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3 years ago

FOR 47 POINTS PLEASE HELP

Mathematics

1 answer:

Julli [10]3 years ago

3 0

Answer:

UV=25 units

Step-by-step explanation:

we know that

UW=UV+VW -----> by addition segment postulate

substitute the given values

4x+10=5x+5

solve for x

5x-4x=10-5

x=5

Find the value of UV

UV=5x

substitute the value of x

UV=5(5)=25 units

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Given: an n-gon

Prove: The sum of the measures of the interior angles is 180(n – 2)°.

Complete the missing parts of the paragraph proof.

We are given an n-gon, which has n sides and n vertices.

Answers:

1. If we choose one of the vertices, we can draw n-3 diagonals.

2. These diagonals form n-2 triangles.

3. The sum of the interior angle measures of a triangle is 180 degrees.

4. n – 2 triangles would have an interior angle measure sum of 180 degrees.

5. Therefore, the sum of the measures of the interior angles of an n-gon is 180(n – 2)°.

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7 cards are drawn from a standard deck of 52 playing cards. How many different 7-card hands are possible if the drawing is done

Vladimir [108]

Answer:

The number of different 7 card hands possibility is 133784560

Step-by-step explanation:

The computation of the number of different 7 card hands possibility is shown below:

Here we use the combination as the orders of choosing it is not significant

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The number of the different hands possible would be

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3 years ago

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3 years ago

An open box is made from a 20-cm by 50-cm piece of tin by cutting a square from each corner and folding up the edges. The area

kipiarov [429]

Answer:

Therefore,

The length of the sides of the squares is

$x=7\ cm$

Step-by-step explanation:

Let "x" be the length of Cut Square,

As the tin size(Dimension) is

20 cm × 50 cm

So the size(Dimension) of box will be

(20 - 2x) × (50 - 2x)

Length = 50 - 2x

Width = 20 - 2x

Area of base of box = 216 cm²

To Find:

x = ?

Solution:

Area of Rectangular field is given by

$(Area\ of\ Rectangle(Box)) = Length\times Width$

Substituting the values we get

$216=(50-2x)(20-2x)$

Applying Distributive property we get

$216=1000-100x-40x+4x^{2}$

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Dividing throughout by 4 we get

$x^{2}-35x+196=0$

On Factorizing we get

$x^{2}-28x-7x+196=0\\\\(x-7)(x-28)=0\\\\x-7=0\ or\ x-28=0\\\\x=7\ or\ x = 28$

As x cannot be 28 because tin size is 20 cm × 50 cm i.e longer than 20

Therefore,

$x=7\ cm$

Therefore,

The length of the sides of the squares is

$x=7\ cm$

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