the smothered steak dinner  is 9800.

Step-by-step explanation:

There are 7 side dishes, and  types of stake and 8 toppings.

The customer will have a smothered steak dinner.

The smothered steak dinner will consist of steak and 3 different toppings and 4\binom{8}{3} = \frac{8!}{3! \times 5!}  = 56 different side dishes.

The number of ways steak can be selected is =\binom{5}{1} = \frac{5!}{1! 4!}  =5

The number of ways toppings can be chosen is  = \binom{8}{3} = \frac{8!}{3! 5!}  = 56

The number of ways side dishes can be chosen = \binom{7}{4} = \frac{7!}{4!3!}  = 35.

Therefore the total number of ways that the customer can order the smothered steak dinner  is

= 5 × 56 × 35  = 9800.

7 0
3 years ago
Evaluate the expression for x= 2 and y=4. Enter your answer in the box. 16x + 2x2 - y2​
Nostrana [21]

Answer:

24

Step-by-step explanation:

Step 1: Define

x = 2

y = 4

16x + 2x² - y²

Step 2: Substitute and Evaluate

16(2) + 2(2)² - 4²

32 + 2(4) - 16

16 + 8

24

8 0
3 years ago
Can someone help to find the missing angle measurements
STatiana [176]

Answer:

Angle 1 = 75°

Angle 2 = 55°

Angle 3 = 55°

Angle 4 = 40°

Angle 5 = 140°

Angle 6 = 40°

Angle 7 = 75°

Angle 8 = 65°

Angle 9 = 115°

Step-by-step explanation:

1) We start with angle 2

Angle 2

Angles on a straight line = 180°

Hence,

b + 125° = 180°

b = 180° - 125°

b = 55°

Angle 2 = 55°

2)Angle 1

The sum of angles in a triangle = 180°

Hence

Let Angle 1 = a

50° + 55° + a = 180°

a = 180° - (50° + 55°)

a = 180° - 105°

a = 75°

3)Angle 3

Angle 2 and Angle 3 are vertical angles

So we use the Vertical angle theorem

This means

Angle 2 = Angle 3

Angle 2 = 55°

Hence, Angle 3 = 55°

4) Angle 4

Sum of Angles in a triangle = 180°

Let Angle 4 = d

Hence:

85° + Angle 3 + d = 180°

85° + 55° + d = 180°

d= 180° - (85° + 55°)

d = 180°- 140°

d = 40°

5)Angle 5

Angle 4 and Angle 5 are angles on a straight line

Sum of angles on a straight line = 180°

Angle 4 = 40°

Let Angle 5 = e

Hence:

40° + e = 180°

Collect like terms

e = 180° - 40°

e = 140°

6) Angle 6

Angle 4 and Angle 6 are vertical angles

Using Vertical angle theorem,

Angle 4 = Angle 6

Angle 4 = 40°

Hence, Angle 6 = 40°

7)Angle 9

Solving for Angle 9,

Sum of angles on a straight line = 180°

Angle 9 = i

i + 65° = 180°

i = 180° - 65°

i = 115°

8) Angle 8

= Angle 9 and Angle 8 are angles in a straight line

= Angle 8 = h

h + 115° = 180°

h = 180° - 115°

h = 65°

9)Angle 7

Sum of angles in a triangle = 180°

Angle 7 = g

g = 180° - (65° + Angle 6)

= 180° - (65 + 40

= 180° - 105°

= 75°

3 0
2 years ago
10. The fifth term of an arithmetic sequence is 11 and the tenth term is 41. What is the first term? ​
9966 [12]

a_{5}=a+4d=11\\a_{10}=a+9d=41

Solve the above equations,

a_{10}-a_{5}=41-11\\a+9d-a-4d=30\\5d=30\\d=6\\a=11-24=-13

First term is -13.

4 0
2 years ago
Read 2 more answers
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