Discuss the process of proving a statement by mathematical induction. What is the importance of verifying the first possible case?

5.7622

step-by-step explanation:

the ten thousandths place is the 2. you round it up if, that number in whatever place is 5 or higher.

1. which statement below is true for hyperbolic geometry?

answer: d  

the sum of the measures of the angles in a triangle is always less than 180 degrees.

2. identify the statement that is true in spherical geometry.

answer: d  

the sum of the measures of the angles of a triangle is greater than 180.

3. what can be said about the vertices of an equilateral triangle drawn in poincaré’s system?

answer: b  

the vertices are equidistant from the center of the circle.

4. satellites sputnik, yeltsin, and plekov often temporarily line up in order in a great circle. the circumference of the earth is 24,900 miles, and the satellites orbit at about 150 miles above the surface. if, while in a great circle, sputnik is 9,000 miles from yeltsin, and yeltsin is 10,500 miles from plekov, how far apart are sputnik and plekov?

answer: b  

6,342 miles

5. identify the statement that is true in spherical geometry.

answer: d  

two distinct lines intersect in two points.

question says to graph a triangle (xyz) and reflect it over the line y=x to create triangle x'y'z'.

we know that line y=x has both coordinates equal like (1,1), (5,5) etc so we can easily graph that reflecting line.

description of transformation:

we can see that x and y coordinate gets switched after transformation like (2,8) changed to (8,2)

what do you notice about the two line segments you drew:

we see that line segments xp and x'p are of same length and perpendicular to the reflecting line y=x.

do you think you would see the same characteristic if you drew the line segment connecting y with the reflecting line and then y' with the reflecting line? :

yes, i would see the same characteristic if you drew the line segment connecting y with the reflecting line and then y' with the reflecting line.

how do you know? :

by measuring the length of yk and y'k.