How much is 1,500 minutes in hours?

Final answer:

The equation |r| = -2 has no solution, and the graph does not exist.

Explanation:

To solve the equation |r| = -2, we need to consider the absolute value. The absolute value of any number is always positive or zero, so it can never be negative. Since there is no number whose absolute value is -2, the equation |r| = -2 has no solution.

Graphically, the equation represents the absolute value function, which is always positive or zero. Therefore, the graph of |r| = -2 does not exist on the coordinate plane.

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x,y - the numbers

one positive number is 5 less than twice a second number

(1)    x - 5 = 2y

their product is 117

(2)    xy = 117

(1)     x - 5 = 2y     add 5 to both sides

x = 2y + 5   substitute it to (2)

(2y + 5)y = 117     use distributive property

(2y)(y) + (5)(y) = 117

2y² + 5y = 117      subtract 117 from both sides

2y² + 5y - 117 = 0

2y² + 18y - 13y - 117 = 0

2y(y + 9) - 13(y + 9) = 0

(y + 9)(2y - 13) = 0 ↔ y + 9 = 0 ∨ 2y - 13 = 0

y + 9 = 0    subtract 9 from both sides

y = -9

2y - 13 = 0     add 13 to both sides

2y = 13     divide both sides by 2

y = 6.5

substitute the values of y to (1)

x = 2(-9) + 5 = -18 + 5 = -13 < 0

x = 2(6.5) + 5 = 13 + 5 = 18

Answer: x = 18 and y = 6.5