Answer:
B
Step-by-step explanation:
12x² - 157x - 40
Consider the factors of the product of the coefficient of the x² term and the constant term which sum to give the coefficient of the x- term
product = 12 × - 40 = - 480 and sum = - 157
The factors are + 3 and - 160
Use these factors to split the x- term
12x² + 3x - 160x - 40 ( factor the first/second and third/fourth terms
= 3x(4x + 1) - 40(4x + 1) ← factor out (4x + 1) from each term
= (4x + 1)(3x - 40) ← in factored form → B
The answer:
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x = (⅔)y ;
y = 3x/2.
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Given:
x + (⅓)y + x - (2/4)<span>y - x = (3/6)y ;
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Take the: x + x - x = 1x + 1x - 1x = 2x - 1x = 1x = x ;
and rewrite:
x + (⅓)y - (2/4)y = (3/6)y ;
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Note that: (2/4)y = (<span>½)y ;
and: (3/6)y = (</span><span>½)y ; so;
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Rewrite as:
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</span>x + (⅓)y - (½)y = (½)y ;
Add "(½)y" to EACH SIDE of the equation;
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x + (⅓)y - (½)y + (½)y = (½)y + (½)y ;
to get: x + (⅓)y = y ;
x = 1y - (⅓)y = (3/3) y - (1/3)y - [ (3-1)/3] y = (⅔)y ;
So: x = (<span>⅔)y ;
In terms of "y" ;
Given: </span>(⅔)y = x ; Multiply each side of the equation by "3" ;
3*[(⅔)y] = 3*x ;
to get: 2y = 3x ;
Now, divide EACH SIDE of the equation by "2" ; to isolate "y" on one side of the equation; and to solve for "y" (in terms of "x"):
2y / 2 = 3x / 2 ;
to get:
y = 3x/2 ;
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Answer:
x = 270 gallons
270 gallons of a 50% antifreeze solution must be mixed with 90 gallons of 10% antifreeze to get a mixture that is 40% antifreeze
Step-by-step explanation:
Let x represent the number of gallons of the 50% antifreeze solution.
The volume of the 10% antifreeze is = 90 gallons
The volume of the mixture that is 40% antifreeze = 90+x
The amount of antifreeze in the two solutions must be equal to the amount of anti freeze in the mixture;
50% of x + 10% of 90 = 40% of (90+x)
0.50(x) + 0.10(90) = 0.40(90+x)
0.50x + 9 = 36 + 0.40x
Collecting the like terms;
0.50x - 0.40x = 36-9
0.10x = 27
x = 27/0.10
x = 270 gallons
270 gallons of a 50% antifreeze solution must be mixed with 90 gallons of 10% antifreeze to get a mixture that is 40% antifreeze
-8/x = 4
-8 = 4x
-8/4 = x
-2 = x
or
x = -2
