Which transformation will always map a parallelogram onto itself?
2 answers:
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Answer:
(x + 6)² + 16 = 0
Step-by-step explanation:
To complete the square we will first need to get our equation to look like: x² + bx = c
Here we have x² + bx + c = 0 → x² + 12x + 52 = 0
- First we need to subtract our c, in this case 52, from both sides to get x² + 12x = -52
- We then need to add
to both sides of the equation
- Here our b value is 12, so plugging this into our formula we get
- Adding 36 to both sides our equation becomes: x² + 12x + 36 = -52 + 36
- Then combining like terms on the right side we get x² + 12x + 36 = -16
- Now making our left side of the equation into a perfect square we get: (x + 6)² = -16
- Finally adding the 16 to both sides of the equation we get: (x + 6)² + 16 = 0
Answer:
Option C) G.
Step-by-step explanation:
Verify each expression
case E) we have
Any number plus zero equals the original number (Identity property of addition)
-----> is a decimal number
case F) we have
Any number plus zero equals the original number (Identity property of addition)
-----> is a decimal number
case G) we have
Any number plus zero equals the original number (Identity property of addition)
-----> is an integer
case H) we have
division by zero is undefined
Answer:
- The scale factor is one-half
- The perimeter of the model is the product of the scale factor and the perimeter of the original rectangle
-The area of the reduced figure is (1/2)^2 = 1/4 times the area of the original figure
Step-by-step explanation:
The ratio of the length of the original rectangle to that of the reduced rectangle is 6 to 3, or a factor of 1/2. The ratio of the width of the original rectangle to that of the reduced rectangle is 2 to 1, or, again, a factor of 1/2. So, because this ratio of 1/2 is constant, we know the total scale factor is 1/2, making B correct.
The perimeter of a rectangle is: , where l is the length and w is the width. The perimeter of the reduced figure is: P = 2 * 3 + 2 * 1 = 6 + 2 = 8 units. The perimeter of the original figure is: P = 2 * 6 + 2 * 2 = 12 + 4 = 16 units.
Notice that 16 * (1/2) = 8, which means that the perimeter of the scale-factored, reduced rectangle is "the product of the scale factor (which is 1/2) and the perimeter of the original rectangle (which is 16)". So, C is correct.
The area of a rectangle is: , where l is the length and w is the width. The area of the reduced figure is: A = 3 * 1 = 3 units squared. The area of the original figure is: A = 6 * 2 = 12 units squared.
Notice that 12 * (1/4) = 3, which means that E is correct, but D is wrong.
Hope this helps!