The system ax-by=-16 and ax+2y=20 has one solution at the point (3,4). Find a and b. (a=4,b=7)
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Answer:
Width: 6
Length: 20
Step-by-step explanation:
So the area of a rectangle can be defined as: where w=width and l=length.
In this case we don't know what the length is, so let's just say the length is the variable l, and since the width is 14 units less than the length, we can express it as (l-14). this gives us the equation: . We can solve for l, since we're given the area which is 120. So let's set the equation equal to that:
Original Equation:
Substitute 120 as A (given)
There is many ways to solve this equation: factoring, quadratic equation, completing the square etc... but in this case I'll just complete the square
Add (b/2)^2 to both sides to complete the square
Simplify
Rewrite right side a square binomial
Take the square root of both sides
Add 7 to both sides
to solve for width simply subtract 14 from the length which is 20, so the width is 6
Width: 6
L: 20