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Congruence Answers
Congruence
asked 2021-03-09
What other information do you need in order to prove the triangles congruent using the SAS Congruence Postulate?
A)
\(\displaystyle\angle{B}{A}{C}\stackrel{\sim}{=}\angle{D}{A}{C}\)
B)
\(\displaystyle\overline{{{A}{C}}}\stackrel{\sim}{=}\overline{{{B}{D}}}\)
C)
\(\displaystyle\angle{B}{C}{A}\stackrel{\sim}{=}\angle{D}{C}{A}\)
D)
\(\displaystyle\overline{{{A}{C}}}\stackrel{\sim}{=}\overline{{{B}{D}}}\)
Congruence
asked 2021-03-09
Show that the congruence
\(\displaystyle{8}{x}^{{2}}-{x}+{4}\equiv{0}{\left(\text{mod}{9}\right)}\)
has no solution by reducing to the form
\(\displaystyle{y}^{{2}}\equiv{a}{\left(\text{mod}{9}\right)}\)
Congruence
asked 2021-03-07
For the following statement, either prove that they are true or provide a counterexample:
Let a, b, c, d,
\(\displaystyle{m}\in{Z}\)
such that c,
\(\displaystyle{d}\ge{1}\)
and m > 1. If
\(\displaystyle{a}\equiv{b}{\left(\text{mod}{m}\right)}\)
and
\(\displaystyle{c}\equiv{d}{\left(\text{mod}{m}\right)}\)
, then
\(\displaystyle{a}^{{c}}\equiv{b}^{{d}}{\left(\text{mod}{m}\right)}\)
Congruence
asked 2021-03-07
Solve the set of congruences
\(\displaystyle{2}{x}\equiv{1}{\left(\text{mod}{5}\right)}\)
\(\displaystyle{x}\equiv{3}{\left(\text{mod}{4}\right)}\)
Congruence
asked 2021-03-07
For each of the following congruences, find all integers N, with N>1, that make the congruence true.
\(10\equiv5(mod\ N)\)
.
Congruence
asked 2021-03-06
Solve the following systems of congruences.
\(x\equiv 4(mod\ 7)\)
Congruence
asked 2021-03-05
Justify Conclusions take a conjecture about the sum of th interior angles of a quadrilateral. Justify your reasoning.
Congruence
asked 2021-03-05
Find the solution of congruence:
\(\displaystyle{x}^{{43}}\equiv{47}{\left(\text{mod}{713}\right)}\)
Congruence
asked 2021-02-25
Find the triangle congruence (SSS SAS AAS HL)
Given: bar(SQ) and bar(PR) bisect each other.
Congruence
asked 2021-02-25
For the following statement, either prove that they are true or provide a counterexample:
Let a, b, c,
\(\displaystyle{m}\in{Z}\)
such that m > 1. If
\(\displaystyle{a}{c}\equiv{b}{c}{\left(\text{mod}{m}\right)},{t}{h}{e}{n}{a}\equiv{b}{\left(\text{mod}{m}\right)}\)
Congruence
asked 2021-02-25
Solve the following linear congruence:
\(17x\ congruence\ 3(mod\ 210)\)
Congruence
asked 2021-02-25
Find the least positive solution for the following congruence:
\(41x=125(mod\ 660)\)
.
Congruence
asked 2021-02-24
Prove that if
\(\displaystyle{a}\equiv{b}{\left(\text{mod}{n}\right)}{\quad\text{and}\quad}{c}\equiv{d}{\left(\text{mod}{n}\right)}\)
, then if
\(\displaystyle{a}-{c}\equiv{b}-{d}{\left(\text{mod}{n}\right)}\)
Congruence
asked 2021-02-23
Find the smallest positive integer solution to the following system of congruence:
\(x\equiv 17(mod\ 35)\)
\(x\equiv 8(mod\ 43)\)
Congruence
asked 2021-02-21
State the third congruence required to prove the congruence of triangles using the indicated postulate.
a)
\(\displaystyle\overline{{{Z}{Y}}}\stackrel{\sim}{=}\overline{{{J}{L}}}\)
b)
\(\displaystyle\angle{X}\stackrel{\sim}{=}\angle{K}\)
c)
\(\displaystyle\overline{{{K}{L}}}\stackrel{\sim}{=}\overline{{{X}{Z}}}\)
d)
\(\displaystyle\angle{Y}\stackrel{\sim}{=}\angle{L}\)
Congruence
asked 2021-02-21
Solve the linear congruence
\(\displaystyle{7}{x}+{3}{y}\equiv{10}{\left(\text{mod}{16}\right)}\)
Congruence
asked 2021-02-21
Use the construction in the proof of the Chinese remainder theorem to find all solutions to the system of congruences
\(\displaystyle{x}\equiv{2}{\left(\text{mod}{3}\right)},{x}\equiv{1}{\left(\text{mod}{4}\right)},{\quad\text{and}\quad}{x}\equiv{3}{\left(\text{mod}{5}\right)}\)
.
Congruence
asked 2021-02-21
Whether the congruence
\(25\equiv 85\ mod\ 12\)
is true or false.
Congruence
asked 2021-02-21
Solve the following systems of congruences.
\(x\equiv 4(mod\ 5)\)
\(x\equiv 3(mod\ 8)\)
\(x\equiv 2(mod\ 3)\)
Congruence
asked 2021-02-19
Solve the linear congruence
\(\displaystyle{7}{x}\equiv{13}{\left(\text{mod}{19}\right)}\)
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