Let the smaller number be x.
The larger number is x + 2.
Given:
x² + (x + 2)² = 100
x² + x² + 4x + 4 = 100
2x² + 4x - 96 = 0
x² + 2x - 48 = 0
(x + 8)(x - 6) = 0
x = -8 or x = 6
If x = -8, larger number = -8 + 2 = -6
If x = 6, larger number = 6 + 2 = 8
Let's denote the number as x. The equation based on the given information is:
6.2x + 8 = 31
Step 1: Solve for x
Subtract 8 from both sides:
6.2x = 23
Step 2: Divide by 6.2
x = 23 / 6.2
x = 3.709677...
x ≈ 3.7
To solve this, we'll convert the numbers from base 5 to decimal, perform the subtraction, and then convert back to base 5 if needed. However, let's directly calculate in base 5.
(432)5 - (234)5
Performing subtraction in base 5:
432
- 234
------
143
The result is (143)5.
The average of the first n natural numbers is given by (n + 1) / 2.
For n = 97:
Average = (97 + 1) / 2
= 98 / 2
= 49
We are told:
Average of 5 numbers = 34
Total sum of 5 numbers = 34 × 5 = 170
Given 3 numbers: 28, 30, 32
Sum of these = 28 + 30 + 32 = 90
Remaining sum = 170 - 90 = 80
Remaining numbers = 2
Average of remaining = 80 ÷ 2 = 40
To find the average, add up all the numbers and divide by the total count.
Step 1: Calculate the sum
Sum = 0 + 0 + 4 + 10 + 5 + 5
= 24
Step 2: Calculate the average
Average = Sum / Count
= 24 / 6
= 4
Given the average of 10, k, and 30 is 21:
(10 + k + 30) / 3 = 21
Multiply both sides by 3:
10 + k + 30 = 63
Combine constants:
40 + k = 63
Subtract 40 from both sides:
k = 23
The perfect squares between 4 and 32 are:
4 = 2²
9 = 3²
16 = 4²
25 = 5²
The largest perfect square between 4 and 32 is 25.
In the number 485.21:
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