A certain regular polygon has sides of length 10 cm; its apothem is 12.1 cm. The polygon’s area is 484 cm². How many sides does the polygon have?

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Answer 1

Answer: Given:
Area of polygon = 484 cm²
apothem 12.1 cm
sides of length = 10 cm
no. of sides = x

Area of a regular polygon = 1/2 perimeter * apothem
484 cm² = 1/2 * (10cm * x) * 12.1cm
484 cm² = 6.05cm * 10cm * x
484 cm² = 60.5 cm² * x
484 cm² ÷ 60.5 cm² = x
8 = x

The polygon is an OCTAGON. It has 8 sides.

Perimeter = 10 cm * 8 sides = 80 cm

484cm² = 1/2 * 80cm * 12.1 cm
484cm² = 1/2 * 968 cm²
484 cm² = 484 cm²

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Write this number in word form. 284,028

The length of a rectangle is 3 meters less than twice is widthA.write an equation to find the length of the rectangle

B.the length of rectangle is 11 meters what is the width the rectangle

Answers

The answer for B is 7 meter

Suppose the lengths of two strings are 10 centimeters and 17 centimeters. Describe how the lengths of these two strings compare

Answers

Answer:

Length of one string is 7 cm less than the length of second string. OR Length of second string is 7 cm longer than length of one string.

Step-by-step explanation:

Given : lengths of two strings are 10 centimeters and 17 centimeters.

To find : Describe how the lengths of these two strings compare.

Solution : We have given that

Length of one string =10 cm.

Length of second string = 17 cm

We can compare both length in many way

Length of one string is 7 cm less than the length of second string.

Length of second string is 7 cm longer than length of one string.

Therefore, Length of one string is 7 cm less than the length of second string. OR Length of second string is 7 cm longer than length of one string.

17 - 10 = 7

The difference is that the second string is 7 centimeters longer.

What is the range of the relation? {(1, 2), (2, 4), (3, 2), (4, 6)}  A.{2, 4}  B.{1, 2, 3, 4, 6}  C.{2, 4, 6}  D.{1, 2, 3, 4}
Which relation is a function?  A.{(1, 2); (2, 3); (3, 4); (2, 5)}  B.{(1, 2); (1, 3); (1, 4); (1, 5)}  C.{(1, 2); (2, 3); (3, 4); (1, 5)}  D.{(1, 2); (2, 2); (3, 2); (4, 2)}

For the function f(x) = 2 – 3x, find f(4).  A.–5  B.12  C.–10  D.14
Which equation represents a direct linear variation?  A.y = x – 3  B.y=1/3x  C.y = x^2  D.y=1/x
Which is the direct linear variation equation for the relationship?

y varies directly with x and y = 12 when x = 4.
   A.y = 3^x  B.y = x + 8  C.y = 2x + 4   D.y = x – 8
Which is the quadratic variation equation for the relationship?

    y varies directly with x2 and y = 48 when x = 2.
   A.y = 4x^2  B.y = 4x  C.y = 12x^2  D.y = x^2 + 25

Write the inverse variation equation for the relationship: y varies inversely with x and y = 4 when x = 2.  A.y = 2x  B.y=8/x  C.y = x + 2  D.y=1/2x

Answers

$(1)\ \ \ \ range:\ \ \ \{2, 4, 6\}\ \ \ \Rightarrow\ \ \ Ans.\ C\n\n(2)\ \ \ function:\ \ \ \{(1, 2); (2, 2); (3, 2); (4, 2)\}\ \ \ \Rightarrow\ \ \ Ans.\ D\n\n(3)\ \ \ f(4)=2-3\cdot4=2-12=-10\ \ \ \Rightarrow\ \ \ Ans.\ C\n\n(4)\ \ \ direct:\ \ \ y=ax\ \ \ \Rightarrow\ \ \ y= (1)/(3) x\ \ \ \Rightarrow\ \ \ Ans.\ B\n\n(5)\ \ \ f(x)=ax\ \ \ and\ \ \ f(4)=12\n.\ \ \ \ \ \Rightarrow\ \ \ 12=a\cdot4\ \ \ \Rightarrow\ \ \ a=3\ \ \ \Rightarrow\ \ \ f(x)=3x\ \ \ \Rightarrow\ \ \ Ans.\ (?)\n\n$

$(6)\ \ \ f(x)=ax^2\ \ \ and\ \ \ f(2)=48\n.\ \ \ \Rightarrow\ \ 48=a\cdot2^2\ \ \Rightarrow\ \ a=48:4=12\ \ \Rightarrow\ \ f(x)=12x^2\ \Rightarrow\ \ Ans.\ C\n\n(7)\ \ \ inversely:\ \ \ f(x)= (a)/(x) \ \ \ and\ \ \ f(2)=4\n.\ \ \ \Rightarrow\ \ \ 4= (a)/(2) \ \ \ \Rightarrow\ \ \ a=4\cdot2=8\ \ \ \Rightarrow\ \ \ y= (8)/(x)\ \ \ \Rightarrow\ \ \ Ans.\ B$

What is 1.794 round to the nearest hundredths

Answers

1.794 to the nearest hundredths is 1.79

it is 1.79 rounded to the nearest hundredths

192.5=1/2(26+12.5)h. What is the unknown measure

Answers

$\bf \textit{area of a trapezoid}\n\n A=\cfrac{h(a+b)}{2}~~ \begin{cases} a,b=\stackrel{bases}{parallel~sides}\n h=height\n[-0.5em] \hrulefill\n a=12.5\n b=26\n A=192.5 \end{cases}\implies 192.5=\cfrac{h(12.5+26)}{2} \n\n\n 385=h(12.5+26)\implies 385=38.5h\implies \cfrac{385}{38.5}=h\implies 10=h$