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masha68 [24]
4 years ago
8

Let R be a ring with identity and let S be a subring of R containing the identity. Prove that if m is a unit in S then u is a un

it in R. Show by example that the converse is false.
Mathematics
1 answer:
kumpel [21]4 years ago
5 0

Explanation:

Since m is a unit in S, then, there exists b ∈ S such that m*b = 1, where 1 is the identity. Since S is a subring of R we have that m ∈ R, and therefore b is also the multiplicative inverse of m in R. The converse isnt true.

The set of real numbers is a Ring with the standard sum and multiplication. Every real number different from 0 has a multiplicative inverse. For example, the inverse of 2 is 1/2. However, 2 is not a unit on the subring of Integers Z.

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When Vlad moved into his home a few years ago, there was a young oak tree in his backyard. He measured it once a year and found
ivanzaharov [21]

Answer:

175 cm

7 years

Step-by-step explanation:

Here is the complete question

When Vlad moved to his new home a few years ago, there was a young oak tree in his backyard.

He measured it once a year and found that it grew by 26 centimeters each year. 4.5 years after he moved into the house, the tree was 292 centimeters tall.

 1. How tall was the tree when Vlad moved into the house?

 2. How many years passed from the time Vlad moved in until the tree was 357 centimeters tall?

The formula for calculating future value:

FV = P + (r x n)

FV = Future height of the tree

P = Present height of the tree

R = growth rate

N = number of years

292 = p + (26 x 4.5)

292 = p + 117

p = 292 - 117

p = 175 cm

b. 357 = 175 + (26 x n)

375 - 175 = 26n

182 = 26n

n = 182 / 26 = 7 years

7 0
3 years ago
Determine the intervals on which the function is (a) increasing and (b) decreasing
Sav [38]
These intervals are measured by the x-values. Additionally, intervals of increase and decrease are always express with parentheses in interval notation. Therefore, the decreasing interval is (-2, 0)U(1, 3) and the increasing interval is (0, 1).

Hope this helps!
5 0
3 years ago
What is the answer to this question
loris [4]
I’m not gonna lie. I’m just answering so I could upload my question
8 0
3 years ago
Read 2 more answers
Ace car rental rents cars for x dollars per day plus y dollars for each time mile driven. Carlos rented a car fir 4 days, drove
kati45 [8]
4x + 160y = 120
and
1x + 240y = 80

that will be be the equations. if we multiply the bottom equation by 4 we get:
4x + 960y = 320

now subtract one equation from another:
4x + 160y = 120
-(4x + 960y = 320)

and get:
-800y = -200
y = $0.25

now plug this into one equation
x +240(.25) = 80
x + 60 = 80
x = $20

so $20 per day and $0.25 per mile
4 0
3 years ago
What is the graph of the function f(x)= 2x^2 -7x^2+2x+3
Dmitriy789 [7]

https://www.mathpapa.com/algebra-calculator.html?q=f(x)%3D2x%5E2-7x%5E2%2B2x%2B3

6 0
3 years ago
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