1) Below is a rectangle that has an unknown component \(x\). The lengths of the sides are expressed using that variable. Using know fact that the area of the rectangle is \(14\) meters squared, find the dimensions of the rectangle.
2) Below is a rectangle that has an unknown component \(x\). The lengths of the sides are expressed using that variable. Using the fact that the area of the rectangle is \(75\) m\(^2\), find the dimensions of the rectangle.
3) You are building a uniform brick patio around your pool which is \(15\) feet by \(10\) feet. Given that the combined area is \(266\) ft\(^2\), what is the possible width of the walkway?
4) Pictured below is a flowerbed that is \(16\) m by \(5\) m. You are hired to create a mulch border that is going to create a total combined area for the bed and mulch to reach \(250\) m\(^2\). What should the width of the mulch border be?
5) Below is an aerial view of the new doughnut shop that is opening in town. The red segments represent the footprint for the shop and outdoor seating which is \(117\) ft (East-West) by \(108\) ft (North-South). The blue segments represent what is going to be dedicated to parking. If the total lot size is \(242\) ft (East-West) by \(233\) ft (North-South), what is the width of the parking lot going to be (what is the length of \(x\))?
Review
6) Solve the following system:
\(2x - 5y = 8\)
\(x - y = 14\)
7) Graph the following linear equation: \(y - 4 = - (x + 2)\)
8) Factor the following completely:
a) \(2x^2+13x-24\)
b) \(28x^2-63\)
c) \(3x^2-3x-36\)
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