Problem solving involving rational equation
1. the reciprocal of 5 plus the reciprocal of 7 is the reciprocal of what number?

2. the reciprocal of the product of two consecutive intergers is 1/72

1. The reciprocal of 5 plus the reciprocal of 7 is the reciprocal of what number?

The reciprocal of 5 plus the reciprocal of 7 is the reciprocal of

1. The reciprocal of 5 plus the reciprocal of 7 is the reciprocal of what number?

From given question,

Given that,

reciprocal of 5 + reciprocal of 7 = ?

On cross-multiplying we get,

Thus reciprocal is

So the reciprocal of 5 plus the reciprocal of 7 is the reciprocal of

2. The reciprocal of the product of two consecutive integers is 1/72

The value of two consecutive numbers are 8 and 9

Let the two consecutive integers be x and x + 1

Given that reciprocal of product of two consecutive integers is

product of two consecutive integers = x(x + 1) =

reciprocal of the product of two consecutive integers =

Solve the above quadratic equation by grouping method

Thus x = -9 or 8

Ignoring negative value,

x = 8

Thus two consecutive integers are x = 8 and x + 1 = 8 + 1 = 9

8 and 9 are two consecutive integers

abde or 1,2,4, 5 is the answer

step-by-step explanation:

when rotating a figure 180 degrees, imagine that you are able to take the figure and turn it clockwise or counterclockwise around a center point. to rotate a figure 180 degrees, you will need to apply the rule (x, y) → (-x, -y). start by using a coordinate grid with coordinates for each vertex of the figure. the center point of the coordinate grid is located at (0, 0), which is what you will rotate the figure around. write down the original coordinates of the shape you are going to rotate. then, apply the rule. for example, coordinate (1, 2) becomes (-1, -2). another example would be, coordinate (-4, -2) becoming (4, 2). after you change each original coordinate to the rotated coordinate, you will draw your new figure.

step-by-step explanation: