Answer:
The slope of the line passing through the points (−3, −5) and (−1, −6) is 
(-0.5)
Step-by-step explanation:
Equation of a straight line:
y = mx + b where m is the slope and b is the y-intercept
(x1, x2) and (y1, y2) : (−3, −5) and (−1, −6)
Calculating Slope (m).
m = 
m = 
m = 
m =
we can take this a step further by finding the equation:
Now putting value of m in equation (i)
y = -0.5x + b
Calculating Y-intercept (b).
Lets choose the first point, (-3,-5) for calculating y-intercept:
y = mx + b
-5 = -0.5(-3) + b
-5 = 1.5 + b
-6.5 = b
b = -6.5
Now putting value of b in equation
y = -0.5x + -6.5
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.
Where is the figure?or is there not
When we say bar magnet, this is a kind of magnet that is rectangular in shape and possesses magnetic properties. Based on the statements above, the one that is true regarding a bar magnet is that, its poles cannot be separated into two isolated poles. The answer would be the third option. Hope this helps.
Answer:
16
Step-by-step explanation:
You plug in the value of y into the expression:
5(2) + 3(2)
10 + 6 = 16
