Answer: y=-5/3 + 2
Step-by-step explanation:
Hope this helps
Answer:
401 MILES
Step-by-step explanation:
miles from A to B:
64 * 5.5 = 352 miles
miles from A to C:
352 + 49 = 401 miles
Answer:
x² + 4xy + 4y²
Step-by-step explanation:
(x + 2y)² = (x + 2y)(x + 2y)
Each term in the second factor is multiplied by each term in the first factor
(x + 2y)(x + 2y)
= x(x + 2y) + 2y(x + 2y) ← distribute both parenthesis
= x² + 2xy + 2xy + 4y² ← collect like terms
= x² + 4xy + 4y²
Answer:
(5,9)
Step-by-step explanation:
3y=4x+7
5y=4x+25
Subtract the two equations to eliminate x
5y=4x+25
-( 3y=4x+7)
------------------
2y = 0x +18
Divide by 2
2y/2 = 18/2
y =9
Now find x
3y = 4x+7
3*9 = 4x+7
27 = 4x+7
Subtract 7
20 = 4x
Divide 4
20/4 = 4x/4
5 =x
(5,9)
Algebra:
A standard parabola is y = x^2. Its vertex is at (0,0)
You can change the position (or vertex) of the parabola.
To move a parabola across the x-axis, you can add or subtract a number from x WITHIN brackets of the ^2
eg. (x + 1)^2 will move the parabola across the x-axis. It will move is one unit to the LEFT (as the sign is opposite to the direction it moves ie. The sign it + but you move the whole parabola in the -ve direction).
Adding or subtracting a number from x OUTSIDE of the ^2 moves the parabola up or down the y-axis
eg. x^2 + 3 will move the parabola UP 3 units (the sign is the same as the direction it moves when the added/subtracted number is outside of the ^2 ie. the sign is positive so the parabola moves up in the positive direction)
From this, we can conclude that because (x + 1)^2 + 3, the vertex will be where x = -1 and where y = 3
Vertex : (-1,3)
Calculus:
f(x) = (x + 1)^2 + 3 = x^2 + 2x + 1 + 3 = x^2 + 2x + 4
Expanding the formular to make it easier to differentiate
f'(x) = 2x + 2
Differentiating (finding the formular the the gradiet of the parabola)
0 = 2x + 2
When the gradient is equal to zero, it must be the vertex
-2 = 2x
-2/2 = x
x = -1
Solve to give the x value at the vertex
f(x) = (x + 1)^2 + 3
= (-1 + 1)^2 + 3
Substitute x = -1 into original equatiom to find y value at the vertex
= (0)^2 + 3
= 0 + 3
= 3
Solve for y
Vertex : (-1,3)
