If DE = 10 in. and GH = 4 in., what is the length of the radius? Round to the nearest tenth. A 5.4 in. B 6.4 in. C 10.8 in. D 29.0 in.

6.4

Step-by-step explanation:

A. 5.4 in

Step-by-step explanation:

At the top of the line segment GH, you can see it ends on Circle D's circumference. Therefore, if you made a line segment from D to G, its length would be the radius. Lines DE and GH are perpendicular and make a 90 degree angle, so you can make line DG a hypotenuse, use pythagoreans theorem, and find the radius. However, since they intersect at a halfway point, you have to divide 10 and 4 by 2. 10/2 = 5  4/2 = 2   5^2 + 2^2 = r^2

5^2 = 25 and 2^2 = 4, so 29 = r^2. The square root of 29 is 5.385, or 5.4 inches.

I got a bit lazy answering this, but I hope it helps!

step-by-step explanation:

we are given

since, we have to isolate x on anyone side

so, we can move all x terms on one side

subtract both sides by 2x

add both sides by 9

divide both sides by 4

we get

18

step-by-step explanation:

draw the shape and you will see that f and k are actually at adjacent vertices (points of the hexagon that are neighboring).   so find the distance between (1,2) and (4,2).   that is easy since (1,2) and (4,2) is just a vertical distance to count, which is 3.   it is a regular polygon which means all sides are congruent.   you have 6 sides (hexa) so multiply 6 by 3 to receive 18.