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VLD [36.1K]
2 years ago
15

Look at the triangle: A right angle triangle is shown with hypotenuse equal to 10 centimeters. An acute angle of the triangle is

labeled as x degrees. The side adjacent to the acute angle has length 6 centimeters and the side opposite to the acute angle has length 8 centimeters. What is the value of tan x°?
Mathematics
1 answer:
trasher [3.6K]2 years ago
7 0
Tan x°= Opposite/ adjacent<span>so tan </span>x°=86
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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
2 years ago
Three times the sum of a number and 21 is at most -26
Anna007 [38]
It would be: 3(x + 21) ≤ -26
3x + 21 ≤ -26
3x ≤ -47
x < -47/3

In short, Your Answer would be -47/3 or 15.67

Hope this helps!

8 0
2 years ago
Please help work this out
BigorU [14]

Answer:

Area=190.091 cm^2

Step-by-step explanation:

Area = 1/2(Pi x r^2)    one-half because it's a semi-circle

Area=1/2(3.14 x 11^2)

11^2=121 so, Area=1/2(3.14 x 121)

Area=1/2(379.94)

Area=189.97 cm^2

adjustment:

Area=1/2(3.142 x 11^2)

Area=1/2(3.142 x 121)

Area=1/2(380.182)

Area=190.091

5 0
2 years ago
Write a quadratic equation with -4 and 3/2 as it’s roots. Write the equation in the form ax^2 + bx + c = 0, where a, b, and c ar
jonny [76]

9514 1404 393

Answer:

  2x² +5x -12 = 0

Step-by-step explanation:

When p and q are roots of a quadratic, its factored form can be written as ...

  (x -p)(x -q) = 0

Here, the roots are given as -4 and 3/2, so the factored form would be ...

  (x -(-4))(x -(3/2) = 0

Multiplying by 2 gives us ...

  (x +4)(2x -3) = 0

Expanding the product, we find the desired quadratic is ...

  2x² +5x -12 = 0

5 0
2 years ago
Consider this right triangle. Determine whether each equation is correct. Select yes or no using the dropdown for each equation.
Romashka [77]

Answer:

Yes

Yes

NO    CosD = 5/13

Yes

5 0
2 years ago
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