Answer:
Choice C Rational
Step-by-step explanation:
Hey There!
If i got this down right,
An = A1 + (n - 1)d
Sn = A1 + A2 + A3 + ... + An
A1 is given by
Sn = n (A1 + An) / 2
For Example
An = A1 + (n - 1)d
= 6 + 3 (n - 1)
= 3 n + 3
n = 50
Hope This Helps!!!
Answer:
Step-by-step explanation:
![17. (a^{m})^{n}=a^{m*n}\\\\a^{m}*a^{n}=a^{m+n}\\\\-3k^{2}*(4k^{5})^{3}=-3k^{2}*4^{3}*k^{5*3}\\\\ = -3k^{2}*64*k^{15}\\\\= (-3)*64*k^{2+15}\\\\= - 192k^{17}](https://tex.z-dn.net/?f=17.%20%20%28a%5E%7Bm%7D%29%5E%7Bn%7D%3Da%5E%7Bm%2An%7D%5C%5C%5C%5Ca%5E%7Bm%7D%2Aa%5E%7Bn%7D%3Da%5E%7Bm%2Bn%7D%5C%5C%5C%5C-3k%5E%7B2%7D%2A%284k%5E%7B5%7D%29%5E%7B3%7D%3D-3k%5E%7B2%7D%2A4%5E%7B3%7D%2Ak%5E%7B5%2A3%7D%5C%5C%5C%5C%20%3D%20-3k%5E%7B2%7D%2A64%2Ak%5E%7B15%7D%5C%5C%5C%5C%3D%20%28-3%29%2A64%2Ak%5E%7B2%2B15%7D%5C%5C%5C%5C%3D%20-%20192k%5E%7B17%7D)
![19. \dfrac{a^{m}}{a^{n}}=a^{m-n}\\\\\\\dfrac{(-7p^{4})*(-8p^{5})}{2p^{3}}= \dfrac{(-7)*(-8)*p^{4}*p^{5}}{2p^{3}}\\\\\\=(-7)*(-4)*p^{4+5-3} \\\\= 28p^{6}\\](https://tex.z-dn.net/?f=19.%20%5Cdfrac%7Ba%5E%7Bm%7D%7D%7Ba%5E%7Bn%7D%7D%3Da%5E%7Bm-n%7D%5C%5C%5C%5C%5C%5C%5Cdfrac%7B%28-7p%5E%7B4%7D%29%2A%28-8p%5E%7B5%7D%29%7D%7B2p%5E%7B3%7D%7D%3D%20%5Cdfrac%7B%28-7%29%2A%28-8%29%2Ap%5E%7B4%7D%2Ap%5E%7B5%7D%7D%7B2p%5E%7B3%7D%7D%5C%5C%5C%5C%5C%5C%3D%28-7%29%2A%28-4%29%2Ap%5E%7B4%2B5-3%7D%20%5C%5C%5C%5C%3D%2028p%5E%7B6%7D%5C%5C)
![20)\dfrac{15a^{16}b^{11}}{(3a^{4}b^{2})^{3}}=\dfrac{15a^{16}b^{11}}{3^{3}*a^{4*3}*b^{2*3}}\\\\\\=\dfrac{15a^{16}b^{11}}{27*a^{12}*b^{6}}\\\\=\dfrac{5*a^{16-12}*b^{11-6}}{9}\\\\\\=\dfrac{5a^{4}b^{5}}{9}](https://tex.z-dn.net/?f=20%29%5Cdfrac%7B15a%5E%7B16%7Db%5E%7B11%7D%7D%7B%283a%5E%7B4%7Db%5E%7B2%7D%29%5E%7B3%7D%7D%3D%5Cdfrac%7B15a%5E%7B16%7Db%5E%7B11%7D%7D%7B3%5E%7B3%7D%2Aa%5E%7B4%2A3%7D%2Ab%5E%7B2%2A3%7D%7D%5C%5C%5C%5C%5C%5C%3D%5Cdfrac%7B15a%5E%7B16%7Db%5E%7B11%7D%7D%7B27%2Aa%5E%7B12%7D%2Ab%5E%7B6%7D%7D%5C%5C%5C%5C%3D%5Cdfrac%7B5%2Aa%5E%7B16-12%7D%2Ab%5E%7B11-6%7D%7D%7B9%7D%5C%5C%5C%5C%5C%5C%3D%5Cdfrac%7B5a%5E%7B4%7Db%5E%7B5%7D%7D%7B9%7D)
Answer:
Step-by-step explanation:
Given the expression (x+11)(2x+3)
We want to expand it and write equivalent expression
Generally if we want to expand an expression we will take one of the expression in one bracket and multiply with the other bracket and then take the other expression and multiply it with the other
E.g, (a+b) × (c + d)
Then, we take a × (c+d) and also b × (c+d)
We can do it the other way round too and it will give the same results.
So, applying this to the given expression
(x+11)(2x+3)
x(2x+3) + 11(2x+3)
2x² + 3x + 22x + 33
2x² + 25x + 33
Then, the equivalent expression is 2x² + 25x + 33
(x + 11)(2x + 3) = 2x² + 25x + 33
Answer:
n° = 62°
p° = 62°
q° = 118°
v° = 84°
w° = 138°
Step-by-step explanation:
angle ABC is 118°
so
m° + 118° = 180
m° = 180° - 118°
m° = 62°
n° = m° = 62° (corresponding angles are equal since AB is parallel to DC, and BC)
p° = n° = 62° (vertical angles are equal)
q° + n° = 180° (linear pair angles)
q° + 62° = 180°
q° = 180° - 62°
q° = 118°
v° + 96° = 180° (linear pair angles)
v° = 180° - 96°
v° = 84°
w° + 42° = 180 (linear pair angles)
w° = 180° - 42°
w° = 138°