Answer:
70 m
Step-by-step explanation:
AB makes a 30-60-90 triangle with the wall.
AC makes a 45-45-90 triangle with the wall.
In a 30-60-90 triangle, the short leg (opposite of the 30° angle) is half the hypotenuse.
In a 45-45-90 triangle, the legs are the same length.
So the distance between the left wall and the laser is 60/2 = 30 m.
The distance between the right wall and the laser is 40 m.
The total distance is therefore 70 m.
Following transformations on Triangle ABC will result in the Triangle A'B'C'
a) Reflection the triangle across x-axis
b) Shift towards Right by 2 units
c) Shift upwards by 6 units
In Triangle ABC, the coordinates of the vertices are:
A (1,9)
B (3, 12)
C (4, 4)
In Triangle A'B'C, the coordinates of the vertices are:
A' (3, -3)
B' (5, -6)
C' (6, 2)
First consider point A of Triangle ABC.
Coordinate of A are (1, 9). If we reflect it across x-axis the coordinate of new point will be (1, -9). Moving it 2 units to right will result in the point (3, -9). Moving it 6 units up will result in the point (3,-3) which are the coordinates of point A'.
Coordinates of B are (3,12). Reflecting it across x-axis, we get the new point (3, -12). Moving 2 units towards right, the point is translated to (5, -12). Moving 6 units up we get the point (5, -6), which are the coordinate of B'.
The same way C is translated to C'.
Thus the set of transformations applied on ABC to get A'B'C' are:
a) Reflection the triangle across x-axis
b) Shift towards Right by 2 units
c) Shift upwards by 6 units
Answer:
y=76 degree(being vertically opposite angle)
y+x=180 degree(being linear pair)
76+x=180
x=180-76
x=104 degree
x=z(being vertically opposite angle)
104=z
therefore z=104 ,y=76,x=104
Step-by-step explanation:
Answer:
x = 1 and x = 2
x = 4 and x = -4
Step-by-step explanation:
Vertical asymptotes appear where the function does not have a value. This is most commonly when the denominator of a rational function is 0. Find the asymptotes by factoring the denominator and setting it equal to 0. Then solve for x.
<u>First equation</u>
x² - 3x + 2 factors into (x-1)(x-2)
When x-1 = 0, x = 1. When x-2=0, x = 2. The V.A. are at x = 1 and x = 2.
<u>Second equation</u>
x² - 16 factors into (x+4)(x-4)
When x+4= 0, x = -4. When x-4 = 0, then x = 4. The V.A. are at x = -4 and x = 4.
