Combine the two equations so that it’s 2x+5=4x-1 and then subtract 2x from both sides. now it’s 5=4x-1 and add 1 to both sides. now is 6=4x 6 divided by 4 is 1.5 so that is the x value. now sub 1.5 as the x value into the first equation so it’s y=2(1.5)+5. you do the math and it’s y=8 (because 1.5 times 2 is 3 and 3+5 is 8) then your point is (1.5,8)
Answer:
x = 10 cm, y = 5 cm gives a minimum area of 300 cm^2.
Step-by-step explanation:
V= x^2y = 500
Surface area A = x^2 + 4xy.
From the first equation y = 500/x^2
So substituting for y in the equation for the surface area:
A = x^2 + 4x * 500/x^2
A = x^2 + 2000/x
Finding the derivative:
dA/dx = 2x - 2000x^-2
dA/dx = 2x - 2000/x^2
This = 0 for a minimum/maximum value of A, so
2x - 2000/x^2 = 0
2x^3 - 2000 = 0
x^3 = 2000/ 2 = 1000
x = 10
Second derivative is 2 + 4000/x^3
when x = 10 this is positive so x = 10 gives a minimum value of A.
So y = 500/x^2
= 500/100
= 5.
First, you add 1 to both sides. Then square both sides to get rid of the square root. After that you just solve it like a normal equation when you are left with 4x-2=9.
Part A:

The first step of completing the square is writing the expression

as

which expands to

.
We have the first two terms exactly the same with the function we start with:

and

but we need to add/subtract from the last term, 49, to obtain 41.
So the second step is to subtract -8 from the expression

The function in completing the square form is

Part B:
The vertex is obtained by equating the expression in the bracket from part A to zero


It means the curve has a turning point at x = -7
This vertex is a minimum since the function will make a U-shape.
A quadratic function

can either make U-shape or ∩-shape depends on the value of the constant

that goes with

. When

is (+), the curve is U-shape. When

(-), the curve is ∩-shape
Part C:
The symmetry line of the curve will pass through the vertex, hence the symmetry line is

This function is shown in the diagram below