Explanation

The sum of the roots of a quadratic equation ax² + bx + c = 0 is given by -b/a.

Given equation:

x² - 3x - 4 = 0

a = 1

b = -3

Sum of roots = -(-3)/1

= 3

Explanation

The formula relating arc length (l), radius (r), and central angle (θ) is:

l = rθ

Given:

l = 45 cm

r = 9 cm

θ = l / r

= 45 / 9

= 5 radians

Explanation

Let's simplify the expression:

tanθ + cotθ

= sinθ/cosθ + cosθ/sinθ

= (sin²θ + cos²θ) / (sinθcosθ)

Since sin²θ + cos²θ = 1:

= 1 / (sinθcosθ)

= 1/sinθ * 1/cosθ

= cosecθ * secθ

= secθcosecθ

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

Let's solve for x:

9 - 3x = 12

Subtract 9 from both sides:

-3x = 3

Divide both sides by -3:

x = -1

Explanation

To convert millimeters to centimeters, divide by 10:

0.6 mm ÷ 10 = 0.06 cm.

Explanation

In Maths, a straight angle is an angle equal to 180°.

It is called straight because it appears as a straight line.

Explanation

To find the number of pages Faraz read in 1 hour, divide the total number of pages by the total hours:

49.5 pages ÷ 11 hours = 4.5 pages/hour.

Explanation

Total trees = Number of rows × Trees in each row

= 243 × 21

= 5103

Explanation

An open sentence contains a variable (like x) and becomes either true or false only when a value is assigned.

x < 3 is open because its truth depends on the value of x.