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sladkih [1.3K]
3 years ago
5

The constant of proportionality is always the point___________, where k is the constant of proportionality

Mathematics
1 answer:
TiliK225 [7]3 years ago
4 0
Let's take as example a linear function of the form:
 y = kx.
 Where,
 k is the constant of proportionality.
 Therefore, the proportionality constant is the point:
 (x, kx)
 Generically it is always the point:
 (x, k * f (x))
 Where, f (x) is a function proportional to x.
 answer:
 The constant of proportionality is always the point (x, k * f (x)), where k is the constant of proportionality. 
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Answer:

\text{sin}(x) is an odd function.

Step-by-step explanation:

We are asked to prove whether \text{sin}(x) is even or odd.

We know that a function f(x) is even if f(x)=f(-x) and a function f(x) is odd, when f(-x)=-f(x).

We also know that an even function is symmetric with respect to y-axis and an odd function is symmetric about the origin.

Upon looking at our attachment, we can see that \text{sin}(x) is symmetric with respect to origin, therefore, \text{sin}(x) is an odd function.

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Given: AB with point C between A and B. AB = 10x + 20, AC = 2x + 13, and CB = 10x - 9.
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Answer:46

Step-by-step explanation:

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This was given to me during a summative test and the teacher didn't bother giving me the correction. I just cannot figure it out
Dmitry [639]
  • Base be y

ATQ

\\ \sf\longmapsto xy=6050\dots 1

\\ \sf\longmapsto 2(x+y)=220\implies x+y=110\dots 2

Now

\\ \sf\longmapsto (x+y)^2=x^2+y^2+2xy

\\ \sf\longmapsto 110^2-2(6050)=x^2+y^2

\\ \sf\longmapsto 12100-12100=x^2+y^2

\\ \sf\longmapsto x^2+y^2=0\dots(3)

From all equations

\\ \sf\longmapsto (x-y)^2=x^2+y^2-2xy

\\ \sf\longmapsto (x-y)^2=0-2(6050)

\\ \sf\longmapsto (x-y)^2=-12100

\\ \sf\longmapsto (x-y)=110\dots(4)

Now

Adding 3 and 4

\\ \sf\longmapsto 2x=220

\\ \sf\longmapsto x=110m

One side won't be covered hence

  • y=2(110)=220m
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Find x<br><br> 9x+3+5x-2+11x-21=180
Bess [88]

Answer:

x = 8

Step-by-step explanation:

Simplifying

(9x + 3) + (5x + -2) + (11x + -21) = 180

Reorder the terms:

(3 + 9x) + (5x + -2) + (11x + -21) = 180

Remove parenthesis around (3 + 9x)

3 + 9x + (5x + -2) + (11x + -21) = 180

Reorder the terms:

3 + 9x + (-2 + 5x) + (11x + -21) = 180

Remove parenthesis around (-2 + 5x)

3 + 9x + -2 + 5x + (11x + -21) = 180

Reorder the terms:

3 + 9x + -2 + 5x + (-21 + 11x) = 180

Remove parenthesis around (-21 + 11x)

3 + 9x + -2 + 5x + -21 + 11x = 180

Reorder the terms:

3 + -2 + -21 + 9x + 5x + 11x = 180

Combine like terms: 3 + -2 = 1

1 + -21 + 9x + 5x + 11x = 180

Combine like terms: 1 + -21 = -20

-20 + 9x + 5x + 11x = 180

Combine like terms: 9x + 5x = 14x

-20 + 14x + 11x = 180

Combine like terms: 14x + 11x = 25x

-20 + 25x = 180

Solving

-20 + 25x = 180

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '20' to each side of the equation.

-20 + 20 + 25x = 180 + 20

Combine like terms: -20 + 20 = 0

0 + 25x = 180 + 20

25x = 180 + 20

Combine like terms: 180 + 20 = 200

25x = 200

Divide each side by '25'.

x = 8

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