Answer: 12 sides
Step-by-step explanation:
The sum of the interior angles of a polygon is 180(n-2), where n is the number of sides
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1 answer:
Answer:
The two column proof is presented as follows;
Statement Reason
1. Parallelogram SUPN ⊥
1. Given
and ⊥
2. ∠SRU = ∠PMN = 90° 2. Definition of perpendicular lines
3. ∠SRU ≅ ∠PMN 2. Definition of congruency
4. ║
4. Opposite sides of a parallelogram are
congruent
5. ∠SNR ≅ ∠PUM 5. Alternate interior angles are congruent
6. ≅
6. Opposite sides of a parallelogram are
congruent
7. ΔPMU ≅ ΔSRN 7. By AAS rule of congruency
By the Angle-Angle-Side (AAS) rule of congruency, we have that, if two angles and a corresponding adjacent side (∠SRU ≅ ∠PMN, ∠SNR ≅ ∠PUM, ≅
) of two triangles (ΔPMU and ΔSRN) are congruent, then the the two triangles are also congruent (ΔPMU ≅ ΔSRN)
Step-by-step explanation:
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Two main facts are needed here:
1. The logarithm , regardless of the base of the logarithm, exists for
.
2. The square root exists for
.
(in both cases we're assuming real-valued functions only)
By (2) we know that exists if
, or
.
By (1), we know that exists if
, or
. But as long as the square root exists, it will always be positive, so this condition will always be met.
Ultimately, then, we only require , so the function has domain
.
To determine the range, we need to know that, in their respective domains, and
increase monotonically without bound. We also know that
at minimum, at which point the square root term vanishes, so the least value the function takes on is
. Then its range would be
.