Answer:
The sum of reciprocals is 2/3.
You don't need complex numbers to solve this, but if you try to find a and b you will need complex numbers.
Step-by-step explanation:
a+b = 2
a*b = 3
1/a + 1/b = x
(a*b)*(1/a + 1/b) = (a*b)x
b + a = (a*b)(x)
2 = 3x
x = 2/3
b = 2 - a
a*(2 - a) = 3
-a^2 + 2a = 3
-a^2 + 2a - 3 = 0
a^2 - 2a + 3 = 0
let's solve the quadratic equation
a^2 - 2a + 3 = a^2 - 2a + 1 + 2 = (a - 1)^2 + 2 = 0
(a - 1)^2 = -2
![a_1 - 1 = \sqrt{2}i\\a_1 = 1+\sqrt{2}i\\\\a_2 - 1 = -\sqrt{2}i\\a_2 = 1 - \sqrt{2}i\\](https://tex.z-dn.net/?f=a_1%20-%201%20%3D%20%5Csqrt%7B2%7Di%5C%5Ca_1%20%3D%201%2B%5Csqrt%7B2%7Di%5C%5C%5C%5Ca_2%20-%201%20%3D%20-%5Csqrt%7B2%7Di%5C%5Ca_2%20%3D%201%20-%20%5Csqrt%7B2%7Di%5C%5C)
these options correspond to a and b from the original question.
Answer:
(m+n) -a = r
Step-by-step explanation:
first, you have to find what m+n is because that is their total budget, then you have to remove how much their apartment costs from their budget, because r is the amount of free cash they have. once A is subtracted from m+n, you have r
Answer:
The area of the triangle is of 8 units of area.
Step-by-step explanation:
Answer:
The area of the triangle is of 21 units of area.
Step-by-step explanation:
The area of a triangle with three vertices
is given by the determinant of the following matrix:
![A = \pm 0.5 \left|\begin{array}{ccc}x_1&y_1&1\\x_2&y_2&1\\1_3&y_3&1\end{array}\right|](https://tex.z-dn.net/?f=A%20%3D%20%5Cpm%200.5%20%5Cleft%7C%5Cbegin%7Barray%7D%7Bccc%7Dx_1%26y_1%261%5C%5Cx_2%26y_2%261%5C%5C1_3%26y_3%261%5Cend%7Barray%7D%5Cright%7C)
In this question:
Vertices (1,0) (5,0) (3,4). So
![A = \pm 0.5 \left|\begin{array}{ccc}1&0&1\\5&0&1\\3&4&1\end{array}\right|](https://tex.z-dn.net/?f=A%20%3D%20%5Cpm%200.5%20%5Cleft%7C%5Cbegin%7Barray%7D%7Bccc%7D1%260%261%5C%5C5%260%261%5C%5C3%264%261%5Cend%7Barray%7D%5Cright%7C)
![A = \pm 0.5(1*0*1+0*1*3+1*5*4-1*0*3-0*5*1-1*1*4)](https://tex.z-dn.net/?f=A%20%3D%20%5Cpm%200.5%281%2A0%2A1%2B0%2A1%2A3%2B1%2A5%2A4-1%2A0%2A3-0%2A5%2A1-1%2A1%2A4%29)
![A = \pm 0.5*(20-4)](https://tex.z-dn.net/?f=A%20%3D%20%5Cpm%200.5%2A%2820-4%29)
![A = \pm 0.5*16 = 8](https://tex.z-dn.net/?f=A%20%3D%20%5Cpm%200.5%2A16%20%3D%208)
The area of the triangle is of 8 units of area.
Answer:
![\frac{1}{8}\ liter](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B8%7D%5C%20liter)
Step-by-step explanation:
we know that
To find out how much solution the scientist used for the experiment multiply 3/4 by 1/6
so
![(\frac{3}{4})(\frac{1}{6})=\frac{3}{24}\ liter](https://tex.z-dn.net/?f=%28%5Cfrac%7B3%7D%7B4%7D%29%28%5Cfrac%7B1%7D%7B6%7D%29%3D%5Cfrac%7B3%7D%7B24%7D%5C%20liter)
simplify
![\frac{3}{24}=\frac{1}{8}\ liter](https://tex.z-dn.net/?f=%5Cfrac%7B3%7D%7B24%7D%3D%5Cfrac%7B1%7D%7B8%7D%5C%20liter)