Simon must maintain an average grade of 80% or better in his math class to be eligible to play sports. His math grades so far are: 80%, 84%, 76%, 77%. At this point, his grades make him ineligible to play. What is the lowest he score on his next grade to bring his average score up to an 80%. Part A: Write an inequality to represent the average of the five grades as greater than or equal to 80%. Part B: Use the inequality from Part A to prove what his lowest score could be on the 5th test.

(a)

(b)83%

Step-by-step explanation:

His math grades so far are: 80%, 84%, 76%, 77%.

Let the lowest score required to bring his average score up to an 80% =x

(A)Average of the five scores

=

=

If the average of the five grades as greater than or equal to 80%.

Then:

(b) To find what his lowest score should be, we solve the inequality derived in part A.

Cross Multiplying

The lowest score he requires is 83%.

∠acb = 8°

step-by-step explanation:

∠xba lies on the circle and is half the measure of the intercepted arc ax

hence

measure of arc ax = 2 × 42° = 84°

∠acb is outside the circle and is

∠acb = (arcab - arcax ), hence

∠acb = 0.5 (100 - 84) = 0.5 × 16° = 8°