Answer:
A valid argument is reasoning that is comprehensive on the foundation of logic or fact. ... Therefore, inductive reasoning moves from specific instances into a generalized conclusion, while deductive reasoning moves from generalized principles that are known to be true to a true and specific conclusion.
17. y = -2/3x + 2
2/3x + y = 2
2x + 3y = 6 <==
18. y = 3x + 7....slope is 3. A parallel line will have the same slope.
y = mx + b
slope(m) = 3
(2,10)...x = 2 and y = 10
now sub and find b, the y int
10 = 3(2) + b
10 = 6 + b
10 - 6 = b
4 = b
so ur equation is : y = 3x + 4 <===
19. - 5x + 10y = 5
10y = 5x + 5
y = 1/2x + 1/2...slope is 1/2
y = -2x + 4....slope is -2
1/2 and -2 are negative reciprocals of each other....so ur lines are perpendicular
20. y = -1/4x + 8....slope is -1/4
-2x + 8y = 4
8y = 2x + 4
y = 1/4x + 1/2...slope here is 1/4
different slope and different y intercepts ...neither parallel or perpendicular
21. slope in the equation is 8/3. A perpendicular line will have a slope of -3/8.
y - y1 = m(x - x1)
slope(m) = -3/8
(-2,3)...x1 = -2 and y1 = 3
now we sub
y - 3 = -3/8(x - (-2) =
y - 3 = -3/8(x + 2) <==
Answer:
The answer is A. Both 1 and 4
Step-by-step explanation:
The answer is b. 72 square units.
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 ...