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Verizon [17]
3 years ago
13

Which of the following statements are the same? (A) x -= x + 4 (B) x = x + 4 - x (C) x = x - (x + 4) (A) and (B) are the same (A

) and (C) are the same (B) and (C) are the same (A), (B), and (C) are the same
Mathematics
1 answer:
Nesterboy [21]3 years ago
5 0

Answer: (A) and (B) are the same

Step-by-step explanation:

for (A)

x-=x+4

x=x-(x+4)

x=x-x-4

x=4

for (B)

x=x+4-x

x=4

for (C)

x=x-(x+4)

x=x-x-4

x=-4

so (A) and (B) are the same because the value of their x is +4

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Sladkaya [172]
11x-6x=5x
30-12=18
5x+18
8 0
3 years ago
Read 2 more answers
3. Let A, B, C be sets and let ????: ???? → ???? and ????: ???? → ????be two functions. Prove or find a counterexample to each o
Fiesta28 [93]

Answer / Explanation

The question is incomplete. It can be found in search engines. However, kindly find the complete question below.

Question

(1) Give an example of functions f : A −→ B and g : B −→ C such that g ◦ f is injective but g is not  injective.

(2) Suppose that f : A −→ B and g : B −→ C are functions and that g ◦ f is surjective. Is it true  that f must be surjective? Is it true that g must be surjective? Justify your answers with either a  counterexample or a proof

Answer

(1) There are lots of correct answers. You can set A = {1}, B = {2, 3} and C = {4}. Then define f : A −→ B by f(1) = 2 and g : B −→ C by g(2) = 4 and g(3) = 4. Then g is not  injective (since both 2, 3 7→ 4) but g ◦ f is injective.  Here’s another correct answer using more familiar functions.

Let f : R≥0 −→ R be given by f(x) = √

x. Let g : R −→ R be given by g(x) = x , 2  . Then g is not  injective (since g(1) = g(−1)) but g ◦ f : R≥0 −→ R is injective since it sends x 7→ x.

NOTE: Lots of groups did some variant of the second example. I took off points if they didn’t  specify the domain and codomain though. Note that the codomain of f must equal the domain of

g for g ◦ f to make sense.

(2) Answer

Solution: There are two questions in this problem.

Must f be surjective? The answer is no. Indeed, let A = {1}, B = {2, 3} and C = {4}.  Then define f : A −→ B by f(1) = 2 and g : B −→ C by g(2) = 4 and g(3) = 4. We see that  g ◦ f : {1} −→ {4} is surjective (since 1 7→ 4) but f is certainly not surjective.  Must g be surjective? The answer is yes, here’s the proof. Suppose that c ∈ C is arbitrary (we  must find b ∈ B so that g(b) = c, at which point we will be done). Since g ◦ f is surjective, for the  c we have already fixed, there exists some a ∈ A such that c = (g ◦ f)(a) = g(f(a)). Let b := f(a).

Then g(b) = g(f(a)) = c and we have found our desired b.  Remark: It is good to compare the answer to this problem to the answer to the two problems

on the previous page.  The part of this problem most groups had the most issue with was the second. Everyone should  be comfortable with carefully proving a function is surjective by the time we get to the midterm.

3 0
3 years ago
Shaun has five coins in his pocket. If he empties the coins onto a table, what is the probability that all five coins will land
Anastasy [175]

Answer:

A. 1/32

Step-by-step explanation:

Ok, the probability for one of the coins to land on heads is 1/2 cause a coin have to sides and chance is 50% that it will land on either of its sides.

If you have 2 coins the probability will be 1/2 for the first coin to land on heads and 1/2 for the second one. The overall probability for 2 coins would be (1/2)*(1/2)=1/4. You could also see it is 1/4 because all of the possible combinations of 2 coins are 4 (HH, HT, TH, TT) and HH is one of four.

It's the same if you have 5 coins. The probability will be (1/2)*(1/2)*(1/2)*(1/2)*(1/2)=1/32 in other words HHHHH is one of 32 possible combinations of 5 coins.

5 0
3 years ago
A company uses two vans to transportworkers from a free parking lot to theworkplace between 7:00 and 9:00 a.m.One van has 6 more
OverLord2011 [107]
X = small van capacity, y = larger van capacity
y = x + 6

2x + y = 57
now we sub in x + 6 for y
2x + x + 6 = 57
3x + 6 = 57
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x = 51/3
x = 17

y = x + 6
y = 17 + 6
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small van (x) has 17 seats and large van (y) has 23 seats

3 0
2 years ago
Circle theorem <br> This is a very easy question but i just can't seem to be able to answer it
xxMikexx [17]

The measure of <FCD is 77 degrees

<h3>Circle geometry</h3>

From the given diagram, we have the following:

m<FCD + 90 + m<F = 180 degrees

Given the following parameters

m<BEO = 13 degrees = m<F

Substitute into the formula:

m<FCD + 90 +13 = 180 degrees

m<FCD = 180 - 103

m<FCD = 77 degrees

Hence the measure of <FCD is 77 degrees

Learn more on circle geometry here; brainly.com/question/24375372

5 0
2 years ago
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