The length of side A is 194
Step-by-step explanation:
a triangular number n is the sum of all natural numbers <= n.
t1 = 1
t2 = 1+2 = 3
t3 = 1+2+3 = 6
t4 = 1+2+3+4 = 10
...
so,
tn = tn-1 + n
47.
1×8 + 1 = 9 is a square number.
3×8 + 1 = 25 is a square number
6×8 + 1 = 49 is a square number
10×8 + 1 = 81 is a square number
48.
1/3 = 0 remainder 1
3/3 = 1 remainder 0
6/3 = 2 remainder 0
10/3 = 3 remainder 1
15/3 = 5 remainder 0
21/3 = 7 remainder 0
28/3 = 9 remainder 1
so, there seems to be a pattern 1 0 0 1 0 0 1 0 0 1 ...
49.
1/4 = 0 remainder 1
4/4 = 1 remainder 0
9/4 = 2 remainder 1
16/4 = 4 remainder 0
25/4 = 6 remainder 1
36/4 = 9 remainder 0
49/4 = 12 remainder 1
so, there seems to be a pattern 1 0 1 0 1 0 1 0 1 0 1 ...
50.
polygonal numbers is the real name for this.
the formula for dimensions = 5 is
(3n² − n)/2
for dimensions = 6 it is
2n² - n
so, dimensions=5 (and therefore dividing also by 5) we get the remainders
1/5 = 0 remainder 1
5/5 = 1 remainder 0
12/5 = 2 remainder 2
22/5 = 4 remainder 2
35/5 = 7 remainder 0
51/5 = 10 remainder 1
70/5 = 14 remainder 0
92/5 = 18 remainder 2
117/5 = 23 remainder 2
145/5 = 29 remainder 0
here the pattern is 1 0 2 2 0 1 0 2 2 0 1 0 2 2 0 ...
dimensions=6 (and therefore dividing also by 6) we get the remainders
1/6 = 0 remainder 1
6/6 = 1 remainder 0
15/6 = 2 remainder 3
28/6 = 4 remainder 4
45/6 = 7 remainder 3
66/6 = 11 remainder 0
91/6 = 15 remainder 1
120/6 = 20 remainder 0
153/6 = 25 remainder 3
190/6 = 31 remainder 4
231/6 = 38 remainder 3
276/6 = 46 remainder 0
325/6 = 54 remainder 1
here the pattern is 1 0 3 4 3 0 1 0 3 4 3 0 1 0 3 4 3 0 ...
Answer:
0
Step-by-step explanation:
To find the slope between the two given points, you can use the given formula for the slope between two points.
__
<h3>given</h3>
The points are (x1, y1) = (-3, 2) and (x2, y2) = (4, 2).
The formula is ...
slope = (y2 -y1)/(x2 -x1)
__
<h3>use the formula</h3>
Substituting the given values into the formula gives ...
slope = (2 -2)/(4 -(-3)) = 0/7 = 0
The slope of the line is zero.
Answer:
Mean volume shipped per trailer load = 2960 ft³
Step-by-step explanation:
Since both trailers are always full,
Total volume in one 30 feet trailer shipment = 8 × 10 × 30 = 2400 ft³
Total volume in one 40 feet trailer shipment = 8 × 10 × 40 = 3200 ft³
Assuming a basis of 10 shipments, 3 shipments are done using the 2400 ft³ trailer and 7 shipments are done using the 3200 ft³ trailer.
Mean volume shipped per trailer load = total volume shipped/number of shipments
Total volume shipped = (3 × 2400) + (7 × 3200) = 7200 + 22400 = 29600 ft³
Number of shipment in the basis used = 10
Mean volume shipped per trailer load = 29600/10 = 2960 ft³
