B is the midpoint of AC, D is the midpoint of CE, and AE = 9. Find BD.
1 answer:
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Answer:
The required inequalities are and
.
Step-by-step explanation:
Consider the provided information.
Daniel moves no more than 30 of his sheep and goats into another field.
Let s represent the number of sheep and g represent the number of goats.
No more than means the number of sheep and goats should be less than or equal to 30.
For less than or equal to use the inequality ≤
Hence the required inequality is:
More than 7 of his animals are sheep.
This can be represented as:
Hence, the required inequalities are and
.
Answer:
1. Juan's marathon training schedule is an example of a geometric sequence
2. Lizzy's marathon training schedule is an example of an arithmetic sequence
3. Lizzy will be better prepared for the marathon
Step-by-step explanation:
In the arithmetic sequence there is a common difference between each two consecutive terms
In the geometric sequence there is a common ratio between each two consecutive terms
Juan's Schedule
∵ Juan's will run one mile on the first day of the week
∴ = 1
∵ He will double the amount he runs each day for the next
6 days
- That means he multiplies each day by 2 to find how many miles
he will run next day
∴ = 1 × 2 = 2 miles
∴ = 2 × 2 = 4 miles
∴ = 4 × 2 = 8 miles
∴ = 8 × 2 = 16 miles
∴ = 16 × 2 = 32 miles
∴ = 32 × 2 = 64 miles
That means there is a common ratio 2 between each two consecutive days
1. Juan's marathon training schedule is an example of a geometric sequence
Lizzy's Schedule
∵ Lizzy's will run 10 miles on the first day of the week
∴ = 10
∵ She will increase the amount she runs by 3 miles each day for
the next six days
- That means she adds each day by 3 to find how many miles
she will run next day
∴ = 10 + 3 = 13 miles
∴ = 13 + 3 = 16 miles
∴ = 16 + 3 = 19 miles
∴ = 19 + 3 = 22 miles
∴ = 22 + 3 = 25 miles
∴ = 25 × 3 = 28 miles
That means there is a common difference 3 between each two consecutive days
2. Lizzy's marathon training schedule is an example of an arithmetic sequence
The rule of the sum of nth term in the geometric sequence is
∵ = 1 , r = 2 and n = 7
∴
∴ = 127
∴ Juan will run 127 miles in the final week
The rule of the sum of nth term in the arithmetic sequence is
∵ n = 7, = 10 and
= 28
∴
∴ = 133
∴ Lizzy will run 133 miles in the final week
∵ 133 miles > 127 miles
∴ Lizzy will run more miles than Juan
3. Lizzy will be better prepared for the marathon