The slope is undefined or -5
0.008 x10 = 0.08
Answer : 0.008
Decimal - 2.75
Fraction - 2 and 3/4
Percent - 275%
Answer:
![3a^4](https://tex.z-dn.net/?f=3a%5E4)
Step-by-step explanation:
What is the cube root of
? This is the question.
We can write:
![\sqrt[3]{27a^{12}}](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B27a%5E%7B12%7D%7D)
We will use the below property to simplify:
![\sqrt[n]{a*b}=\sqrt[n]{a} \sqrt[n]{b}](https://tex.z-dn.net/?f=%5Csqrt%5Bn%5D%7Ba%2Ab%7D%3D%5Csqrt%5Bn%5D%7Ba%7D%20%20%5Csqrt%5Bn%5D%7Bb%7D)
So, we have:
![\sqrt[3]{27a^{12}} =\sqrt[3]{27} \sqrt[3]{a^{12}}](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B27a%5E%7B12%7D%7D%20%3D%5Csqrt%5B3%5D%7B27%7D%20%5Csqrt%5B3%5D%7Ba%5E%7B12%7D%7D)
We will now use below property to further simplify:
![\sqrt[n]{x} =x^{\frac{1}{n}}](https://tex.z-dn.net/?f=%5Csqrt%5Bn%5D%7Bx%7D%20%3Dx%5E%7B%5Cfrac%7B1%7D%7Bn%7D%7D)
Thus, we have:
![\sqrt[3]{27} \sqrt[3]{a^{12}} =3*(a^{12})^{\frac{1}{3}}](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B27%7D%20%5Csqrt%5B3%5D%7Ba%5E%7B12%7D%7D%20%3D3%2A%28a%5E%7B12%7D%29%5E%7B%5Cfrac%7B1%7D%7B3%7D%7D)
We know power to the power rule: ![(a^z)^b=a^{zb}](https://tex.z-dn.net/?f=%28a%5Ez%29%5Eb%3Da%5E%7Bzb%7D)
Now, we have:
![3*(a^{12})^{\frac{1}{3}}\\=3*a^{\frac{12}{3}}\\=3a^4](https://tex.z-dn.net/?f=3%2A%28a%5E%7B12%7D%29%5E%7B%5Cfrac%7B1%7D%7B3%7D%7D%5C%5C%3D3%2Aa%5E%7B%5Cfrac%7B12%7D%7B3%7D%7D%5C%5C%3D3a%5E4)
This is the correct answer: ![3a^4](https://tex.z-dn.net/?f=3a%5E4)
= 9n + 63
generate the first few terms using the recursive equation
f(1) = 72
f(2) = 72 + 9 = 81
f(3) = 81 + 9 = 90
f(4) = 90 + 9 = 99
the sequence is 72, 81, 90, 99, .....
This is an arithmetic sequence whose n th term formula is
=
+ (n - 1 )d
where
is the first term and d the common difference
d = 99 - 90 = 90 - 81 = 81 - 72 = 9 and
= 72
= 72 + 9(n - 1) = 72 + 9n - 9 = 9n + 63 ← explicit formula