Triangle ABC was transformed using the rule (x, y) → (–y, x). The vertices of the triangles are shown. A (–1, 1) B (1, 1) C (1,
4) A' (–1, –1) B' (–1, 1) C' (–4, 1) Which best describes the transformation? The transformation was a 90° rotation about the origin. The transformation was a 180° rotation about the origin. The transformation was a 270° rotation about the origin. The transformation was a 360° rotation about the origin.
2 answers:
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By setting up a system of equations we can easily solve this problem. Let's denote Jane's working hours with x and Jack's working hours with y. Since they don't want to work more than 65 hours, the first equation is x+y=65. The second equation is 14x+7y=770. By solving this system of equation 
, we find that y=20 hours, which is Jack's maximum working hours.
Answer:
Subsets of the given set = 32
Proper subset of the given set = 31
Step-by-step explanation:
Given set is {18, 8, 14, 9, 6} having 5 elements.
We know number of subsets of a set having n elements are represented by
where n is the number of elements in the set.
Therefore, subsets of the given set =
= 32
Since original set itself is a subset of its own, is not a proper subset.
Therefore, proper subset of a set =
=
= 32 - 1
= 31
Answer: Any real number x as long as and
In other words, anything but 0 or -2/3 is valid.
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Explanation:
Set the denominator equal to zero and solve for x
2(3x^2 + 2x) = 0
3x^2 + 2x = 0
x(3x + 2) = 0
x = 0 or 3x+2 = 0 .... zero product property
x = 0 or 3x = -2
x = 0 or x = -2/3
If either x = 0 or x = -2/3, then the denominator 2(3x^2 + 2x) will be zero. But recall that we cannot have zero in the denominator. Dividing by zero is not allowed. The expression is undefined when we divide by zero.
Therefore, we must exclude x = 0 and x = -2/3 from the domain. Any other real number is valid as an x input.