On a map, 1/4 inch between locations represents an actual distance of 2 miles between the locations. What is the actual distance, in miles, between the two cities that are 3 3/4 inches apart on the map?

30 miles

Step-by-step explanation:

1/4 = 2

3  3/4 = x

15/4 = x

So, Cross multiply

=> 1/4 * x = 15/4 * 2

=> 1/4x = 15/4 * 4/2

=> 1/4x = 60/8

=> 1/4x = 7.5

=> 1/4x * 4 = 7.5 * 4

=> x = 30

So, 15/4 inches on the map equals 30 miles.

walter needs to make at least 5 more cookies but no more than 40. 5 ≤ x ≤ 40

step-by-step explanation:

20 ≤ x + 15 ≤ 55

subtract 15 from all parts

20-15 ≤ x + 15-15 ≤ 55-15

5 ≤ x ≤ 40

this means how many more cookies he has to make

walter needs to make at least 5 more cookies, but no more than 40 cookies; 5 ≤ x ≤ 40

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.