Darrin is hanging 200 feet of Christmas garland on the fencing around his house. The fence has the shape of a rectangle and full
1 answer:
Answer:
the width is 17.5 feet and the length is 82.5 feet.
Step-by-step explanation:
The house has a rectangular shape and we know that the length is 5 feet less than 5 times the width.
We will call the width x, thus, the length would be represented as 5x-5 (5 less than 5 times the width).
Since Darrin is going to hang garland around the perimeter of the house, we know that the perimeter is 2 times the length plus two times the width and this equals 200.
Let's write this in algebraic form
Therefore, the width is 17.5 feet.
Now, the length is 5x-5, thus substituting the 17.5 in this equation we have:
feet
Therefore, the width is 17.5 feet and the length is 82.5 feet.
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Answer:
1. Translation: g(x) = f(x-a)+b.
2. Reflection around y-axis: h(x) = f(-x)
3. Reflection around x-axis: k(x) = -f(x)
4. Rotation of 90° :
5. Rotation of 180° : .
6. Rotation of 270° : .
Step-by-step explanation:
Let us assume that the transformations namely translation, reflection are applied to a function f(x) and the rotation is applied to the point ( x,y ).
So, according to the options:
We know that 'translation moves the image in horizontal and vertical direction'.
1. As we have to translate the function f(x) 'a' units to the right and 'b' units up. So, the new form of the function becomes g(x) = f(x-a)+b.
Further, we know that 'reflection means to flip the image around a line'.
2. As, we have to reflect the function f(x) around y-axis. The new form of the function is h(x) = f(-x).
3. As, we have to reflect the function f(x) around x-axis. The new form of the function is k(x) = -f(x).
Since, 'rotation turns the image around a point to a certain degree'.
4. As, we have to rotate ( x,y ) counter-clockwise to 90° about the origin, the new form of the function is .
5. As, we have to rotate ( x,y ) counter-clockwise to 180° about the origin, the new form of the function is .
6. As, we have to rotate ( x,y ) counter-clockwise to 270° about the origin, the new form of the function is .