USING STRUCTURE An athletic facility is building an indoor track. The track is composed of a rectangle and two semicircles, as shown. A drawing shows an indoor track. It is shaped like a rectangle with a semi-circle on each of the shorter sides. The length of the rectangle is labeled x. The radius of each semi-circle is labeled r. A. Write a formula for the perimeter of the indoor track. $P=$ b. Solve the formula for $x$ . $x=$ Question 2 c. The perimeter of the track is 660 feet, and $r$ is 50 feet. Find $x$ . Round your answer to the nearest foot. $x=$ feet

Step-by-step explanation:

Find the digram attached.

Perimeter of the track = perimeter of the rectangle + perimeter of the 2semicircles

Perimter of a rectangle = 2(x+r) where:

x is the length

2r is the width of the rectangle = diameter of the semicircle

Perimeter of semicircle = 2πr/2 = πr

Perimeter of 2semicirle = 2πr

Perimeter of the track = 2(x+2r) + 2πr

r is the radius if the semicircle

Expand

Perimeter of the track = 2x+4r + 2πr

Perimeter of the track = 2(x+2r+πr)

b) Given P = 2(x+2r+πr), we are to make x the subject of the formula.

P = 2x+4r+2πr

P-4r-2πr = 2x

Divide both sides by 2.

(P-4r-2πr)/2 = 2x

x = (P-4r-2πr)/2

c) Given

P = 600fr

r = 50ft

x = (600-4(50)-2π(50))/2

x = (600-200-100(3.14))/2

x = 400-314/2

x = 86/2

x = 43ft

Hence the value of x to nearest foot is 43ft

13

step-by-step explanation:

divide the cost of the total of sodas you bought by the cost of one soda, for example:

$24.57 divided by $1.89 is 13 which means you bought 13 sodas

solution:

we have to construct

∠m nt ≅ ∠p qr

the steps to draw this construction are

step 1: use a compass to draw an arc from point q which intersects the side pq at point a and the side qr at point b.

step 2: draw a segment nt and use the same width of the compass to draw an arc from point n which intersects the segment nt at a point x.

step 3:

step 4: join points n and y using a straightedge.

step 3:

option (d).maintaining the same width of the compass as ab, draw an arc from point x such that it intersects the arc drawn from n in a point y.

to draw   congruent angles , 1. width of compasses while drawing two angles should be same i.e from point at which angle has to be drawn, 2.the distance between the two points where the compass intersects the two sides should be same while drawing any two congruent angles.