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
these options correspond to a and b from the original question.
The Present value of an annuity is given by PV = P(1 - (1 + r/t)^-nt)/(r/t)
where: P is the monthly payment, r is the annual rate = 7% = 0.07, t is the number of periods in one year = 12 and n is the number of years = 3.
18,000 - 6,098 = P(1 - (1 + 0.07/12)^-(3 x 12)) / (0.07/12)
11,902 = P(1 - (1 + 0.07/12)^-36) / (0.07/12)
P = 0.07(11,902) / 12(1 - (1 + 0.07/12)^-36) = 367.50
Therefore, monthly payment = $367.50
Answer:
your answer is 65 for the two missing angles
you take 50 and subtract it from 180 to get 130 then divide that by 2 you get 65
Step-by-step explanation:
or you can use the line which also equals 180 in all it has 115 on it so u would subtract 50 from it to get one of the angles then u would add 65 and 50 to get 115 and subtract 115 from 180 to get 65
Answer:
f=6
g=8
Step-by-step explanation:
If ABCE is a trapezium, AD is parallel to BC, and angle C is a right angle, ABCD must be a rectangle. You know that since ABCE has an area of 60 and ABCD has an area of 48, ADE must have an area of 12. Because the area of a triangle is bh/2, AD must be 6 and therefore f must be as well. Since ABCD has an area of 48, g must be 48/6=8. Hope this helps!
