<span>(5 + 3i)(8 - 2i) =
40 - 10i + 24i - 6i</span>² =
40 + 14i - 6(-1) =
40 + 14i + 6 =
46 + 14i
Answer:
Step-by-step explanation:
Let's call hens h and ducks d. The first algebraic equation says that 6 hens (6h) plus (+) 1 duck (1d) cost (=) 40.
The second algebraic equations says that 4 hens (4h) plus (+) 3 ducks (3d) cost (=) 36.
The system is
6h + 1d = 40
4h + 3d = 36
The best way to go about this is to solve it by substitution since we have a 1d in the first equation. We will solve that equation for d since that makes the most sense algebraically. Doing that,
1d = 40 - 6h.
Now that we know what d equals, we can sub it into the second equation where we see a d. In order,
4h + 3d = 36 becomes
4h + 3(40 - 6h) = 36 and then simplify. By substituting into the second equation we eliminated one of the variables. You can only have 1 unknown in a single equation, and now we do!
4h + 120 - 18h = 36 and
-14h = -84 so
h = 6.
That means that each hen costs $6. Since the cost of a duck is found in the bold print equation above, we will sub in a 6 for h to solve for d:
1d = 40 - 6(6) and
d = 40 - 36 so
d = 4.
That means that each duck costs $4.
Answer:
The answer to your question is number 3.
Step-by-step explanation:
Data
slope = m = 2
Point = (3, 9)
Process
1.- Write the equation of the line in the form point-slope
y - y1 = m(x - x1)
2.- Identify the values of x1 and y1
x1 = 3 y1 = 9
3.- Substitution
y - 9 = 2(x - 3)
4.- Simplify
y - 9 = 2x - 6
y = 2x - 6 + 9
5.- Result
y = 2x + 3 slope y-intercept form
Your answer is 21.7724<span>Kilograms</span>
