Learning Task 2Solve the following problems. (Show your complete solutions.)
1.) What is the sum of the interior angles of a polygon having 8 sides?
2.) Find the measure of the exterior angle of a regular decagon.
3.) Find the number of diagonals of a nonagon.
4.) What is the measure of each angle of a regular nonagon?
5.) if the sum of the measures of the angles of a regular polygon is 900, then
what is the number of sides?

Answers

Answer 1
Answer:

Answer:

1. 1080°

2. 36°

3. 27 diagonals

4. 140°

5. 7 sides

Step-by-step explanation:

1. The sum S of the interior angles of a polygon is given by;

S = (n-2) x 180°

Where;

n = number of sides of the polygon.

Therefore, to get the sum of the interior angles of a polygon having 8 sides, we substitute n = 8 into equation (i) as follows;

S = (8 - 2) x 180°

S = 6 x 180°

S = 1080°

Therefore, the sum of the interior angles of a polygon having 8 sides is 1080°

2. The sum of interior angles of a polygon is given by;

S = (n - 2) x 180°

For a polygon which is a regular decagon where the number of sides n = 10, the sum is;

S = (10 - 2) x 180°

S = 8 x 180°

S = 1440°

Since the decagon is regular, then each of its interior angles is given by;

1440° / 10

=> 144°

Now, since we know that the sum of the interior angle and exterior angle will give 180°, then;

The exterior angle of a regular decagon is;

180° - 144° = 36°

Therefore, the exterior angle of a regular decagon is 36°

3. The number of diagonals N of a polygon with n sides is given by;

N = (1)/(2) n(n-3)

So, for a nonagon which has 9 sides (i.e n = 9), the number of diagonals is;

N = (1)/(2)*9(9-3)

N = (1)/(2)*9(6)

N = 9(3)

N = 27

Therefore, a nonagon has 27 diagonals.

4. The sum of interior angles of a polygon is given by;

S = (n - 2) x 180°

For a polygon which is a nonagon where the number of sides n = 9, the sum is;

S = (9 - 2) x 180°

S = 7 x 180°

S = 1260°

Since the nonagon is regular, then each of its interior angles is given by;

1260° / 9

=> 140°

Therefore, the measure of each angle (interior angle) of a regular nonagon is 140°

5. The sum of the interior angles of a polygon is given by;

S = (n - 2) x 180°

So if the sum is 900, then to get the number of sides of the polygon, we substitute S = 900 into the equation;

900° = (n - 2) x 180°

Divide through by 180°

5 = (n - 2)

Solve for n;

n = 5 + 2

n = 7

Therefore, the regular polygon has 7 sides.


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olivia deposits $6,952 in a savings account paying 3.72% interest. to the nearest dollar, how much money does olivia have in total after sixteen years?

Factorise this
72-6x

Answers

72-6x Factorised is 6(12+-1x)

a rectangle has a length that is 5 inches greater than its width, and its area is 104 square inches. The equation(x+5) x=104 represents the situation, where x represents the width of the rectangle. (x+5) x=104 x2+5x-104=0. Determine the solutions of the equation. What solution makes sense for the situation?

Answers

Answer:

x=8

Step-by-step explanation:

Area of a rectangle=length×width

Area=104

Width=x

Length=5+x

104=x*(5+x)

104=5x+x^2

104-5x-x^2=0

x^2+5x-104=0

Can also be written as

-x^2-5x+104=0

Solve the quadratic equation using formula

−x2−5x+104=0

using the Quadratic Formula where

a = -1, b = -5, and c = 104

x=−b±√b2−4ac/2a

x=−(−5)±√(−5)2−4(−1)(104)/2(−1)

x=5±√25−(−416)/−2

x=5±√441/−2

The discriminant b^2−4ac>0

so, there are two real roots.

Simplify the Radical:

x=5±21/−2

x=-26/2 or 16/2

x=-13 or 8

The value of x can't be negative

So, x=8 is the answer

What is the value of x in 3x+7y=27

Answers

Answer:

x = (-7y)/(3) +9

Step-by-step explanation:

Note the equal sign, what you do to one side, you do to the other side. Do the opposite of PEMDAS. Isolate the variable, x.

PEMDAS is the order of operation, and =

Parenthesis

Exponents (& Roots)

Multiplication

Division

Addition

Subtraction

~

First, subtract 7y from both sides:

3x + 7y (-7y) = 27 (-7y)

3x = -7y + 27

Next, divide 3 from all terms on both sides:

(3x)/3 =  (-7y + 27)/3

x = (-7y/3) + 9

x = (-7y)/(3) +9

What is the value of PI in full form i can start it out which is 3.14 but what is the rest of it?

Answers

3.14159265359 is some of PI
just to let you know pi doesn't end so yh 3.1415926535897932384626433832795028841971693993751058209749445923078164062862089986280348253421170679 
  8214808651328230664709384460955058223172535940812848111745028410270193852110555964462294895493038196 
  4428810975665933446128475648233786783165271201909145648566923460348610454326648213393607260249141273 
  724587006606315588174881520920962829254091715364367892590360011330530548820466521384146951941511609...

A store makes a $0.45 profit on every toy they sell. If they made $237.15 in profit last month, how many toys did they sell?

Answers

Answer:

527

Step-by-step explanation:

237.15/0.45 = 527

Answer:

They sold 527 toys.

Step-by-step explanation:

If they make 0.45$ profit on every toy.

Total profit of a month is $237.15.

then no of toys sold = total profit divided by individual profit

Number of toys= 237.15/0.45 =527

Help please it's due 11:59 pmSuppose there are two car dealerships, A and B. At A, each member of the sales staff is paid a fixed monthly amount of
$2,000 plus a $200 bonus for each car he or she sells. At B, each salesperson is paid a fixed monthly amount of $2,500 but
does not receive a bonus for each car he or she sells. In which setting will a member of the sales staff be more likely to
work harder? Why is this important?

Answers

They would work harder at A because if they sell 3 cars they would get paid more than if they worked at B