From the set {-282, -95, 95}, use substitution to determine which value of x makes the equation true.

Find the area of the regular polygon

Y_Kistochka [10]

Answer:

A = 374.123 ft^2

Step-by-step explanation:

First, lets calculate the perimeter:

Perimeter (p) = side length (s) * number of sides (n)

$p = s * n$

$p = 12 * 6$

$p = 72$

Next, lets find the apothem, which is the shortest length from any side to the middle. It's like the radius in a circle, but more complicated.

Apothem (a) = side length (s) / ( 2 * tan(180/number of sides (n)) )

$a = \frac{s}{2 * tan (\frac{180}{n} )}$

$a = \frac{12}{2 * tan (\frac{180}{6} )}$

$a = \frac{12}{2 * \frac{\sqrt{3} }{3}}$

$a = \frac{12}{\frac{2\sqrt{3} }{3}}$

$a = \frac{12*3}{2\sqrt{3}}$

$a = \frac{6*3}{\sqrt{3}}$

$a = \frac{18}{\sqrt{3}}$

Now, finally, to find the area of a regular polygon, we use the following equation:

Area (A) = ( apothem (a) * perimeter (p) ) / 2

$A = \frac{a * p}{2}$

$A = \frac{\frac{18}{\sqrt{3} } * 72}{2}$

$A = \frac{18}{\sqrt{3}} * 36$

$A = \frac{640}{\sqrt{3}}$

Turning into a decimal:

$A = 374.123 ft ^2$

8 0

2 years ago

Keiko has seven colors of lanyard. She uses three different colors to make a keychain. How many different combinations can she c

AleksAgata [21]

Combination = doesn't matter what order
Permutation = order matters

There are <u>two</u> methods to work out combinations.

Method 1 List out possibilities
123 124 125 126 127 134 135 136 137 145 146 147 156 157 167
234 235 236 237 245 246 247 256 257 267
345 346 347 356 357 367
456 457 467
567

For a total of 35 combinations.

Method 2 Use a formula.
It's a rather complicated one, so only use it if you have a lot of possibilities.

$\frac{n!}{r!(n-r)!} = \frac{7!}{3!(7-3)!} = \frac{7!}{3!*4!} = \frac{7*6*5*4*3*2*1}{3*2*1*4*3*2*1} = \frac{7*6*5}{3*2*1}=\frac{210}6=35$

(n is the number of choices, r is the amount you choose, and ! is a function that multiplies together all numbers down to 1)

7 0

3 years ago

Help pls , graph and linear equations

drek231 [11]

Answer:

4- -1=3

Step-by-step explanation:

7. m=3 (4,-1)

do the () inside first so

4- -1 = 3

hope this helps for number 7

5 0

2 years ago

What is the missing step in this proof?

garri49 [273]

I'm not really sure what I'm looking at... is it possible for you to take a better picture so I can look at the diagram if there is one + the rest of the steps?

7 0

2 years ago

A publisher reports that 30% of their readers own a laptop. A marketing executive wants to test the claim that the percentage is

Ierofanga [76]

Answer:

Test statistic = - 2.29

Pvalue = 0.0110

Step-by-step explanation:

The hypothesis :

H0 : p = 0.3

H1 : p < 0.3

Test statistic :

z=pˆ−p/√p(1−p)/n

pˆ = 0.2

Z = (0.20 - 0.30) / √(0.30(1 - 0.30) / 110

Z = - 0.1 / √0.0019090

Z = - 0.1 / 0.0436931

Z = - 2.29

Test statistic = -2.29

The Pvalue :

P(Z < -2.29) = 0.0110

4 0

2 years ago