Line l is parallel to line e in the figure below.
2 answers:
Answer:
2 Vertical angles prove that Angle 2 is congruent to angle 5
4 The triangles are similar because alternate interior angles are congruent.
5 In the similar triangles, Angle 3 and Angle 6 are corresponding angles.
Step-by-step explanation:
The picture of the question in the attached figure
<u><em>Verify each statement</em></u>
1 Vertical angles prove that Angle 1 is congruent to angle 4.
we know that
----> by alternate interior angles
therefore
The statement is false
2 Vertical angles prove that Angle 2 is congruent to angle 5
we know that
<u><em>Vertical Angles</em></u>, are the angles opposite each other when two lines cross.
They always are equal
so
In this problem
----> by vertical angles
therefore
The statement is true
3 The triangles are similar because corresponding sides are congruent
we know that
In this problem, the corresponding angles are congruent, hence the corresponding sides must be proportional
The triangles are similar, but the corresponding sides are not congruent
therefore
The statement is false
4 The triangles are similar because alternate interior angles are congruent.
The statement is true
The triangles are similar, because the corresponding angles are congruent (one angle is congruent by vertical angles and the other two by alternate interior angles)
5 In the similar triangles, Angle 3 and Angle 6 are corresponding angles
The statement is true
In this problem
The corresponding angles are
∠3 and ∠6
∠1 and ∠4
∠2 and ∠5
6 In the similar triangles, Angle 3 and Angle 4 are corresponding angles
The statement is false
Because
The corresponding angles are
∠3 and ∠6
∠1 and ∠4
∠2 and ∠5
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- $33,336.83
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Step-by-step explanation:
The amortization formula can be used to find the payment value.
A = P(r/2)/(1 -(1 +r/2)^(2n))
where P is the principal amount at the beginning of the loan period, r is the annual interest rate, n is the number of years remaining on the loan
The value of A in this scenario is the semi-annual payment.
Initially, the interest rate is 0.055 and the number of years remaining is 25.
After the first 5-year period, the interest rate goes up by 12%, so is multiplied by a factor of 1.12 to become 6.16% per year. The same growth factor is applied to the interest rate at the beginning of each 5-year period.
Of course, the number of years remaining is decreased by 5 years at the beginning of the next 5-year period.
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The Principal remaining at the end of each 5-year period is the starting principal for the next period. It is calculated from ...
FV = P(1 +r/2)^10 -A((1 +r/2)^10 -1)/(r/2)
Where P is the starting principal, A is the loan payment as calculated above, and r is the annual interest rate.
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These formulas are built into spreadsheet functions, so the desired set of loan payments can be calculated easily by that technology. The result is attached. In the "# pmts" column is the value used to amortize the loan for the 5-year period. The semiannual payment is calculated as though the loan would be completely paid off in that number of payments, keeping the same interest rate for the duration. Of course, that payment series is interrupted and the loan recalculated at the beginning of the next 5 years.
The half-yearly payments for each 5-year interval are ...
$33,336.83
$35,176.68
$36,869.23
$38,266.75
$39,158.08
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<em>Additional comment</em>
The values displayed in the spreadsheet are rounded to the values shown. The values used in calculation have 14 or more significant digits. This means the numbers here may vary from those provided by a lending institution. In the real world, the principal and interest values are rounded to cents with each payment, so actual results may vary by a few cents either way.
