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3 years ago

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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Given:

Angled formed by ray BA and ray BC is 90 degrees.

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The equation of line that bisects the angle formed by ray BA and ray BC.

Solution:

If a line bisects the angle formed by ray BA and ray BC, then it must be passes through point B and makes angles of 45 degrees with ray BA and ray BC.

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3 years ago

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marissa [1.9K]

Step-by-step explanation:

Consider the provided information.

For the condition statement $p \rightarrow q$ or equivalent "If p then q"

The rule for Converse is: Interchange the two statements.
The rule for Inverse is: Negative both statements.
The rule for Contrapositive is: Negative both statements and interchange them.

Part (A) If it snows tonight, then I will stay at home.

Here p is If it snows tonight, and q is I will stay at home.

Converse: If I will stay at home then it snows tonight.

$q \rightarrow p$

Inverse: If it doesn't snows tonight, then I will not stay at home.

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Contrapositive: If I will not stay at home then it doesn't snows tonight.

$\sim q \rightarrow \sim p$

Part (B) I go to the beach whenever it is a sunny summer day.

Here p is I go to the beach, and q is it is a sunny summer day.

Converse: It is a sunny summer day whenever I go to the beach.

$q \rightarrow p$

Inverse: I don't go to the beach whenever it is not a sunny summer day.

$\sim p \rightarrow \sim q$

Contrapositive: It is not a sunny summer day whenever I don't go to the beach.

$\sim q \rightarrow \sim p$

Part (C) When I stay up late, it is necessary that I sleep until noon.

P is I sleep until noon and q is I stay up late.

Converse: If I sleep until noon, then it is necessary that i stay up late.

$q \rightarrow p$

Inverse: When I don't stay up late, it is necessary that I don't sleep until noon.

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Contrapositive: If I don't sleep until noon, then it is not necessary that i stay up late.

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