Answer:
3/1
Step-by-step explanation:
The average rate of change is the distance between y values divided by the distance between x values. We know this as rise/run or slope for linear equations. For non-linear equations, we calculate the average over an interval.
This function has y-values of -1 at x=0 and 5 at x=2.
We add -1+5=6 and divide this by 2-0=2.
6/2=3.
The y-values on average change 3 units for every 1 unit of the x-values.
We have such equation
6x+3=4x+9 /-4x subtract 4x both sides
6x-4x+3=4x-4x+9
2x+3=9 /-3 subtract 3 both sides
2x=6 /:2 divide both sides by 2
x=3 - its result
Step-by-step explanation:
x² + 6x + 9 = 2
(x + 3)² = 2
x + 3 = ±sqrt(2)
x = -3 ± sqrt(2)
so, B and D are correct.
control :
(-3 + sqrt(2))² + 6(-3 + sqrt(2)) + 9 = 2
9 + 2 - 6sqrt(2) - 18 + 6sqrt(2) + 9 = 2
2 = 2
correct
(-3 - sqrt(2))² + 6(-3 - sqrt(2)) + 9 = 2
9 + 2 + 6sqrt(2) - 18 - 6sqrt(2) + 9 = 2
2 = 2
correct
(3 + sqrt(2))² + 6(3 + sqrt(2)) + 9 = 2
9 + 2 + 6sqrt(2) + 18 + 6sqrt(2) + 9 = 2
38 + 12sqrt(2) = 2
wrong.
(3 - sqrt(2))² + 6(3 - sqrt(2)) + 9 = 2
9 + 2 - 6sqrt(2) + 18 - 6sqrt(2) + 9 = 2
38 - 12sqrt(2) = 2
wrong.
So I did this:
y=x +2
y=3x-4
I used the first equation to plug into the second equation.
x+2= 3x -4
I subtracted 3 from both sides so I get
-2x+2=-4
So I subtract 2 from both sides so I get
-2x=-6
I divide -2 on both sides and so I get
x=3
Then I plug the x into either equation. I did the first equation.
y=3+2
y=5
So x=3 and y=5
