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enyata [817]
3 years ago
13

The perimeter of a regular hexagon depends on the length of its side. Write the formula that describes this perimeter as the fun

ction of side’s length.

Mathematics
1 answer:
Basile [38]3 years ago
3 0

Answer:

Step-by-step explanation:

A. Write an equation to represent this direct variation. Make sure to define your variables.

 We define the variables:

 P = perimeter

 L = sides of the square

 The equation that represents this proportional variation is:

 P = 4L

 B. In complete sentences, use a specific example to justify your equation from part A. Include a drawing in your answer.

 Example: consider a square of sides 4 units. Find the perimeter.

The perimeter of the square can be found in two ways:

 Way 1:

 P = 4 + 4 + 4 + 4 = 16

 Way 2: 

 Using equation of part A:

 P = 4L

 P = 4 * (4)

 P = 16

 Note: see attached image.

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Find the sum of the positive integers less than 200 which are not multiples of 4 and 7​
taurus [48]

Answer:

12942 is the sum of positive integers between 1 (inclusive) and 199 (inclusive) that are not multiples of 4 and not multiples 7.

Step-by-step explanation:

For an arithmetic series with:

  • a_1 as the first term,
  • a_n as the last term, and
  • d as the common difference,

there would be \displaystyle \left(\frac{a_n - a_1}{d} + 1\right) terms, where as the sum would be \displaystyle \frac{1}{2}\, \displaystyle \underbrace{\left(\frac{a_n - a_1}{d} + 1\right)}_\text{number of terms}\, (a_1 + a_n).

Positive integers between 1 (inclusive) and 199 (inclusive) include:

1,\, 2,\, \dots,\, 199.

The common difference of this arithmetic series is 1. There would be (199 - 1) + 1 = 199 terms. The sum of these integers would thus be:

\begin{aligned}\frac{1}{2}\times ((199 - 1) + 1) \times (1 + 199) = 19900 \end{aligned}.

Similarly, positive integers between 1 (inclusive) and 199 (inclusive) that are multiples of 4 include:

4,\, 8,\, \dots,\, 196.

The common difference of this arithmetic series is 4. There would be (196 - 4) / 4 + 1 = 49 terms. The sum of these integers would thus be:

\begin{aligned}\frac{1}{2}\times 49 \times (4 + 196) = 4900 \end{aligned}

Positive integers between 1 (inclusive) and 199 (inclusive) that are multiples of 7 include:

7,\, 14,\, \dots,\, 196.

The common difference of this arithmetic series is 7. There would be (196 - 7) / 7 + 1 = 28 terms. The sum of these integers would thus be:

\begin{aligned}\frac{1}{2}\times 28 \times (7 + 196) = 2842 \end{aligned}

Positive integers between 1 (inclusive) and 199 (inclusive) that are multiples of 28 (integers that are both multiples of 4 and multiples of 7) include:

28,\, 56,\, \dots,\, 196.

The common difference of this arithmetic series is 28. There would be (196 - 28) / 28 + 1 = 7 terms. The sum of these integers would thus be:

\begin{aligned}\frac{1}{2}\times 7 \times (28 + 196) = 784 \end{aligned}.

The requested sum will be equal to:

  • the sum of all integers from 1 to 199,
  • minus the sum of all integer multiples of 4 between 1\! and 199\!, and the sum integer multiples of 7 between 1 and 199,
  • plus the sum of all integer multiples of 28 between 1 and 199- these numbers were subtracted twice in the previous step and should be added back to the sum once.

That is:

19900 - 4900 - 2842 + 784 = 12942.

8 0
3 years ago
5. and 6. Show work for full credit please.
Delvig [45]

Answer:

2. YWX

Step-by-step explanation:

<T and <Y are congruent

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8 0
3 years ago
Three brothers, Andy, Bob, and Curly, take a taxi together home from the
MrRa [10]

Answer:

See explanation

Step-by-step explanation:

not sure what class this is for but I\ll try. Each traveller has a 21 km drive so their fare should be equal.

method 1) each traveller can pay for 21 km worth when they get out

method 2) Curly can pay the full fare and Andy and Bob can pay him back later (they're brothers so this should be easy to manage)

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Share 50 in the ratio 3:7
AlexFokin [52]

Answer:

Step-by-step explanation:This Ratio Division Calculator allows you to divide an amount by a specific ratio. ... Alternatively, you can enter separate ratios for multi share ratio split of the ... 50% is a ratio expressed as a percentage; ½ is a ratio expressed as a fraction.

5 0
3 years ago
A garden has an area of 196 square feet. If you want to edge the garden with 1 foot pavers that cost $1.90 each, how much will i
Rainbow [258]

Answer:

197.9

Step-by-step explanation:

4 0
3 years ago
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