Answer:
x= -5/9
That is the answer, try it.
Subtract 3 from both sides
simplify 12 - 3 to 9
break down the problem into these two equations
1 + p = 9 and -(1 + p) = 9
solve the first equation 1 + p = 9 and that would be 8 since 1 + 8 = 9 is true.
solve the second equation -(1 + p) = 9 and just simplify brackets and add 1 to both sides then add 9 + 1 and lastly multiply both sides by -1 and p = -10.
Gather both solutions
Answers: p = -10, 8
Answer:
The answer would be 0.6666666666666666666666666666666666666666667
Step-by-step explanation:
6/9 equals 0.66666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666667
Let's call n the number of days Marika's been training for the race, and 
the distance she runs on the nth day in meters. After the first day, when n = 1, she runs 100 meters, so
On the second day, she runs an additional 4 meters, on the third day, another 4, and so on. Here's what that looks like mathematically:
It would be easier to write this continued addition as multiplication, in which case those same equations would look like
Notice that, in every case, the number 4 is being multiplied by is 1 less than n. We could even write for our first term that 
. In general, we can say that
Which is expressed by option B.
(Bonus: What piece of information from this question did we not need to use here?)
Speed of the plane: 250 mph
Speed of the wind: 50 mph
Explanation:
Let p = the speed of the plane
and w = the speed of the wind
It takes the plane 3 hours to go 600 miles when against the headwind and 2 hours to go 600 miles with the headwind. So we set up a system of equations.
600
m
i
3
h
r
=
p
−
w
600
m
i
2
h
r
=
p
+
w
Solving for the left sides we get:
200mph = p - w
300mph = p + w
Now solve for one variable in either equation. I'll solve for x in the first equation:
200mph = p - w
Add w to both sides:
p = 200mph + w
Now we can substitute the x that we found in the first equation into the second equation so we can solve for w:
300mph = (200mph + w) + w
Combine like terms:
300mph = 200mph + 2w
Subtract 200mph on both sides:
100mph = 2w
Divide by 2:
50mph = w
So the speed of the wind is 50mph.
Now plug the value we just found back in to either equation to find the speed of the plane, I'll plug it into the first equation:
200mph = p - 50mph
Add 50mph on both sides:
250mph = p
So the speed of the plane in still air is 250mph.
