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.
Answer:
(x-7)^2+(y-8)^2=121
Step-by-step explanation:
Answer
Social security tax amount = $3348
Medicare tax amount = $743
Step by step explanation
The amount earned by Marcus = $54000
Social security tax = 6.2% = 6.2/100 = 0.062
Social security tax amount = 54000*0.062
Social security tax amount = $3348
Medicare tax = 1.45% = 1.45/100 = 0.0145
Medicare tax amount = 54000*0.0145
Medicare tax amount = $743
Hope this will help you.
Value of x is 9 and measure of each side is 35 units.
<u>SOLUTION:
</u>
Given, Triangle QRS is an equilateral triangle.
QR is seventeen more than twice x, 
RS is 19 less than six times x, 
And QS is one less four times x, 
We have to find x and measure of each side.
Now, we know that, sides of equilateral triangle are equal,
Then 
So, value of x is 9.
Hence, value of x is 9 and measure of each side is 35.
