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denis-greek [22]
3 years ago
15

4 The perimeter of a regular pentagon is represented by the expression 35d - 25.

Mathematics
1 answer:
Komok [63]3 years ago
3 0

The equivalent expression to Daryl's expression is -5 + 7d ⇒ d

Step-by-step explanation:

In a regular polygon of n-side

  • All sides are equal in lengths
  • All angles are equal in measures
  • Its perimeter is n × the length of one side

∵ The polygon is a pentagon

∴ n = 5

∵ The pentagon is regular

∴ The lengths of its 5 sides are equal

∵ Its perimeter = 5 × length of one side

∵ Its perimeter = 35d - 25

- Equate the two sides of the perimeter

∴ 5 × length of one side = 35d - 25

- Divide both sides by 5

∵ 35d ÷ 5 = 7d and 25 ÷ 5 = 5

∴ The length of one side = 7d - 5

Daryl's expression is 7d - 5

Now lets check the answers

a. 35d - 25 ⇒ No

b. 7d - 15 ⇒ No

c. 5(35 - 25) ⇒ No

d. -5 + 7d ⇒ Yes

e. (35d - 25) ⇒ No

The equivalent expression to Daryl's expression is -5 + 7d

Learn more:

You can learn more about polygons in brainly.com/question/6281564

#LearnwithBrainly

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4. Diego is thinking of two positive numbers. He says, "If we triple the first number and
aleksandr82 [10.1K]

Answer:

3<em>x </em>+ 2<em>y</em> = 34. and two possible pairs of positive numbers are  (<em>x</em>, <em>y</em>) = (10, 2) and (<em>x</em>, <em>y</em>) = (4, 11).

Step-by-step explanation:

 Let the First positive number be <em>x</em> and second positive number be <em>y.</em>

Triple of first number = 3<em>x</em>

double of second number = 2<em>y</em>

According to question,

3<em>x </em>+ 2<em>y</em> = 34

Therefore, the equation is 3<em>x </em>+ 2<em>y</em> = 34

So the two possible pair of numbers Diego would be thinking of must satisfy the equation 3<em>x </em>+ 2<em>y</em> = 34

Now,  3<em>x </em>+ 2<em>y</em> = 34

3<em>x </em>= 34 - 2<em>y</em>

Let x = 10 and by substituting its value in above expression,

3 \times 10 = 34 - 2y

30 = 34 - 2y

2y = 34 - 30

2y = 4

y = 2

Therefore first pair (<em>x</em>, <em>y</em>) = (10, 2)

In the same way put x = 4 then,

3<em>x </em>= 34 - 2<em>y</em>

3 \times 4 = 34 - 2y

2y = 34 - 12

2y = 22

y = 11

Therefore first pair (<em>x</em>, <em>y</em>) = (4, 11)

Therefore, (<em>x</em>, <em>y</em>) = (4, 11) and  (<em>x</em>, <em>y</em>) = (10, 2) are the two possible pairs of numbers Diego could be thinking of as these both values satisfy the equation 3<em>x </em>+ 2<em>y</em> = 34.  

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taurus [48]
<span>73/12 = 6 1/12

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8 0
3 years ago
Read 2 more answers
Two corresponding sides of two similar triangles are 3 cm and 5 cm. The area of the first triangle is 12 cm. What is the area of
gizmo_the_mogwai [7]

Since the are of the first triangle is 12 cm², the area of the second triangle is 33.33 cm².

To answer the question, we need to know what similar triangles are

<h3>What are similar triangles?</h3>

Similar triangles are triangles in which the ratio of their corresponding sides is constant.

Given that the corresponding sides of the two similar triangles are 3 cm and 5 cm respectively. Also, the area of the first triangle is 12 cm². We need to find the area of the second triangle.

<h3 /><h3>Area of second triangle</h3>

Since the triangles are similar, we have that

(side of second triangle/side of first triangle)² = Area of second triangle/Area of first triangle

Area of second triangle = (side of second triangle/side of first triangle)² × Area of first triangle

= (5 cm/3 cm)² × 12 cm²

= 25/9 × 12 cm²

= 25/3 × 4 cm²

= 100 cm²/3

= 33.33 cm²

So, the area of the second triangle is 33.33 cm².

Learn more about similar triangles here:

brainly.com/question/21874065

#SPJ1

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