Explanation

Convert minutes to decimal: 15' ÷ 60 = 0.25

Convert seconds to decimal: 36" ÷ 3600 = 0.01

Add to degrees: 8 + 0.25 + 0.01 = 8.26

Explanation

In division, the quotient is the result of dividing one number by another.

Here, 30 ÷ 5 = 6, so the quotient is 6.

Explanation

To find the value-added tax (VAT), we need to calculate the tax paid on purchase and tax charged on sale, then find the difference.

Purchase price = Rs. 6890

Tax paid on purchase = 4% of 6890

= 0.04 × 6890

= Rs. 275.6

Sale price = Rs. 7900

Tax charged on sale = 6% of 7900

= 0.06 × 7900

= Rs. 474

Value-added tax (VAT) = Tax charged on sale - Tax paid on purchase

= 474 - 275.6

= Rs. 198.4

Explanation

Explanation

Using trigonometry, specifically the sine function:

sin(θ) = opposite side (height) / hypotenuse

Given:

θ = 45°

hypotenuse = 10 feet

Rearrange the formula to solve for height:

height = hypotenuse × sin(45°)

= 10 × (√2 / 2)

= 10 × √2 / 2

= 5√2 feet

Explanation

To find the solution set of 2x² + 2x - 11 = 1:

First, subtract 1 from both sides:

2x² + 2x - 12 = 0

Now, divide by 2:

x² + x - 6 = 0

Factor the quadratic:

(x + 3)(x - 2) = 0

This gives us two possible solutions:

x + 3 = 0 --> x = -3

x - 2 = 0 --> x = 2

So, the solution set is:

(-3, 2)

Explanation

Explanation

Let x = 0.888... (repeating).

Multiply by 10: 10x = 8.888...

Subtract: 10x - x = 8.888... - 0.888...

→ 9x = 8

Solve for x: x = 8/9.

Explanation

When rotating a point (x, y) 90° counterclockwise, the new coordinates are (-y, x).

For P(-5, -3), the new coordinates P' will be (3, -5).

Explanation