Find the sum. 10 + 12 + 14 + ... + 80
1 answer:
Answer:
1620
Step-by-step explanation:
The amount of even integers between 10 and 80 inclusive is 36 (5 for each interval of 10 [e.g., 10-19 has 5, 20-29 has 5] and one extra for 80).
Since the numbers are consecutive even numbers, we can use the fact that the sum of the numbers is equal to the average of the numbers, times the number of numbers.
The average of the numbers is 45, since . We can use only the two outer numbers to determine the average since the numbers are all evenly spaced as they are consecutive even numbers.
, so the sum is 1620.
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Using linear function concepts, a system of equations with no solutions is created when:
A linear function is modeled by:
y = mx + b
In which:
- m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.
- b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.
The intersection of two lines is the solution of a system of equations. If two lines have the <u>same slope and different intercepts</u>, they will never intercept, that is, the system will not have a solution.
The lines are given as follows:
- y = mx + b.
- y = -2x + 3/2.
Hence, for a system with no solution, we need that:
More can be learned about linear function concepts at brainly.com/question/24808124
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