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Marianna [84]
3 years ago
6

Constructing a brick staircase: A brick staircase has a total of 30 steps. The bottom step requires 100 bricks. Each successive

step requires two less bricks than the prior step
a) How many bricks are required for the top shelf?
b) How many bricks are required to build the staircase

Sequences, Pre-Calc
Show all work :)
Mathematics
1 answer:
galben [10]3 years ago
7 0
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.
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baherus [9]
No, it is not.

4/7 ≈ 0.5714

3/5 = 0.6

Actually, 3/5 is greater than 4/7.

Another way you could do this is by multiplying 4/7 with 5/5 and by multiplying 3/5 with 7/7.

4/7 * 5/5 = 20/35

3/5 * 7/7 = 21/35

Have an awesome day! :)
6 0
2 years ago
15 POINTS!!!!!! PLEASE HELP!!The length of a rectangle is four times its width. If the perimeter is at most 130 centimeters, wha
marin [14]
Here is the information we have:

1. The perimeter is at most 130 cm.
2. The length of the rectangle is 4 times the width.
    We can let l stand for length and w for width.

The formula for the perimeter of a rectangle is 2l + 2w.
We have to change the formula a bit.
The length of this rectangle is going to be 4 times the width
So, replace 2l with 2(4w).

Then make this equation equal to 130.

2(4w) + 2w = 130 ; Start
8w + 2w = 130      ; Distribute the 2 across the 4w
10w = 130             ; Combine the like terms 8w and 2w
w = 13                   ; Divide both sides by the coefficient of w. Which is 10

8 0
3 years ago
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Ugo [173]

Answer:

The choice Draw 2

Step-by-step explanation:

3(8 - 4x) < 6(x - 5) \\ 24 - 12x < 6x - 30 \\  24- 12x + 12x < 6x + 12x - 30 \\ 24 < 18x - 30 \\ 24 + 30 < 18x - 30 + 30 \\ 54 < 18x \\ 54 \div 18 < 18x \div 18 \\ 3 < x \\ x > 3

I hope I helped you^_^

6 0
3 years ago
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Answer:

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Step-by-step explanation:

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