Answer:
The first term is 3. The common difference is 2.
Step-by-step explanation:
The first term is x.
The common difference is d.
The second term is x + d.
3rd term: x + 2d
4th term: x + 3d
7th term: x + 6d
"The fourth term of an Arithmetic Sequence is equal to 3 times the first term"
x + 3d = 3 * x Eq. 1
"the seventh term exceeds twice the third term by 1"
x + 6d = 2(x + 2d) + 1 Eq. 2
Simplify Eq. 1:
2x = 3d
Simplify Eq. 2:
x + 6d = 2x + 4d + 1
x = 2d - 1
Multiply both sides of the last equation by 2.
2x = 4d - 2
2x = 3d (simplified Eq. 1)
Since 2x = 2x, then the right sides are equal.
3d = 4d - 2
d = 2
2x = 3d
2x = 3(2)
2x = 6
x = 3
Answer: The first term is 3. The common difference is 2.
Answer:
A
Step-by-step explanation:
If you plug them in you get 2≥-1
Answer:
B
Step-by-step explanation:
Well you can get rid of c and d since 9^2 = 81. so 74 is less than 81 so it's definitely less than 9. Now, we know it's between 8 and 9. try multiplying 8.5 x 8.5 = 72.25. So our ranges are
A) 64 - 72.25
B) 72.25 - 81.
74 falls between 72.25 - 81. So it'll be B
Answer:
Step-by-step explanation:
Give the data
198 sq.yd × 8 sq ft ×7
Note that we have two unit of measurement which are yd and ft and 7 is just a constant
So we need to convert them,
Then, 1 yd = 3ft
Also notice that they are square.
Then square both sides of the comparison
(1 yd)² = (3 ft)²
1 sq.yd = 9 sq.ft
Then, back to our question,
198 sq.yd × 8 sq ft ×7
Let covert to ft
198 sq.yd× (9 sq.ft/1 sq.yd) ×8 sq.ft×7
sq.yd cancels out
99,792 sq.ft × sq.ft
99,792 ft⁴
Let convert to yd
198 sq.yd × 8 sq ft ×7
198 sq.yd×8 sq.ft (1 sq.yd / 9sq.ft )×7
1,232 sq.yd × sq.yd
1,232 yd⁴
9514 1404 393
Answer:
52 measures
Step-by-step explanation:
Let s represent the length of the second song. Then the first song's length is 108 -s, and the difference in length is ...
(108 -s) -(s) = 4
108 -2s = 4 . . . .collect terms
54 -s = 2 . . . . divide by 2
52 = s . . . . . add s-2
Grace's second song is 52 measures long.
