Given points A(−2,0), B(−5,3), C(−9,−1), P(7,6), Q(4,0), and R(−4,4), which of the following proves that △ABC~△PQR?
UNO [17]
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:
brainly.com/question/4163594
So we can set x= width
2x+2 = length
so 2(x)+2(2x+2)= 76
so that will give us 2x+4x+4=76
6x=72
x=12
so 12 is width and 26 is length
Follow the Order of Operations:
(PEMDAS)
<u>Parenthesis</u> (1)
<u>Exponents</u> (2)
<u>Multiplications</u> (3)
<u>Division</u> (3)
<u>Addition</u> (4)
<u>Subtraction</u> (4)
Note: Multiplication and Division are both on the same level, depending if it first came on the left or not. Same goes to Addition and Subtraction.
Answer: 3.50329. <em>3.5, if round to the nearest tenth.</em>
Answer:
Emily has 20 students and Santiago has 18 students in home rooms
Step-by-step explanation:
to figure out the number in Emily's class we need to answer this question - '15 is 75% of what number'?
we can use:
is/of = %/100
is = 15
of = 'n'
75% = 75/100 or 3/4
15/n = 3/4
cross-multiply to get:
3n = 60
n = 20
So there are 20 students in Emily's home room
Now we find the number of students in Santiago's home room:
the question is - '12 is 2/3 of what number'?
we can write this equation:
12 = 2/3n
multiply each side by 3/2 to get:
36/2 = n
18 = n
18 students in Santiago's home room
