Answer:
x=−16/3 or x=2
Step-by-step explanation:
Step 1: Simplify both sides of the equation.
3x2+10x−8=24
Step 2: Subtract 24 from both sides.
3x2+10x−8−24=24−24
3x2+10x−32=0
Step 3: Factor left side of equation.
(3x+16)(x−2)=0
Step 4: Set factors equal to 0.
3x+16=0 or x−2=0
The only thing you can do here is to try to simplify, so I'll assume that's what you want to do.
The numerator is a difference of squares, so it's easy to factorize:
In the denominator, we factorize by grouping:
So we have
Answer: the first fish was 3/20 feet longer.
Explanation: in order to compare the fractions you need to multiply 12/5 by 4 and 9/4 by 5. That leaves us with 48/20 and 45/20 after that you simply subtract and are left with 3/20.
2^10/5 = 2^2 = 4
................................
If it needs to be a rectangle, then the rectangle with the smallest perimeter for
a given area is the square. He needs 32 feet of fence, and should fence off a
square that's 8 x 8 .
But if he's willing to go to the trouble, the perimeter of a circle with the same area
is even less than the square.
A = (pi) (R²)
R = √(64/pi).
Circumference = (2 pi) (R) = 2 pi √(64/pi) = √(256 pi) = 28.359 (rounded).
That's 11.4% less fence to buy, for a circular run.
But on the other hand, what have you got against the dog ? One of
the two main purposes of a dog run is to give the dog a place to <u>run</u>.
Minimizing the perimeter also minimizes the distance where he can get
up some speed and run in a straight line ... freeing up his hips, clearing
the cobwebs from his brain, smelling the air, keeping his claws nice and
worn down. With the emotional well-being of the dog in mind, I'd expect
you'd want to give him the <u>maximum</u> possible straight route inside the
run, which, unfortunately, also maximizes the amount of fence that Malcolm
has to provide.
But I digress. The math is done. The question is answered.
This case is closed.
