If y varies inversely with x, find the constant of variation x= -40 and y= 4

Mathematics

1 answer:

Daniel [21]3 years ago

8 0

Answer:

$y=\frac{-160}{x}, \ \ \ \ k=-160$

Step-by-step explanation:

let $k$ be a constant written as:

$y=\frac{k}{x}$

It is given that y=4, x=-40

#We substitute x, y values in our function:

$y=\frac{k}{x}\\\\4=\frac{k}{-40}\\\\k=4\times-40\\\\k=-160$

We substitute the constant value in the equation:

$y=\frac{k}{x}, k=-160\\\\y=\frac{-160}{x}$

You might be interested in

What would you have to show in order to prove that a quadrilateral is a rectangle?

nekit [7.7K]

Answer:

A. Consecutive sides have opposite reciprocal slopes

Step-by-step explanation:

A rectangle is a special case of parallelogram, in which the diagonals bisect each other and are the same length, and all angles are right angles. In order to prove a quadrilateral is a rectangle, it can be shown to be a parallelogram, but one or the other of these additional characteristics must be proven.

A. Consecutive sides have opposite reciprocal slopes

Sides with opposite reciprocal slopes will be perpendicular. That is, the angle between them will be a right angle. If all pairs of consecutive sides meet at right angles, the figure must be a rectangle.

B. All sides are congruent

A rhombus is a quadrilateral in which all sides are congruent. It will only be a rectangle if the diagonals are the same length, or, equivalently, adjacent sides meet at right angles.

C. Opposite sides are parallel

A parallelogram will have opposite sides parallel. It will only be a rectangle if the diagonals are the same length, and/or adjacent sides meet at right angles.

D. Consecutive sides are congruent, opposite sides are not.

This seems a contradiction, as opposite sides are consecutive to the same side. (For example, sides AB and CD are both consecutive to side BC.) If we take this to mean that there are two pairs of consecutive congruent sides, then the figure may be a kite, but isn't necessarily a rectangle unless the other conditions are met.

_____

Additional comment

If sides are horizontal and vertical, the slope of the vertical sides is "undefined." It cannot be shown to be the opposite reciprocal of the slope of the horizontal sides.

5 0

2 years ago

Using the digits 0-9, at most one time each, create five ordered pair that represent a linear

krok68 [10]

Answer:

(-9, 0), (-8, 1), (-7, 2), (-6, 3) and (-5, 4)

Step-by-step explanation:

From the graph attached,

Ordered pairs which lie on the given line (-9, 0), (0, 3), (3, 4), (6, 5) and (9, 6).

Since all the points lie on the same line, rate of change of the linear function will be defined by the slope of the given line.

Slope of the line passing through (0, 3) and (3, 4) = $\frac{y_2-y_1}{x_2-x_1}$