Answer:
The length side of the original square banner was 9 ft
Step-by-step explanation:
Let
x-----> the length side of the original square banner
we know that
The new area of the banner is equal to

Solve for x

Solve the quadratic equation by graphing
The solution is x=9 ft
see the attached figure
The interval that f(x) is increasing is the distance from 200 to 300.
The minimum value of f(x) in the interval 0<x<300 is 200.
At a value of 500, the value of f(x) is 0.
The function can't be a quadratic function since there are two points in the graph where f(x) changes its rate from increasing to decreasing or the opposite. A quadratic function has only one of that point.
Is that everything for the problem??
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Answer:
27720
Step-by-step explanation:
Given that there are 12 students in a graduate class. The students are to be divided into three groups of 3, 4, and 5 members for a class project.
From 12 students 3 students for group I can be selected in 12C3 ways.
Now from remaining 9, 4 students can be selected for II group in 9C4 ways
The remaining 5 have to be placed in III group.
Hence possible divisions for grouping the 12 students in the class into three groups
= 12C3 *9C4
= 
1/2 would not be a useful benchmark to compare these 2 fractions because both of them are greater than half. The benchmark fraction 1/2 is most useful when one fraction is less than half and the other more than 1/2. 5/8 is more than 4/8(1/2), and 9/10 is more than 5/10(1/2).