Answer:
The area of the given polygon is:
Step-by-step explanation:
To find the area of the polygon in the picture, you can divide the polygon in three rectangles: a 3 cm by 14 cm, a 5 cm by 14 cm rectangle, and the last rectangle must have a base of 12 cm (20 cm - 3 cm - 5 cm), and a height of 10 cm (14 cm - 4 cm). We can calculate the area of the rectangles with the formula below:
- Area of a rectangle = Base * height
Now, we're gonna replace the measurements in the formula.
<em>First rectangle:</em>
- Area of a rectangle = 3 cm * 14 cm
- <u>Area of a rectangle = 42 cm^2</u>
<em>Second rectangle:</em>
- Area of a rectangle = 5 cm * 14 cm
- <u>Area of a rectangle = 70 cm^2</u>
<em>Third rectangle:</em>
- Area of a rectangle = 12 cm * 10 cm
- <u>Area of a rectangle = 120 cm^2</u>
By last, we must add the area of the rectangles:
- Area of the polygon = 42 cm^2 + 70 cm^2 + 120 cm^2
- <u>Area of the polygon = 232 cm^2</u>
As you can see, <em><u>the area of the polygon in the picture is 232 cm^2</u></em>.
Number of pencils x
number of pens y
3x + y = 10
x ≤ y
Draw the line 3x + y = 10 .[it passes by (0,10) and (-10/3,0)
Draw the line y=x [it passes by (0,0), (1,1), (2,2) etc]
Then the solution is the points with integer x and y, that belong to the segment of the line 3x +y = 10 between the x-axis and the line y=x. Those points are (1,7) , (2,4), (3, 1).
Answer:
Advanced tickets=30 Day =20
Step-by-step explanation:
Put them into equations:
x=advanced
y=day
x+y=50
25x+15y=1050
to make it simpler re-arrange x+y=50
x=50-y
Then substitute into 25x+15y=1050
25(50-y)+15y=1050
Expand
1250-25y+15y=1050
Rearrange
25y-15y=1250-1050
Work the above out
10y=200
y=20
and then
20+x=50
meaning....
x=30
showing Advanced tickets=30 Day =20
add up all of the sides together. the perimeter is the outside length of a shape.
Let the width path be x.
Length of the outer rectangle = 26 + 2x.
Width of the outer rectangle = 8 +2x.
Combined Area = (2x + 26)*(2x + 8) = 1008
2x*(2x + 8) + 26*(2x + 8 ) = 1008
4x² + 16x + 52x + 208 = 1008
4x² + 68x + 208 - 1008 = 0
4x² + 68x - 800 = 0. Divide through by 4.
x² + 17x - 200 = 0 . This is a quadratic equation.
Multiply first and last coefficients: 1*-200 = -200
We look for two numbers that multiply to give -200, and add to give +17
Those two numbers are 25 and -8.
Check: 25*-8 = -200 25 + -8 = 17
We replace the middle term of +17x in the quadratic expression with 25x -8x
x² +17x - 200 = 0
x² + 25x - 8x - 200 = 0
x(x + 25) - 8(x + 25) = 0
(x+25)(x -8) = 0
x + 25 = 0 or x - 8 = 0
x = 0 -25 x = 0 + 8
x = -25 x = 8
The width of the path can not be negative.
The only valid solution is x = 8.
The width of the path is 8 meters.
