Answer:
x=9,-1 and 
Explanation:
We are given the quadratic equation 
, which we then compare with the standard form of a quadratic. The general quadratic is identified as 
. From our given equation, it follows that a=1,b=-8,c=-9
. To calculate the discriminant, we insert these values into the formula 
. Now, to find the value of x
The formula is 
. The resulting equation will be obtained by rewriting the original equation through rearranging 9 to the right side and applying negative signs within brackets to convert the expression into the form of
.
Answer:
Answer choice C. 
.
Step-by-step explanation:
The entire question is present in the attached figure.
It is established that
The function f(x) is represented by
,
indicating a parabola that opens upward.
The vertex is situated at the point (0,0).
The function g(x) shares the same parabolic shape.
The vertex of g(x) is located at (-3,1).
Therefore,
The transformation from f(x) to g(x) can be described as:
(0,0) transforms to (-3,1).
(x,y) transforms to (x-3,y+1).
This indicates a shift of 3 units to the left and 1 unit upward.
Thus,
The equation for g(x) in vertex form can be expressed as
.
Answer:
He is dividing the angle BAC into two equal parts.
Step-by-step explanation:
Initially, he places the compass at point A and draws two small arcs intersecting points D and E. Next, setting the compass at D and then at E, he draws two arcs that intersect between the line segments AB and AC.
The bisecting line is drawn from point A through the intersection of these arcs.
Distance formula:
5 units-4.5 units=0.5 units
Segment LM exceeds segment JK by 0.5 units.
Assuming arcs are measured in degrees, let S represent the following sum:
S = sin 1° + sin 2° + sin 3° +... + sin 359° + sin 360°
By rearranging, S can be reformulated as
S = [sin 1° + sin 359°] + [sin 2° + sin 358°] +... + [sin 179° + sin 181°] + sin 180° +
+ sin 360°
S = [sin 1° + sin(360° – 1°)] + [sin 2° + sin(360° – 2°)] +... + [sin 179° + sin(360° – 179)°]
+ sin 180° + sin 360° (i)
However, for any real k,
sin(360° – k) = – sin k
Thus,
S = [sin 1° – sin 1°] + [sin 2° – sin 2°] +... + [sin 179° – sin 179°] + sin 180° + sin 360°
S results in 0 + 0 +... + 0 + 0 + 0 (... since sine of 180° and 360° are both equal to 0)
Therefore, S equals 0.
Each pair within the brackets negates itself, leading the sum to total zero.
∴ sin 1° + sin 2° + sin 3° +... + sin 359° + sin 360° equals 0. ✔
I hope this clarifies things. =)
Tags: sum summatory trigonometric trig function sine sin trigonometry
