Which two expressions , added together , form a function with the following characteristics? -It’s range is all real numbers
- it’s graph has exactly two x-intercepts

Options (B) and (C)

Step-by-step explanation:

We have to form a function which has following characteristics,

1). Its range is all real numbers

 Which means graph of the given function starts from negative side of the y-axis (-∞) and goes towards positive direction of the y-axis (+∞).

It's a typical characteristic of odd degree polynomial/function.

2). The graph has exactly two x-intercepts.

  Which means when we put f(x) = 0, we get exactly two values of x.

Therefore, function will be, f(x) = x³ + x²

Range of the function → (-∞, ∞) Or a set of all real numbers.

x-intercepts → f(x) = x³ + x² = 0

                             x²(x + 1) = 0

                             x = -1, 0

Therefore, Options (B) and (C) will be the answer.

the transverse axis of a hyperbola is the line that contains the two vertices and the two focuses.

in this example (hyperbola of equation x^2/2 - y^2/4 = 1), the transverse axis is the  x-axis  . 

step-by-step explanation:

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.