First, let's convert each line to slope-intercept form to better see the slopes.
Isolate the y variable for each equation.
2x + 6y = -12
Subtract 2x from both sides.
6y = -12 - 2x
Divide both sides by 6.
y = -2 - 1/3x
Rearrange.
y = -1/3x - 2
Line b:
2y = 3x - 10
Divide both sides by 2.
y = 1.5x - 5
Line c:
3x - 2y = -4
Add 2y to both sides.
3x = -4 + 2y
Add 4 to both sides.
2y = 3x + 4
Divide both sides by 2.
y = 1.5x + 2
Now, let's compare our new equations:
Line a: y = -1/3x - 2
Line b: y = 1.5x - 5
Line c: y = 1.5x + 2
Now, the rule for parallel and perpendicular lines is as follows:
For two lines to be parallel, they must have equal slopes.
For two lines to be perpendicular, one must have the negative reciprocal of the other.
In this case, line b and c are parallel, and they have the same slope, but different y-intercepts.
However, none of the lines are perpendicular, as -1/3x is not the negative reciprocal of 1.5x, or 3/2x.
<h3><u>B and C are parallel, no perpendicular lines.</u></h3>
Five dimes and one quarter = .75.
9.75/.75=3.25*4/1=13
there are 13 "5 dimes and 1 quarter"s
so 65 dimes
Subtract corresponding x and y components
- u - v = - <- 8, 4> - <2, 7> = <8, - 4> - <2, 7> = <8 - 2, - 4 - 7> = <6, - 11>
u - v = <- 8, 4> - <2, 7> = <- 8 - 2, 4 - 7> = <- 10, - 3>
v - u = <2, 7> - <- 8, 4> = <2 + 8, 7 - 4> = <10, 3>
1. 13
2. 20
3. 4
4. 40
5. 4
6. 4
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Below are the choices and the answer is C.
A. T<span>he way he or she scores points.
</span>B. <span>The number of turns he or she gets to take
</span>C. <span>The actions expected of him or her.
</span>D, <span>The name of his or her character.</span>
