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2 years ago

What radius of a circle is required to inscribe a regular hexagon with an area of 210.44 cm2 and an apothem of 7.794 cm

1 answer:

8 0

We know that

[area of a regular hexagon]=6*[area of one equilateral triangle]
210.44=6*[area of one equilateral triangle]
[area of one equilateral triangle]=210.44/6-----> 35.07 cm²

[area of one equilateral triangle]=b*h/2
h=7.794 cm
b=2*area/h------> b=2*35.07/7.794------>b= 9 cm

the length side of a regular hexagon is 9 cm
applying the Pythagorean theorem
r²=h²+(b/2)²------>r²=7.794²+(4.5)²------> r²=81--------> r=9 cm

this last step was not necessary because the radius is equal to the hexagon side------> (remember the equilateral triangles)

the answer is
the radius is 9 cm

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Please ASAP help please !!! Help me anyone

worty [1.4K]

difference of squares means that both the terms are square terms. (also there must be a - symbol)

for example

y^2 - 4

square root of y^2 is y

square root of 4 is +2 as well as -2

so you would factorise it like this:

(y+2)(y-2)

1. y^4 has a square root of y^2 as y^2 × y^2 is y^4.

however, -2 doesnt have a whole number square root so it is not a difference of squares.

2. 25 has a square root of 5. m^2 has a square root of m. n^4 has a square root of n^2. so this 25m^2n^4 is a square term.

1 has a square root of +1 and -1.

therefore, this one is a difference of squares. (5mn^2 +1) (5mn^2 -1)

3. p^8 has a square root of p^4. q^4 has a square root of +q^2 and -q^2)

so it is a difference of squares. (p^4+q^2)(p^4 -q^2)

4. 16x^2 is a square term as irs square root is 4x.

however, 24 is not a square term.

therefore, it is not a difference of squares.

6 0

2 years ago

a collection of dimes and quarters is worth $19.85. There are 128 coins in all. How many of each type of coin are in the collect

PolarNik [594]

Number of dimes were 81 and number of quarters were 47

Solution:

Let "d" be the number of dimes

Let "q" be the number of quarters

We know that,

value of 1 dime = $ 0.10

value of 1 quarter = $ 0.25

Given that There are 128 coins in all

number of dimes + number of quarters = 128

d + q = 128 ------ eqn 1

Also given that collection of dimes and quarters is worth $19.85

number of dimes x value of 1 dime + number of quarters x value of 1 quarter = 19.85

$d \times 0.10 + q \times 0.25 = 19.85$

0.1d + 0.25q = 19.85 -------- eqn 2

Let us solve eqn 1 and eqn 2

From eqn 1,

d = 128 - q -------- eqn 3

Substitute eqn 3 in eqn 2

0.1(128 - q) + 0.25q = 19.85

12.8 - 0.1q + 0.25q = 19.85

12.8 + 0.15q = 19.85

0.15q = 7.05

Therefore from eqn 3,

d = 128 - q

d = 128 - 47

Thus number of dimes were 81 and number of quarters were 47

4 0

2 years ago

What is the measure of angle w? Type the number only. Do not type the word degrees.

Margaret [11]

Answer:

w = 34°

Step-by-step explanation:

Every quadrilateral is equal to 360 degrees. If you know 3 out of the 4 angles, then what you need to do is add up each angle and subtract the sum from 360 to find the remaining angle.

90 + 90 + 146 = 326

360 - 326 = 34

w = 34

4 0

2 years ago

A cable company charges $35 for basic subscription and $4 per premium channel. Write a function rule that represents the money c

vampirchik [111]

Answer:

c = 4x + 35

Step-by-step explanation:

Imagine c = cost

$35 is base price so you add that to whatever else you spend.

Let x = number of channels you buy. ($4/CHANNEL)

so cost is equal to $4*channels plus 35

Therefore

c = 4x+35

5 0

2 years ago

Read 2 more answers

x2 + 2x + 7 = 21 The number of positive solutions to this equation is . The approximate value of the greatest solution to the eq

barxatty [35]

I need help and no one is helping me

8 0

2 years ago