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
For the first question it's A for the second one it's D.Hope this helps.
A reduction is represented by option C, (x,y) —> (0.7x, 0.3y). It reduces both the x and y values.
As for the set of lengths that are not the side lengths of a right triangle, option B, 13, 84, 85, doesn't form a right triangle. However, I must say, those are some odd lengths for a triangle. Maybe it's a triangle for aliens or something!
To determine if a transformation represents a reduction, we need to look at the scale factors. A reduction occurs when the scale factor is less than 1.
For the first question:
A: The scale factor is 0.9, which is less than 1. This represents a reduction.
B: The scale factor is 1.4, which is greater than 1. This does not represent a reduction.
C: The scale factors are 0.7 and 0.3, both of which are less than 1. This represents a reduction.
D: The scale factor is 2.5, which is greater than 1. This does not represent a reduction.
Therefore, the correct answer is options A and C.
For the second question:
A right triangle follows the Pythagorean theorem, which states that the square of the length of the hypotenuse is equal to the sum of the squares of the other two sides.
Using this theorem, we can calculate the squares of the side lengths for each option:
A: 28^2 + 45^2 = 784 + 2025 = 2809
53^2 = 2809
B: 13^2 + 84^2 = 169 + 7056 = 7225
85^2 = 7225
C: 36^2 + 77^2 = 1296 + 5929 = 7225
85^2 = 7225
D: 16^2 + 61^2 = 256 + 3721 = 3977
65^2 = 4225
By comparing the squares of the side lengths, we can see that option D does not satisfy the Pythagorean theorem. Therefore, the correct answer is option D.
(x,y)——->(0.9x,0.9y)
(x,y)——->(0.7x,0.3y)
(x,y)——->(1.4x,1.4y)
(x,y)——->(2.5x,2.5y)
Which represents a reduction
sdf
for a reduction, both scales must be the same, and less than 1
For the triangle, just get out your calculator and check!
28^2+45^2 = 2809 = 53^2
so that one works out
Now do the others.