21-6=15
The range of the set is 15
Absolute value equations have more than one solution because when the answer is in abs. value, it is positive, so there could be a negative answer and it would still be positive. For example |-5|=5 and |5|=5 as well.
4+|2x|=-1 would have no solution because you cannot have the equation equal a negative since the 2x is in absolute value.
Answer:
Step-by-step explanation:
- The speed of the boat in the lake = x
- The speed of the current = 3 km/h
<u>Required equation:</u>
- 54 / (x + 3) + 42 / (x - 3) = 96/x
- 9x(x - 3) + 7x(x + 3) = 16(x + 3)(x - 3)
- 9x² - 27x + 7x² + 21x = 16x² - 144
- 6x = 144
- x = 144/6
- x = 24 km/h
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!
9514 1404 393
Answer:
(b) One figure is a rotation image of the other
Step-by-step explanation:
The axis of symmetry is horizontal for the left figure, and vertical for the right figure. The right figure has been rotated 90° CW from the left figure.
