Answer:
y = -
x
Step-by-step explanation:
the equation of a linear function in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Calculate m using the slope formula
m = 
with (x₁, y₁ ) = (- 8, 2) and (x₂, y₂ ) = (1, - 4) ← 2 ordered pairs from the table
m =
=
=
= - 
the ordered pair (0, 0 ) indicates the line crosses through the origin, then
c = 0
y = -
x + 0 , that is
y = -
x ← equation of linear function
Answer:
the two consecutive integers are 6 and 7.
Step-by-step explanation:
Im %99 sure
Given
Expenditures at Manager's Store; expenditures at Competitor's Store.
Find
a) average spent at each store
b) which store is better represented by the mean value
c) an explanation for the answer in ≥ 2 sentences
Solution
a) The sum of expenditures divided by the number of expenditures (15) is ...
... average for Manager's Store: $37.60
... average for Competitor's Store: $48.53
b) The expenditures at Manager's Store are well-represented by the mean (average).
c) The range of expenditures at Competitor's Store is significantly higher than at Manager's store, so a single number such as mean or median does not represent the data well. The expenditures at Manager's store are more compactly grouped around the mean and median, which are closer together, so the mean is a good representation of Manager's Store expenditures overall.
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).
Answer:
1. 2
2. 25
3. 1/3
I'm in 8th grade so not 100% sure about these
I'm gonna try the rest
But this is what I got so far!