in the xy - plain the line of the equation y = 5x - 6 is parallel to the line ax + 2y = 6. Where a is a constant. Determine the value of a

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  a = -10

Step-by-step explanation:

Subtract 5x from the given equation and compare to the desired equation.

  -5x +y = -6

  ax +2y = 6

For the lines to have the same slope, the ratio of x and y coefficients must be the same.

  -5/1 = a/2

  -10 = a . . . . . multiply by 2

answer: given that the roller coaster can accommodate 1600 riders per hour, thus the roller coaster can accomodate 1600 / 60 = 26.67 riders per minute.

given that there are 345 people in the line, the number of minutes it will take for the 345 persons to get into the roller coaster is given by 345 / 26.67 = 12.94 minutes.

therefore, it will take you 12.94 minutes to get to the front of the line.

step-by-step explanation:

answer: 204

step-by-step explanation:

we are told that the revenue is

x⋅(4080−10x)=−10x^2+4080x

this is a quadratic function, so to maximize it we should find the x-value of its vertex. recall that the x-value of the vertex of the parabola ax^2+bx+c is given by the formula −b/2a.

so in this case, we have a=−10 and b=4080, so the x-value of the vertex is

−b/2a= −(4080)/2(−10)=204