We know that a quadrilateral has ten parts in all: four sides, four angles and two diagonals. ... We divide the required quadrilateral into two triangles which can be easily constructed. These two triangles together will form a quadrilateral.
To find the interior angle, you use the formula ((n - 2) x 180) / n (where n is the number of sides).
So, ((20 - 2) x 180) / 20 = 162
To find the exterior angle, you merely take away the interior angle from 180.
180 - 162 = 18, so the exterior angle is 18 degrees
Another, easier, way is to just divide 360 by n. All exterior angles always add to 360. Thus, 360 / 20 = 18 degrees
Answer:
<h2><em>
2ft by 2ft by 1 ft</em></h2>
Step-by-step explanation:
Total surface of the cardboard box is expressed as S = 2LW + 2WH + 2LH where L is the length of the box, W is the width and H is the height of the box. Since the cardboard box is without a lid, then the total surface area will be expressed as;
S = lw+2wh+2lh ... 1
Given the volume V = lwh = 4ft³ ... 2
From equation 2;
h = 4/lw
Substituting into r[equation 1;
S = lw + 2w(4/lw)+ 2l(4/lw)
S = lw+8/l+8/w
Differentiating the resulting equation with respect to w and l will give;
dS/dw = l + (-8w⁻²)
dS/dw = l - 8/w²
Similarly,
dS/dl = w + (-8l⁻²)
dS/dw = w - 8/l²
At turning point, ds/dw = 0 and ds/dl = 0
l - 8/w² = 0 and w - 8/l² = 0
l = 8/w² and w =8/l²
l = 8/(8/l² )²
l = 8/(64/I⁴)
l = 8*l⁴/64
l = l⁴/8
8l = l⁴
l³ = 8
l = ∛8
l = 2
Hence the length of the box is 2 feet
Substituting l = 2 into the function l = 8/w² to get the eidth w
2 = 8/w²
1 = 4/w²
w² = 4
w = 2 ft
width of the cardboard is 2 ft
Since Volume = lwh
4 = 2(2)h
4 = 4h
h = 1 ft
Height of the cardboard is 1 ft
<em>The dimensions of the box that requires the least amount of cardboard is 2ft by 2ft by 1 ft</em>
A is the answer I got hope this helps !!
Answer:
let x = the larger number
let y = the smaller
;
write a equation for each statement
:
1. The sum of two numbers is 87.
x + y = 87
The larger number subtracted from twice the smaller is 18.
2y - x = 18
Rearrange equation for elimination with the first equation
-x + 2y = 18
x + y = 87
--------------addition eliminates x find y
0 + 3y = 105
y = 105/3
y = 35
then
x + 35 = 87
x = 87 - 35
x = 52
Step-by-step explanation:
is this right