All questions of Inequalities for JAMB Exam

Explanation:

Given values:
x = 15
y = 10
z = 9

Calculations:
1. Find the minimum of y and x-z:
min(y, x-z) = min(10, 15-9) = min(10, 6) = 6

2. Find the maximum of x, y, and z:
ma(x, y, z) = max(15, 10, 9) = 15

3. Evaluate the expression:
le(x, min(y, x-z), le(9, 8, ma(x, y, z)) = le(15, 6, le(9, 8, 15))

4. Compare 9 and 8:
le(9, 8) = 0 (as 9 is not less than 8)

5. Evaluate the expression further:
le(15, 6, 0) = 6

Therefore, the value of le(x, min(y, x-z), le(9, 8, ma(x, y, z)) for the given values is 6, which corresponds to option 'b'.

Explanation:

Given:
x, y, and z are three positive integers such that x > y > z.

To find:
The expression closest to the product xyz.

Solution:

Approach:
To find the closest expression to the product xyz, we need to consider the given condition x > y > z.
- We know that x is the largest among x, y, and z. So, the closest expression to xyz would be when we replace x with (x - 1) to get a smaller value.
- This is because if we replace x with (x - 1), the product xyz will decrease, making it closer to the actual value.

Calculations:
Let's consider option A: (x - 1)yz
- If we substitute x with (x - 1), the expression becomes: (x - 1)yz
- The product of this expression is: (x - 1) * y * z
- This expression will be closest to the product xyz because we are replacing the largest value x with (x - 1), making the product smaller.
Therefore, option A: (x - 1)yz is the closest to the product xyz.

To solve the given expression ma(10, 4, le((la10, 5, 3), 5, 3)), we need to follow the order of operations (also known as PEMDAS/BODMAS).

Step 1: Evaluate the innermost expression
The innermost expression is le((la10, 5, 3), 5, 3). Let's break it down further:
- la10 means the largest among 10, 5, and 3, which is 10.
- le(10, 5, 3) means the smallest among 10, 5, and 3, which is 3.

So, the innermost expression evaluates to 3.

Step 2: Substitute the innermost expression in the main expression
Now, we substitute the value of the innermost expression (3) in the main expression: ma(10, 4, 3).

Step 3: Evaluate the main expression
The expression ma(10, 4, 3) means the arithmetic mean (average) of the three numbers: 10, 4, and 3.

Arithmetic Mean Formula: sum of numbers/total number of numbers

Sum of numbers = 10 + 4 + 3 = 17
Total number of numbers = 3

Arithmetic Mean = 17/3 = 5.67

Rounded to one decimal place, the value of ma(10, 4, 3) is 5.7.

Step 4: Corresponding option
The correct option given is 'B' which states the value as 6.5. However, this does not match the calculated value of 5.7. Hence, the correct option should be re-evaluated or reviewed, as it does not match the calculated value.

The expression |x2 - 2x| represents the absolute value of the quadratic expression x^2 - 2x.

To find the absolute value of x^2 - 2x, we need to consider the cases when the expression inside the absolute value is positive and negative.

When x^2 - 2x is positive (greater than or equal to zero):
x^2 - 2x ≥ 0
x(x - 2) ≥ 0

In this case, the absolute value of x^2 - 2x is simply x^2 - 2x.

When x^2 - 2x is negative (less than zero):
x^2 - 2x < />
x(x - 2) < />

In this case, the absolute value of x^2 - 2x is -(x^2 - 2x), which is equal to -x^2 + 2x.

Therefore, the expression |x^2 - 2x| can be written as:

x^2 - 2x, for x ≤ 0 or x ≥ 2
-x^2 + 2x, for 0 < x="" />< 2="" />

I'm sorry, I don't understand the context of your message. Can you please provide more information or clarify your request?

If x = 5, then the equation y = 2x + 3 can be solved as follows:

y = 2(5) + 3
y = 10 + 3
y = 13