Answer:
length = 31 ft
width = 19 ft
Explanation:
Assume that the width of the rectangle is w.
We are given that the length is 12 ft more than the width. This means that the length of the rectangle is w + 12
The perimeter of the rectangle in this case would be:
perimeter = 2 (length + width)
perimeter = 2 (12 + w + w)
perimeter = 24 + 4w
Assume that Dan would use all 100 ft of fencing to surround the yard. This would mean that the largest perimeter is 100 ft.
Therefore:
perimeter = 24 + 4w
100 = 24 + 4w
4w = 100 - 24
4w = 76
w = 19 ft
Since we have calculated that the width of the yard is 19 ft, we can substitute to get the length as follows:
length = 12 + w
length = 12 + 19
length = 31 ft
Hope this helps :)
You know, it is helpful if you post the sets as well.
The signs of the factors will be different. (One will be positive and one will be negative.)
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Here, the "first sign" is considered to be the sign of <em>x²</em>, and the "second sign" is considered to be the sign of <em>c</em>. The above statement will be true regardless of the sign of <em>b</em>. The "signs <em>of</em> the factors" is considered to refer to the signs of the constant terms <em>in</em> the binomial factors.
For (x +p)(x -q) where <em>p</em> and <em>q</em> are both positive so the signs are as shown, the product is x² +(p-q)x -pq. That is <em>x²</em> is positive and <em>-pq</em> is negative, regardless of the relative magnitudes of <em>p</em> and <em>q</em> (thus the sign of <em>p-q</em>).
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If something else is meant by the terminology used, it isn't clear what the intended answer is supposed to be.
Both x² +3x -10 and x² -3x -10 have factorizations that have different signs <em>in</em> the two factors. The first is (x+5)(x-2); the second is (x+2)(x-5). The signs <em>of</em> the factors are all positive: (x+5), not -(x+5), for example.
On the other hand x² -3x +2 = (x-2)(x-1) has same signs <em>in</em> and <em>of</em> the factors. That is, by themselves, the sign of x² (first sign) and the sign of 3x (second sign) don't guarantee the signs <em>in</em> the factors are anything in particular, except that at least one sign in the factors must be negative if the first (x²) and second (3x) signs differ.
Answer:
The solution is x=7
Step-by-step explanation:
We want to solve for x in the equation
Subtract 8 from both sides of the equation:
Simplify to get:
This implies that:
