Answer:
9) Lines AB and CD are parallel lines
31)
- t = (A -P)/(Pr)
- y = (3/4)x -3
- a = -c
- y = ((a-c)x +d)/a
Step-by-step explanation:
9) Lines can be designated by a name on the line or by a pair of points on the line. In this figure, there are not enough angle-value indicators to show any ilnes as being parallel. It appears as though there is a direction indicator between A and B on that line, and possibly a matching one on the line below between C and D. (The figure is cut off.) If so, then that shows AB is parallel to CD.
31a) Your working is correct. You need to be careful with fractions. When the division bar is horizontal, it clearly identifies the numerator and denominator:
[tex]t=\dfrac{A-P}{Pr}[/tex]
When the division bar is slanted, it does not. Parentheses are needed around both the numerator and denominator, if they are anything other than a single number or variable. The answer you wrote would properly say ...
... (A - P)/(Pr) = t
31b) Add the opposite of everything that is not the y-term on the side with the y-term, then divide by the coefficient of y.
... -4y = -3x +12 . . . . . add -3x
... y = (3/4)x -3 . . . . . . divide by the coefficient of y
31c) Another way to work something like this (with the variable on both sides) is to subtract one side from the other. It can work well to subtract the side with the smallest coefficient of the variable of interest. (Here, that's 2 on the left side.) Then simplify, divide by the variable coefficient, and add the opposite of everything that is not the variable.
... 0 = 4a -2(a -c) . . . . . subtract the left side
... 0 = 2a +2c . . . . . . . . simplify
... 0 = a + c . . . . . . . . . . divide by the coefficient of a
... -c = a . . . . . . . . . . . . add the opposite of stuff that is not a
31d) We can work this the same way as the previous problem. Here the variable coefficient is negative on the right, so we'll subtract the right side.
... cx -d -a(x -y) = 0
... x(c -a) -d +ay = 0 . . . . . eliminate parentheses, then collect x-terms
... (x(c -a) -d)/a +y = 0 . . . .divide by a
... y = (x(a -c) +d)/a . . . . . . add the opposite of stuff that is not y
