Answer:
4.1
Step-by-step explanation:
Let the first number of the five we are looking for equal n.
Because the numbers are consecutive, the next four can be expressed as (n+1), (n+2), (n+3) and (n+4).
Our series of 5 numbers is therefore n,(n+1),(n+2),(n+3),(n+4).
We are told the sum of the squares of the first 3 is equal to the sum of the squares of the last 2 therefore:
n² + (n+1)² + (n+2)² = (n+3)² + (n+4)²
expand all the brackets to give
n² + n² + 2n + 1 + n² + 4n + 4 = n² + 6n + 9 + n² + 8n + 16
3n²+6n+5 = 2n²+14n+25
n²-8n-20=0
factorising this gives us
(n+2)(n-10) = 0 so the solutions are n=10 and n=-2
That means that n,(n+1),(n+2),(n+3),(n+4) could be [-2, -1, 0, 1 and 2] or [10, 11, 12, 13 and 14].
Since the question asks for whole numbers, and negative numbers are not classed as whole numbers, the numbers we want must be 10, 11, 12, 13 and 14.
You can check this on a calculator by doing 10² + 11² + 12² (=365) and 13² + 14² (=365).
First you need to multiply 52 x 40 = 2080
then you need to divide 2080 from 60,000.
The answer will be 60000/2080 is approximately $28.85
Answer:
10 units
Explanation:
Create a right triangle, determine the a and b side lengths of the triangle by looking at the graph. (See image)
Then use the Pythagorean theorem to find c.
a² + b² = c²
(8)² + (6)² = c²
64 + 36 = c²
100 = c²
Square root both sides to get c.
= c
10 = c
First, subtract both sides by 25:
x^2 - 6x = -25
Because we're completing the square, we subtract both sides by 9:
x^2 - 6x - 9 = -34
(x - 3) = 5.831 (about)
x = 8.831
