Explanation

x:y = 7:8 → multiply both by 5 ⇒ x:y = 35:40  

y:z = 5:6 → multiply both by 8 ⇒ y:z = 40:48  

So x:z = 35:48

Explanation

2z/5 + 21/3 = 9

=> 2z/5 + 7 = 9

=> 2z/5 = 2

=> 2z = 10

=> z = 5

Explanation

Let's solve for y:

5y/3 + 28/7 = 14

5y/3 + 4 = 14

5y/3 = 10

5y = 30

y = 6

Explanation

Using the identity a² - b² = (a+b)(a-b):

(31)² - (29)² = (31+29)(31-29)

= (60)(2)

= 120

Explanation

sin30° = 1/2

cos60° = 1/2

Calculation

1/2 + 1/2 = 1

Explanation

We can use the formula for the difference of squares:

a² - b² = (a - b)(a + b)

Here a = 21, b = 19

21² - 19² = (21 - 19)(21 + 19)

= (2)(40) = 80

Explanation

4 - 3x = 8 - x

Solve step-by-step:

1. Move all x terms to one side:

   4 - 3x + x = 8  

   ⇒ 4 - 2x = 8

2. Subtract 4 from both sides:

   -2x = 4

3. Divide by -2:

   x = -2

Explanation

a⁶.a³/a⁴ = a⁶+³-⁴ = a⁵

Explanation

Given:  

x/5 - (3x/2) = 7 + x/2

Step 1: Eliminate fractions by finding a common denominator  

The LCM of 5 and 2 is 10. Multiply both sides of the equation by 10:

10 × (x/5 - 3x/2) = 10 × (7 + x/2)

(2x - 15x) = 70 + 5x  

-13x = 70 + 5x

Step 2: Move all terms to one side

-13x - 5x = 70  

-18x = 70

Step 3: Solve for x

x = 70 / -18 = -35/9

Explanation

100x​×60=48
x×0.6=48
x=48/0.6​

$$x=80$$