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.
Answer:
4894
Step-by-step explanation:
I know that it is divisible by 2, because it is an even number, and also the one's digit has 4, which is divisible by 2.
hope this helps :3
This exponential growth/decay (in this case decay because r<1) of the form:
f=ir^t, f=final value, i=initial value, r=common ratio or "rate", t=time.
Since the population decreases by 4.5% each year the common ratio is:
r=(100-4.5)/100=0.955 so we can say
P(t)=8500(0.955^t)
....
7000=8500(0.955^t)
14/17=(955/1000)^t taking the natural log of both sides
ln(14/17)=t ln(955/1000)
t=ln(14/17)/ln(955/1000)
t≈4.22 years (to nearest hundredth of a year)
Since t is the years since 2010, the population will fall to 7000 in the year (2010+4.22=2014.22, more than four years will have elapsed) 2015.
The interest is 11.62% compounded monthly. Converting this to an effective rate:
i = (1 + 0.1162/12)^12 - 1
i = 0.1226
We use this formula to solve the problem:
455.96 = (23860(1.0811) + 1695 + 228 - C) [0.0811(1+0.0811)^3]/[(1+0.0811)^3 - 1]
Solving for C
C = 4413.13
The cost of her car was $4,413.13.
Answer:
Prob = 0.514
A. independent
Step-by-step explanation:
The probability that the club chooses a girl and then a boy for the representative spots
Total = 15
Boys = 6
Girls = 9
Prob of 2 person, a girl and a boy
=( 9C1*6C1)/(15C2)
= (9*6)/(105)
= 54/105
= 0.514
