Hello.
A trinomial is a perfect square if the square root of the first term times the square root of the third term times 2 equals the middle term.
![\boxed{\mathsf{x^{2} + \dfrac{2}{3} x}}](https://tex.z-dn.net/?f=%5Cboxed%7B%5Cmathsf%7Bx%5E%7B2%7D%20%2B%20%5Cdfrac%7B2%7D%7B3%7D%20x%7D%7D)
a) Adding 1/9:
![\cdot \: \mathsf{x^{2} + \dfrac{2}{3} x + \dfrac{1}{9}} \\ \\ \\ \mathsf{\sqrt{x^{2}} \times \sqrt{\dfrac{1}{9}} \times 2 =} \\ \\ \\ \mathsf{x \times \dfrac{1}{3} \times 2 =} \\ \\ \\ \mathsf{\dfrac{2}{3} x \rightarrow it \: is \: a \: perfect \: square \: trinomial}](https://tex.z-dn.net/?f=%5Ccdot%20%5C%3A%20%5Cmathsf%7Bx%5E%7B2%7D%20%2B%20%5Cdfrac%7B2%7D%7B3%7D%20x%20%2B%20%5Cdfrac%7B1%7D%7B9%7D%7D%20%5C%5C%20%5C%5C%20%5C%5C%20%5Cmathsf%7B%5Csqrt%7Bx%5E%7B2%7D%7D%20%5Ctimes%20%5Csqrt%7B%5Cdfrac%7B1%7D%7B9%7D%7D%20%5Ctimes%202%20%3D%7D%20%5C%5C%20%5C%5C%20%5C%5C%20%5Cmathsf%7Bx%20%5Ctimes%20%5Cdfrac%7B1%7D%7B3%7D%20%5Ctimes%202%20%3D%7D%20%5C%5C%20%5C%5C%20%5C%5C%20%5Cmathsf%7B%5Cdfrac%7B2%7D%7B3%7D%20x%20%5Crightarrow%20it%20%5C%3A%20is%20%5C%3A%20a%20%5C%3A%20perfect%20%5C%3A%20square%20%5C%3A%20trinomial%7D)
b) Adding 4/9:
![\cdot \: \mathsf{x^{2} + \dfrac{2}{3} x + \dfrac{4}{9}} \\ \\ \\ \mathsf{\sqrt{x^{2}} \times \sqrt{\dfrac{4}{9}} \times 2 =} \\ \\ \\ \mathsf{x \times \dfrac{2}{3} \times 2 =} \\ \\ \\ \mathsf{\dfrac{4}{3} x \rightarrow it \: is \: not \: a \: perfect \: square \: trinomial}](https://tex.z-dn.net/?f=%5Ccdot%20%5C%3A%20%5Cmathsf%7Bx%5E%7B2%7D%20%2B%20%5Cdfrac%7B2%7D%7B3%7D%20x%20%2B%20%5Cdfrac%7B4%7D%7B9%7D%7D%20%5C%5C%20%5C%5C%20%5C%5C%20%5Cmathsf%7B%5Csqrt%7Bx%5E%7B2%7D%7D%20%5Ctimes%20%5Csqrt%7B%5Cdfrac%7B4%7D%7B9%7D%7D%20%5Ctimes%202%20%3D%7D%20%5C%5C%20%5C%5C%20%5C%5C%20%5Cmathsf%7Bx%20%5Ctimes%20%5Cdfrac%7B2%7D%7B3%7D%20%5Ctimes%202%20%3D%7D%20%5C%5C%20%5C%5C%20%5C%5C%20%5Cmathsf%7B%5Cdfrac%7B4%7D%7B3%7D%20x%20%5Crightarrow%20it%20%5C%3A%20is%20%5C%3A%20not%20%5C%3A%20a%20%5C%3A%20perfect%20%5C%3A%20square%20%5C%3A%20trinomial%7D)
c) Adding 4 and 1/9:
![\cdot \: \mathsf{x^{2} + \dfrac{2}{3} x + \dfrac{1}{9} + 4 = x^{2} + \dfrac{2}{3} x + \dfrac{37}{9}} \\ \\ \\ \mathsf{\sqrt{x^{2}} \times \sqrt{\dfrac{37}{9}} \times 2 =} \\ \\ \\ \mathsf{x \times \dfrac{\sqrt{37}}{3} \times 2 =} \\ \\ \\ \mathsf{\dfrac{2\sqrt{37}}{3} x \rightarrow it \: is \: not \: a \: perfect \: square \: trinomial}](https://tex.z-dn.net/?f=%5Ccdot%20%5C%3A%20%5Cmathsf%7Bx%5E%7B2%7D%20%2B%20%5Cdfrac%7B2%7D%7B3%7D%20x%20%2B%20%5Cdfrac%7B1%7D%7B9%7D%20%2B%204%20%3D%20x%5E%7B2%7D%20%2B%20%5Cdfrac%7B2%7D%7B3%7D%20x%20%2B%20%5Cdfrac%7B37%7D%7B9%7D%7D%20%5C%5C%20%5C%5C%20%5C%5C%20%5Cmathsf%7B%5Csqrt%7Bx%5E%7B2%7D%7D%20%5Ctimes%20%5Csqrt%7B%5Cdfrac%7B37%7D%7B9%7D%7D%20%5Ctimes%202%20%3D%7D%20%5C%5C%20%5C%5C%20%5C%5C%20%5Cmathsf%7Bx%20%5Ctimes%20%5Cdfrac%7B%5Csqrt%7B37%7D%7D%7B3%7D%20%5Ctimes%202%20%3D%7D%20%5C%5C%20%5C%5C%20%5C%5C%20%5Cmathsf%7B%5Cdfrac%7B2%5Csqrt%7B37%7D%7D%7B3%7D%20x%20%5Crightarrow%20it%20%5C%3A%20is%20%5C%3A%20not%20%5C%3A%20a%20%5C%3A%20perfect%20%5C%3A%20square%20%5C%3A%20trinomial%7D)
