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

Given:

LCM = 456

HCF = 6

One number = 24

Let's denote the other number as x. We know:

LCM * HCF = Product of the numbers

456 * 6 = 24 * x

2736 = 24x

x = 2736 / 24

x = 114

Explanation

To evaluate the expression:

Log₁₀ √10

First, rewrite the square root as an exponent:

√10 = 10^(1/2)

Now, apply the logarithm:

Log₁₀ 10^(1/2)

Using the property of logarithms that states logₐ a^x = x:

Log₁₀ 10^(1/2) = 1/2

Explanation

Negative integers are all numbers less than 0 (e.g., -1, -2, -3, ...).

They lie to the left of zero on the number line.

Explanation

0.8

-0.3

0.5

---------

1.0

****

0.8-0.3+0.5=1

Explanation

Universal set (U) = {1, 2, 3, 4, 5, 6}

Set A = {2, 3}

Complement of A means all elements in U that are not in A → {1, 4, 5, 6}

Explanation

The fourth root of 256 is:

⁴√256 = ⁴√(4^4) = 4

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