Answer:
12 (the third one is the greatest common factor of 120 and 84)
The rate of change of the balance was $175 per deposit which is C
Answer:
![32 {x}^{2} \sqrt[3]{ 2x } -8{x}^{3}](https://tex.z-dn.net/?f=32%20%7Bx%7D%5E%7B2%7D%20%5Csqrt%5B3%5D%7B%202x%20%7D%20%20%20%20-8%7Bx%7D%5E%7B3%7D)
Step-by-step explanation:
We want to
![4x \sqrt[3]{4 {x}^{2} } (2 \sqrt[3]{32 {x}^{2} } - x \sqrt[3]{2x} )](https://tex.z-dn.net/?f=4x%20%5Csqrt%5B3%5D%7B4%20%7Bx%7D%5E%7B2%7D%20%7D%20%282%20%5Csqrt%5B3%5D%7B32%20%7Bx%7D%5E%7B2%7D%20%7D%20%20-%20x%20%5Csqrt%5B3%5D%7B2x%7D%20%29)
We expand to obtain:
![4x \sqrt[3]{4 {x}^{2} } \times 2 \sqrt[3]{32 {x}^{2} } -4x \sqrt[3]{4 {x}^{2} } \times x \sqrt[3]{2x} )](https://tex.z-dn.net/?f=4x%20%5Csqrt%5B3%5D%7B4%20%7Bx%7D%5E%7B2%7D%20%7D%20%20%5Ctimes%202%20%5Csqrt%5B3%5D%7B32%20%7Bx%7D%5E%7B2%7D%20%7D%20%20-4x%20%5Csqrt%5B3%5D%7B4%20%7Bx%7D%5E%7B2%7D%20%7D%20%5Ctimes%20%20x%20%5Csqrt%5B3%5D%7B2x%7D%20%29)
We now simplify
![8x \sqrt[3]{4 {x}^{2} \times 32 {x}^{2} } -4 {x}^{2} \sqrt[3]{4 {x}^{2} \times 2x}](https://tex.z-dn.net/?f=8x%20%5Csqrt%5B3%5D%7B4%20%7Bx%7D%5E%7B2%7D%20%20%5Ctimes%2032%20%7Bx%7D%5E%7B2%7D%20%7D%20%20%20%20-4%20%7Bx%7D%5E%7B2%7D%20%20%5Csqrt%5B3%5D%7B4%20%7Bx%7D%5E%7B2%7D%20%20%5Ctimes%202x%7D%20)
We multiply the radicand
![8x \sqrt[3]{64 \times {x}^{3} \times 2x } -4 {x}^{2} \sqrt[3]{8 {x}^{3}}](https://tex.z-dn.net/?f=8x%20%5Csqrt%5B3%5D%7B64%20%5Ctimes%20%7Bx%7D%5E%7B3%7D%20%20%5Ctimes%202x%20%7D%20%20%20%20-4%20%7Bx%7D%5E%7B2%7D%20%20%5Csqrt%5B3%5D%7B8%20%7Bx%7D%5E%7B3%7D%7D%20)
Or
![8x \sqrt[3]{ {(4x)}^{3} \times 2x } -4 {x}^{2} \sqrt[3]{{(2x)}^{3}}](https://tex.z-dn.net/?f=8x%20%5Csqrt%5B3%5D%7B%20%7B%284x%29%7D%5E%7B3%7D%20%20%5Ctimes%202x%20%7D%20%20%20%20-4%20%7Bx%7D%5E%7B2%7D%20%20%5Csqrt%5B3%5D%7B%7B%282x%29%7D%5E%7B3%7D%7D%20)
We take cube root to get:
![8x \times 4x\sqrt[3]{ 2x } -4 {x}^{2} \times 2x](https://tex.z-dn.net/?f=8x%20%20%5Ctimes%204x%5Csqrt%5B3%5D%7B%202x%20%7D%20%20%20%20-4%20%7Bx%7D%5E%7B2%7D%20%20%5Ctimes%202x)
We multiply out to get:
![32 {x}^{2} \sqrt[3]{ 2x } -8{x}^{3}](https://tex.z-dn.net/?f=32%20%7Bx%7D%5E%7B2%7D%20%5Csqrt%5B3%5D%7B%202x%20%7D%20%20%20%20-8%7Bx%7D%5E%7B3%7D)
Answer:
a=8 b=3/2
Step-by-step explanation:
so here a is the initial value which 8
then we can plug in 2 for x and 18 for f(x) to find b
f(x)=8*b^x
18=8*b^2
18/8=b^2
9/4=b^2
b^2=(3/2)^2
b=3/2
Answer: D. 50
Step-by-step explanation:
the sum of opposite angles of a cyclic quadrilateral are always 180 degrees
80 +2x= 180
2x= 180 - 80
x= 100/2
x= 50