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sweet [91]
3 years ago
6

Use the algebraic expressions for the length and width of Marlene's living room found in the

Mathematics
1 answer:
krok68 [10]3 years ago
8 0

Answer:

<em>The area of Marlien's living room is 420 square ft</em>

Step-by-step explanation:

Before calculating the real dimensions of Marlien's living room, we must find the value of x.

Given the total shape of the house is a rectangle, then both widths must be equal and both lengths must be equal.

The widths are already written width identical expressions x-2+x, but the lengths are given as different functions of x. Equating both expressions, we have:

2x-10+x-2+\frac{1}{2}x-4+x-2=2x+2+\frac{1}{2}x-4+x-2

Simplifying:

-10 + x - 2 = 2

x = 10 + 2 + 2

x = 14

Since x=14 feet, the dimensions of Marlien's living room are

width=x=14 feet

length=2x+2=30 feet

Thus the area is:

A = 14*30 = 420 square ft

The area of Marlien's living room is 420 square ft

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Based on the extreme value theorem, what is the maximum value of f(x) = –x2 + 6x over the interval [1, 4]?
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