What is the relationship between the slope of the line and the side lengths of the triangles?
1 answer:
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Step-by-step explanation:
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Answer:
See explanation.
Step-by-step explanation:
Part A.
If two curves intersect, they have the same x- and y-coordinates.
So if we set the y-coordinates equal to each other, we are finding for what x-coordinate those y-coordinates will be the same. Therefore solving 2^(-x)=8^(x+4) gives us an x- so that both sides are the same (where both sides represent the corresponding y- coordinate for that x- in the curves given by y=2^(-x) and y=8^(x+4).
Part B.
x | 2^(-x) | 8^(x+4)
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-3 2^(-(-3))=2^3=8 8^(-3+4)=8^1=8
-2 2^(-(-2))=2^2=4 8^(-2+4)=8^2=64
-1 2^(-(-1))=2^1=2 8^(-1+4)=8^3=512
0 2^(-(0))=2^0=1 8^(0+4)=8^4=4096
1 2^(-(1))=2^(-1)=1/2 8^(1+4)=8^5=32768
2 2^(-(2))=2^(-2)=1/4 8^(2+4)=8^6=262144
3 2^(-(3))=2^(-3)=1/8 8^(3+4)+8^7=2097152
So in the table we see both lists have the same y-coordinate when the x-coordinate is -3.
The solution to equation 2^(-x)=8^(x+4) is therefore x=-3 since the table tells us both sides is the same value, 8, for this x-coordinate.
Part C.
You can graph both curves given by y=2^(-x) and y=8^(x+4) on the same coordinate plane. Where they intersect is the solution.
I use the table in part B to help guide me in plotting the points to help graph the curves for each equation. I have included a visual in an attachment.
They cross at (-3,8) so this is the solution.
So this tells me 2^(-x)=8^(x+4) has solution at x=-3 since both sides will be 8 at that x-.
