Explanation

To find the greatest possible length of each piece, we need to find the greatest common divisor (GCD) of 18, 42, and 24.

Factors of 18: 1, 2, 3, 6, 9, 18

Factors of 42: 1, 2, 3, 6, 7, 14, 21, 42

Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24

The greatest common factor is 6.

Explanation

Let's solve the equation step by step:

3(y - 2) + 4(y - 3) = 5y + 14 - 4(y - 8)

Expanding the equation:

3y - 6 + 4y - 12 = 5y + 14 - 4y + 32

Combine like terms:

7y - 18 = y + 46

Subtract y from both sides:

6y - 18 = 46

Add 18 to both sides:

6y = 64

Divide by 6:

y = 64 / 6

y = 32 / 3

Explanation

The even numbers from 2 to 18 are: 2, 4, 6, 8, 10, 12, 14, 16, 18.

To find the average, we'll add these numbers and divide by 9:

Sum = 2 + 4 + 6 + 8 + 10 + 12 + 14 + 16 + 18 = 90

Average = Sum / Number of terms

= 90 / 9

= 10

Explanation

Let's find the common difference (d) of the arithmetic sequence.

Step 1: Write the formula for the nth term

an = a + (n - 1)d

Step 2: Plug in the values

a = 2, n = 6, an = 27

27 = 2 + (6 - 1)d

27 = 2 + 5d

Step 3: Solve for d

25 = 5d

d = 25/5

d = 5

Explanation

Step-by-step binary addition:

1 + 1 = 10 (0, carry 1)

0 + 1 + 1 (carry) = 10 (0, carry 1)

1 + 1 + 1 (carry) = 11 (1, carry 1)

Final result: (1100)₂

Explanation

Explanation

The equation x = 4 represents a vertical line.

Vertical lines are always parallel to the y-axis.

Explanation

If x - 1 is a factor of x² - kx + 3, then substituting x = 1 should make the expression zero.

Substituting x = 1 in x² - kx + 3 = 0 gives:

(1)² - k(1) + 3 = 0 ⟹ 1 - k + 3 = 0 ⟹ k = 4.

Explanation

The expression is 2x² + 8x + 8. First, factor out 2:

→ 2(x² + 4x + 4)

Now factor the quadratic:

→ x² + 4x + 4 = (x + 2)(x + 2)

So the full factorization is 2(x + 2)(x + 2).

Explanation

To find out what fraction of the whole pizza Madeeha got:

Nida had 3/12 of the pizza and gave 1/8 of that to Madeeha.

First, simplify 3/12 to 1/4.

Madeeha got 1/8 of 1/4:

(1/8) × (1/4) = 1/32

Madeeha got 1/32 of the whole pizza.