Answer:
Part A
![f(n)=52-12(n-1)](https://tex.z-dn.net/?f=f%28n%29%3D52-12%28n-1%29)
![f(n)=\left\{\begin{matrix}52\: \:if \: \:n=1 & \\f(n+1)+12& if\: n\geq 2 \end{matrix}\right.](https://tex.z-dn.net/?f=f%28n%29%3D%5Cleft%5C%7B%5Cbegin%7Bmatrix%7D52%5C%3A%20%5C%3Aif%20%5C%3A%20%5C%3An%3D1%20%26%20%5C%5Cf%28n%2B1%29%2B12%26%20if%5C%3A%20n%5Cgeq%202%20%5Cend%7Bmatrix%7D%5Cright.)
Part B
Geometric Sequence
Part C
1/4,3/4,5/4,7/4,9/4
![g(n)=\frac{1}{4}+\frac{2}{4}(n-1)\\f(n)=\left\{\begin{matrix}1/4if \: \:n=1 & \\ f(n+1)+2/4& if\: n\geq 2 \end{matrix}\right](https://tex.z-dn.net/?f=g%28n%29%3D%5Cfrac%7B1%7D%7B4%7D%2B%5Cfrac%7B2%7D%7B4%7D%28n-1%29%5C%5Cf%28n%29%3D%5Cleft%5C%7B%5Cbegin%7Bmatrix%7D1%2F4if%20%5C%3A%20%5C%3An%3D1%20%26%20%5C%5C%20f%28n%2B1%29%2B2%2F4%26%20if%5C%3A%20n%5Cgeq%202%20%5Cend%7Bmatrix%7D%5Cright)
Part D:
![h(n)=1.1+0.4(n-1)\\h(n)=\left\{\begin{matrix}1.1 & if\:n=1 \\ h(n+1)+0.4 & if\:n\geq 2\end{matrix}\right](https://tex.z-dn.net/?f=h%28n%29%3D1.1%2B0.4%28n-1%29%5C%5Ch%28n%29%3D%5Cleft%5C%7B%5Cbegin%7Bmatrix%7D1.1%20%26%20if%5C%3An%3D1%20%5C%5C%20h%28n%2B1%29%2B0.4%20%26%20if%5C%3An%5Cgeq%202%5Cend%7Bmatrix%7D%5Cright)
Step-by-step explanation:
By definition, an Arithmetic Sequence holds the same difference between each following number.
Part A
![(52,40, 28, 16)\\52-40=12\\40-28=12\\28-16=12\\d=12](https://tex.z-dn.net/?f=%2852%2C40%2C%2028%2C%2016%29%5C%5C52-40%3D12%5C%5C40-28%3D12%5C%5C28-16%3D12%5C%5Cd%3D12)
<u>Explicit Formula</u>
To write an explicit formula is to write it as function.
![f(n)=52-12(n-1)](https://tex.z-dn.net/?f=f%28n%29%3D52-12%28n-1%29)
<u>Recursive Formula</u>
To write it as recursive formula, is to write it as recurrence given to some restrictions:
![f(n)=\left\{\begin{matrix}52\: \:if \: \:n=1 & \\f(n+1)+12& if\: n\geq 2 \end{matrix}\right.](https://tex.z-dn.net/?f=f%28n%29%3D%5Cleft%5C%7B%5Cbegin%7Bmatrix%7D52%5C%3A%20%5C%3Aif%20%5C%3A%20%5C%3An%3D1%20%26%20%5C%5Cf%28n%2B1%29%2B12%26%20if%5C%3A%20n%5Cgeq%202%20%5Cend%7Bmatrix%7D%5Cright.)
Part B
![(2,4,8,16,32)\: \:](https://tex.z-dn.net/?f=%282%2C4%2C8%2C16%2C32%29%5C%3A%20%5C%3A)
Geometric Sequence, since 2*2=4 8*2=16 and 16*2=32 and 8+2=10 8+16=24
Part C
![(\frac{1}{4},\frac{3}{4},\frac{5}{4},\frac{7}{4},\frac{9}{4})\\\](https://tex.z-dn.net/?f=%28%5Cfrac%7B1%7D%7B4%7D%2C%5Cfrac%7B3%7D%7B4%7D%2C%5Cfrac%7B5%7D%7B4%7D%2C%5Cfrac%7B7%7D%7B4%7D%2C%5Cfrac%7B9%7D%7B4%7D%29%5C%5C%5C)
Arithmetic Sequence, difference
![d=\frac{2}{4}](https://tex.z-dn.net/?f=d%3D%5Cfrac%7B2%7D%7B4%7D)
<u>Explicit Formula:</u>
![g(n)=\frac{1}{4}+\frac{2}{4}(n-1)](https://tex.z-dn.net/?f=g%28n%29%3D%5Cfrac%7B1%7D%7B4%7D%2B%5Cfrac%7B2%7D%7B4%7D%28n-1%29)
<u>Recursive Formula</u>
![g(n)=\left\{\begin{matrix}\frac{1}{4} &if\:n=1 \\ g(n+1)+\frac{2}{4} &if\: n\geq 2\end{matrix}\right.](https://tex.z-dn.net/?f=g%28n%29%3D%5Cleft%5C%7B%5Cbegin%7Bmatrix%7D%5Cfrac%7B1%7D%7B4%7D%20%26if%5C%3An%3D1%20%5C%5C%20g%28n%2B1%29%2B%5Cfrac%7B2%7D%7B4%7D%20%26if%5C%3A%20n%5Cgeq%202%5Cend%7Bmatrix%7D%5Cright.)
Part D
(1.1,1.5,1.9,2.3,2.7) Arithmetic Sequence, difference d=0.4
<u>Explicit formula</u>
![h(n)=1.1+0.4(n-1)\\](https://tex.z-dn.net/?f=h%28n%29%3D1.1%2B0.4%28n-1%29%5C%5C)
<u>Recursive Formula</u>
![h(n)=\left\{\begin{matrix}1.1 &if\:n=1 \\ h(n+1)+0.4 &if\: n\geq 2\end{matrix}\right.](https://tex.z-dn.net/?f=h%28n%29%3D%5Cleft%5C%7B%5Cbegin%7Bmatrix%7D1.1%20%26if%5C%3An%3D1%20%5C%5C%20h%28n%2B1%29%2B0.4%20%26if%5C%3A%20n%5Cgeq%202%5Cend%7Bmatrix%7D%5Cright.)
Answer:
x = 2 x = -6
Step-by-step explanation:
2 (x+2) ^2-4=28
Add 4 to each side
2 (x+2) ^2-4+4=28+4
2 (x+2) ^2= 32
Divide by 2
2/2 (x+2) ^2=32/2
(x+2)^2 = 16
Take the square root of each side
sqrt((x+2)^2) =±sqrt( 16)
x+2 = ±4
Subtract 2 from each side
x+2-2 = -2±4
x = -2±4
x = -2+4 and x = -2-4
x = 2 x = -6
numerator = top part of the fraction
denominator = bottom part of the fraction
* means multiply
a.
you can only add the numerator when the denominator is the same
cant add the denominator
denominator has to be the same
1/5 = 4/20
4/20 + 7/20 = 11/20
b.
1 7/8 = 15/8
3/4 ÷ 15/8 =
3/4 * 8/15 =
24/60 = divide both top and bottom by 12 =
2/5