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Answer:
Draw it with 9 cm for length and width.
Step-by-step explanation:
The product is the maximum area when the length and width are as close as possible, or equal to each other. Because length and width are 2 sides each, we can divide 36 by 4, which is 9.
9x9 = 81 cm^2. This is the largest area possible.
Answer:
![\huge\boxed{x=8;\ y=1\to(8;\ 1)}](https://tex.z-dn.net/?f=%5Chuge%5Cboxed%7Bx%3D8%3B%5C%20y%3D1%5Cto%288%3B%5C%201%29%7D)
Step-by-step explanation:
![\left\{\begin{array}{ccc}y=x-7&(1)\\5+2y=7&(2)\end{array}\right\\\\\text{Substitute (1) to (2) and solve for x:}\\\\5+2(x-7)=7\qquad\text{use the distributive property}\\\\5+(2)(x)+(2)(-7)=7\\\\5+2x-14=7\\\\2x+(5-14)=7\\\\2x-9=7\qquad\text{add 9 to both sides}\\\\2x-9+9=7+9\\\\2x=16\qquad\text{divide both sides by 2}\\\\\dfrac{2x}{2}=\dfrac{16}{2}\\\\\boxed{x=8}](https://tex.z-dn.net/?f=%5Cleft%5C%7B%5Cbegin%7Barray%7D%7Bccc%7Dy%3Dx-7%26%281%29%5C%5C5%2B2y%3D7%26%282%29%5Cend%7Barray%7D%5Cright%5C%5C%5C%5C%5Ctext%7BSubstitute%20%281%29%20to%20%282%29%20and%20solve%20for%20x%3A%7D%5C%5C%5C%5C5%2B2%28x-7%29%3D7%5Cqquad%5Ctext%7Buse%20the%20distributive%20property%7D%5C%5C%5C%5C5%2B%282%29%28x%29%2B%282%29%28-7%29%3D7%5C%5C%5C%5C5%2B2x-14%3D7%5C%5C%5C%5C2x%2B%285-14%29%3D7%5C%5C%5C%5C2x-9%3D7%5Cqquad%5Ctext%7Badd%209%20to%20both%20sides%7D%5C%5C%5C%5C2x-9%2B9%3D7%2B9%5C%5C%5C%5C2x%3D16%5Cqquad%5Ctext%7Bdivide%20both%20sides%20by%202%7D%5C%5C%5C%5C%5Cdfrac%7B2x%7D%7B2%7D%3D%5Cdfrac%7B16%7D%7B2%7D%5C%5C%5C%5C%5Cboxed%7Bx%3D8%7D)
![\text{Substitute it to (1):}\\\\y=8-7\\\\\boxed{y=1}](https://tex.z-dn.net/?f=%5Ctext%7BSubstitute%20it%20to%20%281%29%3A%7D%5C%5C%5C%5Cy%3D8-7%5C%5C%5C%5C%5Cboxed%7By%3D1%7D)
Answer:
(i) A truth table shows how the truth or falsity of a compound statement depends on the truth or falsity of the simple statements from which it's constructed.
Since A ∧ B (the symbol ∧ means A and B) is true only when both A and B are true, its negation A NAND B is true as long as one of A or B is false.
Since A ∨ B (the symbol ∨ means A or B) is true when one of A or B is true, its negation A NOR B is only true when both A and B are false.
Below are the truth tables for NAND and NOR connectives.
(ii) To show that (A NAND B)∨(A NOR B) is equivalent to (A NAND B) we build the truth table.
Since the last column (A NAND B)∨(A NOR B) is equal to (A NAND B) it follows that the statements are equivalent.
(iii) To show that (A NAND B)∧(A NOR B) is equivalent to (A NOR B) we build the truth table.
Since the last column (A NAND B)∧(A NOR B) is equal to (A NOR B) it follows that the statements are equivalent.
Answer:
![D = 7\sqrt 2](https://tex.z-dn.net/?f=D%20%3D%207%5Csqrt%202)
Step-by-step explanation:
Given
![A = (-3,-4)](https://tex.z-dn.net/?f=A%20%3D%20%28-3%2C-4%29)
![B = (4,3)](https://tex.z-dn.net/?f=B%20%3D%20%284%2C3%29)
Required
The distance between them
This is calculated as:
![D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}](https://tex.z-dn.net/?f=D%20%3D%20%5Csqrt%7B%28x_2-x_1%29%5E2%2B%28y_2-y_1%29%5E2%7D)
So, we have:
![D = \sqrt{(3-(-4))^2+(4-(-3))^2}](https://tex.z-dn.net/?f=D%20%3D%20%5Csqrt%7B%283-%28-4%29%29%5E2%2B%284-%28-3%29%29%5E2%7D)
![D = \sqrt{7^2+7^2}](https://tex.z-dn.net/?f=D%20%3D%20%5Csqrt%7B7%5E2%2B7%5E2%7D)
![D = \sqrt{2(7^2)}](https://tex.z-dn.net/?f=D%20%3D%20%5Csqrt%7B2%287%5E2%29%7D)
![D = 7\sqrt 2](https://tex.z-dn.net/?f=D%20%3D%207%5Csqrt%202)