Explanation

Given the quadratic equation mx² - 5x + n = 0:

Sum of roots = -(-5/m) = 5/m

Product of roots = n/m

Given both sum and product of roots are equal to 10:

5/m = 10 => m = 1/2

n/m = 10 => n = 10m

n = 10 * (1/2)

n = 5

Explanation

To find the Arithmetic Mean (AM), we need to sum all the values and divide by the number of values:

Values: 2, 3, 4, 5, 6, 7, 8, 9, 10

Sum = 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10

= 54

Number of values = 9

Arithmetic Mean = Sum / Number of values

= 54 / 9

= 6

Explanation

To find the greatest capacity of a measuring jar that can exactly measure 165, 175, and 200 liters, we need to find the greatest common divisor (GCD) or highest common factor (HCF) of these numbers.

Let's find the prime factors:

165 = 3 * 5 * 11

175 = 5 * 5 * 7

200 = 2 * 2 * 2 * 5 * 5

The common factor among these is 5.

The greatest capacity of the measuring jar is: 5 liters

Explanation

Like terms are terms that have the same variable(s) with the same exponent(s).

x² and - √3x² are like terms because they both have the same variable (x) with the same exponent (²).

Explanation

60% of 75 = (60/100) × 75

= 0.6 × 75 = 45

Explanation

To divide the expression, follow the quotient rule:

9y⁴ ÷ 3y² = (9/3) × (y⁴/y²)

Simplify:

3 × y²

So, the correct answer is:

3y²

Explanation

A proper fraction has a numerator smaller than the denominator, meaning its value is less than 1.

7/8 is the only one that meets this condition.

Explanation

To find the length of the chord, we can use the formula:

Length = 2 * √(r² - d²)

where r is the radius and d is the distance from the center.

Given:

r = 5 cm

d = 3 cm

Length = 2 * √(5² - 3²)

= 2 * √(25 - 9)

= 2 * √16

= 2 * 4

= 8 cm

Explanation

1 kilometer = 1,000 meters

1 meter = 1,000 millimeters

So, 1 km = 1,000 × 1,000 = 1,000,000 mm

Explanation

Coterminal angles have the same initial and terminal sides but differ by full rotations (360°, 720°, etc.).

Example: 30° and 390° are coterminal because 390° = 30° + 360°.