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dmitriy555 [2]
3 years ago
12

The variables x and y are proportional. Use the values to find the constant of proportionality. Then write an equation that rela

tes x and y.
When y=72 and x=3.

K = ?

y = ?
Mathematics
1 answer:
Sidana [21]3 years ago
3 0

Answer:

k = 24, y = 24x

Step-by-step explanation:

Given x and y are proportional then the equation relating them is

y = kx ← k is the constant of variation

To find k use the condition when y = 72, x = 3 , then

72 = 3k ( divide both sides by 3 )

k = 24

y = 24x ← equation of proportion

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3 years ago
Find the coordinates of the circumcenter for ∆DEF with coordinates D(1,3) E (8,3) and F(1,-5). Show your work.
luda_lava [24]

Answer: The coordinates of the circumcenter is (\frac{9}{2}, -1).

Explanation:

The coordinates of triangle DEF are D(1,3) E (8,3) and F(1,-5).

Distance formula,

d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}

DE=\sqrt{(8-1)^2+(3-3)^2}=7

FE=\sqrt{(1-8)^2+(-5-3)^2}=\sqrt{7^2+8^2}

DF=\sqrt{(1-1)^2+(-5-3)^2}=8

Since triangle follows pythagoras theorem,

(DF)^2+(DE)^2=(FE)^2

Therefore the given triangle is a right angle triangle.

Or plot these points on a coordinate plane. From the figure we can say that the triangle DEF is a right angle triangle.

The circumcenter of a right angle triangle is the midpoint of the hypotenuse.

The hypotenuse is EF. The midpoint of EF is,

Midpoint =(\frac{8+1}{2}, \frac{3-5}{2} )=(\frac{9}{2}, -1)

Therefore, the coordinates of the circumcenter is (\frac{9}{2}, -1).

5 0
3 years ago
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MA_775_DIABLO [31]

Step-by-step explanation:

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4 years ago
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