Marine fuel is a combination of gasoline and motor oil. The standard gasoline and oil mixture is about 98% gasoline and about 2% motor oil. The "break in" mixture for a new engine is about 96% gasoline and about 4% motor oil. a. Write an equation in standard form that models the possible combinations of each kind of mixture you can prepare using 6 gallons of gasoline. b. If you prepare 4 gallons of the "break in" mixture, how much gasoline will you have for the standard mixture?

With 6 gallons of gasoline you could obtain 6.12 gallons of standard mixture or 6.25 gallons of break in mixture. In turn, if 4 gallons of break in mixture were prepared, there would be 2.16 gallons of gasoline left to prepare standard mixture.

Since the standard gasoline and oil mixture is about 98% gasoline and about 2% motor oil, and the "break in" mixture for a new engine is about 96% gasoline and about 4% motor oil, to determine the possible combinations of each kind of mixture you can prepare using 6 gallons of gasoline and, if you prepare 4 gallons of the "break in" mixture, how much gasoline will you have for the standard mixture, the following calculations should be performed:

A)

Therefore, with 6 gallons of gasoline you could obtain 6.12 gallons of standard mixture or 6.25 gallons of break in mixture.

B)

Therefore, if 4 gallons of break in mixture were prepared, there would be 2.16 gallons of gasoline left to prepare standard mixture.

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0.98g+ 0.02m= 7.1224 gallons standard mixture

0.96g+ 0.04m= 6.25 gallons break oil

3.92 gallons of gasoline  is required for  4 gallons the standard mixture

Step-by-step explanation:

If we have to use 6 gallons of gasoline this means that 98%= 6 gallons and 2% would be 6/98*2

Gasoline: Motor oil

6              :    x

98        : 2

Using the product rule

x= 6*2/98= 0.1224 gallons of motor oil is required.

Let the gasoline be represented by g and motor oil by m then for the standard oil the equation would be

0.98g+ 0.02m= 7.1224 gallons standard mixture

For break in oil

Gasoline: Motor oil

6              :    x

96        : 4

Using the product rule

x= 6*4/96= 0.25 gallons of motor oil is required.

Let the gasoline be represented by g and motor oil by m then for the break oil the equation would be

0.96g+ 0.04m= 6.25 gallons break oil

Part b. For  4 gallons of the "break in" mixture

96% of the 4 gallons of the "break in" mixture is gasoline =  3.84 gallons of gasoline

4% of 4 = 0.16 gallons of motor oil

Now the standard mixture 4 gallons would contain 98 % of gasoline and 2 % of motor oil

98% of 4 gallons= 3.92 gallons of gasoline

2% of  4 gallons= 0.08 gallons of motor oil.

hello from mrbilldoesmath!

answer:

(7 x + 6 y) (49 x^2 - 42 x y + 36 y^2)

discussion:

the trick is to recognize that 343 = 7^3 and 216 = 6^3 and, in general,

a^3 + b^3 =   (a + b) (a^2 - a b + b^2).

in our case

343x^3+216y^3   =   (7x)^3 + (6y)^3

so take a = 7x and b = 6y in the above equation to get the answer.

you,

mrb

the equation of the parallel line would be y = 2x + 9

step-by-step explanation:

to start we need to find the slope of the original line. we can do that by looking at the coefficient of x, which is 2

since the slope of the original line is 2 and parallel lines have the same slope, we know the new line will also have 2 slope. now we can use that along with the point given in point-slope form to get the find equation.

y - y1 = m(x - x1)

y - 5 = 2(x + 2)

y - 5 = 2x + 4

y = 2x + 9