Hope I helped.
Answer:
wow thats one hard equationnnnn
Step-by-step explanation:
Answer:
First you have to find x.
A stratight line is 180 degree.
Therefore, we have:
16x+8+4x-8=180
20x= 180
x= 9
Angle BAT = 16x+8= 16(9)+8= 152 degree.
Angle CAT= 180-152= 28 degree.
Using the concept of probability and the combination formula, it is found that there is a 0.4444 = 44.44% probability they get to be on the same team.
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- A probability is the <u>number of desired outcomes divided by the number of total outcomes.</u>
- The order in which the children are chosen is not important, which means that the combination formula is used to find the number of outcomes.
--------------------
<u>Combination formula:
</u>
is the number of different combinations of<u> x objects from a set of n elements</u>, given by the following formula.
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Finding the number of desired outcomes:
- Andy and Ollie on the same team, plus 3 children from a set of 8.
- Can be on either team, blue or red, so multiplied by 2.
![D = 2C_{8,3} = 2\frac{8!}{3!5!} = 112](https://tex.z-dn.net/?f=D%20%3D%202C_%7B8%2C3%7D%20%3D%202%5Cfrac%7B8%21%7D%7B3%215%21%7D%20%3D%20112)
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Finding the number of total outcomes:
- <u>5 children from a set of 10</u>, thus:
![T = C_{10,5} = \frac{10!}{5!5!} = 252](https://tex.z-dn.net/?f=T%20%3D%20C_%7B10%2C5%7D%20%3D%20%5Cfrac%7B10%21%7D%7B5%215%21%7D%20%3D%20252)
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The probability is:
![p = \frac{D}{T} = \frac{112}{252} = 0.4444](https://tex.z-dn.net/?f=p%20%3D%20%5Cfrac%7BD%7D%7BT%7D%20%3D%20%5Cfrac%7B112%7D%7B252%7D%20%3D%200.4444)
0.4444 = 44.44% probability they get to be on the same team.
A similar problem is given at brainly.com/question/22931444
See the picture to better understand the problem
we know that
A regular dodecagon has 12 sides
Central angle of a regular polygon is an angle whose vertex is the center of the polygon with two consecutive radii
thus
the measure of a central angle is
m∠AOC=360/n
where n is the number of sides
so
m∠AOC=360/12-----> 30°
therefore
the answer Part a) is <span>
the measure of the angle formed by two consecutive radii is 30 degrees
Part b)
we know that
OAC is an isosceles triangle
so
OA=OC
m</span>∠OAC=m∠OCA
<span>the sum of the internal angles of a triangle is 180 degrees
</span>so
180=2*m∠OAC+m∠AOC-----> m∠OAC=[180-30]/2----> 75°
the answer part b) is <span>
the measure of the angle formed by a radius and a side is 75</span>
°