Answer:
50
Step-by-step explanation:
- 8i = √-64
8i + 6
- -4i = -√-16
-4i + 3
[8i + 6][-4i + 3] → FOIL
>> -32i² + [24i - 24i] + 18
↑ ↑
-1 0
>>> 32 + 18 = 50
Information on Imaginary Numbers
√-1 = i
-1 = i²
-i = i³
1 = i⁴ [And every other exponent that is a multiple of 4; this cycle then repeats itself every time you go up one number at a time]
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Answer:
Quadrilateral
Step-by-step explanation:
The definition of a parallelogram is a quadrilateral that has two sets of parallel sides.
<span><span>the basic formula is
</span><span>
c(x) = ax² + bx + c,
where x is the number of widgets produced, and c(x) is cost to produce x number
of widgets.
first we need to calculate a, b, and c from the quadratic formula using the
system of 3 equations.
So, the equations are:
1. c(2) = 16= a(2)² + b(2) + c = 4a + 2b + c </span></span><span>= </span><span><span>4a + 2b + c = 16
</span>
2. c(4) = 18= a(4)² + b(4) + c = 16a + 4b + c </span><span>= </span><span><span>16a + 4b + c = 18
</span>
3. c(10) = 48= a(10)² + b(10) + c = 100a + 10b + c </span><span>= </span><span><span>100a + 10b + c = 48
</span><span>
subtract equation 1 from equation 2:
16a + 4b + c - 4a - 2b - c = 18 - 16 </span></span>=<span><span> 12a + 2b = 2
</span><span>
subtract equation 1 from equation 3:
100a + 10b + c - 4a - 2b - c = 48 - 16 </span></span>=<span><span> 96a + 8b = 32
</span><span>
We have two equations now, multiply the first by 4 ( to equal out b):
12a + 2b = 2 = 48a +8b =8
now subtract these equations:
96a + 8b - 48a - 8b = 32 - 8
48a = 24 </span></span><span> </span>
<span><span>a = 24/48 = 1/2
</span><span>
If we know a, we can calculate b from the equation:
12a + 2b = 2
2b = 2 - 12a = 2 - 12 * 1/2 = 2 - 6 = -4
b = -4 ÷ 2 = -2
We have a and b. Let's calculate c:
4a + 2b + c = 16
c = 16 - 4a - 2b = 16 - 4 * 1/2 - 2 * (-2) = 16 - 2 + 4 = 18
so a = ½ , b = -2, c = 18
now calculate c(6)
<span> c(6) = 1/2(6)² - 2(6) + 18 = 1/2 * 36 - 12
+ 18 = 18 - 12 + 18 = 24</span></span></span>
<span><span><span>
</span></span></span>
<span><span><span> it costs $24 to produce 6 widgets</span></span></span>
