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Verizon [17]
3 years ago
5

What does it mean by find the slope of each line

Mathematics
1 answer:
beks73 [17]3 years ago
6 0

Answer:

.

Step-by-step explanation

Find the run and the rise.

To do that:

- There is a right angle where the points meet. The bottom one (2,-2) is three units away from the top one, (-2,-1)and then one upwards and they will meet.

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Determine,in each of the following cases, whether the described system is or not a group. Explain your answers. Determine what i
zheka24 [161]

Answer:

(a) Not a group

(b) Not a group

(c) Abelian group

Step-by-step explanation:

<em>In order for a system <G,*> to be a group, the following must be satisfied </em>

<em> (1) The binary operation is associative, i.e., (a*b)*c = a*(b*c) for all a,b,c in G </em>

<em>(2) There is an identity element, i.e., there is an element e such that a*e = e*a = a for all a in G </em>

<em> (3) For each a in G, there is an inverse, i.e, another element a' in G such that a*a' = a'*a = e (the identity) </em>

<em> </em>

If in addition the operation * is commutative (a*b = b*a for every a,b in G), then the group is said to be Abelian

(a)  

The system <G,*> is not a group since there are no identity.  

To see this, suppose there is an element e such that  

a*e = a

then  

a-e = a which implies e=0

It is easy to see that 0 cannot be an identity.

For example  

2*0 = 2-0 = 2

Whereas

0*2 = 0-2 = -2

So 2*0 is not equal to 0*2

(b)

The system <G,*> is not a group either.

If A is a matrix 2x2 and the determinant of A det(A)=0, then the inverse of A does not exist.

(c)

The table of the operation G is showed in the attachment.

It is evident that this system is isomorphic under the identity map, to the cyclic group

\mathbb{Z}_{5}

the system formed by the subset of Z, {0,1,2,3,4} with the operation of addition module 5, which is an Abelian cyclic group

We conclude that the system <G,*> is Abelian.

Attachment: Table for the operation * in (c)

4 0
3 years ago
What are the zeros of the graphed function y = 1/3 (x + 3)(x + 5)?
Darya [45]

One factor will be zero, hence y will be zero, when x=-3.

The other factor will be zero, hence y will be zero, when x=-5.

The zeros of the function are x ∈ {-5, -3}.

_____

This solution makes use of the "zero product rule," which states a product is zero if and only if one or more factors is zero.

5 0
3 years ago
Pentagon DEFGH is translated 4 units to the right to create pentagon UVXYZ. DE is 5cm long. What is the length of UV?
creativ13 [48]
If a shape is translated (has it's vertex' coordinates moved/changed), then it retains its original values but just has different vertex coordinates.

Thus since DE is equal to UV, then,

DE = UV; substitution:
5=5
5 0
3 years ago
A. y=82x + 998<br> b. y=247.7x - 335<br> c. y=743x - 1647<br> d. y=998x + 82
MrMuchimi
A is the answer for the question
3 0
3 years ago
Read 2 more answers
PLEASE HELP 10 POINTS!!!
inna [77]

Answer:

Step-by-step explanation:

B.

7 0
3 years ago
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