Answer:
m∠1 = 85°, m∠2 = 85°, m∠3 = 64°, m∠4 = 31°
Step-by-step explanation:
1. Since ∠3 and the angle labeled 64° are vertical, they are congruent, therefore m∠3 = 64°
2. By the same logic, since ∠4 and the angle labeled 31° are vertical, they are also congruent, meaning m∠4 = 31°
3. ∠4, ∠1, and 64° make up 180°, thus a straight line around them, so m∠1 + 31° + 64° = 180° --> m∠1 = 85°
4. ∠1 and ∠2 are vertical, so they are congruent, meaning m∠2 = 85°
A u B u C A=(a,b,c,d,e) B=(d,e,f,g,h,i) C=(a,e,i,o,u) help class 8
BlackZzzverrR [31]
Answer:
If U = { a, b, c, d, e, f, g, h} , find the complements of the following sets:(i) A = {a, b, c} (ii) B = {d, e, f, g} (iii) C = {a, c, e, g} (iv) D = { f, g, h, a}
Answer:
$57.50
Step-by-step explanation:
find 10% of 50 first, which is 5, because 5 × 10 = 50, then add $10 to the $50 beacause 50 × 0.2 = 10, next, remove 5%, to do this divide 10% by 2 to get $2.50, 60 - 2.5 = 57.5
Answer: Choice C) 124 square cm
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Explanation:
Let's calculate the area of the trapezoid shown
b1 and b2 are the parallel bases; h is the height of the 2D trapezoid
b1 = 2
b2 = 5
h = 1.5
A = h*(b1+b2)/2
A = 1.5*(2+5)/2
A = 1.5*7/2
A = 10.5/2
A = 5.25
The area of one 2D trapezoid is 5.25 sq cm
There are two of these trapezoids that form the base faces of the trapezoidal prism. So the total base area is 2*5.25 = 10.5 sq cm
Keep this value (10.5) in mind. We'll use it later.
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Now onto the lateral surface area (LSA)
It turns out that the formula for the LSA is
LSA = p*d
where
p = perimeter of the trapezoid shown
d = depth or height of the 3D trapezoid (I'm not using h as it was used earlier)
This formula works for any polygonal base. It doesn't have to be a trapezoid.
In this case the perimeter is,
p = 1.7+2+2.65+5
p = 11.35
So
LSA = p*d
LSA = 11.35*10
LSA = 113.5
Add this LSA to the base area found earlier
10.5+113.5 = 124
The total surface area is 124 square cm
