Answer:
The tarp needed to complete your tent = 93.67 ft².
Step-by-step explanation:
See the attached figure.
The tent has a shape of a triangular prism.
The size of tarp needed to complete your tent = total surface area of the triangular prism
The length will be 6ft, the width 4 ft and the height 4ft.
Total surface area of the triangular prism = area of the floor(6 ft by 4 ft) + area of 2 triangles( 4 ft and the height 4ft. ) + area of 2 rectangles (edge by 6 ft)
The edge (the hypotenuse) = ![\sqrt{4^2+2^2} =\sqrt{16+4}= \sqrt{20} =\sqrt{4*5} =2\sqrt{5}](https://tex.z-dn.net/?f=%5Csqrt%7B4%5E2%2B2%5E2%7D%20%3D%5Csqrt%7B16%2B4%7D%3D%20%5Csqrt%7B20%7D%20%3D%5Csqrt%7B4%2A5%7D%20%3D2%5Csqrt%7B5%7D)
Area of the floor = 4 * 6 = 24 ft²
Area of 2 triangles = 2 * (0.5 * width* height) = 2 * 0.5 * 4 * 4 = 16 ft²
Area of 2 sides = 2 * edge * length = 2 * 2√5 * 6 = 24√5 ft²
Total surface area = 24 + 16 + 24√5 = (40 + 24√5) ft²
Expressing as decimal number 40 + 24√5 = 93.67 ft².
so, the tarp needed to complete your tent = 93.67 ft².
Answer:
Options b) and c) are correct
Step-by-step explanation:
Given: fractions are ![\frac{5}{8},\frac{5}{4}](https://tex.z-dn.net/?f=%5Cfrac%7B5%7D%7B8%7D%2C%5Cfrac%7B5%7D%7B4%7D)
To find: the common denominator
Solution:
Multiply both numerator and denominator of
by 2
![\frac{5}{4}=\frac{5(2)}{4(2)}=\frac{10}{8}](https://tex.z-dn.net/?f=%5Cfrac%7B5%7D%7B4%7D%3D%5Cfrac%7B5%282%29%7D%7B4%282%29%7D%3D%5Cfrac%7B10%7D%7B8%7D)
So,
have same denominator 8.
Now multiply numerator and denominator of
by 2, ![\frac{5}{8}=\frac{5(2)}{8(2)}=\frac{10}{16}](https://tex.z-dn.net/?f=%5Cfrac%7B5%7D%7B8%7D%3D%5Cfrac%7B5%282%29%7D%7B8%282%29%7D%3D%5Cfrac%7B10%7D%7B16%7D)
Now multiply numerator and denominator of
by 4, ![\frac{5}{4}=\frac{5(4)}{4(4)}=\frac{20}{16}](https://tex.z-dn.net/?f=%5Cfrac%7B5%7D%7B4%7D%3D%5Cfrac%7B5%284%29%7D%7B4%284%29%7D%3D%5Cfrac%7B20%7D%7B16%7D)
So,
have same denominator 16.
Hence, options b) and c) are correct
Percent formula : is/of = %/100
18 is what percent of 20...
is = 18
of = 20
% = x
sub and solve
18/20 = x/100
cross multiply
(20)(x) = (100)(18)
20x = 1800
x = 1800/20
x = 90 <=== so 18 is 90% of 20
Move the 8 over
-x=3x-8
Move the 3x over
-x-3x=8
-4x=8
Divide by -4
x=-2