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xz_007 [3.2K]
2 years ago
11

The sum of three consecutive even integers is 108. What is the largest number?

Mathematics
1 answer:
horrorfan [7]2 years ago
3 0

Answer:

The largest of three numbers  is 38.

Step-by-step explanation:

Given : The sum of three consecutive even integers is 108.

We have to find the largest of three consecutive even integer.

Consecutive integers are integer having a difference of one between each term . example 14 , 15, 16 ..

consecutive even integers are integers having a difference of two between them such that first term is in the form of 2n , where n is integers.

Consider the three consecutive even integers are 2n , 2n + 2 , 2n + 4

Also, given The sum of three consecutive even integers is 108.

that is 2n + 2n + 2 + 2n + 4 = 108

Simplify, we get,

6n + 6 = 108

Subtract 6 both side, we get,

6n = 102

Divide by 6 both side, we get,

n = 17

Thus, numbers are 2n = 2 × 17 = 34

2n + 2 = 34 + 2 = 36

2n + 4 = 34 + 4 = 38

Thus, The sum of three consecutive even integers is 108 then integers are 34, 36, 38 .

Thus, The largest of three numbers  is 38.

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Nata [24]

9514 1404 393

Answer:

  vertex: (2, -3.2)

  axis of symmetry: x = 2

  zeros: x=0, x=4

  formula for axis of symmetry:

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  • x = -b/(2a) . . . . . . . where the quadratic is ax^2 +bx +c
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Step-by-step explanation:

a) The vertex x-coordinate is halfway between the zeros, so is x = (0+4)/2 = 2. It is where the graph has a turning point.

The vertex y-coordinate is the low point of this graph. It is not on a grid line, so we can only guess at its value. I choose to call it -3.2.

The vertex is (2, -3.2).

__

b) The axis of symmetry is the vertical line through the vertex. The constant in its equation is the x-coordinate of the vertex:

  x = 2

__

c) The zeros of the function are where the function crosses the x-axis. These are marked on the graph with red dots. The zeros are x=0 and x=4.

__

d) When the quadratic is written in standard form, ax^2 +bx +c, the equation of the axis of symmetry is ...

  x = -b/(2a) . . . . . perhaps this is the formula you're being asked for (?)

When there is no equation, the axis of symmetry can be found from the graph a couple of ways. One is to identify the x-coordinate of the vertex.

  x = <x-coordinate of the vertex>

Another is to average the zeros, since they are symmetrical about the axis of symmetry.

  x = average of zeros = (z1 +z2)/2

If the quadratic is written in vertex form, the vertex coordinate is the constant in the equation for the axis of symmetry.

  y = a(x -h)^2 +k . . . . . quadratic with vertex (h, k)

  x = h . . . . . . equation of axis of symmetry

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