The linear function f(x) = 0.5x + 80 represents the average test score in your math class, where x is the number of the test taken. The linear function g(x) represents the average test score in your science class, where x is the number of the test taken. xg(x) 181
283
385

Part A: Determine the test average for your math class after completing test 2. (2 points)

Part B: Determine the test average for your science class after the completing test 2. (2 points)

Part C: Which class had a higher average after completing test 4? Show work to support your answer. (6 points)

Part A:

After completing 2 tests, the average test score in math class is 81

Part B:

After completing 2 tests, the average test score in science class is 83

Part C

Science class has the highest test score after 4 tests

Step-by-step explanation:

Part A:

The given function for the average test score in math class is f(x) = 0.5·x + 80

After completing 2 tests, we have the average test score in math class is f (2) = 0.5 × 2 + 80 = 81

Part B:

For science class

From the table given, the average test score, after completing 2 test is x = 2 g(x) = 83

The average test score, after completing 2 test is 83

Part C

After completing 4 tests, we have;

The average test score for math f ( 4 ) = 0.5 × 4 + 80 = 82

For science, we have that the equation for the average test score, g(x) is found as follows;

The rate of change of g(x) with x for point 1 and 2 = (83 - 81)/(2 - 1) = 2

For point 3 and 2 = (85 - 83)/(3 - 2) = 2

Therefore we have;

(y - 81)/(x - 1) = 2

y - 81 = 2×(x - 1)

y = 2·x -2 + 81 = 2·x + 79

g(x) = 2·x + 79

After completing 4 test, we have;

g (4) = 2 × 4 + 79 = 87

Since 87 > 82, science class has the highest test score after 4 tests.

δabc ≅ δdcb by sas because

db ≅ ac . . given (side)

bc ≅ bc . . reflexive property (side)

∠dbc ≅ ∠ acb . . alternate interior angles where transversal bc crosses parallel lines bd and ac (included angle)

step-by-step explanation: