Each edge of the inner square has a length of √[(x/2)²+(x/2)²]=√2x²/4=(x√2)/2
Then, the area is 2x²/4=x²/2 ☺☺☺☺
Answer:
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Given lines:
- 3x + y = 1 and y + 6 = - 3x
Convert both equations to slope-intercept form of y = mx + b:
- 3x + y = 1 ⇒ y = - 3x + 1
- y + 6 = - 3x ⇒ y = - 3x - 6
Slopes are same, so these are parallel lines, and the distance between parallel lines is:
- , where b₁, b₂ - y-intercepts, m- slope
Substitute and calculate:
(10x+5) + (6x-1)=180
10x+5+6x-1=180
16x+4=180
16x+4=180
16x=180-4
16x=178
x=11
1. The linear equation:
y = m x + b
m = 3
- 2 = 3 · 1 + b
- 2 = 3 + b
b = - 5
Answer: A ) y = 3 x - 5
2. We will solve the system of equations:
12 = - 4 m + b / · ( - 1 )
23 = 7 m + b
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- 12 = 4 m - b
+
23 = 7 m + b
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11 = 11 m, m = 1, b = 16
Answer: A ) y = x + 16