Explanation

To find LCM of fractions:

$$text{LCM} = frac{text{LCM of numerators}}{text{HCF of denominators}}$$HCF of denominators​

Numerators: 2, 3, 6 → LCM = 6
Denominators: 5, 10, 25 → HCF = 5

$$$$

text{LCM} = frac{6}{5}

Explanation

Step-by-step:

$$frac{31 times 3}{100} = frac{93}{100}, quad frac{7}{5} = frac{140}{100}, quad 20 = frac{2000}{100}$$

Add all:

93+140+2000​/100=2233​/100=22.33

Explanation

Multiply both sides by 2:

$$|3x| = 6 Rightarrow 3x = ±6 Rightarrow x = ±2$$

Explanation

Explanation

If4^a=8^b, find the ratio $frac{a}{b}$

Write both sides with base 2:

$$4^a = (2^2)^a = 2^{2a} \ 8^b = (2^3)^b = 2^{3b} Rightarrow 2^{2a} = 2^{3b} Rightarrow 2a = 3b Rightarrow frac{a}{b} = frac{3}{2}$$

⇒2^2a=2^3b⇒2a=3b⇒a​/b=3/2​

Explanation

Given:

(1+x)(1+x2)(1+x4)(1+x8)(1−x),

$$$$(1+x)(1+x2)(1+x4)(1+x8)(1−x)

This is a well-known identity in algebra that builds up as a geometric progression product:

Identity:

(1−x)(1+x)(1+x^2)(1+x^4)(1+x^8)=1−x^16

$$$$(1−x)(1+x)(1+x2)(1+x4)(1+x8)=1−x16

So,

(1+x)(1+x^2)(1+x^4)(1+x^8)(1−x)=1−x^16

$$$$(1+x)(1+x2)(1+x4)(1+x8)(1−x)=1−x16

Explanation

 24 is split into two parts such that 7 times the first plus 5 times the second is 146.

Let the first part be 

x, then the second is 

7x+5(24−x)=146

7x+120−5x=146

2x=26⇒x=13

Explanation

If $a + 3b = 6$ and $ab=3$, then the value of $a^2 + 9b^2$ is:

We are given:

a+3b=6(1),ab=3(2)

$$$$a+3b=6(1),ab=3(2)

Now square equation (1):

$$(a + 3b)^2 = 6^2 = 36 Rightarrow a^2 + 9b^2 + 6ab = 36$$

Use $ab = 3$

$$a^2 + 9b^2 + 6(3) = 36 Rightarrow a^2 + 9b^2 + 18 = 36 Rightarrow a^2 + 9b^2 = 18$$

Explanation

In the 2018 general elections, the Election Commission of Pakistan (ECP) declared 20,789 polling stations as sensitive out of a total of 85,307 established across the country. ​

These sensitive polling stations were distributed across the provinces as follows:​

• Khyber Pakhtunkhwa: 7,386
• Sindh: 5,776
• Punjab: 5,686
• Balochistan: 1,768
• Islamabad Capital Territory: 173​

Explanation

 In the 2018 general elections in Pakistan, approximately 80,000 prisoners across the country were denied their right to vote.