We will use demonstration of recurrences<span>1) for n=1, 10= 5*1(1+1)=5*2=10, it is just
2) assume that the equation </span>10 + 30 + 60 + ... + 10n = 5n(n + 1) is true, <span>for all positive integers n>=1
</span>3) let's show that the equation<span> is also true for n+1, n>=1
</span><span>10 + 30 + 60 + ... + 10(n+1) = 5(n+1)(n + 2)
</span>let be N=n+1, N is integer because of n+1, so we have
<span>10 + 30 + 60 + ... + 10N = 5N(N+1), it is true according 2)
</span>so the equation<span> is also true for n+1,
</span>finally, 10 + 30 + 60 + ... + 10n = 5n(n + 1) is always true for all positive integers n.
<span>
</span>
Answer:
Smaller number-47.5
Larger number-52.5
Step-by-step explanation:
We will make the smaller number x. If the smaller number is x, then the larger number will be equal to x+5. We also know that when we add the two numbers, we get 100. We can make the equation
x+x+5=100
100-5=95
2x=95
95/2=47.5
x=47.5
The smaller number equals 47.5 and the larger number is 47.5+5 which equals 52.5
Ok, so basically, proportionate pieces mean that the lengths in each section of the diagram are proportional:
2/q = 3/4 = 4/p
Using this, you could find that q = 2/3 and p = 4/3
For 15 to 20, change the equation from y=mx+b into mx-y=-b
Example: 15) y=-5x+2 into -2=-5x-y or 2=5x+y
For 21-29, the numbers in the parenthesis are coordinates (x, y) so uh the equation y=mx+b plug in the m that is given and x and y and then solve for b to complete the equation
Ex: 21) (-8,3) m=2
Y=mx+b
3=2(3)+b
3=6+b
-3=b
So y=2x-3
Do the same to the others
