How many line segments can be drawn between each 15 points? No three points are in straight line.
Which five consecutive numbers equals 175?
Farmer has ducks and cows in his farm. If all together t animals have 60 heads and 70 feet how many ducks and how many cows does farmer has?
<<Which five consecutive numbers equals 175?>>
The average is 175/5 = 35, and that must be the "middle" number.
Since they are consecutive integers, they are 33, 34, 35, 36 and 37
You must have copied the last question incorrectly, unless there are a lot on one-legged cows and ducks
Consider one of the points. If there are n points, you can draw n-1 lines from that point to the others.
By the time you have drawn all lines from n points, you have drawn n(n-1) lines. But each line is drawn twice. The line from point 6 to point 3 is the same line as was already drawn from point 3 to point 6.
There are thus n(n-1)/2 lines.
For this problem, n=15.
To find the number of line segments that can be drawn between 15 points, you can use the formula for the number of line segments formed by n points, which is given by nC2, also known as the binomial coefficient. In this case, you have 15 points, so the number of line segments is calculated as:
15C2 = (15 * 14) / (2 * 1) = 105
Therefore, there can be 105 line segments drawn between the 15 points.
To find five consecutive numbers that equal 175, you can use algebraic equations. Let's assume the five consecutive numbers are n, n+1, n+2, n+3, and n+4. Then, you can set up the equation:
n + (n+1) + (n+2) + (n+3) + (n+4) = 175
Simplifying the equation:
5n + 10 = 175
5n = 165
n = 165/5
n = 33
So, the consecutive numbers that equal 175 are 33, 34, 35, 36, and 37.
To determine the number of ducks and cows the farmer has based on the total number of animals and the number of heads and feet, you can set up a system of equations. Let's assume the farmer has d ducks and c cows.
The number of heads can be represented as:
d + c = 60
The number of feet can be represented as:
2d + 4c = 70 (since each duck has 2 feet and each cow has 4 feet)
To solve this system of equations, we can multiply the first equation by 2 and subtract it from the second equation to eliminate the variable d:
2d + 4c - 2d - 2c = 70 - 2 * 60
2c = -50
c = -50/2
c = -25
Since we cannot have a negative number of cows, there must be an error in the given information or assumptions.