Simplifying
5y + -2 = 4y + 7
Reorder the terms:
-2 + 5y = 4y + 7
Reorder the terms:
-2 + 5y = 7 + 4y
Solving
-2 + 5y = 7 + 4y
Solving for variable 'y'.
Move all terms containing y to the left, all other terms to the right.
Add '-4y' to each side of the equation.
-2 + 5y + -4y = 7 + 4y + -4y
Combine like terms: 5y + -4y = 1y
-2 + 1y = 7 + 4y + -4y
Combine like terms: 4y + -4y = 0
-2 + 1y = 7 + 0
-2 + 1y = 7
Add '2' to each side of the equation.
-2 + 2 + 1y = 7 + 2
Combine like terms: -2 + 2 = 0
0 + 1y = 7 + 2
1y = 7 + 2
Combine like terms: 7 + 2 = 9
1y = 9
Divide each side by '1'.
y = 9
Simplifying
y = 9
Answer:
C. The x-coordinate of the vertex must be 6
Step-by-step explanation:
The parabola intercepts the x-axis when y = 0.
Therefore, if the quadratic equation has the points (2, 0) and (10, 0) then the x-intercepts or "zeros" are x = 2 and x = 10.
The x-coordinate of the vertex is the midpoint of the zeros.

Therefore, the solution is option C.
<u>Additional Information</u>
The leading coefficient of a quadratic tells us if the parabola opens upwards or downwards:
- Positive leading coefficient = parabola opens upwards
- Negative leading coefficient = parabola opens downwards
We have not been given this information and so therefore cannot determine the way in which it opens.
As we do not know the way in which way the parabola opens, we cannot determine if the parabola will have a negative or positive y-intercept.
We have not been given the full quadratic equation, and so we cannot determine if the parabola is wider (or narrower) than the parent function.
Answer:
a)27-x
b)27+x
Step-by-step explanation:
when a boat travels in the same direction as the current is downstream-->speeds the boat. If the rate of the boat in still water is 27 mph and the rate of the current of a river is x mph, the rate of the boat when the boat is going downstream is 27+x
when a boat travels against the current is upstream-->slow down. If the rate of the boat in still water is 27 mph and the rate of the current of a river is x mph, the rate of the boat when the boat is going upstream is 27-x
Answer:
$2.50
Step-by-step explanation: