<u>Statement </u> <u>Reason</u>
1. AB = x + 16 1. Given
BC = 4x + 11
AC = 77
2. AB + BC = AC 2. Segment Addition Postulate
3. x + 16 + 4x + 11 = 77 3. Substitution Property
4. 5x + 27 = 77 4. Simplification <em>(added like terms)</em>
5. 5x = 50 5. Subtraction Property of Equality
6. x = 10 6. Division Property of Equality
7. AB = 10 + 16 7. Substitution Property
8. AB = 26 8. Simplification <em>(added like terms)</em>
Answer:Marvin burned more calories per hour.
Step-by-step explanation:
Thomas went for a long hike and burned 657 calories in 2 1/2 hours. Converting 2 1/2 hours to improper fraction, it becomes 5/2 hours
This means that the amount of calories that Thomas burnt in 1 hour would be 657 × 2/5 = 262.8 calories per hour
Marvin decided to go for a bike ride and burned 1,035 calories in 3 1/4 hours. Converting 3 1/4 hours to improper fraction, it becomes 13/4 hours
This means that the amount of calories that Thomas burnt in 1 hour would be 1035 × 13/4 = 3363.75 calories per hour
Therefore, Marvin burns more calories per hour.
Given:
Arithmetic sequence -5, 13, 31, 49..........
We are to find the explicit formula of the sequence above. An explicit formula provides a binding formula for finding nth term.
To find the formula, we need to know the first term and the common difference.
The common difference is the difference between each successive terms of the sequence.
In the given sequence, the common difference is 18;
13-(-5) = 18
31 - 13 = 18
49 - 31 = 18
n calculation of the nth term
1 -5 -5 + 18(0) = -5
2 13 -5 + 18(1) = 13
3 31 -5 + 18(2) = 31
4 49 -5 + 18(3) = 49
Since the common difference is 18, we can now derive the formula;
b(n) = -5 + 18(n-1)
n is the position of the term
Any number in the sequence can be derived using the explicit formula
-5 + 18(n-1)
Answer:
x = 114 inches
Step-by-step explanation:
The ratio of height to shadow length will be identical
x/72 = 76/48
x = 76(72)/48 114 inches
To find the number you can set up a small equation (x being the number) and solve for x.
It can be written as 2 ( x + 4) < 12
Solve for x to find the number.
2 ( x + 4) < 12
Distribute the 2
2x+8<12
Subtract 8 on both sides
2x<4
Divide by 2 on both sides
x<2
Therefore the number is any number less than 2
~I hope this helps!~
