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Alexxandr [17]
3 years ago
13

Find the values of x and y that satisfy the equation –21 + 5yi = 7x – 10i.

Mathematics
1 answer:
kap26 [50]3 years ago
8 0

Answer:

The values of x and y are x = -3 and y = -2

Step-by-step explanation:

In the complex numbers if a + bi = c + di, then the real parts are equal and the imaginary parts are equal

  • a = c
  • b = d

Let us use this rule to solve the question

∵ -21 + 5yi = 7x - 10i

∴ The real parts are -21 and 7x

∴ The imaginary parts are 5y and -10

∵ The real parts are equal

∴ 7x = -21

→ Divide both sides by 7

∴ \frac{7x}{7} = \frac{-21}{7}

∴ x = -3

∵ The imaginary parts are equal

∴ 5y = -10

→ Divide both sides by 5

∴ \frac{5y}{5} = \frac{-10}{5}

∴ y = -2

∴ The values of x and y are x = -3 and y = -2

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Two kinds of crated cargo, A and B, are to be shipped by truck. Each crate of cargo A is 50 cubic feet in volume and weighs 200
BlackZzzverrR [31]

Answer:

The correct answer is option b)

50a+10b<1000; 200a+360b < 7200; a> 0; b>0

Step-by-step explanation:

We are given that Two kind of crated cargo namely A and B to be shipped by truck.

<u>Cargo A:</u>

Volume of each crate of cargo A = 50 cubic ft

Weight of each crate of cargo A = 200 pounds

Let number of crates of cargo A to be shipped = a

Total volume of 'a' crates of cargo A = 50a cubic ft

Total weight of 'a' crates of cargo A = 200a pounds

<u>Cargo B:</u>

Volume of each crate of cargo B = 10 cubic ft

Weight of each crate of cargo B = 360 pounds

Let number of crates of cargo B to be shipped = b

Total volume of 'b' crates of cargo B = 10b cubic ft

Total weight of 'b' crates of cargo B = 360b

Total volume allowed in the truck is 1000 cubic ft

Total volume of 'a' crates of Cargo A and Total volume of 'b' crates of Cargo B = 50a+10b cubic ft (This sum should be less than volume of truck so that it can fit in the truck)

So, the inequality becomes

50a+10b ....... (1)

Total weight allowed (load limit) in the truck is 7200 pounds

Total weight of 'a' crates of Cargo A and Total weight of 'b' crates of Cargo B = 200a+360b cubic ft (This sum should be less than volume of truck so that it can fit in the truck)

So, the inequality becomes

200a+360b ....... (1)

And number of crates of cargo A and B are always a positive number.

So, a > 0 and b > 0.

So, the correct answer is option b.

<em>b. 50a+10b<1000; 200a+360b < 7200; a> 0; b>0</em>

3 0
3 years ago
F(x) = x2 + 1<br> g(x) = 5 – x
xz_007 [3.2K]

Answer:

g(x) = 5 – x

Step-by-step explanation:

7 0
3 years ago
E = mc2<br> please help ive been looking and i can’t find an answer for math.
goldfiish [28.3K]

Answer:

Don't really understand the question, but

7 0
3 years ago
2,4...16,32 what comes next<br>​
laiz [17]
The next one would be 64
3 0
2 years ago
Read 2 more answers
12(43)
IrinaVladis [17]
I’m not entirely sure how to answer this without a word problem, but from what I see, all you have to do is multiply the two numbers.
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3 0
3 years ago
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