Explanation

Step 1: Let the numbers be

Three consecutive odd numbers:

$$x-2,x,x+2$$

Step 2: Form an equation

$$(x-2)+x+(x+2)=57$$$$3x = 57$$

Step 3: Solve

$$x=19$$

$$Last\; updated\; by\; NA\; on\; 24-April-2026$$

Explanation

Let original = x  

x + 20% of x = 540  

1.2x = 540  

x = 540 / 1.2 = 450  

Last verified on 14-04-2026

Explanation

LCM of 16, 24, 30:  

16 = 2⁴  

24 = 2³ × 3  

30 = 2 × 3 × 5  

LCM = 2⁴ × 3 × 5 = 240  

240 is three-digit, so that’s it.  

Last verified on 14-04-2026

Explanation

Explanation

What are the factors ofx^2−5?

We use the identity:

a^2−b^2=(a−b)(a+b)

x^2−5=x^2− √5

(x − √5)(x + √5)

 Last updated NA 13-04-2026

Explanation

We are given:

$$(2a-7b,5b)=(-10a,3+b)$$

Step 1: Equate corresponding components

Since ordered pairs are equal:

1. First components:

$$2a-7b=-10a$$

2. Second components:

5b=3+b

Step 2: Solve second equation

5b=3+b
5b−b=3
$$4b=3$$

b=3/4​

Step 3: Substitute into the first equation

2a−7(3/4)=−10a
2a−21/4​=−10a

Bring like terms together:

$$2a + 10a = frac{21}{4}$$ $$12a = frac{21}{4}$$a=21​/48=7/16​

Final Answer:

a=7/16,b=3/4

 Last updated NA 13-04-2026
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Explanation

In the proportion 5 : 5 :: 6 : X, find X

We use the proportion rule:

$frac{a}{b} = frac{c}{d}$

Apply the values:

5/5​=6/X​
1=6/X​
$$X=6$$

$$Last\; updated\; NA\; 13-04-2026$$

Explanation

We use the triangle angle rule

A+B+C=180∘

50∘+40∘=90∘

180∘−90∘=90∘

 Last updated NA 13-04-2026

Explanation

s² - 8s + 16 = 0  

Discriminant = b² - 4ac = (-8)² - 4(1)(16) = 64 - 64 = 0  

When D = 0, roots are Real and Equal.

Here: (s - 4)² = 0 → s = 4, 4  

Last verified on 12-04-2026

Explanation

Two quantities are in inverse proportion when one increases and the other decreases.

Their product always remains constant.

Common in real-life situations like speed & time.

If one doubles, the other becomes half.

It is also called indirect proportion.

Direct Proportion → Both increase or decrease together.

Last verified on 12-04-2026