1. Given any triangle ABC with sides BC=a, AC=b and AB=c, the following are true :
i) the larger the angle, the larger the side in front of it, and the other way around as well. (Sine Law) Let a=20 in, then the largest angle is angle A.
ii) Given the measures of the sides of a triangle. Then the cosines of any of the angles can be found by the following formula:
![a^{2}=b ^{2}+c ^{2}-2bc(cosA)](https://tex.z-dn.net/?f=%20a%5E%7B2%7D%3Db%20%5E%7B2%7D%2Bc%20%5E%7B2%7D-2bc%28cosA%29%20%20%20)
2.
![20^{2}=9 ^{2}+13 ^{2}-2*9*13(cosA) 400=81+169-234(cosA) 150=-234(cosA) cosA=150/-234= -0.641](https://tex.z-dn.net/?f=%2020%5E%7B2%7D%3D9%20%5E%7B2%7D%2B13%20%5E%7B2%7D-2%2A9%2A13%28cosA%29%0A%0A400%3D81%2B169-234%28cosA%29%20%20%20150%3D-234%28cosA%29%0A%0AcosA%3D150%2F-234%3D%20-0.641)
3. m(A) = Arccos(-0.641)≈130°,
4. Remark: We calculate Arccos with a scientific calculator or computer software unless it is one of the well known values, ex Arccos(0.5)=60°, Arccos(-0.5)=120° etc
Answer:
![Width= 13 cm](https://tex.z-dn.net/?f=Width%3D%2013%20cm)
![length=30cm](https://tex.z-dn.net/?f=length%3D30cm)
Step-by-step explanation:
Let the length of the rectangle be 'L'
And the width of the rectangle be 'W'
![Perimeter= 86 cm](https://tex.z-dn.net/?f=Perimeter%3D%2086%20cm)
According to the statement:
![Length= 2*Width+4\\L=2W+4](https://tex.z-dn.net/?f=Length%3D%202%2AWidth%2B4%5C%5CL%3D2W%2B4)
Perimeter of a rectangle= 2(Length+Width)
![86=2(2W+4+W)\\86/2=3W+4\\43=3W+4\\3W=43-4\\3W=39\\W=39/3\\W=13 cm\\\\Length(L)=2W+4\\=2(13)+4=26+4=30 cm\\Length=30 cm](https://tex.z-dn.net/?f=86%3D2%282W%2B4%2BW%29%5C%5C86%2F2%3D3W%2B4%5C%5C43%3D3W%2B4%5C%5C3W%3D43-4%5C%5C3W%3D39%5C%5CW%3D39%2F3%5C%5CW%3D13%20cm%5C%5C%5C%5CLength%28L%29%3D2W%2B4%5C%5C%3D2%2813%29%2B4%3D26%2B4%3D30%20cm%5C%5CLength%3D30%20cm)
![Width= 13 cm](https://tex.z-dn.net/?f=Width%3D%2013%20cm)
![length=30cm](https://tex.z-dn.net/?f=length%3D30cm)
Answer:
1.
is a perfect square trinomial
Step-by-step explanation:
2. Perfect square trinomials are algebraic expressions with three terms that are created by multiplying a binomial to itself.
3. I will upload a picture showing my work
Answer:
-2
Step-by-step explanation:
Add them up: -14
Divide by how many there are: -14 / 7 = -2