Answer: The 3 pieces of candy- one candy under that costs only 40 cents. The five pieces separated cost 50 cents each
Answer:
1. x = +/- 2
- 7
2. x = 
+/- 
3. n = 
+/- 
Step-by-step explanation:
1. Divide both sides by 2: (x + 7)^2 = 8
Square root both sides: x + 7 = +/- 2
Subtract 7 from both sides: x = +/- 2 - 7
2. Square root both sides: x - 3 = 
Since there is a negative inside the radical, we need to have an imaginary number: 
. So, 
Add 3 to both sides: x = +/-
3. Divide by -5 from both sides: (n - 2)^2 = -2
Square root both sides: n - 2 = 
Again, we have to use i: 
Add 2 to both sides: n = +/-
Hope this helps!
Answer:
D. A number of books and their cost that is not possible with either subscription.
Step-by-step explanation:
If you look at the 2 lines on the graph, you see that the blue line represents the first subscription which charges a 96 dollar annual fee, and the red line represents the other subscription which charges 3 dollars per book.
Every point along these lines shows a price that could possibly be paid and a number of books that could be bought. The point where these two lines meet is where the amount of books borrowed and the price for those books is the same for both subscriptions.
Because point S is not at this intersection, nor is it on either of these lines, it is not possible to pay that price for that amount of books with either subscription.
Answer:
Step-by-step explanation:
Firstly, note that -2i really is just z = 0 + (-2)i, so we see that Re(z) = 0 and Im(z) = -2.
When we're going from Cartesian to polar coordinates, we need to be aware of a few things! With Cartesian coordinates, we are dealing explicitly with x = blah and y = blah. With polar coordinates, we are looking at the same plane but with angle and magnitude in consideration.
Graphing z = -2i on the Argand diagram will look like a segment of the y axis. So we ask ourselves "What angle does this make with the positive x axis? One answer you could ask yourself is -90°! But at the same time, it's 270°! Why do you think this is the case?
What about the magnitude? How far is "-2i" stretched from the typical "i". And the answer is -2! Well... really it gets stretched by a factor of 2 but in the negative direction!
Putting all of this together gives us:
z = |mag|*(cos(angle) + isin(angle))
= 2*cos(270°) + isin(270°)).
To verify, let's consider what cos(270°) and sin(270°) are.
If you graph cos(x) and look at 270°, you get 0.
If you graph sin(x) and look at 270°, you get -1.
So 2*(cos(270°) + isin(270°)) = 2(0 + -1*i) = -2i as expected.
-1 = (x-1)/3
(multiply both sides by 3)
-3 = x-1
(add 1 on both sides)
x=-2
