1/2 x = 20
x = 2 x 20 = 40
The answer is letter B. Every polygon tesselates. Since the word 'tesselate' here means a pattern of shapes put together without any gaps, then I think every polygon tesselates if they are put side by side together in varying amounts and leave absolutely no gaps or spaces between each other.
Answer: 4x² + 4x - 2 - 
<u>Step-by-step explanation:</u>
You can use either synthetic or long division. I am using synthetic division:
2x + 3 = 0 ⇒ x = 
| 4 10 4 -6
<u>| ↓ -6 -6 3 </u>
4 4 -2 -3 ← <em>-3 is the remainder</em>
↓ ↓ ↓
4x² +4x -2 ← <em>factored polynomial</em>
Find the equation of the first line using the two given points: (1,-1) (-1,-5)
Slope = change in Y over change in x:
Slope = (-5-(-1)) / (-1-(1) = -4/-2 = 2
Now find y intercept: y - y1 = m(x-x1) = y -(-1) = 2(x-1)
Simplify to get y = 2x-3
Now a perpendicular line has a opposite reciprocal slope.
The perpendicular line would be y = -1/2x - 3
You are told the y intercept is -4 units greater, so add -4 to -3 to get -7
The answer would be A. y = -1/2x-7
Answer:
15
Step-by-step explanation:
To find the minimum amount of items, x, that need to be sold for the manufacturer to make a profit, we can use the quadratic formula





In context of the problem, we can only rely on the positive value, as the negative value would lead to a loss of profit.

Furthermore, we must round to the nearest whole number, as you cannot make part of an item.
Lastly, if you were to plug in 14 into the equation for Profit, you would still have a negative number (i.e. a negative profit), thus requiring the manufacturer to make no less than 15 items to make a profit:
