What is lcm of 3,6,9

You have to answer to other question before answering this one, just in case anyone was confused

Nuetrik [128]

Answer: C

Explanation: You first convert the mixed numbers into improper fractions ( including the ones inside and outside of the parentheses) Then, subtract the fractions inside of the parentheses. Then whatever you got, add it to the fraction that was outside of the parentheses.

(7^5/6 - 5^1/3) + 1^1/9
^
(47/6 - 16/3) + 10/9
^
5/2 + 10/9

65/18 = 3^11/18

3 0

3 years ago

A regular decagon has a radius of 14'. Determine the length of the apothem. Then determine the perimeter of the decagon

pav-90 [236]

Answer:

Part 1) The length of the apothem is 13.32'

Part 2) The perimeter of the decagon is 86.5'

Step-by-step explanation:

we know that

A regular decagon has 10 equal sides and 10 equal interior angles

A regular decagon can be divided into 10 congruent isosceles triangle

(they are isosceles since their two sides are the radii of the polygon and the unknown side is the side of the polygon)

The vertex angle of each isosceles triangle is equal to

$\frac{360^o}{10}=36^o$

To find out the side length of the decagon, we can use the law of cosines

so

$c^2=a^2+b^2-2(a)(b)cos(C)$

where

c is the length side of decagon

a and b are the radii

we have

$a=14'\\b=14'\\C=36^o$

substitute the values

$c^2=14^2+14^2-2(14)(14)cos(36^o)$

$c^2=392-(392)cos(36^o)$

$c=8.65'$

To fin out the perimeter of decagon multiply the length side by 10

so

$P=8.65(10)=86.5'$

To find out the apothem we can apply the Pythagorean Theorem in one isosceles triangle

see the attached figure to better understand the problem

$r^2=a^2+(c/2)^2$

substitute the given values

$14^2=a^2+(8.65/2)^2$

solve for a

$a^2=14^2-(8.65/2)^2$

$a=13.32'$

8 0

3 years ago

Two-thirds of the T-shirts in a T-shirt shop are blue. Three-fifths of those T-shirts are on sale. One-half of the blue T

katrin2010 [14]

Let, total number of T-shirts are x.

Number of blue T-shirts = (2/3)x = 2x/3 .

Number of blue shirts on sale = (3/5)(2x/3) = 2x/5 .

Number of medium sized blue shirts on sale = (1/5)(2x/5) = 2x/25 .

Fraction of the shop's T-shirts are blue T-shirts that are on sale and are size medium = $\dfrac{2x/25}{x}$ = 2/25 . ( Number of medium sized blue shirts on sale divided by total number of T-shirts )