Identify the least common multiple of x2 − 10x + 24 and x2 − x − 12.

(x-4)(x-6)(x+3) or in more compressed form x³-7x²-6x+72

Step-by-step explanation:

To find the L.C.M, w first factorize each of the expressions.

x²-10x+24

Two numbers that when added give -10 but when multiplied give 24

will be, -4 and -6

Thus the expression becomes:

x²-4x-6x+24

x(x-4)-6(x-4)

=(x-4)(x-6)

Let us factorize the second expression.

x²-x-12

Two numbers when added give -1 and when multiplied give -12

are 3 and -4

Thus the expression becomes: x²-4x+3x-12

x(x-4)+3(x-4)

(x-4)(x+3)

Therefore the LCM between  (x-4)(x-6) and (x-4)(x+3)

will be

(x-4)(x-6)(x+3)

We can multiply the expression as follows.

(x-4)(x-6)

x²-6x-4x+24 = x²-10x+24

(x+3)(x²-10x+24)

=x³-10x²+24x+3x²-30x+72

=x³-7x²+-6x+72

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.

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step-by-step explanation: