Which represents a reduction?
A
(x,y) —> (0.9x, 0.9y)
B
(x,y) —> (1.4x, 1.4y)
C
(x,y) —> (0.7x, 0.3y)
D
(x,y) —> (2.5x, 2.5y)
11
Which set of lengths are not the side
lengths of a right triangle?
A
28, 45, 53
B
13, 84, 85
C
36, 77, 85
D
16, 61, 65
i dont know them pls help me
well, the scale factors must be the same for an expansion or reduction.
And of course, for a reduction, the scale must be less than 1, right?
For the Pythagorean triples a,b,c, you must have
a^2 + b^2 = c^2
where c is the largest of the three values.
So, check the triples to see which doesn't fit the bill.
For example, 13^2 + 84^2 = 169 + 7056 = 7225 = 85^2
thanks and i think the first one is a?
yes, it is
To determine which option represents a reduction, we need to understand what reduction means in this context. In mathematics, a reduction is a transformation that decreases the size or magnitude of an object or its components.
For example, in option A, the points (x, y) are transformed to (0.9x, 0.9y). Since the scale factor is less than 1 (0.9), the resulting points are closer to the origin, indicating a decrease in size. Therefore, option A represents a reduction.
Similarly, in option C, the points (x, y) are transformed to (0.7x, 0.3y). Again, the scale factor is less than 1 (0.7), resulting in a decrease in size. Option C also represents a reduction.
On the other hand, in option B, the points (x, y) are transformed to (1.4x, 1.4y). Here, the scale factor is greater than 1 (1.4), indicating an increase in size. Option B does not represent a reduction.
Finally, in option D, the points (x, y) are transformed to (2.5x, 2.5y). As the scale factor is greater than 1 (2.5), there is an increase in size, and option D does not represent a reduction.
Therefore, the options that represent reductions are A and C.
Moving on to the second question regarding right triangles, let's analyze each option to determine which lengths cannot form the sides of a right triangle. To be the side lengths of a right triangle, the values must satisfy the Pythagorean theorem, which states that the sum of the squares of the two shorter sides is equal to the square of the longest side (the hypotenuse).
For option A, the lengths are 28, 45, and 53. We can check if they satisfy the Pythagorean theorem:
28^2 + 45^2 = 784 + 2025 = 2809
And 53^2 = 2809
Since they are equal, the lengths form a right triangle. So option A is a valid right triangle.
For option B, the lengths are 13, 84, and 85. Let's check if they satisfy the Pythagorean theorem:
13^2 + 84^2 = 169 + 7056 = 7225
And 85^2 = 7225
Again, they are equal, so option B is a valid right triangle.
For option C, the lengths are 36, 77, and 85. Applying the Pythagorean theorem:
36^2 + 77^2 = 1296 + 5929 = 7225
But 85^2 = 7225
Once again, they are equal, so option C is also a valid right triangle.
Lastly, for option D, the lengths are 16, 61, and 65. Checking with the Pythagorean theorem:
16^2 + 61^2 = 256 + 3721 = 3977
But 65^2 = 4225
They are not equal, indicating that option D does not satisfy the Pythagorean theorem. Therefore, option D does not represent the side lengths of a right triangle.
In summary, the option that does not represent the side lengths of a right triangle is option D.