Answer:
A. ∠ QPR = 17°
Step-by-step explanation:
From the given information, let QP be the length of the ramp.
Then, ∠ QPR is the angle between the ramp and the ground.
∠ PQR is the angle between the ramp and the doorpost and
∠ QRP is the angle between the doorpost and the ground.
Clearly, ∠ PQR = 73° (given)
∠ QRP = 90° (since doorpost and the ground are perpendicular to each other)
Now, use triangle sum propoerty of ΔQPR, we get,
∠ QPR + ∠ PQR + ∠ QRP = 180°
∠ QPR + 73 + 90 = 180°
∠ QPR + 163 = 180°
∠ QPR = 180 - 163
∠ QPR = 17°
Step-by-step explanation:
let Sean be 4 years old and Rachel be 2 years old on April 17
part (A)
R=S-2 --(A)
is an equation that can be used to determine Rachel's age
likewise,
S=R+2--(B)
can be used to determine Sean's age
part (B)
use equation(A) for table (1) and equation(B) for table 2
Table (1) : R=S-2=11-2= R=9
12-2=10=»R=10
13-2=11=»R=11
14-2=12=»R=12
15-2=13=»R=13
16-2=15=»R=14
likewise use equation B for the table (2)
the outputs must be 3,4,5,6,7,8
and 9
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).
-7 ÷ 2 1/2
Okay, so first, put the -7 over one and make 2 1/2 an improper fraction. so now:
-7/1 ÷ 5/2
Then, take the reciprocal of 5/2 and multiply it by -7/1
-7/1 × 5/2
Which would be -35/2