Answer:
Step-by-step explanation:
x/4-y/2=8, x-2y=32, x=32+2y
x/2+3y/4=-5, 2x+3y=-20, x=(-20-3y)/2
32+2y=(-20-3y)/2
64+4y=-20-3y
7y=-84
y=-12, since x=32+2y
x=32+2(-12), x=32-24=8
So the solution is the point (8, -12)
The abscissa is the x coordinate whereas the ordinate is the y coordinate. Both x and y are positive in the first quadrant only.
Answer:
A
Step-by-step explanation:
9 > 3 + 2x
6 > 2x
3 > x
or
x < 3
and that means 3 is NOT included (otherwise there must be a smaller or equal sign). hence A is the right answer.
Answer: y=-1/5x+4
Step-by-step explanation: use the equation y=mx+b (x,y)->(5,3) 5 is an x value and 3 is a y value so you want to plug in these values into the equation. 3=-1/5(5)+b. We already know our slope so just plug it into m. Now multiply -1/5 and 5 which is -1. 3=-1+b you want to isolate b so you can find the intercept. Add one to both sides so it cancels out. 4=b we found our y-intercept so we can write the equation now. y=-1/5x+4
Answer:
2,674.14 g
Step-by-step explanation:
Recall that the formula for radioactive decay is
N = N₀ e^(-λt)
where,
N is the amount left at time t
N₀ is the initial amount when t=0, (given as 42,784 g)
λ = coefficient of radioactive decay
= 0.693 ÷ Half Life
= 0.693 ÷ 18
= 0.0385
t = time elapsed (given as 72 years)
e = exponential constant ( approx 2.7183)
If we substitute these into our equation:
N = N₀ e^(-λt)
= (42,787) (2.7183)^[(-0.0385)(72)]
= (42,787) (2.7183)^(-2.7726)
= (42,787) (0.0625)
= 2,674.14 g
