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:
y=-x+3
Step-by-step explanation:
y=-x+3
you can see the negative slope in the direction
the +3 comes from the 3 in the x and y intercepts
m=-1
Answer:
Hexagon
Step-by-step explanation:
It has more than 3 sides because it is more sides than a triangle and less than 5 since it has to be fewer sides than a pentagon. A hexagon has 6 sides meaning it has more sides than the pentagon.
Answer: the required sample size = 155
Step-by-step explanation:
If the standard deviation of the prior study is known, then the formula to compute required sample size:
, where E = Margin of error, z* = Critical value, 
= populion standard deviation.
Given: E = 3.7 , 
Critical value for 90% confidence = 1.645
Required sample size: 
Hence, the required sample size = 155
Answer:
1/3 is the slope.
Step-by-step explanation:
First, we need to find the y-intercept of x + 4y = 20.
x + 4y = 20
Subtract x from both sides.
4y = -x + 20
Divide both sides by 4.
y = -1/4x + 5
Input 0 as x to find the y-intercept.
y = -1/4(0) + 5
Simplify.
y = 5
Now we know the y-intercept is (0,5). Now we need to include to find a slope that contains (0,5) and (3,6). We can use the slope formula:
(5 - 6)/(0 - 3) = m
-1/-3 = m
Simplify.
1/3 = m
1/3 is the slope.
