A number that is a factor of 2 or more numbers is called a ______ of those number
2 answers:
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Answer:
Part 1:
The solution set of the system of equations is x = 1, y = 1
Part 2:
The solution set is x = 1, y = 1
Part 3:
The similarity of the system of equations in Parts 1 and 2 is that they have the same solution set
The difference of the system of equations in Parts 1 and 2 is that they are arranged differently
Step-by-step explanation:
Part 1:
The system of equation is given as follows;
2·x + y = 3...(1)
x = 2·y - 1...(2)
The above system of equations can be written in terms of the variable, y, as follows;
For equation (1), we have;
y = 3 - 2·x
For equation (2), we have;
y = (x + 1)/2
From the attached graph created with Microsoft Excel, we have;
The solution set (the point of intersection) of the system of equations is x = 1, y = 1
To accurately find the common solution, we have;
(x + 1)/2 = 3 - 2·x
x + 1 = 2·(3 - 2·x) = 6 - 4·x
x + 1 = 6 - 4·x
x + 4·x = 6 - 1
5·x = 5
x = 5/5 = 1
x = 1
Therefore, y = 3 - 2·x = 3 - 2× 1 = 1, at the common solution
Part 2:
y = -2x + 3
x - 2y = -1
∴ x = 2y -1
y = -2(2y -1) + 3
y = -4y + 2 + 3
5y = 5
y = 1
x = 2y - 1 = 2 - 1 = 1
x = 1
The solution set is x = 1, y = 1
Part 3
The system of equations are similar in terms of their solution
The system of equations are different in terms of their arrangement
The number of white and grey blocks in the quilts follows a sequence given by the Design number of the quilt
The numbers and patterns of the blocks are;
a. Patterns;
- The height of the white blocks is the Design number, while the rows are one more than the design number
- The height of the outer grey blocks is 2 blocks more than the Design number, while their rows are 3 blocks more than the Design number
b. The function is
c. The function is
d.
e. The design chosen is <u>Design 9</u>
The number of blocks is <u>132 blocks</u>
Reasons:
The pattern of the design are;
a. The column height of the grey blocks = 2 blocks more than the column height of the white blocks
Width of the outer grey blocks = 2 blocks more than the width of the inner white blocks
The number of white blocks in a design, <em>n</em> is the product of <em>n</em> and (n + 1)
The number of grey blocks in a design <em>n</em>, is the product of (n + 2) and (n + 3) less the number of white blocks in the design
b. Based on the above, the function that represent the number of picture blocks in Design <em>n</em>, is therefore;
- p(n) = n·(n + 1)
c. Based on the above, the function that represent the number of border blocks in Design <em>n</em>, is therefore;
- b(n) = (n + 2)·(n + 3) - n·(n + 1)
d. The total number of blocks, t(n) = (n + 2)·(n + 3)
t(n) = (n + 2)·(n + 3) - n·(n + 1) + n·(n + 1)
- t(n) = p(n) + b(n)
e. The given number of picture blocks = 90
The number of picture blocks in a design, n = n × (n + 1)
Therefore, given that the number of picture blocks is 90, we have;
90 = n × (n + 1)
n² + n - 90 = 0
(n + 10)·(n - 9) = 0
n = 9, or n = -10
Therefore, the design museum chooses is <u>Design 9</u>
The total number of blocks in a quilt design, t(n) = (n + 2)·(n + 3)
Total blocks in the design the art museum choses, t(9), is given as follows;
t(9) = (9 + 2)·(9 + 3) = <u>132 blocks</u>
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