The following diagram shows part of the graph of the function f(x)= -12x + 26 and g(x) = -(1/5) ^ -x + 2 + 3 what are the soluti
ons of the equation -12 x + 26 = -(1/5) -x + 2 + 3
A. x = -22 and x = 3
B. x = 2 and x = 3
C. x = 2 and x = -22
D. x = 2 and x = 4
A. x = -22 and x = 3
B. x = 2 and x = 3
C. x = 2 and x = -22
D. x = 2 and x = 4
1 answer:
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Answer:
Step-by-step explanation:
Okay, so attached is a diagram of the triangle we are solving. Because buildings are almost always perpendicular (90 degrees) to the ground, it is a right triangle.
You can now use the pythagorean theorem with the sides to fill in the other side:
a^2+ b^2= c^2
5^2 + b^2= 22^2
25+b^2=484
b^2= 459
b=21.42
Okay, so for slope you need 2 points- think of the wall as your y axis, and the ground as your x axis. The ladder is the line.
Your first point is (-5,0) because the bottom of the ladder is touching the ground (no y movement) and the bottom of the ladder is 5 feet from the base of the wall and ground (origin).
The second point is going to be (0, 21.42) because that is the height of the wall where the ladder is touching (x is at origin). The 21.42 is positive, because you can't have negative height.
Okay so far? :)
(-5,0) and (0, 21.42)
(x1, y1) and (x2, y2)
slope= (y2-y1)/(x2-x1)
slope= (21.42-0)/ (0-(-5)) ---- becomes positive
slope= 4.284
(Note: slope could also be negative if you put the ladder on the other side of the wall- 5 would become positive... google "positive vs negative slopes" for more info)
Hopefully that answers your question!
