(a+bi)(2+3i)-i=(-11+5i)(1-i)
2a+3ai+2bi+3bi²-i=-11+11i+5i-5i²
2a+(3a+2b-1)i-3b=-11+16i+5
(2a-3b)+(3a+2b-1)i=-6+16i
Therefore; we have the next system of equations:
2a-3b=-6
3a+2b-1=16
Finally, the system of equations is:
2a-3b=-6
3a+2b=17
We can solve this system of equations by reduction method
2(2a-3b=-6)
3(3a+2b=17)
----------------------
13a=39 ⇒a=39/13=3
3(2a-3b=-6)
-2(3a+2b=17)
----------------------
-13b=-52 ⇒ b=52/13=4
Answer: a=3; b=4
Answer:
3.75 hours
Step-by-step explanation:
Bob completes his homework in 2.5 hours.
In 1 hour, he completes 1/2.5 of his homework.
Joe completes his homework in x hours.
In 1 hour, he completes 1/x of his homework.
Together, they complete the homework in 1.5 hours.
In 1 hour, they do 1/1.5 of the homework.
1/2.5 + 1/x = 1/1.5
Convert the decimal numbers in the numerators into fractions.
1/(5/2) + 1/x = 1/(3/2)
2/5 + 1/x = 2/3
Multiply both sides by the LCD, 15x.
6x + 15 = 10x
-4x = -15
x = 3.75
Answer: 3.75 hours
Considering that the square root of 49 is 7, and 52 > 49, Alejandro was not correct, as the correct integer is of 48.
<h3>What is the integer that has the square root closest to n, without going over?</h3>
The integer that has square root n is given by:
S(n) = n².
Hence the closest is given by:
C(n) = n² - 1.
In this problem, we have n = 7, hence:
C(7) = 7² - 1 = 48.
Which means that Alejandro was not correct.
More can be learned about square roots at brainly.com/question/27678604
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Answer:The left side 13 is greater than right side -3.6 which means statement is true
