Prove : the graphs of the function f(x)=x4
and g(x)=x3-x2 have aunique intersection
point.

The unique intersection point for the given functions which is at x = 0.

The intersection point is (0,0)

Step-by-step explanation:

We are given the following information in the question.

We have to find the intersection point.

Equating the two equations we get,

Since the quadratic equation gives complex root, thus there is a unique intersection point for the given functions which is x = 0.

The attached image shows the graph for the given function.

The red line represent f(x) and blue line represent g(x).

The intersection point is (0,0)

answer: the price of one pound cabbage = $ 0.8

the point (10,8) represents that the cost of 10 pounds cabbage is $ 8

step-by-step explanation:

since, here is a proportional relation between the number of pounds of cabbage (x) and the price in dollars (y).

therefore, we can write,

⇒ y = k x

where k is the constant of proportionality.

now, point (5,4) is in the line.

thus, it will satisfies the above equation of line.

⇒ 4 = 5 k

⇒ k = 0.8

thus, the equation of the line is,

y = 0.8 x

a) for x = 1,

y = 0.8

therefore, the cost of one pound of cabbage is 0.8 dollars.

b) in the below graph (10,8) represents that the cost of 10 pounds of cabbage is 8 dollars.

first, we define the variables:

x: number of years after 1950

f (x): amount of vinyl sold.

then, with the variables defined, we have:

68594 vinyl records were sold in 1958 > f (8) = 68594

91299 vinyl records were sold in 1961 > f (11) = 91299

38720 vinyl records were sold in 1952 > f (2) = 38720

161743 vinyl records were sold in 1967 > f (17) = 161743

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step-by-step explanation: