What is the answer for this math problem
1 answer:
Answer:
The group of all ordered pairs lie on the line is (3, 7), (2, 6), (-2, 2) ⇒ D
Step-by-step explanation:
<em>To solve this type of question, Form the equation of the line and substitute the x-coordinate of each ordered pair to find y, if the value of y equal to the value of the y-coordinate of the point, then the point is on the line</em>
The 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 that passes through points (x1, y1) and (x2, y2) is m =
From the given figure
∵ The line passes through points (-4, 0) and (0, 4)
∴ x1 = -4 and y1 = 0
∴ x2 = 0 and y2 = 4
→ Substitute them in the rule above
∵ m = =
=
∴ m = 1
∵ b is the value of y at x = 0
∵ y = 4 at x = 0
∴ b = 4
→ Substitute the values of m and b in the form of the equation above
∴ y = 1(x) + 4
∴ y = x + 4 ⇒ equation of the given line
Let us check every group
∵ The ordered pairs are (7, 3), (6, 2), (2, -2)
∵ y = x + 4
∵ x = 7
∵ y = 7 + 4 = 11
∵ y-coordinate = 3
∴ Point (7, 3) doesn't lie on the line
∵ The ordered pairs are (5, 1), (3, 7), (2, 6)
∵ x = 5
∴ y = 5 + 4 = 9
∵ y-coordinate = 1
∴ Point (5, 1) doesn't lie on the line
∵ The ordered pairs are (3, 7), (2, 6), (2, 2)
∵ x = 3
∴ y = 3 + 4 = 7
∵ y-coordinate = 7
∴ Point (3, 7) lies on the line
∵ x = 2
∴ y = 2 + 4 = 6
∵ y-coordinate = 6
∴ Point (2, 6) lies on the line
∵ x = 2
∴ y = 6
∵ y-coordinate = 2
∴ Point (2, 2) doesn't lie on the line
∵ The ordered pairs are (3, 7), (2, 6), (-2, 2)
∵ x = 3
∴ y = 3 + 4 = 7
∵ y-coordinate = 7
∴ Point (3, 7) lies on the line
∵ x = 2
∴ y = 2 + 4 = 6
∵ y-coordinate = 6
∴ Point (2, 6) lies on the line
∵ x = -2
∴ y = -2 + 4 = 2
∵ y-coordinate = 2
∴ Point (-2, 2) lies on the line
∵ The three ordered pairs lie on the line
∴ The group of all ordered pairs lie on the line is (3, 7), (2, 6), (-2, 2)
∵ The ordered pairs are (1, 5), (-6, 2), (-7, -3)
∵ x = 1
∴ y = 1 + 4 = 5
∵ y-coordinate = 5
∴ Point (1, 5) lies on the line
∵ x = -6
∴ y = -6 + 4 = -2
∵ y-coordinate = 2
∴ Point (-6, 2) doesn't lie on the line
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Answer: Manager has evidence that the filling machine is over dash filling the cans.
Step-by-step explanation:
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Given claim : A can of soda is labeled as containing 15 fluid ounces.
i.e.
The quality control manager wants to verify that the filling machine is not over dash filling the cans.
i.e.
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So, the set of hypothesis for the given situation will be :-
Also, the quality control manager obtains a sample of 78 cans and measures the contents.
The sample evidence leads the manager to reject the null hypothesis.
That means he has evidence that the filling machine is over dash filling the cans.