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:
y = 1/3x + 5/3
Step-by-step explanation:
An equation contains a slope and y-intercept, in the form y = mx + b. To find the slope or m, you need to plug the coordinates into the slope formula.
y2 - y1/ x2 - 1
3 - 0/ 4 - (-5)
= 3 / 9
= 1/3
Now that we know the slope, we need to plug the values of x and y to find the y-intercept.
y = 1/3x + b
3 = 1/3(4) + b
3 = 4/3 + b
5/3 = b
The equation is y = 1/3x + 5/3
Answer:
where's the picture bro?
Step-by-step explanation:
Answer:
See attachment
Step-by-step explanation:
We want to graph 
on the interval -10 to 10.
Let 
be the parent absolute value function.
We can easily graph , if we use translation.
When the parent function is shifted downwards by 12 units, we obtain the graph of .
The parent function is a v-shaped graph with vertex at the origin.
We shift the parent function down so that its vertex is now at (0,-12) to get the graph of .
See attachment for the graph of on the specified interval.
Answer:
Thus the last row has 119 seats.
The total number of seats in 24 rows = 1476
Step-by-step explanation:
The number of seats in each row make an arithmetic series. We will use arithmetic equation to find the number of seats in last row:
An = a1+ (n-1)d
An = 4+(24-1)5
An = 4 + (23)(5)
An = 4 + 115
An = 119
Thus the last row has 119 seats.
Now to find the sum of seats we will apply the formula:
Sn = n(a1 + an)/2
Sn = 24(4+119)/2
Sn = 24(123) /2
Sn = 1476 .....
The total number of seats in 24 rows = 1476....
