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1 year ago

Drag a statement or reason to each box to complete this proof.

Mathematics

1 answer:

alukav5142 [94]1 year ago

8 0

The table to complete the proof is as follows

Equation statement

1. m∠ABD = 60°, m∠DBC=40° Given

2. m∠ABD + m∠DBC = m∠ABC Angle Addition Postulate

3. 60° + 40° = m∠ABC Substitution Property of Equality

4. 100° = m∠ABC Simplifying

5. ∠ABC is an obtuse angle. greater than 90 degrees

6. △ABC is an obtuse triangle. Definition of obtuse triangle

<h3>What is obtuse angles?</h3>

When an angel is greater than 90 degrees the angle is said to be an obtuse angle.

For the question solved here m∠ABC is greater than 90 degrees hence an obtuse angle.

Read more on angles here: brainly.com/question/25716982

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Find the smallest positive integer solution to the following system of congruences: x = 0 (mod 5) x = 8 (mod 11) The solution is

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Answer:

The smallest positive integer solution to the given system of congruences is 30.

Step-by-step explanation:

The given system of congruences is

$x=0(mod5)$

$x=8(mod11)$

where, m and n are positive integers.

It means, if the number divided by 5, then remainder is 0 and if the same number is divided by 11, then the remainder is 8. It can be defined as

$x=5m$

$x=11n+8$

$5m\cong 11n+8$

Now, we can say that m>n because m and n are positive integers.

For n=1,

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19 is not divisible by 5 so m is not an integer for n=1.

For n=2,

$5m=11(2)+8$

$5m=30$

$m=6$

The value of m is 6 and the value of n is 2. So the smallest positive integer solution to the given system of congruences is

$x=5(6)=30$

Therefore the smallest positive integer solution to the given system of congruences is 30.

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