13, start with 24, right? 24 plus 6 is 30. 30 minus 12 is 18. 18 minus 5 is 13.
Call the smaller of the two odds = n
Call the next number in the sequence = n + 2
n*(n +2) = 782 Remove the brackets.
n^2 + 2n = 782 Subract 782 from both sides.
n^2 + 2n - 782 = 0 We are going to have to factor this.
Discussion
This problem can't be done the way it is written. The product of an odd integer with another odd integer is and odd integer. There are no exceptions to this. So you need to give a number that has two factors very near it's square root for this question to work.
For example, you could use 783, (which factors) instead of 782 .
Solve
n^2 + 2n - 783 = 0
(n + 29)(x - 27) = 0
<u>Solution One</u>
n - 27 = 0
n = 27
The two odd consecutive integers are 27 and 29.
<u>Solution Two</u>
n + 29 = 0
n = - 29
The two solution integers are -29 and - 27 Notice that - 29 is smaller than - 27.
Answer:
The answer would be 150,000 to 249,999
F(2)=2(3*2)+1
f(2)=2(6)+1
=13
answer is 13
In each case, you can use the second equation to create an expression for y that will substitute into the first equation. Then you can write the result in standard form and use any of several means to find the number of solutions.
System A
x² + (-x/2)² = 17
x² = 17/(5/4) = 13.6
x = ±√13.6 . . . . 2 real solutions
System B
-6x +5 = x² -7x +10
x² -x +5 = 0
The discriminant is ...
D = (-1)²-4(1)(5) = -20 . . . . 0 real solutions
System C
y = 8x +17 = -2x² +9
2x² +8x +8 = 0
2(x+2)² = 0
x = -2 . . . . 1 real solution
