Let x = the first number
x+1 = the second number
The sum of our two numbers is therefore: x + (x+1)
When you subtract 13 from the above you get 18 left over.
So our equation is:
x + (x+1) - 13 = 18
Now we can just solve for x:
x + (x+1) = 31
2x + 1 = 31
2x = 30
x = 15
So our first number is 15 and our second number must be 16.
Since a triangles angles add up to 180 you would add the other sides and then
180-161=19
So angle 1 is 19 degrees
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Answer:
1: proportional
2: non-proportional
3: non-proportional
4: non-proportional
5: proportional
6: proportional
7: non-proportional
8: proportional
9. proportional.
10. proportional.
11. non-proportional.
12. proportional.
Step-by-step explanation:
I'm unsure how the proportional ones are actually calculated depending if it requires a dot on the exact origin, but depending on what I can graphically view and assume; every graph with the line running through the origin is proportional and every graph where the line does not run through the origin is non-proportional.
Let's make a table of differences
0 3 8 15 24
3 5 7 9
2 2 2
Constant second difference means a quadratic polynomial,
f(n)=an² + bn +c
f(1)=0, f(2)=3, f(3)=8
0 = a+b+c
3 = 4a + 2b + c
8 = 9a + 3b + c
Subtracting pairs
3 = 3a+b
5 = 5a + b
Subtracting,
2 = 2a
a = 1
b = 5 - 5a = 0
c = -a-b = -1
f(n)=n² -1
Duh, shoulda noticed that at the beginning.
f(17)=17²-1 = 288
a₁ =5
aₙ = aₙ₋₁ - 7
aₙ = a₁ + d(n-1)
aₙ = 5 - 7(n-1)
a₇ = 5 - 7(6) = -37
Answer: -37
