The dimension of a rectangular garden are represented by (x+7) and (x-7)
A. What is the area of the garden?
B. It is possible that x=7?how about x=-7?explaine why or why not.
C. What could be the value of x?
Please answer steve
what, still no thoughts of your own?
A. (x+7)(x-7) = x^2-49
B. What are the dimensions if x=7?
C. both dimensions must be positive, so x > 7
A. To find the area of the garden, we multiply the dimensions together. So the area is:
Area = (x+7)(x-7)
B. To check if x=7 is possible, we substitute it into the equation for the dimensions:
(x+7)(x-7) = (7+7)(7-7) = 14 * 0 = 0
Since the area is 0, this means the garden has no dimensions and is not possible.
Similarly, we check if x=-7 is possible:
(x+7)(x-7) = (-7+7)(-7-7) = 0 * (-14) = 0
Again, the area is 0, so the garden has no dimensions and is not possible.
Therefore, x=7 and x=-7 are not possible values for the dimensions.
C. To find the possible value of x, we need to consider the factors of the area equation. In this case, we have:
(x+7)(x-7) = 0
This equation will be true when either (x+7) or (x-7) equals zero. So the possible values for x are:
x+7=0 or x-7=0
Solving these equations gives us:
x=-7 or x=7
However, since we already determined that x=7 and x=-7 are not possible values for the dimensions, there are no valid values for x that satisfy the given conditions.
A. To find the area of the garden, we need to multiply the length and width. In this case, the length is (x+7) and the width is (x-7). So, the area of the garden is given by the expression (x+7) * (x-7).
B. To determine if it is possible that x = 7 or x = -7, we need to check if those values would result in valid dimensions for a rectangular garden. For a valid rectangular garden, both the length and the width should be positive.
1. If x = 7:
Plugging in x = 7 into the expressions, we get:
Length = (7+7) = 14
Width = (7-7) = 0
Since the width is 0, it means there would be no width and hence no garden. So, it is not possible for x to be 7.
2. If x = -7:
Plugging in x = -7 into the expressions, we get:
Length = (-7+7) = 0
Width = (-7-7) = -14
Similarly, since the length and width are negative or zero, it means there would be no valid dimensions for a garden. Thus, it is not possible for x to be -7 either.
C. To determine possible values of x, we need to consider the conditions for a valid rectangular garden. Both the length and width should be positive.
- From the expression (x+7) * (x-7), we can see that for the length to be positive, x > -7.
- Also, for the width to be positive, x < 7.
Based on these conditions, the possible values for x would be within the range -7 < x < 7.