A) The first step needs 100 bricks, the second needs 98, the third needs 96, and so on. Therefore the number of bricks for the nth step is: a_n = a_1 + d(n-1), where a_1 = 100 (the first term), d = -2 (difference).
a_n = 100 - 2(n-1) = 102 - 2n, and for the 30th step, a_30 = 102 - 2*30 = 42. So the top step will need 42 bricks.
b) The total staircase will need: 100 + 98 + 96 + ... + 44 + 42, and there are n = 30 terms. Using the formula for the sum of an arithmetic sequence:
S = (a_1 + a_n)*n/2 = (100 + 42)*30/2 = 2130
Therefore, 2130 bricks are required to build the entire staircase.
The empty jug weighs 0.75 lb
With the 3c, the total weighs 2.25 lb. That means:
3c + empty jug = 3c + 0.75 = 2.25
3c = 2.25 - 0.75
3c = 1.5
and 1c = 0.5 (so c is a constant -or the slope-)
Then the equation is:
y = 0.5x + 0.75
Answer:
The answer is True.
Step-by-step explanation:
- <u>Estimate the Answer Before Solving Having a general idea of a ballpark answer .</u>
- <u>Or the problem lets students know if their actual answer is reasonable or not.</u>
Answer:
There you go , happy to help
Answer:
x = 20
Step-by-step explanation:
(3x + 50) = (6x - 10)
Subtract 6x on each side
3x + 50 - 6x = -10
Combine the x values together
-3x + 50 = -10
Subtract 50 on each side
-3x = -60
Divide each side by -3
x = 20
