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vredina [299]
3 years ago
5

Find the indicated side of the right triangle x=

Mathematics
1 answer:
adell [148]3 years ago
6 0

9514 1404 393

Answer:

  • x = 9
  • y = 9√2

Step-by-step explanation:

Side lengths in an isosceles right triangle have the reduced ratios ...

  1 : 1 : √2

Yours have the ratios ...

  9 : x : y

If you multiply the reduced ratios by 9, you can find the values of x and y.

  9 : 9 : 9√2 = 9 : x : y

  x = 9

  y = 9√2

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Daisy will need 6 sticks of clay
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What is the minimum amount of saran wrap that Tyler will need to cover the pencil holder, to ensure that no sand leaks out? *
liberstina [14]

Answer:

e

Step-by-step explanation:

To find the surface area of the triangular prism, you need to find the area of all the sides and add them together. The two triangular bases have already been established to have an area of 3 square units each, so together they have an area of 6 units. Two of the rectangular sides have dimensions of 3.5 by 2.5 units, while one has dimensions 3.5 by 3 units. Adding all of this together, you get a total of 34 square inches, or option e. Hope this helps!

7 0
3 years ago
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
Will mark brainliest <br> 20 pionts<br> Show work
Rufina [12.5K]

Answer:

Part A) The percentage increase was 6.1\%

Part B) Michael is financially better off this year than last year

Step-by-step explanation:

Part A)

we know that

Using proportion

Let

x-----> the percentage increase

\frac{100\%}{33,000}=\frac{x\%}{35,000-33,000}\\ \\x=2,000*100\%/33,000\\ \\x=6.1\%

Part B) Compare the percentage increase with the inflation

6.1\%>5\%

The percentage increase is greater than the inflation

therefore

Michael is financially better off this year than last year

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Answer:

7, 10, 17

Step-by-step explanation:

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As a rule, the measure of a side of a triangle must be less than the sum of the measures of the 2 other sides

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3 years ago
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