This is a fairly tedious problem. The only way to solve that I see is to simply list out all the possible cases and go through each one by one. You'll use the triangle inequality theorem to see if the triangles can be formed. The theorem says that a+b > c must be true for all sets of pairs. In other words, take any two sides and add them up. The sum must be greater than the third side.
Going through all the combos possible (that I could find), this is what I got
Blue9,Green7,Orange4
Blue9,Green7,Purple12
Blue9,Green7,Red3
Blue9,Green7,Yellow5
Blue9,Orange4,Purple12
Blue9,Purple12,Yellow5
Green7,Orange4,Yellow5
Green7,Red3,Yellow5
Orange4,Red3,Yellow5
In all, I count 9 cases. So the answer to problem 1 is 9.
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For problem 2, the best way may be to pick two segments at a time instead of one. However, I have a feeling that will take just as long as the first method. I haven't tried it out. Even though going through the rods one at a time takes a while, it's probably the best option so you don't overlook any cases.
So,
y = mx + b is the slope-intercept form.
"m" represents the slope. It will allow you to find additional points on the specified line by determining the "rise" and the "run." The "rise" means vertical movement, and the "run" means horizontal movement.
"b" represents the y-intercept, which is the point on the line where x = 0. When x = 0, the line crosses, or intercepts, the y-axis.
Answer:
Step-by-step explanation:
let x be one part of the money invested.
let y be the other part of the money invested.
x *(10/100) -- amount on 10% of interest per annum
y*(7/100)- amount invested on 7% of interest per annum
x *(10/100) + y*(7/100) =1400
on simplifying it
10x +7y =140000 --(1)
On interchanging the interest rate on x amount and y amount of the investor
x *(7/100) + y*(10/100) =1490
7x +10y =149000-(2)
on solving equation (1) and (2) we get
70x +49y =980000
70x + 100y =1490000
-51y= -510000
y=10000
and x=7000
So our total amount invested is 17000
Answer:
13, -4
Step-by-step explanation:
If S is at 4, then for ST to = 8, you would add 8 to S, which you would get 13. You can also subtract 8 from S, which you would get -4.
