A. Multiplication is the ONLY function that reverses what division did. If you did 56/-14 = n, then n x -14 should equal 56.
To prove two sets are equal, you have to show they are both subsets of one another.
• <em>X</em> ∩ (⋃ ) = ⋃ {<em>X</em> ∩ <em>S</em> | <em>S</em> ∈ }
Let <em>x</em> ∈ <em>X</em> ∩ (⋃ ). Then <em>x</em> ∈ <em>X</em> and <em>x</em> ∈ ⋃ . The latter means that <em>x</em> ∈ <em>S</em> for an arbitrary set <em>S</em> ∈ . So <em>x</em> ∈ <em>X</em> and <em>x</em> ∈ <em>S</em>, meaning <em>x</em> ∈ <em>X</em> ∩ <em>S</em>. That is enough to say that <em>x</em> ∈ ⋃ {<em>X</em> ∩ <em>S</em> | <em>S</em> ∈ }. So <em>X</em> ∩ (⋃ ) ⊆ ⋃ {<em>X</em> ∩ <em>S</em> | <em>S</em> ∈ }.
For the other direction, the proof is essentially the reverse. Let <em>x</em> ∈ ⋃ {<em>X</em> ∩ <em>S</em> | <em>S</em> ∈ }. Then <em>x</em> ∈ <em>X</em> ∩ <em>S</em> for some <em>S</em> ∈ , so that <em>x</em> ∈ <em>X</em> and <em>x</em> ∈ <em>S</em>. Because <em>x</em> ∈ <em>S</em> and <em>S</em> ∈ , we have that <em>x</em> ∈ ⋃ , and so <em>x</em> ∈ <em>X</em> ∩ (⋃ ). So ⋃ {<em>X</em> ∩ <em>S</em> | <em>S</em> ∈ } ⊆ <em>X</em> ∩ (⋃ ).
QED
• <em>X</em> ∪ (⋂ ) = ⋂ {<em>X</em> ∪ <em>S</em> | <em>S</em> ∈ }
Let <em>x</em> ∈ <em>X</em> ∪ (⋂ ). Then <em>x</em> ∈ <em>X</em> or <em>x</em> ∈ ⋂ . If <em>x</em> ∈ <em>X</em>, we're done because that would guarantee <em>x</em> ∈ <em>X</em> ∪ <em>S</em> for any set <em>S</em>, and hence <em>x</em> would belong to the intersection. If <em>x</em> ∈ ⋂ , then <em>x</em> ∈ <em>S</em> for all <em>S</em> ∈ , so that <em>x</em> ∈ <em>X</em> ∪ <em>S</em> for all <em>S</em>, and hence <em>x</em> is in the intersection. Therefore <em>X</em> ∪ (⋂ ) ⊆ ⋂ {<em>X</em> ∪ <em>S</em> | <em>S</em> ∈ }.
For the opposite direction, let <em>x</em> ∈ ⋂ {<em>X</em> ∪ <em>S</em> | <em>S</em> ∈ }. Then <em>x </em>∈ <em>X</em> ∪ <em>S</em> for all <em>S</em> ∈ . So <em>x</em> ∈ <em>X</em> or <em>x</em> ∈ <em>S</em> for all <em>S</em>. If <em>x</em> ∈ <em>X</em>, we're done. If <em>x</em> ∈ <em>S</em> for all <em>S</em> ∈ , then <em>x</em> ∈ ⋂ , and we're done. So ⋂ {<em>X</em> ∪ <em>S</em> | <em>S</em> ∈ } ⊆ <em>X</em> ∪ (⋂ ).
QED
Hi! So because all the sides of the square are the same side, you multiple two of the side lengths together, so the area of the painting is 18 x 18 = 324 :) Good luck and do well in school!!!!!!!!
Answer:
y = (3/8)x - 1.5
Step-by-step explanation:
Use the slope-intercept form y = mx + b. Substitute -1.5 for b, 4 for x and 0 for y. Then: 0 = m(4) - 1.5, or
4m = 1.5, or
The slope is m = 1.5/4, or m = 0.375, or m = 3/8.
Note that the x-intercept can be treated just like any other point: (4, 0)
Then the desired equation is y = (3/8)x - 1.5
Answer:
-2
Step-by-step explanation:
Y = mx+c
M here being the number in front of x
