Find four consecutive even integers such that the sum of the third and fourth is 6 less than four times the first

The numbers are 2, 4, 6 and 8

Step-by-step explanation:

let the four numbers be x, y, z and l respectively

then:

x+y+z+l

(z+l)–6=4x

since they are all four consecutive even integers

then y=x+2

z=y+2=x+4

l=z+2=x+6

since (z+l)–6=4x

then ((x+4)+(x+6))–6=4x

2x+4=4x

4=4x–2x

4=2x

2=x

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

step-by-step explanation:

659