Answer:
144 in^2
Step-by-step explanation:
There are four triangular sides to this square pyramid. According to the area-of-a-triangle formula, A = (1/2)(b)(h), which here is A = (1/2)(8 in)(5 in) = 20 in^2.
Thus, the total lateral (side) area is 4(20 in^2) = 80 in^2.
The area of the bottom is (8 in)^2, or 64 in^2.
Thus, the total surface area is 80 in^2 + 64 in^2, or 144 in^2.
Answer:
B) Sin^-1(-1) = 3pi/2 or 270°
D) Sin^-1(-1) = -pi/2 or -90°
Step-by-step explanation:
Sine function:
The sine function is -1 at 270º(-90º), which is 3pi/2 = -pi/2.
Inverse sine:
The input of the inverse sine function is a value, and the output are the angles which have the sine equal to the input.
Sin^-1(-1)
Angles for which the sine are -1, that is 3pi/2 or 270° and -pi/2 or -90°. Thus, options B and D are correct.
There is a theorem that says if parallel lines are cut by a transversal, then same-side interior angles are supplementary (add up to 180 degrees).
If lines p and r were parallel, then angles 28 and (3x + 2) would add up to 180 degrees.
(28) + (3x + 2) = 180
3x + 30 = 180
3x = 150
x = 50
<h3>
Answer: C. If two lines are parallel, then the alternate interior angles formed are congruent.</h3>
This is through the alternate interior angles theorem. Angles Q and T pair up as one alternate interior set of angles that are the same measure. The same thing applies to angles X and R.
The identical arrow markers on segments XQ and TR show that those segments are parallel. Segment TQ is one transversal cut (forming alternate interior angles Q and T). Segment XR is the other transversal cut (forming alternate interior angles X and R).
We could say "angle XRT" or "angle TRX" instead of "angle R", though its ideal to use shortcuts whenever possible. The same applies for the other angles as well.
