Answer: I think its B 333.3mm
Step-by-step explanation:
Answer: no
Step-by-step explanation:
117% equals 1.17 and 50/33 equals 1.51 repeating so they aren’t equal.
Answer:
35 2/3
Step-by-step explanation:
49 1/3 - 13 2/3
First convert both into improper fractions, which is
148/3 - 41/3
Then subtract!
107/3
Next simplify the fraction.
35 2/3
Answer:
see below
Step-by-step explanation: 5 23 8 03
the lenght of the longer leg of a right triangle is 9 ft longer than the lenght of the shorter leg x. The hypotenuse is 9 ft shorter than twice the lenght of the shorter leg.
shorter leg = x
longer leg = x + 9
hypotenuse = 2x - 9
Pythagorean theorem = a² + b² = c²
shorter-leg² + longer-leg² = hypotenuse²
x² + (x+9)² = (2x - 9)² solve for x
x² + (x+9) (x+9) = (2x - 9)(2x - 9)
x² + (x²+18x+81) = (4x² - 36x + 81)
(2x²+18x+81) = (4x² - 36x + 81)
0 = 2x² -54x
0 = x(2x - 54)
0 = x and 0 = 2x -54
54 = 2x
27 = x
shorter leg = 27
longer leg = 36
hypotenuse = 45
divided all the values by 9 and you get a 3, 4, 5 right triangle, so the answer checks correct
Answer:
220
Step-by-step explanation:
we want to figure out Sum of the following series:
![\rm(1) + (1+2) + (1+2+3) + { \dots}+ (1+2+3+{\dots}+10)](https://tex.z-dn.net/?f=%20%5Crm%281%29%20%2B%20%281%2B2%29%20%2B%20%281%2B2%2B3%29%20%2B%20%7B%20%5Cdots%7D%2B%20%281%2B2%2B3%2B%7B%5Cdots%7D%2B10%29)
notice that, the nth term is equal to the sum of <em>all </em><em>the</em><em> </em><em>previous</em><em> </em>and the <em>nth</em> term , therefore the nth term of the sequence is <u>1</u><u>0</u><u> </u>. The sum of the sequence is equal to
![\displaystyle S _{n} = \frac{n(n + 1)(n + 2)}{6}](https://tex.z-dn.net/?f=%20%5Cdisplaystyle%20S%20_%7Bn%7D%20%3D%20%20%5Cfrac%7Bn%28n%20%2B%201%29%28n%20%2B%202%29%7D%7B6%7D%20)
see the following question for more information
since we've already figured out <em>n</em><em>=</em><em>1</em><em>0</em><em> </em>therefore substitute:
![\displaystyle S _{10} = \frac{10(10+ 1)(10+ 2)}{6}](https://tex.z-dn.net/?f=%20%5Cdisplaystyle%20S%20_%7B10%7D%20%3D%20%20%5Cfrac%7B10%2810%2B%201%29%2810%2B%202%29%7D%7B6%7D%20)
simplify parentheses:
![\displaystyle S _{10} = \frac{10(11)(12)}{6}](https://tex.z-dn.net/?f=%20%5Cdisplaystyle%20S%20_%7B10%7D%20%3D%20%20%5Cfrac%7B10%2811%29%2812%29%7D%7B6%7D%20)
simplify multiplication:
![\displaystyle S _{10} = \frac{1320}{6}](https://tex.z-dn.net/?f=%20%5Cdisplaystyle%20S%20_%7B10%7D%20%3D%20%20%5Cfrac%7B1320%7D%7B6%7D%20)
simplify division:
![\displaystyle S _{10} = \boxed{220}](https://tex.z-dn.net/?f=%20%5Cdisplaystyle%20S%20_%7B10%7D%20%3D%20%20%20%5Cboxed%7B220%7D)
hence, the Sum of the series is <u>2</u><u>2</u><u>0</u>