Answer:
Part 1) Helen's age is 32 years old and Jane's age is 24 years old
Part 2) 13 twenty-dollar bills
Step-by-step explanation:
Part 1) Helen is 8 years older than Jane. Twenty years ago Helen was three times as old as Jane. How old is each now and what is the equation?
Let
x----> Helen's age
y---> Jane's age
we know that
x=y+8 ----> equation A
(x-20)=3(y-20) -----> equation B
substitute equation A in equation B and solve for y
(y+8-20)=3(y-20)
y-12=3y-60
3y-y=60-12
2y=48
y=24 years
Find the value of x
x=y+8
x=24+8=32 years
Part 2)
Let
x-----> the number of five-dollar bills
y----> the number of twenty-dollar bills
we know that
5x+20y=305 -----> equation A
y=x+4 ------> x=y-4 ------> equation B
substitute equation B in equation A and solve for y
5(y-4)+20y=305
5y-20+20y=305
25y=325
y=13 twenty-dollar bills
Find the value of x
x=y-4
x=13-4=9 five-dollar bills
Simplifying
9 + -2x = 35
Solving
9 + -2x = 35
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '-9' to each side of the equation.
9 + -9 + -2x = 35 + -9
Combine like terms: 9 + -9 = 0
0 + -2x = 35 + -9
-2x = 35 + -9
Combine like terms: 35 + -9 = 26
-2x = 26
Divide each side by '-2'.
x = -13
Simplifying
x = -13
The square root of a -36 simplifies to "6i". So you have 3+/- [6i/6]. The 6's cancel each other out leaving 3+/-i. So the "a" is 3 and the "b" is 1
X-intercept: (7,0)
y-intercept: (0,2)
