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2 answers:
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Answer:
CNBD
Step-by-step explanation:
From the diagram, we can see that:
Then by Alternate Interior Angles:
From vertical angles, we also know that:
This is all we can gather from the given image. Knowing only three pairs of angles cannot prove congruence, as proving congruence requires at least one side.
Congruence cannot be determined.
Answer:
See below
Step-by-step explanation:
To find the values of a and b, we use the intersection point P.
Since the graph of f is intersected by P=(-2,2), f(-2)=2, that is, a(2)^(-2)=2. Then a=2(2)²=8.
Since the graph of g is intersected by P=(-2,2), g(-2)=2, that is, -2+b=2. Then b=2+2=4.
Hence a=8, b=4.
To find the other point of intersection Q, we need to find a number x such that f(x)=g(x), that is, 8(2)^(x)=x+4. Rewrite this equation as follows:
It is not easy to solve this equation analitically. Instead, you can apply a quantitative method. First, the left hand side is an exponential function, so it is always positive. Then the solution will be a number in which the right side (x+4) is positive, that is, x > -4. The solution is an integer, then the possible values are x=-3,-2,-1,0,1,2,...
Now, the RHS must be a power of two, so the possible integers are x=-3,-2,0,4,12,28,... However, the LHS grows very quickly, while the LHS grows slowly. Then, it is only necessary to test small integer values (we already know that x=-2 is a solution).
If we test with x=-1, we get 2²=4=3, then x=-1 is not a solution. Any x>-1 will not be a solution, because f increases much faster than g, and then they won't intersect. So our possibilities reduce to x=-3,-2. Taking x=-3, we get f(-3)=2⁰=1=-3+4=g(-3). Thus, (-3,0) is the other point of intersection Q. (r=-3, s=0).