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)
Answer:
multiply 460 by 5
Step-by-step explanation:
460 * 5 = 2,300
Answer:
vases per hour
Step-by-step explanation:
To find the unit rate, solve the total amount of vases that Emily arranged divided by the amount of time that Emily took to arrange the vases.
Or, in other words, solve 20 ÷ 6, since Emily arranged 20 vases and it took her 6 hours to complete it.
You can do this by hand or you can do it on a calculator.
After you solved it, you should get , or 3.33333...
So, Emily's rate is vases per hour.
<h2><u><em>
Please mark as Brainliest!!!</em></u></h2>
Answer:
100 packets
Step-by-step explanation:
Given :
Cost = fixed cost + variable cost
Fixed cost = $500
Variable cost = $10
Sales price = $15
Let :
Number of packets = x
To break even :
fixed cost + variable cost = sales made
500 + 10x = 15x
500 = 15x - 10x
500 = 5x
x = 500 / 5
x = 100
100 packets
Hello!
So, we know she earns x. However, 23% of it is used to pay in taxes.
Then, the expression is:
x - 0,23x = 0,77x or 77% of what she earns.
Stay safe! x
