Symbolically, write this:
C
7 5. Know how to evaluate that?
C stands for "combination."
Y = |x² - 3x + 1|
y = x - 1
|x² - 3x + 1| = x - 1
|x² - 3x + 1| = ±1(x - 1)
|x² - 3x + 1| = 1(x - 1) or |x² - 3x + 1| = -1(x - 1)
|x² - 3x + 1| = 1(x) - 1(1) or |x² - 3x + 1| = -1(x) + 1(1)
|x² - 3x + 1| = x - 1 or |x² - 3x + 1| = -x + 1
x² - 3x + 1 = x - 1 or x² - 3x + 1 = -x + 1
- x - x + x + x
x² - 4x + 1 = -1 or x² - 2x + 1 = 1
+ 1 + 1 - 1 - 1
x² - 4x + 1 = 0 or x² - 2x + 0 = 0
x = -(-4) ± √((-4)² - 4(1)(1)) or x = -(-2) ± √((-2)² - 4(1)(0))
2(1) 2(1)
x = 4 ± √(16 - 4) or x = 2 ± √(4 - 0)
2 2
x = 4 ± √(12) or x = 2 ± √(4)
2 2
x = 4 ± 2√(3) or x = 2 ± 2
2 2
x = 2 ± √(3) or x = 1 ± 1
x = 2 + √(3) or x = 2 - √(3) or x = 1 + 1 or x = 1 - 1
x = 2 or x = 0
y = x - 1 or y = x - 1 or y = x - 1 or y = x - 1
y = (2 + √(3)) - 1 or y = (2 - √(3)) - 1 or y = 2 - 1 or y = 0 - 1
y = 2 - 1 + √(3) or y = 2 - 1 - √(3) or y = 1 or y = -1
y = 1 + √(3) or y = 1 - √(3) (x, y) = (2, 1) or (x, y) = (0, -1)
(x, y) = (2 ± √(3), 1 ± √(3))
The solution (0, -1) can be made by one function (y = x - 1) while the solution (2 ± √(3), 1 ± √(3)) can be made by another function (y = |x² - 3x + 1|). So the solution (2, 1) can be made by both functions, making the two solutions equal.
Linear functions can be written in the form y=mx+b, where:
y is a y coordinate on the line
m is the slope of the line
x is the x coordinate on the line that corresponds with the y coordinate in the equation
b is the y-intercept of the line
So for the equation y=-10x+1:
m=-10 and b=1 so the slope of the line is -10, and the y-intercept is 1. Your answer is B.
Answer: 122.5
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Explanation:
First thing to do is to find the perimeter of figure B. Add up all the sides and we get: 5+9+9+12 = 14+21 = 35.
The scale factor 7:2 means that if the perimeter of figure A was 7, then the perimeter of figure B would be 2. Or it could be 14 for A and 4 for B. And so on. The idea is that the two perimeters scale up or down together. This allows us to set up the proportion below in which we can solve for x
(perimeter of A)/(perimeter of B) = 7/2
x/35 = 7/2
x*2 = 35*7 .... cross multiply
2x = 245
2x/2 = 245/2 .... divide both sides by 2
x = 122.5
The perimeter of figure A is 122.5
