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Mariana [72]
3 years ago
7

I need help plz i will make u a brainllest

Mathematics
1 answer:
k0ka [10]3 years ago
5 0

Answer:  1) C. Reflexive Property of Congruence

               2) A. MD ≅ SG

               3) C. 5.3

               4) D. LK || MJ & JK ≡ LM

<u>Step-by-step explanation:</u>

1) An angle <em>or side</em> is congruent to itself by the Reflexive Property

2) TM ≡ LG       Sides are congruent (given)

   ∠M ≡ ∠G       Angles are congruent (given)

   MD ≡ SG      <u> Sides are congruent                  </u>

ΔTMD ≡ ΔLGS  Side-Angle-Side (SAS) Theorem

<em>Note: The angle must connect the two sides</em>

3) Use similarity proportion

\dfrac{6}{x}=\dfrac{9}{8}\\\\\\48=9x\\\\\\\dfrac{48}{9}=x\\\\\\5.3=x

4) In order to prove a polygon is a parallelogram, you must show

  • opposite sides are parallel
  • opposite sides are congruent

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3 years ago
Find the length and width of a rectangle that has the given perimeter and a maximum area. perimeter: 28 meters
11Alexandr11 [23.1K]
The perimeter is given by:
 P = 2x + 2y = 28
 The area is given by:
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 Writing the area based on x we have:
 A (x) = x * (14-x)
 Rewriting:
 A (x) = 14x-x ^ 2
 Deriving we have:
 A '(x) = 14-2x
 We equal zero and clear x:
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3 0
3 years ago
A water tower in New York City has the shape of a cylinder with a cone on top. The cylinder has a diameter of 12 feet and a heig
vazorg [7]

Answer:

number of minutes to drain the entire tower = 241 minutes(nearest minutes)

Step-by-step explanation:

The water tower has the shape of  a cylinder with a cone on top . The volume of the water tower can be find when you find the sum of the volume of the cylinder and the cone.

Therefore,

volume of the cylinder = πr²h

where

r = 12/2 = 6 ft

h = 15 ft

volume = π × 6² × 15

volume = π × 36 × 15

volume of the cylinder = 540π

Volume of the cone = 1/3πr²h

r = 6 ft

Using tangential ratio we can find the height which is the opposite side of the triangle

tan 25° = opposite/adjacent

tan 25° = h/6

cross multiply

h = 6 tan 25°

h = 6 × 0.46630765815

h = 2.79784594893

h = 2.8 ft

volume of the cone  =  1/3πr²h

volume = 1/3 × π × 36 × 2.8

volume = 100.8π/3

volume = 33.6π

Volume of the tower system = 540π + 33.6π =  573.6π

volume of the tower system = 573.6 × 3.14 = 1801.104 ft³

1 cubic ft  = 7.48 gallons

1801.104 cubic fit = ? gallons

cross multiply

gallons = 1801.104 × 7.48

gallons = 13472.25792  gallons

The residents drains the water at the rate of 56 gallons per minute. Therefore,

56 gallons = 1 minutes

13472.25792  gallons = ? minutes

number of minutes = 13472.25792  /56

number of minutes = 240.576034286

number of minutes to drain the entire tower = 241 minutes(nearest minutes)

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