This looks complicated
lets simplify both sides
By multiplying top and bottom by the conjugate:-
left side = (5-3i)(x + iy) (4+5i) (5-3i)(x + iy) (4+5i)
------------------------ = ------------------------
(4-5i)(4+5i) 41
right side = (2 + i + 3-4)(2+i - 3 + 4i) (by Difference of 2 squares)
= 5-3i)(-1 + 4i)
so as left side = right side
(5-3i)(x+yi)(4+5i) = 41 (5-3i)(-1+5i)
5-3i is common so:-
(x + iy)(4+5i) = 41(-1+5i)
4x +5xi + 4yi - 5y = -41 + 205i
4x - 5y + (5x + 4y)i = -41 + 205i
EQuating coefficients we are left with the system of equations
4x - 5y = -41
5x + 4y = 205
solving this gives x = 21 and y = 25
Answer:
AB = 5/4 y - 1 = 5/4 (12/13) -1 = 2/13
AC= 7/3 y - 2 = 7/3 (12/13) -2 = 2/13
Step-by-step explanation:
Because it is a equilateral triangle, it means all sides have the same length.
AB = AC
5/4 y - 1 = 7/3 y - 2
5/4 y - 7/3 y = -2 +1
-13/12 y = -1
y = 12/13
input y to the equation.
AB = 5/4 y - 1 = 5/4 (12/13) -1 = 2/13
AC= 7/3 y - 2 = 7/3 (12/13) -2 = 2/13
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1.
8 < x(7 - x)
We can now substitute the given values to see which one satisfies the inequality.
8 < 2(7 - 2)
8 < 10
A is the correct answer.
2.
D.
This lists all of the factors of 24.
Answer:
B
Step-by-step explanation:
if its less than 1, the side lengths are smaller than the original.
Answer:
18
Step-by-step explanation:
Let number of girls be 'x'.
So, Number of boys = Number of girls - 4
= x - 4
Total number of students in a class = 40
Number of girls + Number of boys = Total number of students in a class
x + x - 4 = 40
2x - 4 = 40
2x - 4 + 4 = 40 + 4
2x = 44
x = 22
Number of boys = 22 - 4
= 18
