Answer:
Step-by-step explanation:
Simplifying
2m + -6n + 5n + 3m = 0
Reorder the terms:
2m + 3m + -6n + 5n = 0
Combine like terms: 2m + 3m = 5m
5m + -6n + 5n = 0
Combine like terms: -6n + 5n = -1n
5m + -1n = 0
Solving
5m + -1n = 0
Solving for variable 'm'.
Move all terms containing m to the left, all other terms to the right.
Add 'n' to each side of the equation.
5m + -1n + n = 0 + n
Combine like terms: -1n + n = 0
5m + 0 = 0 + n
5m = 0 + n
Remove the zero:
5m = n
Divide each side by '5'.
m = 0.2n
Simplifying
m = 0.2n
Answer:
974
Step-by-step explanation:
Initial × Increase percentage ^ Time
500 × (1 + 10%)^(70/10)
500 × 1.1^7
= 974.36
The population of the town in 70 years will be 974.
Answer:
√3 is irrational
Step-by-step explanation:
The location of the third point of a triangle can be found using a rotation matrix to transform the coordinates of the given points.
<h3 /><h3>Location of point C</h3>
With reference to the attached figure, the slope of line AC is √3, an irrational number. This means the line AC <em>never passes through a point with integer coordinates</em>. (Any point with integer coordinates would be on a line with rational slope.)
<h3>Equilateral triangle</h3>
The line segments making up an equilateral triangle are separated by an angle of 60°. If two vertices are on grid squares, the third must be a rotation of one of them about the other through an angle of 60°. The rotation matrix is irrational, so the rotated point must have irrational coordinates.
The math of it is this. For rotation of (x, y) counterclockwise 60° about the origin, the transformation matrix is ...
![\left[\begin{array}{cc}\cos(60^\circ)&\sin(60^\circ)\\-\sin(60^\circ)&\cos(60^\circ)\end{array}\right] \left[\begin{array}{c}x\\y\end{array}\right]=\left[\begin{array}{c}x'\\y'\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D%5Ccos%2860%5E%5Ccirc%29%26%5Csin%2860%5E%5Ccirc%29%5C%5C-%5Csin%2860%5E%5Ccirc%29%26%5Ccos%2860%5E%5Ccirc%29%5Cend%7Barray%7D%5Cright%5D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7Dx%5C%5Cy%5Cend%7Barray%7D%5Cright%5D%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7Dx%27%5C%5Cy%27%5Cend%7Barray%7D%5Cright%5D)
Cos(60°) is rational, but sin(60°) is not. For any non-zero rational values of x and y, the sum ...
cos(60°)·x + sin(60°)·y
will be irrational.
As in the attached diagram, if one of the coordinates of the rotated point (B) is zero, then one of the coordinates of its image (C) will be rational. The other image point coordinate cannot be rational.
Answer:
3 each
Step-by-step explanation:
36 / 12 = 3
.................................................
5x+4y = 73
-4x + 4y = -8
5x + 4y -(-4x+4y) = 73 -(-8)
5x + 4y + 4x - 4y = 81
5x + 4x + 4y - 4y = 81
9x = 81
x = 81÷9
x = 9
Substitute x = 9 into any of the equations to find y.
5(9) + 4y = 73
45 + 4y = 73
4y = 73 - 45
4y = 28
y = 28÷4
y=7
Answers :
x = 9
y = 7