6x - 3y = 15.....multiply by 4
7x + 4y = 10....multiply by 3
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24x - 12y = 60 (result of multiplying by 4)
21x + 12y = 30 (result of multiplying by 3)
---------------add
45x = 90
x = 90/45
x = 2
6x - 3y = 15
6(2) - 3y = 15
12 - 3y = 15
-3y = 15 - 12
-3y = 3
y = -3/3
y = -1
solution is (2,-1) <==
Solve for x:
2 (6 - x) = x (x + 5)
Expand out terms of the left hand side:
12 - 2 x = x (x + 5)
Expand out terms of the right hand side:
12 - 2 x = x^2 + 5 x
Subtract x^2 + 5 x from both sides:
-x^2 - 7 x + 12 = 0
Multiply both sides by -1:
x^2 + 7 x - 12 = 0
x = (-7 ± sqrt(7^2 - 4 (-12)))/2 = (-7 ± sqrt(49 + 48))/2 = (-7 ± sqrt(97))/2:
Answer: x = (-7 + sqrt(97))/2 or x = (-7 - sqrt(97))/2
If x is length of the diagonal then
x^2 = 3^2 + 4^2 = 25
x = sqrt25 = 5
Diagonal is 5 units long
So the possible answer of the following questions are the following and i hope you would be satisfied with my answer and feel free to ask for more if you have question and further clarification:
#1.A. 120 minutes
#2.A. 96 minutes
#3.A. 1 over 3 minus 1 over x equals 1 over 5
#4.C. 12 minutes
#5.<span>B. 1 over 4 plus 1 over 3 equals 1 over x</span>
