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3 years ago

Hello I need help Find the missing side lengths, leave your answers as radicals in simplest form

Mathematics

1 answer:

Jet001 [13]3 years ago

4 0

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$y = \frac{1}{2} \times \frac{8 \sqrt{3} }{3} \\$

$y = \frac{4 \sqrt{3} }{3} \\$

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$x = \frac{ \sqrt{3} }{2} \times \frac{8 \sqrt{3} }{3} \\$

$x = \frac{8 \times { \sqrt{3} }^{2} }{2 \times 3} \\$

$x = \frac{8 \times 3}{2 \times 3} \\$

$x = \frac{8}{2} \\$

$x = 4$

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Prove each of the following statements below using one of the proof techniques and state the proof strategy you use.

pochemuha

Answer:

See below

Step-by-step explanation:

a) Direct proof: Let m be an odd integer and n be an even integer. Then, there exist integers k,j such that m=2k+1 and n=2j. Then mn=(2k+1)(2j)=2r, where r=j(2k+1) is an integer. Thus, mn is even.

b) Proof by counterpositive: Suppose that m is not even and n is not even. Then m is odd and n is odd, that is, m=2k+1 and n=2j+1 for some integers k,j. Thus, mn=4kj+2k+2j+1=2(kj+k+j)+1=2r+1, where r=kj+k+j is an integer. Hence mn is odd, i.e, mn is not even. We have proven the counterpositive.

c) Proof by contradiction: suppose that rp is NOT irrational, then rp=m/n for some integers m,n, n≠. Since r is a non zero rational number, r=a/b for some non-zero integers a,b. Then p=rp/r=rp(b/a)=(m/n)(b/a)=mb/na. Now n,a are non zero integers, thus na is a non zero integer. Additionally, mb is an integer. Therefore p is rational which is contradicts that p is irrational. Hence np is irrational.

d) Proof by cases: We can verify this directly with all the possible orderings for a,b,c. There are six cases:

a≥b≥c, a≥c≥b, b≥a≥c, b≥c≥a, c≥b≥a, c≥a≥b

Writing the details for each one is a bit long. I will give you an example for one case: suppose that c≥b≥a then max(a, max(b,c))=max(a,c)=c. On the other hand, max(max(a, b),c)=max(b,c)=c, hence the statement is true in this case.

e) Direct proof: write a=m/n and b=p/q, with m,q integers and n,q nonnegative integers. Then ab=mp/nq. mp is an integer, and nq is a non negative integer. Hence ab is rational.

f) Direct proof. By part c), √2/n is irrational for all natural numbers n. Furthermore, a is rational, then a+√2/n is irrational. Take n large enough in such a way that b-a>√2/n (b-a>0 so it is possible). Then a+√2/n is between a and b.

g) Direct proof: write m+n=2k and n+p=2j for some integers k,j. Add these equations to get m+2n+p=2k+2j. Then m+p=2k+2j-2n=2(k+j-n)=2s for some integer s=k+j-n. Thus m+p is even.

7 0

3 years ago

At the state fair, admission at the gate is $9. In addition, the cost of each ride is $3. Suppose that Deshaun will go on x ride

pshichka [43]

SOLUTION:

Step 1:

In this question, we are given the following:

Step 2:

The details of the solution are as follows:

Step-by-step explanation:

Given :

At the state fair, admission at the gate is $9.

In addition, the cost of each ride is $3.

Suppose that Sam will go on x rides.

Then, cost of x rides ( in dollars) = Cost per ride x Number of rides

=3x

Total cost ( in dollars) : Admission fee + cost of x rides

= 9+3x

Sam wants the total number of dollars he spends on admission and rides to be at most t ( less than or equal to t )

$9\text{ + 3x }\leq\text{ t}$

CONCLUSION:

The final answer is:

Using the values and variables given, write an inequality describing this.

$9\text{ + 3x }\leq\text{ t}$

4 0

1 year ago

What is the capacity of a building

dusya [7]

The capacity of a building is 222,500 tons

4 0

3 years ago

Read 2 more answers

Help me please ty ty ‍♀️❤️ Appreciate it

Cloud [144]

Answer:

Pretty Simple!

Now that you know about ratios and all that, this is pretty tame compared to the last problem.

Now, the problem is talking 2D(2 Dimensions)

The ratio is not going to work because it has only one parameter.

Thus, we need to square it!

$(\frac{1}{20})^{2} =\frac{1}{400}$

Thus, we have your correct ratio.

Now, we only need to do the same thing for the triangle problem. Meaning that, we need to compare the ratios, with x as the thing we are looking for.

$\frac{1}{400}=\frac{219}{x} \\x=87,600$

See? X is practically handed to us.

Hope this helps!

8 0

3 years ago

THEIR AGES

snow_tiger [21]

Answer:

Tom’s age is 7 years

Mary’s age is 13 years

Step-by-step explanation:

Since we do not know the ages, let’s represent the ages by variables at first.

Let m represent mary’s age will t represent Tom’s age.

Now, let’s proceed to have equations.

Adding square of Tom’s age (t^2) to mary’s age give 62

t^2 + m = 62 •••••••(i)

Adding square of mary’s age (m^2) to Tom’s age give 176

m^2 + t = 176 •••••••(ii)

Now, to get the individual ages, we will need to solve both equations simultaneously.

Solving both equations simultaneously without mathematical softwares can be a little hard.

By the use of mathematical software ( wolfram alpha to be specific), we can input both equations and allow the software to solve.

By inputing these equations, we have the values of t to be 7 and m to be 13

And if we try to check by inspection, we can see that these values are actually correct.

7^2 + 13 = 62

13^2 + 7 = 176

6 0

3 years ago