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Nastasia [14]
2 years ago
10

Solve for × and then find the missing angle in the triangle below. SHOW ALL WORK.

Mathematics
2 answers:
Sholpan [36]2 years ago
8 0

Answer:

x = 4°

Step-by-step explanation:

all angles in a triangle sum up to 180°

6x + 38° + 5x + 8° + 90° = 180 °

11x +136° = 180°

11x = 44°

x = 4°

JulsSmile [24]2 years ago
3 0

Answer:

The value of x is <u>4</u>.

  • ∠E = 62⁰
  • ∠G = 28⁰
  • ∠O = 90⁰

Step-by-step explanation:

As we know that the sum of interior angles of triangle is 180⁰.

So, adding all the given sides and subtracting to 180⁰, to find the value of x.

\begin{gathered} \quad{\implies{\sf{Sum\:of\:all\: angles={180}^{\circ}}}}\\\\\quad{\implies{\tt{6x + {38}^{\circ} +  {90}^{\circ} +5x + {8}^{\circ} = {180}^{\circ}}}}\\\\\quad{\implies{\tt{(6x + 5x) + ({38}^{\circ} + {90}^{\circ} + {8}^{\circ}) = {180}^{\circ}}}}\\\\\quad{\implies{\tt{(11x) + ({128}^{\circ} + {8}^{\circ}) = {180}^{\circ}}}}\\\\\quad{\implies{\tt{(11x) + ({136}^{\circ}) = {180}^{\circ}}}}\\\\\quad{\implies{\tt{11x + {136}^{\circ} = {180}^{\circ}}}}\\\\\quad{\implies{\tt{11x = {180}^{\circ} -  {136}^{ \circ}}}}\\\\\quad{\implies{\tt{11x = {44}^{ \circ}}}}\\\\\quad{\implies{\tt{x = \dfrac{44}{11}}}}\\\\\quad{\implies{\tt{\underline{\underline{x = 4}}}}}\end{gathered}

Hence, the value of x is 4.

Now, we know the value of x. So, calculating the mission angles of triangle :

  • ➠ ∠E = 6x+38⁰ = 6×4+38 = 62⁰
  • ➠ ∠G = 5x+8⁰ = 5×4+8 = 28⁰
  • ➠ ∠O = 90⁰

\rule{300}{2.5}

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Three balls are packaged in a cylindrical container as shown below. The balls just touch the top, bottom, and the sides of the c
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Answer:

a. 5177 cm³

b. 3,451 cm³

c. 67%

Step-by-step explanation:

Given:

Diameter of each ball (d) = 13 cm

Radius of the ball (r) = radius of the cylinder = ½(13) = 6.5 cm

Height of the cylinder (h) = the sum of the diameters of the 3 balls = 3(13) = 39 cm

a. Volume of cylinder = πr²h

Plug in the values

Volume of cylinder = π*6.5²*39 = 5176.56 ≈ 5177 cm³

b. Total volume of the three balls = 3(volume of 1 ball) = 3(volume of sphere) = 3(⁴/3πr³)

Plug in the value

Total volume of the 3 balls = 3(⁴/3*π*6.5³) = 3(1150.35) = 3,451.05 ≈ 3,451 cm³

c. % of volume of the container occupied by the 3 balls = total volume of the three balls / volume of cylinder × 100

Plug in the values

= 3,451/5177 × 100

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≈ 67%

6 0
2 years ago
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A logical conclusion would say “Kelly is 15 minutes late to school.”
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2 years ago
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Rom4ik [11]
<h3>Answer:  10 cm  (choice A)</h3>

====================================================

Explanation:

One equation we could solve is

x/2.5 = 30/7.5

Note the x/2.5 has us dividing the vertical sides, while 30/7.5 is the same idea for the horizontal sides. The order is large over small. You could do small over large, but make sure you keep both sides consistent.

Solving for x leads to...

x/2.5 = 30/7.5

x*7.5 = 2.5*30

7.5x = 75

x = 75/7.5

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There are many other possible equations that lead to the same answer. One other possible equation is x/30 = 2.5/7.5

These proportions are possible due to the fact we have similar triangles.

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2 years ago
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Step-by-step explanation:

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B=base

H=height

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So let's put it in.

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Answer:

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Step-by-step explanation:


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