Answer:
1
+6
x
+
12
x
2
+
8x
3
Explanation:
We must use our knowledge of the binomial expansion:
Method 1:
We can use:
(
x
+
1
)
n
=
1
+
n
x
+
n
(
n
−
1
)
2
!
x
2
+
n
(
n
−
1
)
(
n
−
2
)
3
!
x
3
+
...
Substituting
n
=
3
and
x
for
2
x
⇒
(
2
x
+
1
)
3
=
1
+
(
3
⋅
2
x
)
+
3
⋅
2
2
!
⋅
(
2
x
)
2
+
3
⋅
2
⋅
1
3
!
⋅
(
2
x
)
3
=
1
+
6
x
+
12
x
2
+
8
x
3
Method 2:
We can use:
(
A
+
B
)
n
=
A
n
+
(
n
1
)
A
n
−
1
B
1
+
(
n
2
)
A
n
−
2
B
2
+
...
Letting
A
=
2
x
and
B
=
1
for this circumstance:
(
2
x
+
1
)
3
=
(
2
x
)
3
+
(
3
1
)
(
2
x
)
2
(
1
)
+
(
3
2
)
(
2
x
)
1
(
1
)
2
+
(
3
3
)
(
2
x
)
0
(
1
)
3
=
8
x
3
+
12
x
2
+
6
x
+
1
Step-by-step explanation:
The correct answer is 702.
To solve for the next number, we need to assign a variable for the unknown number and let that be equal to X.
Then we have the solution below:
7+2+0+7=16
2+0+7+8=17 where 17=16+1
0+7+8+4=19 where 19=17+2
7+8+4+3=22 where 22=19+3
8+4+3+x=26 where 26=22+4
Therefore, the value of x is 11.
Answer:
The answers to all the questions are given below.
Step-by-step explanation:
8)The ratio of the numbers 27 feet and 54 yard
1 foot = 0.3333 yard
27 feet = 9 yard
Required ratio = 
= 0.167
9)A 17 ounce bag costs $5.27.
Hence cost of 1 ounce bag = 
= $0.31
12)For trip of 240 miles ,it uses 8 gallons.
13)1 quart = 0.25 gallons
Hence the ratio would be 
14)1 pound = 0.0005 tonnes.
Hence the ratio would be 
19)1 week = 7 days
So the ratio would be 
These are the required ratios
Formula for triangle area = base times height over two. area of smallest triangle: 2*2/2, so 2. area of medium sized triangle: 2*6/2, so 6. the square in between those triangles has an area of four (2*2). the base of the largest triangle is 2+2+6, so 10, and the height is 4. use the formula to find its area is 20. add them all together to get 4+6+4+20 is 34 units^2.
