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.
Answer:
The answer is the second option
(2,3), (-1,3), (-1,6)
Step-by-step explanation:
Solve for w: by simplifying both sides of the equation, then isolating the variable.
w=-217
Work: 1. Subtract 13 from both sides (w/7 = -18 - 13), 2.Simplify -18-13 to -31 (w/7=-31), 3.Multiply both sides by 7 (w = -31 * 7), 4. Simplify 31*7 to 217 (w=-217)
Answer:
(-5,2)
Step-by-step explanation:
It alogns with negative 5 on the X axis, and positive 2 on the Y axis, meaning its written as (-5,2)
Let's rearrange the equation x + y = 6 to slope-intercept form. Solve for y.
x + y = 6
To get the y variable on the left-hand side alone, subtract x from each side.
x + y - x = 6 - x
y = 6 - x
Rearrange the right-hand side.
y = -x + 6
Now we have it in the slope-intercept form. And to find the slope, we look at the coefficient of x. But there is no coefficient of the -x term!
In all reality, there is. However, it's just 1. -1x is the same thing as -x. We don't show the 1 because it has no effect.
So, -1 is the slope.
