Cos² 2x = (1+cos 4x )/2
cos² 6x = (1+cos 12x)/2
subtract to get 1/2 (cos 4x - cos 12x )
= 1/2 (2 sin 4x sin 8x ) as cos A - cos B = 2 [ sin (A+B)/2 sin (A-B)/2 ]
so the answer
Answer:
30 miles in the morning and 60 in the afternoon.
Step-by-step explanation:
15+15= 30 or 2 hours
15+15+15+15= 4 hours (60miles)
A. 3x + y = 13 → 15x + 5y = 65
x - 5y = 15 → x - 5y = 15
16x = 80
16 16
x = 5
x - 5y = 15
5 - 5y = 15
- 5 - 5
-5y = 10
-5 -5
y = -2
(x, y) = (5, -2)
b. 6x - y = 14
2x + y = 12
8x = 26
8 8
x = 3¹/₄
6x - y = 14
6(3¹/₄) - y = 14
19¹/₂ - y = 14
- 19¹/₂ - 19¹/₂
-y = -5¹/₂
-1 -1
y = 5¹/₂
(x, y) = (3¹/₄, 5¹/₂)
c. 3x - 4y = 22 → 15x - 20y = 110
2x + 5y = 7 → 8x + 20y = 28
23x = 138
23 23
x = 6
3x - 4y = 22
3(6) - 4y = 22
18 - 4y = 22
- 18 - 18
-4y = 4
-4 -4
y = -1
(x, y) = (6, -1)
Answer:
Option C. 
Step-by-step explanation:
we know that
The equation of the parent function f(x) (red graph) is
This is a vertical parabola open upward
The vertex is the point (0,0) (the origin)
The function g(x) (blue graph) is a vertical parabola open upward
The vertex is the point (-5,0)
The transformation of f(x) to g(x) has the following rule
f(x) -----> g(x)
(0,0) ----> (-5,0)
(x,y) ----> (x-5,y)
That means----> The transformation is a translation of 5 units at left
therefore
The equation of g(x) is
In every right triangle, if you add up the squares of the two
shorter sides, you get the square of the longest side. If you
don't then it's not a right triangle.
10² = 100
24² = 576
100 + 576 = 676
676 is the square of 26.
It's NOT the square of 28.
So 10 - 24 - 28 is not a right triangle.
