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:
Left 7 down 6 Then count two spaces left right up and down and draw a circle
Step-by-step explanation:
Your answer is going to be in the bottom left corner, you count 7 vertical lines to the left, then from there you count 6 horizontal lines down. Since the Radius is 2 the diameter is 4. Good luck, if this wasn't helpful enough you can get a graphing calculator for yourself.
X= number of tubs Kasey sold
3x= number tubs sister sold
Add the number sold by Kasey and her sister to equal the total sold (88).
x + 3x= 88
combine like terms
4x= 88
divide both sides by 4
x= 22 number tubs Kasey sold
Number Sold by Sister
3x= 3(22)= 66
CHECK:
x + 3x= 88
22 + 3(22)= 88
22 + 66= 88
88= 88
ANSWER: Kasey sold 22 tubs and her sister sold 66 tubs.
Hope this helps! :)
Answer:
Trial- 2 shows the conservation of momentum in a closed system.
Step-by-step explanation:
Given: Mass of balls are 
Conservation of momentum in a closed system occurs when momentum before collision is equal to momentum after collision.
- Let initial velocity of ball
- Initial velocity of ball
- Final velocity of ball
- Final velocity of ball
- Momentum before collision
- Momentum after collision
Now, According to conservation of momentum.
Momentum before collision = Momentum after collision
We will plug each trial to this equation.
Trial 1
Trial 2
Trial 3
Trial 4
We can see only Trial 2 satisfies the princple of conservation of momentum. That is momentum before collison should equal to momentum after collision.
The rate at which the college student earns credit is 13 credits per semester.
<h3>What is an equation?</h3>
An equation is the statement that illustrates the variables given. In this case, two or more components are taken into consideration to describe the scenario.
Let the credit earned each semester be x.
This will be illustrated as:
5 + 2x = 31
Collect like terms
2x = 31 - 5
2x = 26
Divide
x = 26/2
x = 13
The rate is 13 credits per semester.
Learn more about equations on:
brainly.com/question/2972832
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