Answer:
- x=8, x=2
- no solution
- no solution
Step-by-step explanation:
For the equation ...
y = a(x -h)² +k
you can find the x-intercepts by setting y=0 and solving for x.
0 = a(x -h)² +k
-k = a(x -h)² . . . . . . subtract k
-k/a = (x -h)² . . . . . divide by a
±√(-k/a) = x -h . . . . take the square root
h ± √(-k/a) = x . . . . add h . . . . this is the general solution
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So, for each of your problems, fill in the corresponding numbers and do the arithmetic. If (-k/a) is a negative number, the square root gives imaginary values, so there is "no solution".
1. x = 5 ± √9 = {5 -3, 5 +3} = {2, 8} . . . . the x-intercepts are 2 and 8
2. x = -3 ± √(-2) . . . . . . no solution; the roots are complex
3. x = 5 ± √(-8/4) . . . . . no solution; the roots are complex
3 × 7 × 12 × 2
3 + 7 + 12 + 2
12 - 7 - 3 - 2
Answer:
Therefore (2.30-0.03747)= 2.2625 M of HI remains from an initial concentration of 2.30 M after 4.5 hours.
Step-by-step explanation:
second order reaction: The rate of reaction proportional to the square of the concentration of reactant.
For second order reaction

K is rate constant = 1.6×10⁻³M⁻¹hr⁻¹
a = initial concentration of reactant = 2.30 M
a-x = concentration of reactant after t h
t = time = 4.5 h
Putting the values in the above equation,





Therefore (2.30-0.03747)= 2.2625 M of HI remains from an initial concentration of 2.30 M after 4.5 hours.
You have to evaluate the slopes of these lines. For line AB you have a slope of

For line CD you have a slope of

Because the slopes are equal and the two lines are not one and the same, they are parallel.