Explanation

"Whom are you looking for?"

"Whom" is the objective case of "who" and should be used when it functions as the object of a verb or preposition.

In this sentence, "whom" is the object of the preposition "for," making it grammatically correct.

Explanation

Step 1: Perform polynomial long division or synthetic division

To find the quotient when (2x³ - 5x²y + 5xy² - 3y³) is divided by (2x - 3y), let's try factoring or direct division.

Step 2: Factor the numerator if possible

Notice that (2x³ - 5x²y + 5xy² - 3y³) can be factored as:

(2x³ - 3x²y) + (-2x²y + 3xy²) + (2xy² - 3y³)

= x²(2x - 3y) - xy(2x - 3y) + y²(2x - 3y)

= (2x - 3y)(x² - xy + y²)

Step 3: Identify the quotient

Given the factorization (2x - 3y)(x² - xy + y²), the quotient when (2x³ - 5x²y + 5xy² - 3y³) is divided by (2x - 3y) is x² - xy + y².

Explanation

Sigmund Freud's Psychoanalytic Model focuses on the unconscious mind, childhood experiences, and the structure of personality (Id, Ego, Superego).

It differs from other models by emphasizing inner conflicts and unconscious motives.

Explanation

Given:

α + β = 5 (sum of roots)

αβ = k (product of roots)

3α + 2β = 16

From α + β = 5, we get:

α = 5 - β

Substitute α in 3α + 2β = 16:

3(5 - β) + 2β = 16

15 - 3β + 2β = 16

-β = 1

β = -1

Now, α = 5 - β

α = 5 - (-1)

α = 6

k = αβ

k = 6 × (-1)

k = -6

Explanation

Erik Erikson proposed the Psychosocial Development Theory, which includes 8 stages, each marked by a specific conflict (e.g., trust vs. mistrust).

Successful resolution of these conflicts leads to healthy personality development.

Explanation

Given x = -1 and y = -3:

Let's evaluate the expression 5y² - 2(x² - 4xy) - 5y:

1. Calculate 5y² = 5(-3)² = 5(9) = 45

2. Calculate x² = (-1)² = 1

3. Calculate 4xy = 4(-1)(-3) = 12

4. Calculate x² - 4xy = 1 - 12 = -11

5. Calculate -2(x² - 4xy) = -2(-11) = 22

6. Calculate -5y = -5(-3) = 15

Now, combine the results:

5y² - 2(x² - 4xy) - 5y = 45 + 22 + 15

= 82

Explanation

The Soviet Union suffered approximately 50,000 military casualties during their occupation of Afghanistan (1979–1989).

These heavy losses, along with economic strain and Afghan resistance, contributed to their withdrawal in 1989.

Explanation

To find the LCM of 90, 110, and 150:

Step 1: Prime factorize each number.

90 = 2 × 3² × 5

110 = 2 × 5 × 11

150 = 2 × 3 × 5²

Step 2: Identify the highest power of each prime factor.

Highest power of 2: 2¹

Highest power of 3: 3²

Highest power of 5: 5²

Highest power of 11: 11¹

Step 3: Calculate the LCM.

LCM = 2 × 3² × 5² × 11

= 2 × 9 × 25 × 11

= 4950

Explanation

He asked her why she had lied to him.

The reporting verb “said to” becomes “asked” for a question.

In indirect speech, the past simple “did lie” changes to past perfect → “had lied”.

Explanation

Jean Piaget proposed that cognitive growth occurs through assimilation (taking in new info) and accommodation (modifying ideas).

His theory of cognitive development explains how children build knowledge through active exploration.