The answer should be A.
When we see the equation y=a^x we can relate to all the exponential functions, however, when the problem asked what points does all equations in that form pass through. I was instantly reminded by two facts.
One is that any number to the first is equal to itself. In other words, a^1=a
Another is that any number to the zero is equal to 1. a^x=1
if that is true, 1 will always be the x value since y=a^x and 0 will always be the x value because that is how y can be equal to one.
therefore, the answer is A: (0,1)
Answer:
Step-by-step explanation:
A 45 degree angle in a right triangle produces 2 equal sides. In this case z and the perpendicular line are equal. So that's were we'll start. Then you move on to the 60 degree angle to get x and y.
Finding z
z^2 + z^2 = (24√2) Combine the left
2z^2 = 24^2 * 2 Divide both sides by 2
2z^2/2 = 24^2/2
z^2 = 24^2 Take the square root of both sides
√z^2 = √24^2
z = 24
Finding x and y
The perpendicular = 24. Because it is a 60 degree angle that's given, we can do this without a calculator.
Tan 60 = opposite over adjacent
sqrt(3) = Perpendicular / z Multiply both sides by z
z*sqrt(3) = perpendicular
The above calculation tells us the perpendicular is 24
z*sqrt(3) = 24 Divide by sqrt 3
z = 24/√3
z = 24/1.73
z = 8√3
Finding x
Use Pythagoras to determine x
Perpendicular^2 + (8√3)^2 = x^2
24^2 + 8^2*3 = x^2
576 + 192 = x^2
768 = x^2
√x^2 = √768
x = 27.71
-6 + x = -7
+6 +6 add 6 to both sides, 6's cancel out on the left.
________
x = -1, is the answer.
Hope this helps! Let me know if you have any other questions related to this problem. :)
