Is y=5x-3 perpendicular to x+5y=2
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Answer:
yes to both
Step-by-step explanation:
For a relationship to be a function then each value of x must relate to exactly one unique value of y.
This is the case in this table as
2 → 76
4 → 152
6 → 228
All unique values thus a function
To determine if it is linear then the rate of change is constant for each set of ordered pairs. This is measured using the slope formula.
m =
with (x₁, y₁ ) = (2, 76) and (x₂, y₂ ) = (4, 152 ) ← ordered pair from table
m = =
= 38
Repeat with (x₁, y₁ ) = (4, 152) and (x₂, y₂ ) = (6, 228)
m = =
= 38
Since rate of change is constant then function is linear
The height of the ball initially is 54 inches. The common ratio has been provided which is 0.750.
The explicit formular for the geometric sequence is shown as;
The explicit formula is shown as;
54 x (0.750)^9
The rest is simply to solve for the height on the 10th bounce