Explanation

The line y = 3 is a horizontal line that intersects the y-axis at y = 3.

Since it's horizontal, it's parallel to the x-axis.

Explanation

Given equations:

1. x - 2y = 5

2. 2x - y = 6

Step-by-Step Solution

Step 1: Solve one equation for one variable

From equation (2):

2x - y = 6

⇒ y = 2x - 6

Step 2: Substitute into the other equation

Substitute y = 2x - 6 into equation (1):

x - 2(2x - 6) = 5

x - 4x + 12 = 5

-3x + 12 = 5

Step 3: Solve for x

-3x = 5 - 12

-3x = -7

x = 7/3

Step 4: Solve for y

Substitute x = 7/3 back into y = 2x - 6:

y = 2(7/3) - 6

y = 14/3 - 6

y = 14/3 - 18/3

y = -4/3

Explanation

Given:

Breadth = 1/5 × Length

Perimeter = 24m

Let length = L

Breadth = L/5

Perimeter formula: P = 2(L + B)

24 = 2(L + L/5)

24 = 2(6L/5)

24 = 12L/5

24 × 5 = 12L

120 = 12L

L = 10m

Explanation

Let the younger sister's present age be x.

Fareeha's present age = x + 4

After 10 years:

Younger sister's age = x + 10

Fareeha's age = x + 4 + 10 = x + 14

Given:

x + 10 + x + 14 = 48

2x + 24 = 48

2x = 24

x = 12

Fareeha's present age = x + 4

= 12 + 4

= 16 years

Explanation

Calculating the Total Bill

1. Sandwiches: 3 × 250 = Rs. 750

2. Cold drinks: 2 × 180 = Rs. 360

3. Coffee: Rs. 210

4. Total food cost: 750 + 360 + 210 = Rs. 1320

5. Tax: Rs. 112

6. Total bill: 1320 + 112 = Rs. 1432

Change Calculation

Amount paid: Rs. 5000

Change = 5000 - 1432 = Rs. 3568

Explanation

According to BODMAS, Division (÷) and Multiplication (×) are done first — from left to right, followed by Addition (+) and Subtraction (-).

So, if division appears before multiplication in the expression, it is done first.

Explanation

To determine which set of numbers has an LCM of 6384:

Prime factorization:

42 = 2 × 3 × 7

38 = 2 × 19

16 = 2⁴

LCM = 2⁴ × 3 × 7 × 19 = 6384

Explanation

Given:

Cost of 19 pairs = Rs. 23750

Cost per pair = 23750 / 19

= Rs. 1250

Cost of 65 pairs = 65 × 1250

= Rs. 81250

Explanation

Given fraction: 12/500

To find the decimal form:

12 ÷ 500 = 0.024

Explanation

Given expression: 1830 + 20 × 50 - 396 ÷ 3

Following order of operations:

1. Multiplication: 20 × 50 = 1000

2. Division: 396 ÷ 3 = 132

3. Now, the expression becomes:

1830 + 1000 - 132

= 1830 + 1000 = 2830

= 2830 - 132 = 2698