The exponential model best represents the data is B. f(x) = 5(0.2)^x
<h3>How to determine the
exponential model?</h3>
From the table of values, we have the following points:
(x, y) = (0,5) and (1,1)
An exponential model is represented as:
y = ab^x
Substitute (x, y) = (0,5)
5 = ab^0
5 = a
This gives
a = 5
So, we have:
y = 5b^x
Substitute (x, y) = (1,1)
1 = 5b^1
This gives
5b = 1
Divide by 5
b = 0.2
Substitute b = 0.2 in y = 5b^x
y = 5(0.2)^x
Hence, the exponential model best represents the data is B. f(x) = 5(0.2)^x
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Answer:
12.449899598
Step-by-step explanation:
You would use pythagoras thereom.
C^2=A^2+B^2
The hypotenuse is C (which is the longest side of the triangle - 18).
18×18=13×13+B^2
324=169+B^2
324-169=B^2
155=B^2
Square root B to get B on it's own which would be 12.449899598.
Measure angle ACD = 3x - 2
measure angle BCD = 5x - 20
measure angle ACD = measure angle BCD
3x - 2 = 5x - 20
-2 = 2x - 20
18 = 2x
9 = x
x = 9
measure angle BCD = 5x - 20
measure angle BCD = 5(9) - 20
measure angle BCD = 45 - 20
measure angle BCD = 25
measure angle CDA = 90
measure angle BDC = measure angle CDA
measure angle BDC = 90
measure angle DBF = measure angle BCD + measure angle BDC
measure angle DBF = 25 + 90
measure angle DBF = 115
