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Vsevolod [243]
3 years ago
6

Consider the function represented by 9x + 3y= 12 with x as the independent variable. How can this function be written

Mathematics
1 answer:
Elena-2011 [213]3 years ago
8 0

Answer: f(x) = -3x + 4

Step-by-step explanation:

The function is represented by

9x + 3y= 12

This is a linear equation with x as the independent variable. This means that if x is the independent variable, the y is the dependent variable. The values of y depends on the values of x. In order to represent the function, 9x + 3y= 12, we would rearrange the function such that y stands alone on the left hand side of the equation. This becomes

9x + 3y= 12

Subtracting 9x from both sides,

9x -9x + 3y = 12 - 9x

3y = 12-9x

Dividing the lefthand side and right hand side of the equation by 3, it becomes

3y/3 = (12-9x)/3

y= -3x + 4

using function notation,

y = f(x) = -3x + 4

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3 years ago
Use a Venn diagram to answer the question. A survey of 180 families showed that 67 had a​ dog; 52 had a​ cat; 22 had a dog and a
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Answer:

There are 13 families had a parakeet only

Step-by-step explanation:

* Lets explain the problem

- There are 180 families

- 67 families had a dog

- 52 families had a cat

- 22 families had a dog and a cat

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- 4 had a​ cat, a​ dog, and a parakeet (4 is a part of 22 and 22 is a part

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* We will explain the Venn-diagram

- A rectangle represent the total of the families

- Three intersected circles:

 C represented the cat

 D represented the dog

 P represented the parakeet

- The common part of the three circle had 4 families

- The common part between the circle of the cat and the circle of the

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- The common part between the circle of the dog and the circle of the

 parakeet only had a families

- The common part between the circle of the cat and the circle of the

 parakeet only had b families

- The non-intersected part of the circle of the dog had 67 - 22 - a =

  45 - a families

  had dogs only

- The non-intersected part of the circle of the cat had 52 - 22 - b =  

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  had cats only

- The non-intersected part of the circle of the parakeet had c families

  had parakeets only

- The part out side the circles and inside the triangle has 70 families

- Look to the attached graph for more under stand

∵ The total of the families is 180

∴ The sum of all steps above is 180

∴ 45 - a + 18 + 4 + 30 - b + b + c + a + 70 = 180 ⇒ simplify

- (-a) will cancel (a) and (-b) will cancel (b)

∴ (45 + 18 + 4 + 30 + 70) + (-a + a) + (-b + b) + c = 180

∴ 167 + c = 180 ⇒ subtract 167 from both sides

∴ c = 180 - 167 = 13 families

* There are 13 families had a parakeet only

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Lol this is hard try using multiplication or division...
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