Answer:
The Texas Declaration of Independence was signed in 1836 and the Texas Republic ratified its own constitution shortly after. In 1837, the U.S. formally recognized Texas as a nation, but the new country struggled economically without any of the resources of its larger neighbors, leading most (but not all) residents to welcome statehood by the time it came through in 1845. Only a little more than a decade passed, however, before the state tried to secede from its national government again, joining with the Confederacy in 1861.
Step-by-step explanation:
Area of a triangle= 1/2 (ab) (sin C)
= 1/2 (9 x 11.5) (sin 63.4)
= 46.27
Perpendicular lines refers to a pair of straight lines that intercept each other. The slopes of this lines are opposite reciprocal, meaning that it's multiplication is -1.
On this case they give you the equation of a line and a point, and is asked to find the equation of a line that is perpendicular to the given one, and that passes through this point.
-2x+3y=-6 Add 2x in both sides
3y=2x-6 Divide by 3 in both sides to isolate y
y=2/3x-6/3
The slope of the given line is 2/3, which means that the slope of a line perpendicular to this one, needs to be -3/2. Now you need to find the value of b or the y-intercept by substituting the given point into the formula y=mx+b, where letter m represents the slope.
y=mx+b Substitute the given point and the previous slope found
-2=(-3/2)(6)+b Combine like terms
-2=-9+b Add 9 in both sides to isolate b
7=b
The equation that represents the line perpendicular to -2x+3y=-6 and that passes through the point (6,-2), is y=-3/2x+7.
Answer: The answer is (C) 180° rotation.
Step-by-step explanation: Given that the point A maps to the point A' by a rotation. We are to select the statement that describes the rotation.
In the given figure, the co-ordinates of point A are (-3, 5) and after rotation, the co-ordinates of point A' are (3, -5).
Therefore, the point (x, y) changes to (-x, -y) after rotation. This is the result of 180° rotation.
Therefore, the point A is rotated through an angle of 180° to reach at the point A'.
Thus, the correct option is (C) 180° rotation.
