An open box is to be made from a rectangular piece of cardboard that measures 6 in. by 3 in., by cutting out squares of the same size from each corner and bending up the sides. is it possible to cut the squares so that the volume of the box is 40 in.3? volume of the box find all real solutions of this equation to answer the question. (6 – 2x)(3 – 2x)x = 40 yes. because mc001-1.jpg is a root, you can cut squares with sides of mc001-2.jpg in. to make the box no. this equation has no real solutions. no. the only real solution is x = 4. it is not possible to cut squares of this size.

No. The only real solution is x = 4. It is not possible to cut squares of this size.

Step-by-step explanation:

Volume of the box is (6 - 2x)(3 - 2x)x = 40

2(3 - x)(3 - 2x)x = 40

Divide both sides by 2.

(3 - x)(3 - 2x)x = 20

On inspection, x = 4 is one of the solutions of the above cubic equation.

Now, divide the equation by x - 4, we get

The discriminant of this equation is:

= -39 < 0

Hence, x = 4 is the only real solution.

Since, 6 - 2x < 0, it is not possible to cur squares of side 4 in. at the corners.

Hence, the correct answer is:

No. The only real solution is x = 4. It is not possible to cut squares of this size.

x=-2

infinite number of lines, so there is an infinite number of equations.

step-by-step explanation:

there are an infinite number of line that passes through the point (-2,5)

x=-2   is one line that passes through the point

y = 5 is another line that passes through the point

(these two lines are perpendicular to each other).

since the number of   numbers are infinite and the slope is the ratio of two numbers,(change in y over change in x) we can have an infinite number of slopes.     our only condition is that it passes through the point (-2,5)

the answer is b.)

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