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3 years ago

What’s the length of the segments variable expressions ??

Mathematics

1 answer:

maxonik [38]3 years ago

4 0

Answer:

$EF=9\ units$

Step-by-step explanation:

we know that

The <u><em>Trapezoid Mid-segment Theorem</em></u> states that: A line connecting the midpoints of the two legs of a trapezoid is parallel to the bases, and its length is equal to half the sum of lengths of the bases

so In this problem

$EF=\frac{1}{2}[AD+BC]$

substitute the given values

$x=\frac{1}{2}[(x-6)+(2x-3)]$

$x=\frac{1}{2}[3x-9]$

$2x=(3x-9)\\3x-2x=9\\x=9$

$AD=x-6=9-6=3\ units$

$EF=x=9\ units$

$BC=2x-3=2(9)-3=15\ units$

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viva [34]

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2 years ago

A soccer game lasts 90 minutes without running into overtime. The coach

KatRina [158]

Answer: 7 Switches will be made.

Step-by-step explanation:

$\frac{90}{12.5}=$ number of switches

$7.2=$ number of switches

however you cannot have a fraction of a switch so you must round it to a whole number, which in this case is 7.

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1 year ago

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ra1l [238]

Answer:

Step-by-step explanation:

well, yes we know what coins there are and that they’re in jars right? but to find which jar is worth the most, we need to know how many coins are in each. she could have 300 pennies, 2 quarters, 4 dimes, and 7 nickels. we need more information to answer this question so E is the only correct option!

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2 years ago

12. (07.06 LC) A library building is in the shape of a rectangle. Its floor has a length of (3x + 5) meters and a width of (5x −

Goshia [24]

ANSWER

$15 {x}^{2} + 22x - 5$

EXPLANATION

It was given that, the length of the rectangular building is

$(3x + 5) \: meters$

and the width of the is

$(5x - 1) \: meters$

The area of a rectangular building is calculated using the formula for finding the area of a rectangle.

$A = l \times w$

Since the dimensions are given in terms of x, the area is also a function of x,

$A(x) = (3x +5 )(5x - 1)$

We expand to get,

$A(x) = 3x(5x - 1) + 5(5x - 1)$

$A(x) = 15 {x}^{2} - 3x + 25x - 5$

$A(x) = 15 {x}^{2} + 22x - 5$

meters square

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3 years ago

QuizBIGPOINT

lianna [129]

The number of permutations of the problem is

This = 24
Outfit = 360

<h2>Combination</h2>

$\:$

Combinations are the number of ways to choose members from a certain number, namely from members of a set, combinations can also be interpreted as many ways to make subsets, namely with a certain number of members, namely from members of a set, if a set has n members then the selection of r members, and the combination of n is where r is less than n.

$\:$

<h3>The Formula : </h3>

$\:$

$\:$

<h2>Permutation</h2>

$\:$

Permutations are a way to determine the number of arrangements that occur by paying attention to the order. So in permutations, position/order is very important, namely AB is considered different from BA (AB ≠ BA). Permutation formula

$\:$

<h3>The Formula :</h3>

$\:$

$\frac {n!}{k!}$ (With Double Elements)

n! (Without Double Elements)

$\:$

<h2>Factorial</h2>

$\:$

The factorial of a natural number is the successive multiplication of a natural number that begins with the number one and arrives at the natural number, the factorial is used in calculating combinations, probabilities, and permutations.

$\:$

<h3>For example</h3>

$\:$

》2! = 1 × 2
》3! = 1 x 2 x 3
》4! = 1 x 2 x 3 x 4
》5! = 1 x 2 x 3 x 4 x 5
》6! = 1 × 2 × 3 × 4 × 5 × 6
》7! = 1 × 2 × 3 × 4 × 5 × 6 × 7
》8! = 1 × 2 × 3 × 4 × 5 × 6 × 7 × 8
》9! = 1 × 2 × 3 × 4 × 5 × 6 × 7 × 8 × 9
》10! = 1 × 2 × 3 × 4 × 5 × 6 × 7 × 8 × 9 × 10

$\:$

The following is an example of a factorial that does not involve mixed arithmetic operations, so if you want to add it up we just need to calculate it like a normal number, a factorial number that only multiplies the difference between a factorial number that is added up by addition, subtraction, multiplication, division, for example see below.

$\:$

6! x2! - 3! : 4!

$\:$

The example above is a mixed arithmetic operation that contains multiplication, subtraction, and division. Remember that in mixed arithmetic operations, multiplication/division must be completed before addition/subtraction.

$\:$

<h3>The Formula : </h3>

$\:$

n! (Combined Multiplication)

$\:$

<h2>Place Filling Rules</h2>

$\:$

The Place Fill Rule is a method or method that can be used to determine the number of ways an object occupies its place. The filling slots rule is a method of calculating how many possible ways there are in an experiment or event. If a first event can be done in m different ways and the second event can be done in a different way and so on until the last event in k.

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<h3>The formula</h3>

$\:$

n1 × n2 × n3 × ... × nr

$\:$

<h2><u>Question</u></h2>

Find the number of permutations of letters of the word

- this

- outfit

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<h2><u>Answer</u></h2>

"Number One"

=》This = Four Letters ( 4! )

P = 4!

P = 1 × 2 × 3 × 4

P = 2 × 3 × 4

P = 6 × 4

P = 24

==========

"Number Two"

=》Outfit = Six Letters ( 6! )

=》Outfit = Two Letters The Same ( "T" ) = 2!

P = $\frac {1×2×3×4×5×6}{2×1}$

P = $\frac {2×3×4×5×6}{2}$

P = $\frac {6×4×5×6}{2}$

P = $\frac {24×5×6}{2}$

P = $\frac {120×6}{2}$

P = $\frac {720}{2}$

P = 360

$\:$

<h2><u>Conclusion</u></h2>

So, the number of permutations of the problem is

This = 24
Outfit = 360

$\:$

<h2>Learn More</h2>

$\:$

<h2>Answer Detail</h2>

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➽ Subject: Mathematics
➽ Class : 12
➽ Chapter : 7 - The Rule of Counting:
➽ Maple Code
➽ Categorization code : 12.2.7
➽ Keywords : This, Outfit

5 0

2 years ago