Answer:
x³ - (√2)x² + 49x - 49√2
Step-by-step explanation:
If one root is -7i, another root must be 7i. You can't just have one root with i. The other roos is √2, so there are 3 roots.
x = -7i is one root,
(x + 7i) = 0 is the factor
x = 7i is one root
(x - 7i) = 0 is the factor
x = √2 is one root
(x - √2) = 0 is the factor
So the factors are...
(x + 7i)(x - 7i)(x - √2) = 0
Multiply these out to find the polynomial...
(x + 7i)(x - 7i) = x² + 7i - 7i - 49i²
Which simplifies to
x² - 49i² since i² = -1 , we have
x² - 49(-1)
x² + 49
Now we have...
(x² + 49)(x - √2) = 0
Now foil this out...
x²(x) - x²(-√2) + 49(x) + 49(-√2) = 0
x³ + (√2)x² + 49x - 49√2
Answer:
64%
Step-by-step explanation:
16/25 = 0.64
0.64*100 = 64
64%
One way to look at this is to make 2 equations and treat it as a set of equations. We will make the cost of a donut equal to x, and the cost of a coffee equal to y.
Harold's order:
4x + 2y = 4.08
Melinda's order:
2x + 3y = 3.92
To combine these equations, we need to cancel out either x or y:
4x + 2y = 4.08
<span>2x + 3y = 3.92
</span>
4x + 2y = 4.08
<span>4x + 6y = 7.84
</span>
4x + 2y = 4.08
<span>-4x - 6y = -7.84
</span>
We can now combine these equations:
4x + 2y = 4.08
<span>-4x - 6y = -7.84
</span>
-4y = -3.76
y = 0.94
Therefore the cost of a large coffee is $0.94. We can plug this into either original equation to find the cost of a donut.
<span>4x + 2y = 4.08
</span>4x + 2(0.94) = 4.08
4x + 1.88 = 4.08
4x = 2.20
x = 0.55
The cost of a donut is $0.55, and the cost of a large coffee is $0.94.
