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Step-by-step explanation:

51)

Let n be the first even number.

So the four consecutive even numbers are:

● n

● n+2

● n+4

●n+6

The smallest minus twice the larger is 4

● n-2(n+6)= 4

●n-2n-12 =4

● -n -12 =4

● -12 = 4+n

● -12-4 = n

● -16 = n

so the first even number is -16 and the largest one is -10

● -16+6= -10

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Let m be the first integer

So the five consecutive integers are:

● m

● m+1

● m+2

● m+3

● m+4

The sum of this terms is 5.5 times the middle(m+2)

● m+m+1+m+2+m+3+m+4 = 5.5(m+2)

● 5m + 10 = 5.5 m +11

● -0.5 m = 1

●-m = 2

● m= -2

So the integers are;

● -2

● -1 (-2+1)

● 0

● 1

● 2

step-by-step explanation:

here's what happens:

1) the graph of f   = x^2 is shifted 2 units to the right.

2) the resulting graph is reflected in the x-axis, so that the parabola now opens down.

3) this final result is transformed up by 5 units.

597

step-by-step explanation: