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Arisa [49]
2 years ago
6

It didn't let me put the whole picture, so here are the words/word it cut out.

Mathematics
1 answer:
tangare [24]2 years ago
5 0

Answer:

The options to complete the proof are placed in the boxes of the attached drawing created with Microsoft Word

Step-by-step explanation:

Please see attached drawing of the proof created with Microsoft Word

The two column proof can be  presented as follows;

Statement     {}                                    Reason

 \underset{m}{\leftrightarrow } \parallel \underset{n}{\leftrightarrow }        {}                                        Given

m∠3 + m∠4 = 180°   {}                         Linear pair postulate

∠1 ≅ ∠3     {}                                        Corresponding Angle Theorem

m∠1 + m∠4 = 180°   {}                          Transitive Property      

m∠1 and m∠4 are supplementary  {} Definition of supplementary angles

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Three balls are packaged in a cylindrical container as shown below. The balls just touch the top, bottom, and sides of the cylin
lianna [129]
We know the following:
Cylinder volume: V₁ = π r² h
Ball (sphere) volume:V₂ = \frac{4}{3} π r³
where:
V - volume
r - radius of base of cylinder and diameter of ball
h - height of cylinder.

R = 13 cm ⇒ r = 13 ÷ 2 = 6.5
π = 3.14

a) Since balls touch all sides of cylinder (as shown in image), it can be concluded that height of cylinder is equal to sum of diameters of 3 balls and that radius of base of cylinder is equal to radius of ball:
h = 3 × r = 3 × 13 cm = 39 cm
r = 6.5 cm
So,
V₁ = <span>π r² h
</span><span>V₁ = </span>3.14 × (6.5 cm)² × 39 cm
V₁ = 5,173.9 cm³

b. The total volume of three balls is the sum of volumes of each ball:
Vₐ = 3 × <span>V₂ 
</span>Vₐ = 3 × <span>\frac{4}{3} π r³
</span>Vₐ = 3 × \frac{4}{3} 3.14<span> (6.5 cm)³</span>
Vₐ = 3,449.3 cm³

c. Percentage of the volume of the container occupied by three balls ould be expressed as ratio of volume of three balls and volume of cylinder:
V = \frac{ V_{1}}{ V_{a} } ×100 
V = \frac{3,449.3}{5,173.9} ×100
V = 0.6666 ×100
V = 66.66%
4 0
2 years ago
Read 2 more answers
Linda is buying a new computer the shipping cost 8 percent of the purchase price if Windows computer cost $585 how much will it
Sauron [17]

Answer:

46.8

Step-by-step explanation:

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3 years ago
A flashlight shines straight up into the sky, 9 ft to the right of a tent located at the origin. For which values of A, B, and C
lina2011 [118]

Answer:

Im not sure but i think its A=1, B=0, and C=9

Step-by-step explanation:

hope this helps

8 0
3 years ago
Question 3<br> In the triangle below, what is the side opposite to
cluponka [151]

Answer:

In the given diagram the side opposite angle J is LR which is :

<h2>Option D</h2>
5 0
3 years ago
If {4x-3y=17 and 2x-5y=-11 then y=?
anyanavicka [17]
You need to solve this "system of linear equations."  In other words, find a point (x,y) that satisfies both 4x-3y=17 and 2x-5y=-11.

Try solution by elimination.  Multiply the 2nd equation by -2 to obtain -4x+5y=22.  Add this result to the 1st equation.  I'd suggest you write this out to see what is happening.  

 4x-3y=17

-4x+10y=22
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Now find x.  To do this, substitute 39/7 for y in either of the given equations.  Solve the resulting equation for x.

Write your solution in the form (x, y):  ( ? , 39/7).
3 0
2 years ago
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