Which polynomial is in standard form?
1 answer:
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The two-column proof that proves that ∠O ≅ ∠R using the SSS and CPCTC theorems is shown in the image attached below.
<h3>What is the Side-side-side Congruence Theorem (SSS)?</h3>The side-side-side congruence theorem (SSS) states that when three sides of a triangle are congruent to the corresponding three sides of another triangle, then both triangles are considered congruent to each other.
<h3>What is the CPCTC Theorem?</h3>The CPCTC theorem states that when two triangles are proven to be congruent by any triangle congruent theorem, then all the corresponding parts of the congruent triangle are congruent. This implies that the corresponding sides and angles of both triangle are equal or congruent.
We are asked to prove that ∠O ≅ ∠R.
With the given image, we would draw segment UP. Thus, based on the reflexive property, UP ≅ UP (one pair of congruent sides).
We are given two pairs of corresponding sides already, which are: UO ≅ UR and PO ≅ PR.
This means that triangles OUP and RUP have three pairs of corresponding congruent sides. Therefore, ΔOUP ≅ ΔRUP.
Applying the CPCTC theorem, ∠O ≅ ∠R.
The two-column proof is attached in the image below.
Learn more about the Side-side-side Congruence Theorem (SSS) on:
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Answer:
The correct option is (a) 3759.
Step-by-step explanation:
The complete question is:
The natural resources of an island limit the growth of the population. The population of the island is given by the logistic equation where t is the number of years after 1980. What is the limiting value of the population?
(a) 3759
(b) 23
(c) 761
(d) 1017
Solution:
The limiting value is the value of the function P (t) for <em>t</em> → ∞.
As <em>t</em> → ∞, the expression → 0.
Thus, making the denominator of P (t) 1.
So, the limiting value of the population is, 3759.
Thus, the correct option is (a) 3759.