A glass is 1
6
full. Then 95cm3 of orange juice is poured in.
The glass is now
4
5
full. What is the total volume of the glass?

let x = the amount of orange juice in a full glass.

the glass is 1/6 full = 1/6 * x

add 95 cubic centimeters and the glass becomes 4/5 full.

equation for that is:

1/6 * x + 95 = 4/5 * x

subtract 1/6 * x from both sides of this equation to get:

95 = 4/5 * x - 1/6 * x

multiply 4/5 * 6/6 and multiply 1/6 * 5/5 and the equation becomes:

95 = 24/30 * x - 5/30 * x

combine like terms to get 95 = 19/30 * x

multiply both sides of the equation by 30/19 to get:

30/19 * 95 = 30/19 * 19/30 * x

simplify to get:

30/19 * 95 = x

solve for x to get x = 150.

the volume of the glass is 150 cubic centimeters.

1/6 * 150 = 25

4/5 * 150 = 120

the difference between 4/5 full and 1/6 full is 95 cubic centimeters.

solution is that the volume of the glass is 150 cubic centimeters.

Step-by-step explanation:

if the eqn of the parabola is f(x) = (x-4)(x+2), we need to mult. this out to find the coordinates of the vertex.

then f(x) = x^2 + 2x - 4x - 8, and f(x) = x^2 - 2x - 8.

one way in which you can find the vertex is to calculate x = -b / (2a).   here, that comes to

        )

x = = 1.   f(1) = 1^2 - 2(1) - 8 = - 9.   vertex is at (1, -9).

        2(1) 

find another point on the curve:   let x=0, for which y=-8.   then (0, -8) is on the curve.   plot the vertex and this point and draw a smooth parabola thru both.

hope this

step-by-step explanation:

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