Answer:

Step-by-step explanation:
This is a short and simple question, but it's good!
We are given the expression
, and simply being asked to combine like elements to simplify the expression. Take a look at the procedure below -
- Remove ( ),
- Add like elements,
- And further simplify to derive solution

<u><em>Hope that helps!</em></u>
Answer:
a, a + 1, a + 2
55, 56. 57
Step-by-step explanation:
Let the integers be :
a, a + 1, a + 2 (consecutive integers)
Hence, sum of the integers equals 168
a + (a + 1) + (a + 2) = 168
a + a + 1 + a + 2 = 168
3a + 3 = 168
3a = 168 - 3
3a = 165
a = 165 / 3
a = 55
first integer, a = 55
Second, a +1 = 56
Third, a + 2 = 57
Answer:
The ratio of the first term to the common difference is 1 : 2
Step-by-step explanation:
The rule of the sum of the AP is
, where
a is the first number
d is the common difference
n is the position of the number
∵
= 4 ×
⇒ (1)
→ Find
and 
∵ In
n = 10
∴ ![S_{10}=\frac{10}{2}[2a+(10-1)d]](https://tex.z-dn.net/?f=S_%7B10%7D%3D%5Cfrac%7B10%7D%7B2%7D%5B2a%2B%2810-1%29d%5D)
∴ ![S_{10}=5[2a+9d]](https://tex.z-dn.net/?f=S_%7B10%7D%3D5%5B2a%2B9d%5D)
∴
= 10a + 45d ⇒ (2)
∵ In
n = 5
∴ ![S_{5}=\frac{5}{2}[2a+(5-1)d]](https://tex.z-dn.net/?f=S_%7B5%7D%3D%5Cfrac%7B5%7D%7B2%7D%5B2a%2B%285-1%29d%5D)
∴ ![S_{5}=2.5[2a+4d]](https://tex.z-dn.net/?f=S_%7B5%7D%3D2.5%5B2a%2B4d%5D)
∴
= 5a + 10d ⇒ (3)
→ Substitute (2) and (3) in (1)
∵ 10a + 45d = 4[5a + 10d]
∴ 10a +45d = 20a + 40d
→ Subtract 40d from both sides
∴ 10a + 45d - 40d = 20a + 40d - 40d
∴ 10a + 5d = 20a
→ Subtract 10a from both sides
∴ 10a - 10a + 5d = 20a - 10a
∴ 5d = 10a
→ Divide both sides by 5
∴ d = 2a
→ That means d is twice a or a is half d
∴ a : d = 1 : 2
The ratio of the first term to the common difference is 1 : 2
Answer:
The unknown side (x) is 11.9 ft.
Step-by-step explanation:
x= 34.6 - 5.2 - 11.1 - 6.4 = 11.9
x = 11.9