Explanation

 Let original price = x

Selling price = x + 15% of x = 1.15x = 1500

x = 1500 / 1.15 = 1275

Explanation

Given:

HCF = x - 3

LCM = x³ - 9x² + 26x - 24

First polynomial = x² - 5x + 6 (corrected to x² - 5x - 6 doesn't seem right with given HCF, assuming it's x² - 5x + 6 for calculation purposes)

Product of two polynomials = Product of HCF and LCM

Let's denote the second polynomial as P(x).

(x² - 5x + 6) × P(x) = (x - 3) × (x³ - 9x² + 26x - 24)

Factoring LCM:

x³ - 9x² + 26x - 24 = (x - 3)(x² - 6x + 8)

Now, factoring the first polynomial:

x² - 5x + 6 = (x - 3)(x - 2)

(x - 3)(x - 2) × P(x) = (x - 3) × (x - 3)(x² - 6x + 8)

P(x) = (x - 3)(x² - 6x + 8) / (x - 2)

= (x - 3)(x - 2)(x - 4) / (x - 2)

= (x - 3)(x - 4)

= x² - 7x + 12

Explanation

Let's denote the first number as x and the second number as y.

Given equations:

1. 2x + 3y = 61

2. 4x - 5y = 45

We can solve these equations using substitution or elimination. Let's use elimination.

Multiplying equation 1 by 2:

4x + 6y = 122

Now subtracting equation 2 from this:

(4x + 6y) - (4x - 5y) = 122 - 45

11y = 77

y = 7

Explanation

The common difference (d) is the difference between consecutive terms:

d = 3 - (-1) = 4

d = 7 - 3 = 4

d = 11 - 7 = 4

The common difference is:

4

Explanation

To find the area of the path, we need to find the area of the larger rectangle and subtract the area of the smaller rectangle.

Area of larger rectangle = Length × Width

= 60 × 40

= 2400 m²

Length of inner rectangle = 60 - 2 × 2.5 = 55 m

Width of inner rectangle = 40 - 2 × 2.5 = 35 m

Area of inner rectangle = 55 × 35

= 1925 m²

Area of path = Area of larger rectangle - Area of inner rectangle

= 2400 - 1925

= 475 m²

Explanation

First bottle: 3 liters 240 milliliters

Second bottle: 5 liters 350 milliliters

Liters: 3 + 5 = 8 liters

Milliliters: 240 + 350 = 590 milliliters

Total = 8 liters 590 milliliters

Explanation

1 kilometer = 1,000 meters

1 meter = 1,000 millimeters

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

Explanation

Perimeter = AB + BC + AC = 4 + 5 + 3 = 12 cm.

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 circumference of the circle is:

2 × π × r = 2 × π × 15 = 30π m

Distance traveled in 3.5 revolutions:

= 3.5 × 30π

= 105π m