Mathematics, 17.09.2019 21:30, miraculousdollh

Can someone me with this ?
what are the steps for constructing an inscribed circle in δabc using only a compass and a straightedge?

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Let abc be a triangle
1.
construct the angle bisectors of ∠bac and of ∠abc

2.
intersection point o of the bisectors is the center of the inscribed circle

3.
draw the distance oh from o to any of the sides, let's say ab
oh is the radius of the inscribed circle

1a.
to construct the angle bisector of an angle abc draw a circle with center the vertex b of the angle which intersects the side ab at the point d and the side bc at the point e
then with center in d draw a circle and with center in e and the same radius draw another circle which intersects the first one in the point p
bp is the line bisector of the angle abc

3a.
to draw the distance from a point o to a external line ab draw an arc with center in o which intersects ab in two distinct points f and g
then draw a circle with center f and a circle with center g and the same radius
they intersect outside the triangle in a point k. call h the intersection point of ab and ok
oh is the distance from o to ab

follow the steps on this diagram

and try to do it by yourself

use a huge triangle : )

answered: Guest

hello from mrbilldoesmath!

answer:

x - 3

discussion:

x^2 - 9 = (x-3) (x+3) so

(x^2-9)/ (x + 3) = x-3

you,

mrb

answered: Guest

when functions are first introduced, you will probably have some simplistic "functions" and relations to deal with, usually being just sets of points. these won't be terribly useful or interesting functions and relations, but your text wants you to get the idea of what the domain and range of a function are. small sets of points are generally the simplest sorts of relations, so your book starts with those.

step-by-step explanation:

state the domain and range of the following relation. is the relation a function?

{(2, –3), (4, 6), (3, –1), (6, 6), (2, 3)}

the above list of points, being a relationship between certain x's and certain y's, is a relation. the domain is all the x-values, and the range is all the y-values. to give the domain and the range, i just list the values without duplication:

domain: {2, 3, 4, 6}

range: {–3, –1, 3, 6}

(it is customary to list these values in numerical order, but it is not required. sets are called "unordered lists", so you can list the numbers in any order you feel like. just don't duplicate: technically, repetitions are okay in sets, but most instructors would count off for this.)

while the given set does indeed represent a relation (because x's and y's are being related to each other), the set they gave me contains two points with the same x-value: (2, –3) and (2, 3). since x = 2 gives me two possible destinations (that is, two possible y-values), then this relation is not a function.

note that all i had to do to check whether the relation was a function was to look for duplicate x-values. if you find any duplicate x-values, then the different y-values mean that you do not have a function. remember: for a relation to be a function, each x-value has to go to one, and only one, y-value.

state the domain and range of the following relation. is the relation a function?

{(–3, 5), (–2, 5), (–1, 5), (0, 5), (1, 5), (2, 5)}

i'll just list the x-values for the domain and the y-values for the range:

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