Answer:
The rectangle has rotational symmetry of order = 2
The rectangle's rotational symmetry occurs for angles of 90 degrees.
Answer:
![\sqrt[4] {x^3}](https://tex.z-dn.net/?f=%5Csqrt%5B4%5D%20%7Bx%5E3%7D)
Step-by-step explanation:
At this point, we can transform the square root into a fourth root by squaring the argument, and bring into the other root:
![\sqrt x \cdot \sqrt[4] x =\sqrt [4] {x^2} \cdot \sqrt[4] x = \sqrt[4]{x^2\cdot x} = \sqrt[4] {x^3}](https://tex.z-dn.net/?f=%5Csqrt%20x%20%5Ccdot%20%5Csqrt%5B4%5D%20x%20%3D%5Csqrt%20%5B4%5D%20%7Bx%5E2%7D%20%5Ccdot%20%5Csqrt%5B4%5D%20x%20%3D%20%5Csqrt%5B4%5D%7Bx%5E2%5Ccdot%20x%7D%20%3D%20%5Csqrt%5B4%5D%20%7Bx%5E3%7D)
Alternatively, if you're allowed to use rational exponents, we can convert everything:
![\sqrt x \cdot \sqrt[4] x = x^{\frac12} \cdot x^\frac14 = x^{\frac12 +\frac14}= x^{\frac24 +\frac14}= x^\frac34 = \sqrt[4] {x^3}](https://tex.z-dn.net/?f=%5Csqrt%20x%20%5Ccdot%20%5Csqrt%5B4%5D%20x%20%3D%20x%5E%7B%5Cfrac12%7D%20%5Ccdot%20x%5E%5Cfrac14%20%3D%20x%5E%7B%5Cfrac12%20%2B%5Cfrac14%7D%3D%20x%5E%7B%5Cfrac24%20%2B%5Cfrac14%7D%3D%20x%5E%5Cfrac34%20%3D%20%5Csqrt%5B4%5D%20%7Bx%5E3%7D)
$160 (if uncle, granny, aunt, gave $100 in total) $260 if they gave $100 each
Answer:
33/20
Step-by-step explanation:
1/12 - 1/15 = 5/60 - 4/60 = 1/60
d = 1/60
a_n = a_1 + d(n - 1)
a_11 = 1/15 + (1/60)(11 - 1)
a_11 = 1/15 + 1/6
a_11 = 4/60 + 10/60
a_11 = 14/60
a_11 = 7/30
a_12 = 14/60 + 1/60
a_12 = 15/60
a_12 = 1/4
s_n = n(a_1 + a_n)/2
s_11 = 11(1/15 + 7/30)/2
s_11 = 11(2/30 + 7/30)/2
s_11 = 11(9/30)/2
s_11 = 99/60
s_11 = 33/20
The answer is 12.
Steps
If that number is x
(3+x)/(8+x)=3/4
"Cross multply"
4(3+x)=3(8+x)
12+4x=24+3x
x=12
To check: add 12 to 3 and 8. 3+12=15 and 8+12=20. 15/20=3/4
