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1 answer:
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Answer:
b. 3.775
Step-by-step explanation:
The question is worded incorrectly since the sum of the first 100 counting numbers is actually greater than the sum of the first 50 counting numbers.
The sum of any set of consecutive numbers of size 'n' is given by:
Where A1 is the first number on the set and An is the last number.
The sum of the first 100 counting numbers (1 through 100) is:
The sum of the first 50 counting numbers (1 through 50) is:
The difference between those two values is:
Therefore, the sum of the first 100 counting numbers is 3,775 greater than the sum of the first 50 counting numbers.
Answer:
1. The slope of the line is -2
2. The y-intercept is 10
3. The equation in slope-intercept form is y = -2x + 10
Step-by-step explanation:
The slop-intercept form of the linear equation is y = m x + b, where
- m is the slope of the line
- b is the y-intercept (value y at x = 0)
- The rule of the slope of the line using two points on the line (x1, y1) and (x2, y2) is m =
From the given table
∵ (2, 6) and (3, 4) are two points on the line
∴ x1 = 2 and y1 = 6
∴ x2 = 3 and y2 = 4
→ Substitute them in the rule of the slope above to find it
∵ m = =
= -2
∴ m = -2
∴ The slope of the line is -2 ⇒ (1)
→ Substitute it in the form of the equation above
∴ y = -2x + b
→ To find b substitute x and y in the equation by the coordinates of
any point in the table
∵ (5, 0) is a point on the table
∴ x = 5 and y = 0
∵ 0 = -2(5) + b
∴ 0 = -10 + b
→ Add 10 to both sides
∵ 0 + 10 = -10 + 10 + b
∴ 10 = b
∴ The y-intercept is 10 ⇒ (2)
→ Substitute the value of b in the equation
∵ y = -2x + 10
∴ The equation in slope-intercept form is y = -2x + 10 ⇒ (3)