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3 years ago

Find k, the constant of proportionality, for the data in this table. Then write an equation for the relationship.

Mathematics

1 answer:

VashaNatasha [74]3 years ago

7 0

Answer:

$k=\frac{32}{5}$ , $y=\frac{32}{5}x$

$k=6.4$ , $y=6.4x$

Step-by-step explanation:

we know that

A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form $k=\frac{y}{x}$ or $y=kx$

Find the value of the constant of proportionality k

take any ordered pair from the data

For x=25, y=160

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

substitute the values of x and y

$k=\frac{160}{25}$

simplify

$k=\frac{32}{5}$

The linear equation is equal to

$y=\frac{32}{5}x$

$y=6.4x$

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3 years ago

A blue jay lives in a nest that is 12 meters high in a tree the blue jay flies 15 meters to get from its nest to a flower on the

Ivan

Answer:

The distance between the base of the tree and the flower is 9m

Step-by-step explanation:

Here, we have to paint a picture.

The flower is on the ground, the height of the tree is 12m.

The distance from the nest to the flower on the floor is 15m

Indisputably, what we have is a right angled triangle, with the height being 12m, the length of the hypotenuse being 15 and we are asked to calculate the adjacent which represents the distance from the base of the tree to the flower

To get this distance, we simply apply the Pythagoras’ theorem which states that the square of the hypotenuse(longest side of the triangle) is equal to the sum of the squares of the other two sides.

Thus mathematically, we know that our hypotenuse is 15m and the height is 12m

The length we are to calculate is the adjacent and it is equal to;

15^2 - 12^2

= 225 - 144

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The length is thus

√(81) = 9m

Please check attachment for a diagrammatic picture of the triangle