These two lines create vertical angles, which are congruent. That means angle z = 60 degrees. Since angle z and the angle represented by the expression 6x + 60 are supplementary (they are adjacent angles that add to equal 180 degrees), you can set up the following equation to find x:
6x + 60 + 60 = 180
6x + 120 = 180
6x = 60
x = 10
Answers:
x = 10
z = 60
(6+18)^2 = m^2 + m^2
=> 2m^2 = (24)^2
=> m = 24/sqrt(2)
Answer:
Q13. y = sin(2x – π/2); y = - 2cos2x
Q14. y = 2sin2x -1; y = -2cos(2x – π/2) -1
Step-by-step explanation:
Question 13
(A) Sine function
y = a sin[b(x - h)] + k
y = a sin(bx - bh) + k; bh = phase shift
(1) Amp = 1; a = 1
(2) The graph is symmetrical about the x-axis. k = 0.
(3) Per = π. b = 2
(4) Phase shift = π/2.
2h =π/2
h = π/4
The equation is
y = sin[2(x – π/4)} or
y = sin(2x – π/2)
B. Cosine function
y = a cos[b(x - h)] + k
y = a cos(bx - bh) + k; bh = phase shift
(1) Amp = 1; a = 1
(2) The graph is symmetrical about the x-axis. k = 0.
(3) Per = π. b = 2
(4) Reflected across x-axis, y ⟶ -y
The equation is y = - 2cos2x
Question 14
(A) Sine function
(1) Amp = 2; a = 2
(2) Shifted down 1; k = -1
(3) Per = π; b = 2
(4) Phase shift = 0; h = 0
The equation is y = 2sin2x -1
(B) Cosine function
a = 2, b = -1; b = 2
Phase shift = π/2; h = π/4
The equation is
y = -2cos[2(x – π/4)] – 1 or
y = -2cos(2x – π/2) - 1
Step-by-step explanation:
f(x)=2x+1 and g(x)=x²-7
(f/g)(x) = (2x+1)/(x²-7)
I believe it is -8 since the point where the line is x=80 and y=-10. Then you divide x/y (80/-10) and get -8.
