Perpendicular lines refers to a pair of straight lines that intercept each other. The slopes of this lines are opposite reciprocal, meaning that it's multiplication is -1.
On this case they give you the equation of a line and a point, and is asked to find the equation of a line that is perpendicular to the given one, and that passes through this point.
-2x+3y=-6 Add 2x in both sides
3y=2x-6 Divide by 3 in both sides to isolate y
y=2/3x-6/3
The slope of the given line is 2/3, which means that the slope of a line perpendicular to this one, needs to be -3/2. Now you need to find the value of b or the y-intercept by substituting the given point into the formula y=mx+b, where letter m represents the slope.
y=mx+b Substitute the given point and the previous slope found
-2=(-3/2)(6)+b Combine like terms
-2=-9+b Add 9 in both sides to isolate b
7=b
The equation that represents the line perpendicular to -2x+3y=-6 and that passes through the point (6,-2), is y=-3/2x+7.
Second question isn't well formatted
Answer:
Number of republicans = 207
Number of democrats = 245
Step-by-step explanation:
Let :
Number of republicans = x
Number of democrats = x + 38
Total number of representatives from the two parties = 452
Tge number of representatives from each party can be calculated thus ;
Number of democrats + number of republicans = total number of representatives
(x + 38) + x = 452
x + 38 + x = 452
2x = 452 - 38
2x = 414
x = 414 / 2
x = 207
Number of republicans = 207
Number of democrats = 207 + 38 = 245
He will earn $427.50 because $4.27 times 90 equals $427.50
24-3x=2x-1
+3x. +3x
24=5x-1
+1. +1
25=5x
X=5
Answer:
Step-by-step explanation:
9 quarters and 8 dimes
9Q= 2.25
8D= 0.80
If you add then together you would get 2.05
