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Elis [28]
3 years ago
14

Two numbers are in the ratio 3:4 when 4 is added to each term their ratio becomes 10:13. Find the numbers.​

Mathematics
1 answer:
Alex17521 [72]3 years ago
7 0
So there’s 2 steps to this. First we subtract what was added on both sides. 10-4 : 13-4 and we get 6:9. This ratio is true, but is not in simplest form, since both numbers are divisible by 3. So after dividing both sides by 3, the answer in simplest form will be 2:3. The correct answer is 2:3
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Find the real numbers x and y if -3+ix^2y and x^2+y+4i are conjugate of each other. Pls solve with the steps
Firdavs [7]
ANSWER
x = ±1 and y = -4.
Either x = +1 or x = -1 will work

EXPLANATION
If -3 + ix²y and x² + y + 4i are complex conjugates, then one of them can be written in the form a + bi and the other in the form a - bi. In other words, between conjugates, the imaginary parts are same in absolute value but different in sign (b and -b). The real parts are the same

For -3 + ix²y
⇒ real part: -3
⇒ imaginary part: x²y

For x² + y + 4i
⇒ real part: x² + y (since x, y are real numbers)
⇒ imaginary part: 4

Therefore, for the two expressions to be conjugates, we must satisfy the two conditions. 

Condition 1: Imaginary parts are same in absolute value but different in sign. We can set the imaginary part of -3 + ix²y to be the negative imaginary part of x² + y + 4i so that the 

   x²y = -4 ... (I)

Condition 2: Real parts are the same

   x² + y = -3 ... (II)

We have a system of equations since both conditions must be satisfied

   x²y = -4 ... (I)
   x² + y = -3 ... (II)

We can rearrange equation (II) so that we have

   y = -3 - x² ... (II)

Substituting into equation (I)

   x²y = -4 ... (I)
   x²(-3 - x²) = -4
   -3x² - x⁴ = -4
   x⁴ + 3x² - 4 = 0
   (x² + 4)(x² - 1) = 0
   (x² + 4)(x-1)(x+1) = 0

Therefore, x = ±1.
Leave alone (x² + 4) as it gives no real solutions.

Solve for y:

   y = -3 - x² ... (II)
   y = -3 - (±1)²
   y = -3 - 1
   y = -4

So x = ±1 and y = -4. We can confirm this results in conjugates by substituting into the expressions:

   -3 + ix²y 
   = -3 + i(±1)²(-4)
   = -3 - 4i

   x² + y + 4i
   = (±1)² - 4 + 4i
   = 1 - 4 + 4i
   = -3 + 4i

They result in conjugates
4 0
3 years ago
Read 2 more answers
SOLVED I NEED THE ANSWER ASAP
Mademuasel [1]

Answer: -5

Step-by-step explanation:

15.5z=-77.5\\z=-\frac{77.5}{15.5} \\z=-5

4 0
3 years ago
Read 2 more answers
Of 10<br> Find the gradient of the line segment between the points (2,-2) and (0,-6).
Veseljchak [2.6K]

Answer:

<h3>The answer is 2</h3>

Step-by-step explanation:

The gradient of a line given two points can be found by using the formula

m =  \frac{ y_2 - y _ 1}{x_ 2 - x_ 1}  \\

From the question we have

m  =  \frac{ - 6 -  - 2}{0 - 2}  =  \frac{ - 6 + 2}{ - 2}   =   \frac{ - 4}{ - 2}  = 2 \\

We have the final answer as

<h3>2</h3>

Hope this helps you

6 0
3 years ago
5. In which quadrant does the terminal side of al 18° angle lie?
Softa [21]

Answer:

c. first quadrant

Step-by-step explanation:

First Quadrant : 0° to 90°

Second Quadrant : 90° to 180°

Third Quadrant : 180° to 270°

Fourth Quadrant : 270° to 360° (or 0°)

3 0
3 years ago
Read 2 more answers
If x-2y=10 and x≠0, what is the value of 2x/y+5
VladimirAG [237]

Answer: 4

Step-by-step explanation:

x - 2y =10

x = 10 + 2y

\frac{2x)}{y + 5}

\frac{2(10+2y)}{y+5}

\frac{20+4y}{y+5}

\frac{4(5+y)}{y+5} ... cancel like terms (y + 5)

= 4

5 0
2 years ago
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