Explanation

Given:

ab + bc + ca = -4

a² + b² + c² = 17

Using the identity (a + b + c)² = a² + b² + c² + 2(ab + bc + ca):

(a + b + c)² = 17 + 2(-4)

= 17 - 8

= 9

a + b + c = ±√9

= ±3

Explanation

A puppy is a young dog, just as cubs are young lions.

The relationship is of young one to its adult form.

Explanation

والدین بچوں کے سب سے قریب ہوتے ہیں، اس لیے وہ ان کے رویوں اور جذبات کا گہرا مشاہدہ کر سکتے ہیں۔

وہ گھر کے ماحول میں بچوں کے مسائل کو بہتر سمجھ کر ان کی جذباتی اور تعلیمی رہنمائی کر سکتے ہیں۔

Explanation

The phrase "on the way" means something is physically blocking or present along the path.

"There was a parked van on the way" is grammatically and contextually correct.

Explanation

"Last night" tells when the action happened.

Adverbs of time describe when something occurs (e.g., today, yesterday, last night).

Explanation

BTES stand for Beginning Tender Evaluation Study.

The BTES suggests that acquiring knowledge is best viewed as an ongoing process over multiple years.

It emphasizes that learning doesn't happen instantly but develops progressively over time.

Explanation

Let's denote the son's current age as x. Then the father's current age is 13x.

After 4 years:

Son's age = x + 4

Father's age = 13x + 4

According to the problem, after 4 years, the father's age will be 5 times the son's age:

13x + 4 = 5(x + 4)

13x + 4 = 5x + 20

8x = 16

x = 2

So, the father's current age is 13x = 13 * 2 = 26.

Explanation

Given A = [a b; b a] and A² = [l m; ...], let's calculate A²:

A² = [a b; b a] * [a b; b a]

= [a² + b² 2ab; 2ab a² + b²]

Comparing A² = [l m; ...] with our calculation:

l = a² + b²

m = 2ab

The correct answer is l = a² + b², m = 2ab.

Explanation

Let's simplify the expression:

log6 25 − 2 log6 5 + log6 a

Since 25 = 5^2:

log6 25 = log6 (5^2) = 2 log6 5

So, the expression becomes:

2 log6 5 - 2 log6 5 + log6 a

= log6 a

If this expression equals 0 (assuming that's the goal):

log6 a = 0

This implies:

a = 6^0

a = 1

Explanation

The words like on, over, at, under, by etc. are called Prepositions.

"Under" is a preposition showing the relationship between the cat and the table.

Prepositions indicate position, direction, or time in a sentence.