Answer:
The correct options are;
1. Definition of supplementary angles
2. m∠1 + m∠2 = m∠1 + m∠3
3. m∠2 = m∠3
4. Definition of Congruent Angles
Step-by-step explanation:
The two column proof is presented as follows;
Statement 
Reason
1. ∠1 and ∠2 are supplementary Given
∠1 and ∠3 are supplementary
2. m∠1 + m∠2 = 180° Definition of supplementary angles
m∠1 + m∠3 = 180°
3. m∠1 + m∠2 = m∠1 + m∠3 Transitive Property
4. m∠2 = m∠3 Subtraction Property of Equality
5. ∠2 ≅ ∠3 Definition of Congruent Angles
Given that angles ∠1 and ∠2 are supplementary angles and angles ∠1 and ∠3 are are also supplementary angles, then the sums of m∠1 + m∠2 and m∠1 + m∠3 are equal, therefore, ∠2 and ∠3 have equal quantitative value and therefore ∠2 = ∠3 and by definition, ∠2 ≅ ∠3.
Answer:
Step-by-step explanation:
((14×3) + 1 )/3 = (43/3)
Answer:
Step-by-step explanation:
So we have the expression:
And we wish to factor it.
First, let's make a substitution. Let's let u be equal to x². Therefore, our expression is now:
This is a technique called quadratic u-substitution. Now, we can factor in this form.
We can use the numbers -3 and -2. So:
For the first two terms, factor out a u.
For the last two terms, factor out a -3. So:
Grouping:
Now, substitute back the x² for u:
And this is the simplest form.
And we're done!
Given conditions are :
In 1980's, a typical middle-income household earned= $34,757
In 2009, a similar middle-income household earned= $38,550
And we have to find relative increase in income for these households from 1980 to 2009.
So first we will find the total increase in amounts.
Relative increase = 
= 10.91% or rounding it off we get approx 11%.
Hence, the answer is 11%.
The basic equation for interest is the investment amount(x) times the time in years(y) times the percent of interest(z).
That makes the equation:
x·y·z= amount with interest.
Lets plug in the numbers:
$900 x 1.5 x 2.4%
Now turn the percent into a decimal:
2.4% ----> .024
Now the equation is:
$900 x 1.5 x .024
Now do the math:
$900 x 1.5 = 1350
1350 x .024 = 32.4
1350 + 32.4 = 1382.4
The final answer is $1382.40
Hope this helps!
