Answer:
Step-by-step explanation:
REcall the following definition of induced operation.
Let * be a binary operation over a set S and H a subset of S. If for every a,b elements in H it happens that a*b is also in H, then the binary operation that is obtained by restricting * to H is called the induced operation.
So, according to this definition, we must show that given two matrices of the specific subset, the product is also in the subset.
For this problem, recall this property of the determinant. Given A,B matrices in Mn(R) then det(AB) = det(A)*det(B).
Case SL2(R):
Let A,B matrices in SL2(R). Then, det(A) and det(B) is different from zero. So
.
So AB is also in SL2(R).
Case GL2(R):
Let A,B matrices in GL2(R). Then, det(A)= det(B)=1 is different from zero. So
.
So AB is also in GL2(R).
With these, we have proved that the matrix multiplication over SL2(R) and GL2(R) is an induced operation from the matrix multiplication over M2(R).
The percentage decrease is 60% decrease because it changed by 81 and 81 is 60% of 135
Answer:
Money owned by Steve = $11
Money owned by Ben = $13
Step-by-step explanation:
Let x denotes the money owned by Steve and y denotes the money owned by Ben.
Then, Steve gives $3 to Ben
Money left with Steve = x-3 and Ben = y+3
Now, Ben will have twice as much as Steve.
⇒ y+3 = 2(x-3) .............(1)
If Ben gives Steve $7
Money left with Steve = x+7 and Ben = y-7
Then, the amount Ben has will be one-third that of Steve’s.
⇒ y-7 = 
(x+7) ..........(2)
Solving equation (1) and (2) by elimination method, we get
x = 11 and y = 13
⇒ Money owned by Steve = $11
Money owned by Ben = $13
Answer:
<em><u>$432</u></em>
Step-by-step explanation:
Students:24
Ticket:$9
Lunchbox:$9
9+9=18
24x18=$432
The given functions are
Now these are exponential curves and the bases for the functions are 3.5 & 1.5
Also the graph of g(x) is between f(x) & h(x)
Hence the value of base called the scale factor must be between 3.5 & 1.5.
4 & 5 are more than 3.5
0.9 is smaller than 1.5
But π = 3.14 lies between 3.5 & 1.5.
Hence the only option which can represent the graph of g(x) is
Option D) is the right answer
