Find the prime factorization of 54
54 = 2 × 3 × 3 × 3
Find the prime factorization of 99
99 = 3 × 3 × 11
To find the GCF, multiply all the prime factors common to both numbers:
Therefore, GCF = 3 × 3
GCF = 9
The two numbers are 120 and 60
Let's call the two numbers x and y. The first sentence translates into

from which we can derive

So, their product can be written as

This expression is a quadratic polynomial with negative leading coefficient, so it represents a parabola concave down. So, the vertex of the parabola is its maximum, which we can find as usual: given the parabola
, its extreme point is located at
.
So, in your case, since
and
, the maximum is located at

Now that we know y, we can deduce the value of x:

So, the two numbers are 120 and 60
Answer:
Step-by-step explanation:
Answer:
196.6 feet
Step-by-step explanation:
Draw the right triangle formed by the zip-line. Use SOH-CAH-TOA to write and solve an equation:
tan 11.5° = 40 / x
x = 40 / tan 11.5°
x = 196.6