1. x - 16
2. x + 5
3. x divided by 48 (I don’t have the division symbol.)
Answer:
(2x - 1)^2
Step-by-step explanation:
We can reverse engineer the solution...
to complete the square, we know (2x + __)^2 will generate the 1st term 4x^2
To generate the 2nd term, we will need -1, so (2x - 1)^2....
When expanded, we will have 4x^2 - 4x + 1, which we completed the square.
Every proportional relationship is an equation like y = a number times 'x'. When you graph that equation it's a straight line that goes through the origin and every point on the line satisfies the equation. Line B is the only graph that looks like that. The others all have a piece of a proportional relationship. Their bottom pieces are proportional relationships but then they break and the top pieces are not.
This is an exercise you should actually do with real physical objects. The objects don't have to be wood and they don't have to be square for you to be able to arrange them into a rectangular shape. You can cut squares from paper, or use Scrabble™ tiles, poker chips, pennies, M&M™ candies, bottle caps, Legos™, Cheez-It™ crackers, pebbles, or any other objects of similar size and shape.
What you will find is that there are 8 possibilities, corresponding to the number of divisors of 24:
1×24, 2×12, 3×8, 4×6, 6×4, 8×3, 12×2, 24×1
_____
If you make rectangles from numbers of pieces other than 24, you will find that only two rectangles are possible for prime numbers, like 23: 1×23 or 23×1. Even numbers of tiles will all have rectangles of 1×_ and 2×_ (as well as _×1 and _×2).
Doing this sort of playing with physical objects helps you develop number sense that can serve you well later. Don't discount it.
