For each of the following shapes, state whether or not it has rotation symmetry. If it does, draw the rotational
1 answer:
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Answer:
PA = 6.6 units
XP = 2.4 units
Explanation:
1- We are given that:
perimeter of RXA = 24 units
RX = 4
RA = 11
This means that:
XA = 24 - 4 - 11 = 9 units
2- For XA:
XA = XP + PA
XA = 9 units
This means that :
XP + PA = 9 units
XP = 9 - PA
3- Triangle angle bisector theorem:
"In a triangle, the angle bisector divides the opposite side into two segments that are proportional to the other two sides"
Applying this to the given triangle, we can set the ratio as follows:
We have:
XP = 9 - PA
RX = 4
RA = 11
4- Substitute with the givens in the above ratio and solve for PA as follows:
11(9-PA) = 4(PA)
99 - 11PA = 4PA
99 = 15PA
PA = 99/15
PA = 6.6 units
5- Substitute to get XP as follows:
XP = 9 - PA
XP = 9 - 6.6
XP = 2.4 units
Hope this helps :)
PA = 6.6 units
XP = 2.4 units
Explanation:
1- We are given that:
perimeter of RXA = 24 units
RX = 4
RA = 11
This means that:
XA = 24 - 4 - 11 = 9 units
2- For XA:
XA = XP + PA
XA = 9 units
This means that :
XP + PA = 9 units
XP = 9 - PA
3- Triangle angle bisector theorem:
"In a triangle, the angle bisector divides the opposite side into two segments that are proportional to the other two sides"
Applying this to the given triangle, we can set the ratio as follows:
We have:
XP = 9 - PA
RX = 4
RA = 11
4- Substitute with the givens in the above ratio and solve for PA as follows:
11(9-PA) = 4(PA)
99 - 11PA = 4PA
99 = 15PA
PA = 99/15
PA = 6.6 units
5- Substitute to get XP as follows:
XP = 9 - PA
XP = 9 - 6.6
XP = 2.4 units
Hope this helps :)
Answer: First option.
Step-by-step explanation:
Given two sets <em>A</em> and <em>B, </em>the union (<em>A</em>∪B) will be the set of elements which belong to either <em>A</em> or to <em>B</em> or to both.
Inf this case you have these two sets:
{
} and
{
}
To find the union of these sets, put together the elements of the set <em>P</em> and the elements of the set <em>Q</em> (you need to remember that no element must be repeated).
Then, you get that the union of sets <em>P </em>and <em>Q</em> is:
∪
{
}
This matches with the first option.