Explanation

Equation: (4x + 1)/5 = (x + 9)/2

Step 1: Cross multiply to remove fractions

2(4x + 1) = 5(x + 9)

Step 2: Expand both sides

8x + 2 = 5x + 45

Step 3: Move x terms to one side, numbers to the other side

8x - 5x = 45 - 2

3x = 43

Step 4: Divide by 3

x = 43/3

Last verified on 25-05-2026

Explanation

Original equation: x^2 - 11x + 30 = 0

Factor it to find roots:

x^2 - 11x + 30 = (x - 5)(x - 6) = 0

So roots are 5 and 6.

Increase each root by 2:

New roots are 5 + 2 = 7 and 6 + 2 = 8.

New equation with roots 7 and 8 is:

(x - 7)(x - 8) = 0

x^2 - 8x - 7x + 56 = 0

x^2 - 15x + 56 = 0

Last verified on 25-05-2026

Explanation

Let the factors be (x - n) and (x - n - 1).

Multiply: (x - n)(x - n - 1) = x^2 - (2n + 1)x + n(n + 1).

Set n(n + 1) = 110, which gives n = 10.

Then p = 2n + 1 = 21.

Last verified on 25-05-2026

Explanation

If you multiply (a + bi) and (a - bi), you get:

(a + bi)(a - bi) = a_a - a_bi + bi_a - bi_bi

                 = a^2 - abi + abi - b^2_i^2

The middle terms cancel out. And i^2 = -1, so -b^2_i^2 = -b^2*(-1) = b^2.

That leaves a^2 + b^2.

You are told (a + bi)(a - bi) = 89, so a^2 + b^2 = 89.

Last verified on 25-05-2026

Explanation

• Pulpit means منبر

Last verified on 25-05-2026

Explanation

• Resurrection means حشر

Last verified on 25-05-2026

Explanation

• In indirect speech, present perfect (“have finished”) changes to past perfect (“had finished”) when the reporting verb is in past tense.
• So, “I have finished my work” becomes “she had finished her work.”

Last verified on 25-05-2026

Explanation

• In indirect speech, “can” changes to “could” when the reporting verb is in past tense (“said”).
• So, “I can drive” becomes “he could drive” in reported speech.

Last verified on 25-05-2026

Explanation

• Passive voice shows the action done to the subject instead of the subject doing the action.
• Here, “A song is sung by him” is in passive form.

Last verified on 25-05-2026

Explanation

• The sentence is in present continuous tense (“are writing”).
• So in passive voice it becomes is/am/are + being + past participle.
• Here, “a letter” (object) becomes the subject, and the action is ongoing.
• So “is being written” is correct.

Last verified on 25-05-2026