Explanation

In ax² + bx + c = 0, if > 0, b > 0, and c > 0, the parabola opens upward and lies entirely above the x-axis unless discriminant D = b² - 4ac ≥ 0.

If real roots exist, they are negative because both b and c are positive.

Explanation

The formula ∑x/n calculates the arithmetic mean of a set of numbers, where:

∑x = sum of all values

n = number of values

This formula provides the average value of the dataset.

Explanation

The given solution is already solved:

5x + 8 = 23

5x = 23 - 8

5x = 15

x = 15/5

x = 3

Explanation

To find g(3), substitute t = 3 into the equation:

g(3) = (3)³ + (3)² - 9(3) - 9

= 27 + 9 - 27 - 9

= 0

Explanation

The number 1 is called the multiplicative identity because multiplying any real number a by 1 leaves it unchanged: a × 1 = 1 × a = a.

This property holds for all real numbers (∀ a ∈ R).

Explanation

Range is the simplest measure of data spread, calculated by subtracting the smallest value from the largest value.

It gives an idea of how widely the data values are spread.

Explanation

Given the conditions:

1. √x requires x ≥ 1 (from x - 1 ≥ 0)

2. Denominator x² - 2x ≠ 0 implies x ≠ 0 and x ≠ 2

The domain is indeed x ≥ 1, excluding x = 2.

So, the domain is (1, 2) ∪ (2, ∞).

Explanation

60% of 50 = 60/100 × 50

= 0.6 × 50

= 30

Explanation

The rate of change of cost with respect to the number of units produced is called Marginal Cost.

It represents the additional cost of producing one more unit.

Explanation

In the quadratic equation ax² + bx + c = 0, a cannot be zero.

If a = 0, the equation becomes linear (bx + c = 0), and it's no longer a quadratic equation.