Answer:
161y - 45
Step-by-step explanation:
Answer:
(1) length AB = 21.0
(2) length BC = 45.0
Step-by-step explanation:
(1) To determine AB, apply Cosine rule;
![|AB|^2 = |AC|^2 + |BC|^2 \ - \ 2[|AC| \times |BC]cos \ C\\\\|AB|^2 = 13^2 + 29^2 \ - \ 2(13 \times 29) cos(41)\\\\|AB|^2 = 1010 - 569.05\\\\|AB|^2 = 440.95\\\\|AB|= \sqrt{ 440.95} \\\\|AB| = 21.0](https://tex.z-dn.net/?f=%7CAB%7C%5E2%20%3D%20%7CAC%7C%5E2%20%2B%20%7CBC%7C%5E2%20%5C%20-%20%5C%202%5B%7CAC%7C%20%5Ctimes%20%7CBC%5Dcos%20%5C%20C%5C%5C%5C%5C%7CAB%7C%5E2%20%3D%2013%5E2%20%2B%2029%5E2%20%5C%20-%20%5C%202%2813%20%5Ctimes%2029%29%20cos%2841%29%5C%5C%5C%5C%7CAB%7C%5E2%20%3D%201010%20-%20569.05%5C%5C%5C%5C%7CAB%7C%5E2%20%3D%20440.95%5C%5C%5C%5C%7CAB%7C%3D%20%5Csqrt%7B%20440.95%7D%20%5C%5C%5C%5C%7CAB%7C%20%3D%2021.0)
(2) To determine BC, also apply cosine rule;
![|BC|^2 = |AB|^2 + |AC|^2 \ - \ 2[|AB| \times |AC]cos \ A\\\\|BC|^2 = 30^2 + 21^2 \ - \ 2(30 \times 21) cos(123)\\\\|BC|^2 = 1341 - (-686.245)\\\\|BC|^2 = 1341 + 686.245\\\\ |BC| = 2027.245\\\\|BC|= \sqrt{ 2027.245} \\\\|BC| = 45.0](https://tex.z-dn.net/?f=%7CBC%7C%5E2%20%3D%20%7CAB%7C%5E2%20%2B%20%7CAC%7C%5E2%20%5C%20-%20%5C%202%5B%7CAB%7C%20%5Ctimes%20%7CAC%5Dcos%20%5C%20A%5C%5C%5C%5C%7CBC%7C%5E2%20%3D%2030%5E2%20%2B%2021%5E2%20%5C%20-%20%5C%202%2830%20%5Ctimes%2021%29%20cos%28123%29%5C%5C%5C%5C%7CBC%7C%5E2%20%3D%201341%20-%20%28-686.245%29%5C%5C%5C%5C%7CBC%7C%5E2%20%3D%201341%20%2B%20686.245%5C%5C%5C%5C%20%7CBC%7C%20%3D%202027.245%5C%5C%5C%5C%7CBC%7C%3D%20%5Csqrt%7B%202027.245%7D%20%5C%5C%5C%5C%7CBC%7C%20%3D%2045.0)
Answer:
2x squared + 25
Step-by-step explanation:
Answer:
x = 18
Step-by-step explanation:
First, let's find the ratios between the two triangles
We'll use AV and AC
372 ÷ 589 = 12/19
All of the sides of the smaller triangle are 12/19 of the bigger triangle
Now let's find x
We know that AU + UB = AB
So it's 20x + 108 + 273 = AB
12/19 of a bigger triangle side equals a small triangle side
(12/19)AB = AU
For this equation multiply both sides by 19/12 to isolate AB
(12/19)AB x 19/12 = AU x 19/12
AB = (19/12)AU
Now we have this
20x + 108 + 273 = (19/12)(20x + 108)
20x + 381 = (19/12)(20x + 108)
Distribute the 19/12
20x + 381 = 95/3x + 171
Move all like terms to one side
20x + 381 = 95/3x + 171
- 171 - 171
20x + 210 = 95/3x
- 20x - 20x
Don't forget about common denominators
210 = 95/3x - 60/3x
210 = 35/3x
Multiply both sides by 3
210 x 3 = 35/3x x 3
630 = 35x
Divide both sides by 35
630/35 = 35x/35
x = 18
1) 1.2756 x 10^4
2) 1.16464 x 10^5
3) 1.42984 x 10^5
4) 1.392 x 10^6
5) 5.977 x 10^7
6) 9.035 x 10^8
7) 2.6448 x 10^9
