Answer:
1. D. (-1,9)
2. B. (-5/3,2)
3. True
4. 9/5
5. A = -√-4 + 1, √-4 + 1
Step-by-step explanation:
1.
7x²-56x = 63
7x²-56x/7 = 63/7
x²-8x = 9
x²-8x+16 = 9+16
(x-4)² = 25
√(x-4)² = √25
x-4 = ±5
x-4 = -5
x = -5+4
x = -1
x-4 = 5
x = 5+4
x = 9
2.
6y²-2y-20 = 0
a = 6, b = -2, c = -20
x = (-b±√b²-4ac)/2a
x = [-(-2)±√(-2)²-4(6)(-20)]/2(6)
x = (2±√4+480)/12
x = (2±√484)/12
x = (2±22)/12
x = (2-22)/12
x = -20/12
x = -5/3
x = (2+22)/12
x = 24/12
x = 2
4.
r²-2r = -5
r²-2r+1 = -5+1
(r-1)² = -4
√(r-1)² = √-4
r-1 = ±√-4
r-1 = -√-4
r = -√-4 + 1
r-1 = √-4
r = √-4 + 1
5.
90e - 81 = 25e²
25e²-90e+81 = 0
(5e-9)² = 0
√(5e-9)² = √0
5e-9 = 0
5e = 9
e = 9/5
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Answers & Comments
Answer:
1. D. (-1,9)
2. B. (-5/3,2)
3. True
4. 9/5
5. A = -√-4 + 1, √-4 + 1
Step-by-step explanation:
1.
7x²-56x = 63
7x²-56x/7 = 63/7
x²-8x = 9
x²-8x+16 = 9+16
(x-4)² = 25
√(x-4)² = √25
x-4 = ±5
x-4 = -5
x = -5+4
x = -1
x-4 = 5
x = 5+4
x = 9
2.
6y²-2y-20 = 0
a = 6, b = -2, c = -20
x = (-b±√b²-4ac)/2a
x = [-(-2)±√(-2)²-4(6)(-20)]/2(6)
x = (2±√4+480)/12
x = (2±√484)/12
x = (2±22)/12
x = (2-22)/12
x = -20/12
x = -5/3
x = (2+22)/12
x = 24/12
x = 2
4.
r²-2r = -5
r²-2r+1 = -5+1
(r-1)² = -4
√(r-1)² = √-4
r-1 = ±√-4
r-1 = -√-4
r = -√-4 + 1
r-1 = √-4
r = √-4 + 1
5.
90e - 81 = 25e²
25e²-90e+81 = 0
(5e-9)² = 0
√(5e-9)² = √0
5e-9 = 0
5e = 9
e = 9/5