Let width and length be x and y respectively.
Perimeter (32in) =2x+2y=> 16=x+y => y=16-x
Area, A = xy = x(16-x) = 16x-x^2
The function to maximize is area: A=16 x-x^2
For maximum area, the first derivative of A =0 => A'=16-2x =0
Solving for x: 16-2x=0 =>2x=16 => x=8 in
And therefore, y=16-8 = 8 in
Answer is highlighted in blue. If you have any questions feel free to ask.
Answer:
The coordinates of the reflected triangle are 
, 
and 
.
Step-by-step explanation:
Let be a point 
, reflections across x- and y-axes are represented by the following operations:
x-Axis reflection:
y-Axis reflection:
If we know that 
, 
and 
, the coordinates after both reflections are, respectively:
The coordinates of the reflected triangle are , and .
This problem tackles the place values of numbers. From the rightmost end of the number to the leftmost side, these place values are ones, tens, hundreds, thousands, ten thousands, hundred thousands, millions, ten millions, one hundred millions, and so on and so forth. My idea for the solution of this problem is to add up all like multiples. In this problem, there are 5 multiples expressed in ones, thousands, hundred thousands, tens and hundreds. Hence, you will add up 5 like terms. The solution is as follows
30(1) + 82(1,000) + 4(100,000) + 60(10) + 100(100)
The total answer is 492,630. Therefore, the number's identity is 492,630.
Answer:
Distributive Property
Step-by-step explanation:
7 equals (3+4).
Therefore, 4*7 equals 4*(3+4).
By distributive property, this will equal (4*3) + (4*4)
