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Complete each statement with a number that makes the statement true. A._____ < 7°c. B.___<-3°c. C.-0.8°c <_____ < -0
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Refer to the image attachment Figure 1 for the letter references. Hopefully the reference image is handy to keep track of all of the empty boxes.
The answers are given in Figure 2 which is also attached.
===================================================================================================================
Focus on the first Magic Square for now (the one in the top row, left side).
The middle row has 9+6+3 = 18 as the magic constant (aka magic sum). Every row, column and diagonal must add to this constant
A = 7 because the first column of values must add to 18
A+9+2 = A+11 = 18 leads to A = 7
----------
C = 10 since that solves 2+6+C = 18 (northeast diagonal)
----------
Solve the equation A+6+E = 18 for E to get E = 5 (plug in A = 7)
As a check, note how C+3+E = 10+3+5 = 18
----------
We know that A = 7 and C = 10 so B must be B = 1 since A+B+C = 7+1+10 = 18
----------
Similarly, 2+D+E = 18 and E = 5, so D must be 11.
As a check, note how B+6+D = 1+6+11 = 18
----------
----------
In summary we have
A = 7
B = 1
C = 10
D = 11
E = 5
See Figure 2 for the completed magic square
----------
Check:
Row1: 7+1+10 = 18
Row2: 9+6+3 = 18
Row3: 2+11+5 = 18
Column1: 7+9+2 = 18
Column2: 1+6+11 = 18
Column3: 10+3+5 = 18
NorthEast Diagonal: 2+6+10 = 18
NorthWest Diagonal: 7+6+5 = 18
As you can see, we get the same magic constant of 18
===================================================================================================================
Second Magic Square (Top Right)
For this magic square, the magic constant isn't known. So this is mainly a guess and check type of problem. This is what I got
F = 9
G = 6
H = 10
J = 12
K = 5
See Figure 2 for the completed magic square
----------
Check:
Row 1: 11+4+9 = 24
Row 2: 6+8+10 = 24
Row 3: 7+12+5 = 24
Column 1: 11+6+7 = 24
Column 2: 4+8+12 = 24
Column 3: 9+10+5 = 24
NorthEast Diagonal: 7+8+9 = 24
NorthWest Diagonal: 11+8+5 = 24
===================================================================================================================
Third Magic Square at the very bottom
The magic constant is 12+6+7+9 = 34
----------
Bottom row: 13+3+S+16 = 34 which solves to S = 2
----------
Northeast Diagonal: 13+Q+7+4 = 34 which solves to Q = 10
----------
Second Column: 3+Q+6+M = 34 turns into 3+10+6+M = 34 after substitution and that solves to M = 15
----------
For values R, P, L and N, I couldn't figure out an algebraic way to solve for them. So I had to resort to trial and error (guess and check). This is what I got
R = 11
P = 8
L = 1
N = 14
----------
----------
In summary we have
L = 1
M = 15
N = 14
P = 8
Q = 10
R = 11
S = 2
See Figure 2 for the completed magic square
----------
Check:
Row 1: 1+15+14+4 = 34
Row 2: 12+6+7+9 = 34
Row 3: 8+10+11+5= 34
Row 4: 13+3+2+16 = 34
Column 1: 1+12+8+13 = 34
Column 2: 15+6+10+3 = 34
Column 3: 14+7+11+2 = 34
Column 4: 4+9+5+16 = 34
NorthEast Diagonal: 13+10+7+4 = 34
NorthWest Diagonal: 1+6+11+16 = 34
The answers are given in Figure 2 which is also attached.
===================================================================================================================
Focus on the first Magic Square for now (the one in the top row, left side).
The middle row has 9+6+3 = 18 as the magic constant (aka magic sum). Every row, column and diagonal must add to this constant
A = 7 because the first column of values must add to 18
A+9+2 = A+11 = 18 leads to A = 7
----------
C = 10 since that solves 2+6+C = 18 (northeast diagonal)
----------
Solve the equation A+6+E = 18 for E to get E = 5 (plug in A = 7)
As a check, note how C+3+E = 10+3+5 = 18
----------
We know that A = 7 and C = 10 so B must be B = 1 since A+B+C = 7+1+10 = 18
----------
Similarly, 2+D+E = 18 and E = 5, so D must be 11.
As a check, note how B+6+D = 1+6+11 = 18
----------
----------
In summary we have
A = 7
B = 1
C = 10
D = 11
E = 5
See Figure 2 for the completed magic square
----------
Check:
Row1: 7+1+10 = 18
Row2: 9+6+3 = 18
Row3: 2+11+5 = 18
Column1: 7+9+2 = 18
Column2: 1+6+11 = 18
Column3: 10+3+5 = 18
NorthEast Diagonal: 2+6+10 = 18
NorthWest Diagonal: 7+6+5 = 18
As you can see, we get the same magic constant of 18
===================================================================================================================
Second Magic Square (Top Right)
For this magic square, the magic constant isn't known. So this is mainly a guess and check type of problem. This is what I got
F = 9
G = 6
H = 10
J = 12
K = 5
See Figure 2 for the completed magic square
----------
Check:
Row 1: 11+4+9 = 24
Row 2: 6+8+10 = 24
Row 3: 7+12+5 = 24
Column 1: 11+6+7 = 24
Column 2: 4+8+12 = 24
Column 3: 9+10+5 = 24
NorthEast Diagonal: 7+8+9 = 24
NorthWest Diagonal: 11+8+5 = 24
===================================================================================================================
Third Magic Square at the very bottom
The magic constant is 12+6+7+9 = 34
----------
Bottom row: 13+3+S+16 = 34 which solves to S = 2
----------
Northeast Diagonal: 13+Q+7+4 = 34 which solves to Q = 10
----------
Second Column: 3+Q+6+M = 34 turns into 3+10+6+M = 34 after substitution and that solves to M = 15
----------
For values R, P, L and N, I couldn't figure out an algebraic way to solve for them. So I had to resort to trial and error (guess and check). This is what I got
R = 11
P = 8
L = 1
N = 14
----------
----------
In summary we have
L = 1
M = 15
N = 14
P = 8
Q = 10
R = 11
S = 2
See Figure 2 for the completed magic square
----------
Check:
Row 1: 1+15+14+4 = 34
Row 2: 12+6+7+9 = 34
Row 3: 8+10+11+5= 34
Row 4: 13+3+2+16 = 34
Column 1: 1+12+8+13 = 34
Column 2: 15+6+10+3 = 34
Column 3: 14+7+11+2 = 34
Column 4: 4+9+5+16 = 34
NorthEast Diagonal: 13+10+7+4 = 34
NorthWest Diagonal: 1+6+11+16 = 34