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Mrrafil [7]
2 years ago
12

1. In ABC, m Which expression correctly relates the lengths of the sides of this triangle? (1) ABC BC< CA (3)

AC< BC < AB
(2) ABC AC< BC
(4) BC< AC < AB

Mathematics
1 answer:
wlad13 [49]2 years ago
5 0

Answer:

4 d

Step-by-step explanation:

Given D is mid-point of BC and AD⊥AC

From right angle △DAC

cosC=

a/2

b

=

a

2b

...(i)

also from cosine formulae

cosC=

2ab

a

2

+b

2

−c

2

...(ii)

From (i) and (ii) we get

a

2b

=

2ab

a

2

+b

2

−c

2

⇒4b

2

=a

2

+b

2

−c

2

⇒b

2

=

3

a

2

−c

2

∴cosAcosC=

2bc

b

2

+c

2

−a

2

.

a

2b

=

ca

[(

3

a

2

−c

2

)+c

2

−a

2

]

=

3

2

(

ca

c

2

−a

2

)

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madreJ [45]

Step-by-step explanation:

F= 9/5(C + 32)

5/9 F = C + 32

C = 5/9 F - 32

3 0
3 years ago
Given klmn is a trapezoid, kl = mn, m&lt;1 = m&lt;2, lm/kn = 8/9, pklmn = 132. Find: the length of the legs
Ilia_Sergeevich [38]

Answer:

The length of legs lm, mn, and lk is 32 while that of kn is 36.

Step-by-step explanation:

The diagram is attached in the answer.

As both the angles are equal thus the two forms isosceles triangles. This is true because the converse of base angle theorem is applicable here. The theorem clearly states that when a trapezoid is divided by the diagonal, it forms two set of angles where m<1=m<2 and m<lmk=m<nmk

This leads the two set of legs such as

\dfrac{lm}{kn}=\dfrac{8}{9}

Or this could be written as

lm=8x\\kn=9x

Now the remaining two sides are given as

lk=lm as this form an isosceles triangle so

lk=8x

Similarly

mn=lm\\

Or

mn=8x

Now the perimeter is given as

\text{perimeter}=lm+mn+kn+lk\\

Here perimeter is given as 132 so this gives:

\text{perimeter}=lm+mn+kn+lk\\132=8x+8x+8x+9x\\132=33x\\x=\dfrac{132}{33}\\x=4

So the four legs are of length as given below:

lm=8x=8\times 4=32\\mn=8x=8\times 4=32\\lk=8x=8\times 4=32\\kn=9x=9\times4=36

So the length of legs lm, mn, and lk is 32 while that of kn is 36.

6 0
2 years ago
Which represents the solution set of an any quality 5X-9 greater than 21
Svet_ta [14]

Answer:

The last one

Step-by-step explanation:

5x<30

x<6

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the symbol cannot change.

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X + y = 17
sashaice [31]

Answer:

x = 8 and y=9 or y = 8 and x = 9

Step-by-step explanation:

8 x 9 = 72

8+9 = 17

9 x 8 = 72

9+8 = 17

6 0
2 years ago
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