Answer:
(-3, 0) and (1, 0)
(0, 4)
Step-by-step explanation:
x-intercept is the point where y = 0.
y-intercept is the point where x = 0.
or points ...
f(x) = y = -4×|x + 1| + 8
let's start with the y-intercept (x = 0)
y = -4×1 + 8 = -4 + 8 = 4
the y-intercept point (only 1 point) is (0, 4).
for x = 0 the absolute value function contains 0+1. and that is always +1.
the x-intercept(s) :
0 = -4×|x + 1| + 8 (dividing by -4)
0 = |x + 1| - 2
|x + 1| = 2
because of the absolute value we have 2 possibilities :
+(x + 1) = 2
x + 1 = 2
x = 1
and
-(x + 1) = 2
-x - 1 = 2
-x = 3
x = -3
so the points of x-intercept are (-3, 0) and (1, 0)
The largest common multiple of 2 and 3 is 24.
x = 30°.
The triangle drawn inside the circle is an equilateral and equiangular triangle which means that its three sides and its internal angles (that measure 60°) are equal.
To find x°:
First, we can see from the image that the tangent line to circle with arrows is formed a right angle, the angle of one side of the equilateral triangle, and the angle formed with the other side of the equilateral triangle, this three angles has to form 180° respect to the tangent line:
90° + 60° + y° = 180°
y° = 180° + 150°
y° = 30°
Second, the line in the right side of the equilateral triangle form an angle of 180°, so:
60° + z° = 180°
z° = 180° - 60°
z° = 120°
Finally, the triangle formed by this lines its internal angles are x°, y°, and z° and its sum is 180°, then:
x° + y° + z° = 180°
x° + 30° + 120° = 180°
x° + 150° = 180°
x° = 180° - 150°
x° = 30°
