Explanation

Let's denote the numbers as 8x and 3x.

Given: 8x - 3x = 20

5x = 20

x = 4

Step 1: Find the numbers

First number = 8x = 8 * 4 = 32

Second number = 3x = 3 * 4 = 12

Step 2: Find the sum

Sum = 32 + 12 = 44

Explanation

Given equation:

0.5x + 1.1 = 2.3

Step-by-step:

Subtract 1.1 from both sides:

0.5x = 2.3 - 1.1 = 1.2

Divide both sides by 0.5:

x = 1.2 ÷ 0.5 = 2.4

Explanation

Convert all fractions to decimals:

2/3 = 0.666...,

4/9 ≈ 0.444,

5/8 = 0.625,

7/16 = 0.4375

2/3 (≈ 0.666) is the greatest among them.

Explanation

To find the cost of painting, we need to calculate the surface area of the cuboid:

Surface Area = 2(lw + lh + wh)

= 2(43.5 + 46 + 3.5*6)

= 2(14 + 24 + 21)

= 2 * 59

= 118 square meters

Now, cost of painting:

Cost = Surface Area * Rate

= 118 * 43.78

= 5166.04

Explanation

A line extends infinitely in both directions and has no end points.

In contrast, a line segment has two end points, and a ray has one.

Explanation

The opposite of an integer is its additive inverse.

The opposite of -21 is +21.

Explanation

Supplementary angles add up to 180°. Given:

One angle = 122°

Let the other angle be x. Then:

x + 122° = 180°

Subtract 122° from both sides:

x = 58°

Explanation

To find the Highest Common Factor (HCF), list the factors of each number:

135: 1, 3, 5, 9, 15, 27, 45, 135

540: 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 27, 30, 36, 45, 54, 60, 90, 108, 135, 180, 270, 540

675: 1, 3, 5, 9, 15, 25, 27, 45, 75, 135, 225, 675

765: 1, 3, 5, 9, 15, 17, 27, 45, 51, 85, 135, 153, 255, 765

The highest common factor among these numbers is: 45.

Explanation

Equations use "=" (equality sign), like 7x - 1 = 0 and ax + b = 0.

In-equations (inequalities) use "<, >, ≤, or ≥", like 5x - 1 < 0.

Explanation

The formula for the interior angle of a regular polygon is (180° × (n - 2)) / n, where n = 5 for a pentagon.

Substituting n = 5, we get (180 × 3) / 5 = 108° per angle.