<em>Answer is 2</em>
<em>If 8x = 16y </em>
<em>on rearranging question,</em>
<em> x/y = 16/8 = 2</em>
Y = 11.5x + 22
y = -13x + 218
when will their balance be the same.....ur basically just subbing in 1 y for the other and u get :
11.5x + 22 = -13x + 218....now we solve for x
11.5x + 13x = 218 - 22
24.5x = 196
x = 196 / 24.5
x = 8 <== they will be the same at 8 weeks
11.5(8) + 22 = 114
-13(8) + 218 = 114
and they will both have $ 114 at 8 weeks <===
Answer:
-2
Step-by-step explanation:
Given that:
A = (3, 4) ; B = (7, 6)
In triangle ABCD, AB and BC are Perpendicular lines :
Slope AB = Rise / Run = (y2 - y1) / (x2 - x1)
y2 = 6 ; y1 = 4 ; x2 = 7 ; x1 = 3
Slope AB = (6 - 4) / (7 - 3) = 2 / 4 = 1 / 2
To obtain the slope of BC:
RECALL:
product of the slope of 2 Perpendicular lines = - 1
Slope AB * Slope BC = - 1
1 / 2 * slope BC = - 1
Slope BC = - 1 ÷ 1/2
Slope BC = - 1 * 2/1
Slope BC = - 2
HENCE, slope of BC = - 2
Recall some identities:
tan(x) = sin(x) / cos(x)
cos(x + y) = cos(x) cos(y) - sin(x) sin(y)
cos(x - y) = cos(x) cos(y) + sin(x) sin(y)
sin(x - y) = sin(x) cos(y) - cos(x) sin(y)
This means we have
• cos²(90° - x) = [cos(90°) cos(x) + sin(90°) sin(x)]²
… = sin²(x)
• tan(180° - x) = sin(180° - x) / cos(180° - x)
… = [sin(180°) cos(x) - cos(180°) sin(x)] / [cos(180°) cos(x) + sin(180°) sin(x)]
… = sin(x) / (-cos(x))
… = -tan(x)
(and we also get sin(180° - x) = sin(x))
• cos(180° + x) = cos(180°) cos(x) - sin(180°) sin(x)
… = -cos(x)
So, the given expression reduces to
sin²(x) (-tan(x)) (-cos(x)) / sin(x) = sin²(x)
since tan(x) and cos(x)/sin(x) = 1/tan(x) will cancel.
