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Helga [31]
3 years ago
10

A square has side lengths of 2x inches. An equilateral triangle has side lengths of (2x+1/3) inches. If the square and the trian

gle have the same perimeter, what is the value of x?
Mathematics
2 answers:
Arte-miy333 [17]3 years ago
7 0
Size square × 4 = size triangle × 3
(2X × 4 ) = [(2X +1/3) × 3]

8X = [(6X+1)/3×3]
8X = 6X+1
8X -6X = 1
2X = 1
X= 1/2
raketka [301]3 years ago
4 0

Answer : The value of 'x' is \frac{1}{2}

Step-by-step explanation :

As we know that,

The perimeter of square = 4a

The perimeter of equilateral triangle = 3s

('a' is the side square and 's' is the side of equilateral triangle)

Given:

Side of square = a = 2x

Side of equilateral triangle = s = (2x+1/3)

As per question, the square and the triangle have the same perimeter. That means,

Perimeter of square = Perimeter of equilateral triangle

4a = 3s

Now put the value of 'a' and 's', we get the value of 'x'.

4\times (2x)=3\times (2x+\frac{1}{3})

8x=6x+1

8x-6x=1

2x=1

x=\frac{1}{2}

Therefore, the value of 'x' is \frac{1}{2}

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Taye recruits two people to be election campaign volunteers. The next week he ask each of those volunteers to recruit two more c
jeka94

Using a geometric sequence, it is found that:

a) For the first 5 weeks, the numbers are: 2, 4, 8, 16, 32

b) Hence some of the volunteers can stop recruiting new volunteers during the 7th week.

<h3>What is a geometric sequence?</h3>

A geometric sequence is a sequence in which the result of the division of consecutive terms is always the same, called common ratio q.

The nth term of a geometric sequence is given by:

a_n = a_1q^{n-1}

In which a_1 is the first term.

For this problem, on the first week there are 2 people, and since each new people involve two more, the common ratio is of 2, hence the parameters for the geometric sequence are:

a_1 = 2, q = 2

Hence the number of people after n weeks is:

a_n = 2 \times 2^{n - 1}

For the first 5 weeks, the numbers are:

  • a_1 = 2 \times 2^{1 - 1} = 2
  • a_2 = 2 \times 2^{2 - 1} = 4
  • a_3 = 2 \times 2^{3 - 1} = 8
  • a_4 = 2 \times 2^{4 - 1} = 16
  • a_5 = 2 \times 2^{5 - 1} = 32

There will be 150 volunteers when a_n = 150, hence:

2 \times 2^{n - 1} = 150

2^{n-1} = 75

\frac{2^n}{2} = 75

2^n = 150

n = 7...

The above is because 2^7 = 128 and 2^8 = 256, and 128 < 150 < 256.

Hence some of the volunteers can stop recruiting new volunteers during the 7th week.

More can be learned about geometric sequences at brainly.com/question/11847927

#SPJ1

3 0
1 year ago
Please please help I am stuck and idk I tried so many times.
zhuklara [117]

Answer:

58.8 in^2

Step-by-step explanation:

The area of triangle given two sides and included angle.

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Answer is:<span>
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Does the following picture represent a linear function?
nekit [7.7K]

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