This result is actually true for any exterior angle. The exterior angle of a triangle is equal to the sum of the two remote angles, and above is a short proof of it.
Frank will use 3/8 cup of sugar, 61 1/2 cups of flour, and 9 eggs. I know this because...
3/4 divided by 2 is 3/8
20 1/2 times 3 is 61 1/2
3 times 3 is 9
Answer:
n=-6
Step-by-step explanation:
Answer:
- dimensions: 12 ft by 5 ft
- area: 60 ft²
Step-by-step explanation:
Let x represent the shorter dimension in feet. Then the longer one is x+7 and the Pythagorean theorem tells us the relation of these to the diagonal is ...
x² + (x+7)² = 13²
2x² +14x + 49 = 169 . . . . eliminate parentheses
x² +7x -60 = 0 . . . . . subtract 169 and divide by 2
(x +12)(x -5) = 0 . . . . factor the equation
x = -12 or +5 . . . . . . . only the positive value of x is useful here.
The short dimension is 5 ft, so the long dimension is 12 ft. The area is their product, 60 ft².
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<em>Comment on finding the area</em>
The quadratic equation above can be rearranged and factored as ...
x(x +7) = 60
Since the dimensions of the garden are x and (x+7), this product is the garden's area. This equation tells us the area is 60. We don't actually have to find the dimensions.
There would be 60 houses left
