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.
(2m + 7) - (3 - 4m)
First distribute the (-) in front of the quantity of 3 - 4m.
Think of it as this:
-1(3 - 4m)
You multiply each number inside the parenthesis by -1.
So:
3*-1 = -3
-4m * -1 = 4m
Now that you've distributed the negative you can remove the parenthesis.
Now you'll just set it all up like you would any normal problem. Because -3 is negative you'll make it subtract.... I'll show you what I mean:
2m + 7 - 3 + 4m
Combine like terms (Terms which have the same variables... in this case the same number of m's)
Rearranging them can help!
4m + 2m + 7 - 3
6m + 7 - 3
6m + 4, is our difference!
Answer: Choice B
A net is shown with a pentagon in the middle and 5 identical triangles on the 5 sides of the pentagon
The pentagon forms the base of the pentagonal pyramid. Each lateral side is a triangle that meets at the very top of the pyramid. The base stays on the floor while the sides are folded up.
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There are other possible net configurations to form a pentagonal pyramid, but the other answer choices do not make a pentagonal pyramid.
- Choice A produces a square pyramid.
- Choice C makes a triangular pyramid (aka tetrahedron).
- Choice D makes a hexagonal pyramid.
So we can rule choices A, C and D out.
Answer:
t=0 Sugar = 0 Kg
t=1min Sugar=0.27 Kg
Step-by-step explanation:
Data
Tank = 2640 L (pure water)
Sol=0.09kg Sugar per liter
Vin = Vout = 3L/min
Sugar in the beginning = ?
if beginning is t = 0min Amount of sugar = 0, this is due to the fact that at the moment of entering the tank the content is only water
, but if beginning is t= 1min then;
<u>First, find the perpendicular slope</u>
y = 0.3x + 6 ⇒ m = 0.3 = 
perpendicular slope = 
<u>Next, input</u> the point (x₁, y₁) and slope (m) into the Point-Slope formula
y - y₁ = m(x - x₁)
y - (-8) = (x - 3)
y + 8 = 
+ 10
y = + 2
