Step-by-step explanation:
6x²–5x–4 = 0
6×4 = 24..
write many ways 24 can be written..
24 = (6×4), (1×24), (12×2), (8×3)
(8×3) --> –8+3 = –5
6x²+3x–8x–4 = 0
6x(x+½)–8(x+½) = 0
(6x–8)(x+½) = 0
6x–8 = 0, x+½ = 0
6x = 8, x = –½
x = 4/3, –½
Answer:
(6,1)
Step-by-step explanation:
1.) group the x and y terms (and move the constant to the other side)
x²-12x+y²-2y= -12
divide the coeficcents for the terms with just 1 or 1 x variable by 2 and then square it (and add that to both sides)
x²-12x+36+y²-2y+1= -12+36+1
factor
(x-6)²+(y-1)²= 25
the center is therefore (6,1)
Answer:
Beaker: $3, Goggles: $7
Step-by-step explanation:
Answer:
(3, 2), (2, 3)
Step-by-step explanation:
x + y = 5
xy = 6
Solve the first equation for x.
x = 5 - y
Substitute 5 - y for x in the second equation.
xy = 6
(5 - y)y = 6
5y - y² = 6
y² - 5y + 6 = 0
Factor.
(y - 2)(y - 3) = 0
y - 2 = 0 or y - 3 = 0
y = 2 or y = 3
Now substitute 2 for y in the first equation and solve for x.
x + y = 5
x + 2 = 5
x = 3
One solution is x = 3; y = 2, or (3, 2).
Now substitute 3 for y in the first equation and solve for x.
x + y = 5
x + 3 = 5
x = 2
Another solution is x = 2; y = 3, or (3, 2).
Answer: (3, 2), (2, 3)
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