Answer:
Figure A - hexagon
Figure B - triangle
Figure C - rectangle
Figure D - octagon
Step-by-step explanation:
If figure B has 3 vertices (angles), then that means it is a triangle (3 sides)
So that means figure A has 6 sides, (hexagon)
And figure D has 8 vertices, so 8 sides (octagon)
And if C has half as many, that would be 4 (rectangle)
Answer:
5√2
Step-by-step explanation:
The 45-45-90 triangle theorem states that the length of a triangle's hypotenuse is √2 times the length of the triangle's leg. In this problem, the triangle's leg is equal to 5, meaning that the hypotenuse would be 5 x √2, which is equal to 5√2.
Answer:
a) 1/2
b) 250
Step-by-step explanation:
The start of the question doesn't matter entirely, although is interesting to read. What we are trying to do is find the value for such that is maximized. Once we have that , we can easily find the answer to part b.
Finding the value that maximizes is the same as finding the value that maximizes , just on a smaller scale. So, we really want to maximize . To do this, we will do a trick called completing the square.
.
Because there is a negative sign in front of the big squared term, combined with the fact that a square is always positive, means we need to find the value of such that the inner part of the square term is equal to .
.
So, the answer to part a is .
We can then plug into the equation for p to find the answer to part b.
.
So, the answer to part b is .
And we're done!
A. Because an expression with one or more terms is called a polynomial