Let x be the common ratio / or scale factor
the sides of the triangle are
5x, 12x and 13x
sum of the sides defines perimeter
that is
5x + 12x + 13x = 15
30x = 15
x = 15/30
x = 0.5
The sides of the triangle are 0.5(5) = 2.5
0.5(12)=6
0.5(13) = 6.5
2.5, 6, 6.5 all in inches
So let's get k on one side:
2k = 2
Divide by 2:
k = 1
If you want to check your work:
1 + 1 = 3 - 1
2 = 2
$75 to his 401k each month......75(12) = 900 in a yr.
his employee matched 16% of his contributions..
16% of 900 =
0.16(900) = 144
so the total amount contributed was : 900 + 144 = $ 1044
Answer : y - 1 = 1/2 (x-3)
The formula for point slope is y - y1 = m (x - x1)
M is the slope of the line. The nine and three come from the point given. I used the point (3, 1). Hope this helps !
Question 1:
I'm actually not sure which term you ment exactly, so I calculated the solution for three possible variations of your term, depending on how one sets the brackets.
To calculate an ordered pay just set x or y to some value, insert it into the equation and you get the solution for the other variable.
In these calculations I always picked x so values would get eliminated or as close to 0 as possible to make it easier.
variation 1 of term:
y=(5^4)*(x-3)
insert x=3
y=(5^4)*(3-3)==(5^4)*0=0
pair: (3,0)
variation 2 of term:
y=(5^4)*x-3
insert x=0:
y=(5^4)*0-3=0-3=-3
pair: (0,-3)
variation 3 of term:
y=5^(4*x-3)
insert x=1:
y=5^(4*1-3)=5^1=5
pair: (1,5)
question 2:
2y=-5x-4
just insert the pairs as (x,y) into the equation:
a. (-2,3)
2*3=-5*-2-4
6=10-4 yes
b. (1,-4)
2*-4=-5*1-4
-8=-9 no
c. (0,2)
2*2=-5*0-4
4=-4 no
d. (-1,1)
2*1=-5*-1-4
2=5-4 no