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deff fn [24]
3 years ago
15

A.loana established all necessary conditions but then used an inappropriate congruence cirterion

Mathematics
1 answer:
PtichkaEL [24]3 years ago
6 0

Answer:

The correct option is

a. Loana established all necessary conditions but then used an inappropriate congruence criterion

Step-by-step explanation:

The two column proof is presented as follows;

Statement          {}                    Reason

1. PQ = RQ = 9      {}                  Given

2. m∠O = m∠S = 90° {}             Given

3. m∠PQO = m∠RQS = 63° {}   Given

4. ΔOPQ ≅ ΔSRQ {}                  Angle-Side-Angle Congruence

The given parameters shows that the side, adjacent angle, and next adjacent angle of triangle ΔOPQ are congruent to the corresponding side, adjacent angle, and next adjacent angle of triangle ΔSRQ, therefore, the appropriate congruency criterion that shows that ΔOPQ is congruence to ΔSRQ {}is the Side-Angle-Angle which is the same as the Angle-Angle-Side AAS, congruency criterion

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The first term of a geometric series is -3, the common ratio is 6, and the sum of the series is -4,665. Using a table of values,
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Answer:

Option A. 5

Step-by-step explanation:

From the question given above, the following data were obtained:

First term (a) = –3

Common ratio (r) = 6

Sum of series (Sₙ) = –4665

Number of term (n) =?

The number of terms in the series can be obtained as follow:

Sₙ = a[rⁿ – 1] / r – 1

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Cross multiply

–4665 × 5 = –3[6ⁿ – 1]

–23325 = –3[6ⁿ – 1]

Divide both side by –3

–23325 / –3 = 6ⁿ – 1

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Collect like terms

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Express 7776 in index form with 6 as the base

6⁵ = 6ⁿ

n = 5

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\bf n^{th}\textit{ term of a geometric sequence}\\\\
a_n=a_1\cdot r^{n-1}\qquad 
\begin{cases}
n=n^{th}\ term\\
a_1=\textit{first term's value}\\
r=\textit{common ratio}\\
----------\\
a_1=30\\
r=0.75\\
n=4
\end{cases}
\\\\\\
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4 0
3 years ago
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