How many distinct products can be formed using two different integers from the given set: {–6, –5, –4, –3, –2, –1, 0, 1, 2, 3, 4
zhannawk [14.2K]
Number of distinct products that can be formed is 144
<h3>Permutation</h3>
Since we need to multiply two different integers to be selected from the set which contains a total of 12 integers. This is a permutation problem since we require distinct integers.
Now, for the first integer to be selected for the product, since we have 12 integers, it is to be arranged in 1 way. So, the permutation is ¹²P₁ = 12
For the second integer, we also have 12 integers to choose from to be arranged in 1 way. So, the permutation is ¹²P₁ = 12.
<h3>
Number of distinct products</h3>
So, the number of distinct products that can be formed from these two integers are ¹²P₁ × ¹²P₁ = 12 × 12 = 144
So, the number of distinct products that can be formed is 144
Learn more about permutation here:
brainly.com/question/25925367
3 (x + 7) = 5x - 2
3x + 21 = 5x - 2
3x - 5x = -2 - 21
-2x = -23
x = -23/-2
x = 23/2
The values of x and y are 8 and 0 respectively.
<em><u>Explanation</u></em>
As 'p' is located at (0,0) and 'r' is located at (-12,0) , that means both 'p' and 'r' are on the x-axis. So point 'q' will be also on the x-axis , and 'q' is located at (x,y)
So, the value of y will be 0. That means the co ordinate of point 'q' is (x, 0)
Now, using the Distance formula, length of 'pq' 
and length of 'pr' 
Given that, pq : pr =2/3
So....

Thus, the values of x and y are 8 and 0 respectively.
The slope of RS, RT, and ST are 1/2, -1 and -4 respectively
<h3>Triangle and slopes</h3>
Given the folllowing coordinates R (2,3), S (4,4), and T (5,0) os triangle RST
The formula for calculating the distance is expressed as:
For length RS:
D = √(4-3)²+(4-2)²
RS = √1+4
RS= √5
For length RS:
RT = √(0-3)²+(5-2)²
RT = √9+9
RT= 3√2
For length ST:
D = √(0-4)²+(5-4)²
ST = √16+1
ST= √17
Since all the sides are different, the triangle is a scalene triangle.
For the slope of the sides
For the side RS;
Slope = 4-3/4-2
Slope of RS = 1/2
For the side RT:
Slope = 0-3/5-2
Slope of RT = -3/3 = -1
For the side ST
Slope of ST = 0-4/5-4
Slope of ST = -4/1 = -4
Hence the slope of RS, RT, and ST are 1/2, -1 and -4 respectively
Learn more on slope and distance here: brainly.com/question/2010229
Answer:
The answer is x =7 and x= - 15
<em>Explanation</em>
