Solve the following inequality algebraically.
1 answer:
You might be interested in
Based on the SSS similarity theorem, △ABC ~ △PQR because AB/PQ = BC/QR = CA/RP = √2/√5 = √10/5 (option D).
<h3>The SSS Similarity Theorem</h3>Two triangles having three pairs of sides that are proportional can be proven to be similar by the SSS similarity theorem.
If the triangle ABC and triangle PQR are similar, their corresponding sides will be proportional, meaning that: AB/PQ = BC/QR = CA/RP.
Therefore, using the distance formula, , the sides of each triangle is found.
Therefore, it shows that:
AB/PQ = BC/QR = CA/RP = √2/√5 = √10/5
Therefore, based on the SSS similarity theorem, △ABC ~ △PQR because AB/PQ = BC/QR = CA/RP = √2/√5 = √10/5 (option D).
Learn more about the SSS similarity theorem on:
Answer:
I would say the correct answer is 2^3 • 5 • 11
Step-by-step explanation:
To find the prime factors, you start by dividing the number by the first prime number, which is 2. If there is not a remainder, meaning you can divide evenly, then 2 is a factor of the number. Continue dividing by 2 until you cannot divide evenly anymore. Write down how many 2's you were able to divide by evenly. Now try dividing by the next prime factor, which is 3. The goal is to get to a quotient of 1.Here are the first several prime factors: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29...
<u>Let's start by dividing 440 by 2 </u>
440 ÷ 2 = 220 - No remainder! 2 is one of the factors!
220 ÷ 2 = 110 - No remainder! 2 is one of the factors!
110 ÷ 2 = 55 - No remainder! 2 is one of the factors!
55 ÷ 2 = 27.5 - There is a remainder. We can't divide by 2 even anymore. Let's try the next prime number
55 ÷ 3 = 18.3333 - This has a remainder. 3 is not a factor.
55 ÷ 5 = 11 - No remainder! 5 is one of the factors!
11 ÷ 5 = 2.2 -There is a remainder. We can't divide by 5 evenly anymore. Let's try the next prime number
11 ÷ 7 = 1.5714 - This has a remainder. 7 is not a factor.
11 ÷ 11 = 1 - No remainder! 11 is one of the factors!
If we put all of it together we have the factors 2 x 2 x 2 x 5 x 11 = 440. It can also be written in exponential form as 2^3 x 5^1 x 11^1.
here is also the factor tree method : -
