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2 years ago

The sum of two consecutive numbers is n+1. What are the numbers?

Mathematics

1 answer:

Mariulka [41]2 years ago

8 0

Answer: n/2, n/2+1

Step-by-step explanation:

Consecutive numbers are always 1 more than the previous (n, n+1, n+2, n+...), and their sums are (like) n+n+1 or 2n+1 (n is the first number).

So in this situation (x is the first number);

n+1=x+x+1

n=x+x, n=2x

n/2=x

Meaning that the first number is n/2, and the second (n/2)+1 or just n/2+1.

I'm bad at explaining.

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Y=-x^2+6x-4 Find the Axis of Symmetry and the Vertex, Also solve the whole equation.

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1. Axis of symmetry: x = 3

2. Vertex: (3,5)

3. Solution of the equation:

x-intercepts:

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y-intercept: (0, -4)

Explanation:

1. Equation:

$y=-x^2+6x-4$

2. Axis of symmetry:

That is the equation of a parabola, whose standard form is:

$y=ax^2+bx+c$

Where:

$a=-1;b=6;c=-4$

The axis of symmetry is the vertical line with equation:

$x=-b/2a$

Substitute $a=-1,\text{ and }b=6$

$x=-6/[(2)(-1)]=-6/(-2)=3$

Thus, the axis of symmetry is:

$x=3$

3. Vertex

The x-coordinate of the vertex is equal to the axys of symmetry, i.e x = 3.

To find the y-xoordinate, substitute this value of x into the equation for y:

$y=-x^2+6x-4\\\\y=-(3)^2+6(3)-4=-9+18-4=5$

Therefore, the vertex is (3, 5)

4. Find the x-intercepts

The x-intercepts are the roots of the equation, which are the points wher y = 0.

$y=-x^2+6x-4=0$

Use the quadratic equation:

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5. Find the y-intercept

The y-intercet is the value of y when x=0:

$y=-x^2+6x-4\\\\y=-(0)^2+6(0)-4=-4$

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