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3 years ago

12 9 6 3 60 45 30 15 what is the constant of proportionality

Mathematics

1 answer:

Mice21 [21]3 years ago

6 0

Answer:

Step-by-step explanation:

A constant of proportionality is the ratio that forms between each x y pair as the fraction y/x. In a proportional relationship it is constant or the same every time.

60/12 = 5

45/9 = 5

30/6 = 5

15/3 = 5

The constant of proportionality is 5.

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NikAS [45]

Answer:

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Step-by-step explanation:

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2 years ago

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a ski shop has a markup rate of 50% find the selling price of skis that cost the store owner $300. tell me how you got the answe

rusak2 [61]

If nthe shop has a mark up rate of 50% and they cost 300 to buy you multiply 300 by 50% convert 50% to decimal
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then you add 150 to 300 which means that the shop sells the skis for 450 dollars.

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3 years ago

Which two tables represent the same function?

topjm [15]

Answer:

The 1st and the 5th tables represent the same function

Step-by-step explanation:

* Lets explain how to solve the problem

- There are five tables of functions, two of them are equal

- To find the two equal function lets find their equations

- The form of the equation of a line whose endpoints are (x1 , y1) and

(x2 , y2) is $\frac{y-y_{1}}{x-x_{1}}=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

* Lets make the equation of each table

# (x1 , y1) = (4 , 8) and (x2 , y2) = (6 , 7)

∵ x1 = 4 , x2 = 6 and y1 = 8 , y2 = 7

∴ $\frac{y-8}{x-4}=\frac{7-8}{6-4}$

∴ $\frac{y-8}{x-4}=\frac{-1}{2}$

- By using cross multiplication

∴ 2(y - 8) = -1(x - 4) ⇒ simplify

∴ 2y - 16 = -x + 4 ⇒ add x and 16 for two sides

∴ x + 2y = 20 ⇒ (1)

# (x1 , y1) = (4 , 5) and (x2 , y2) = (6 , 4)

∵ x1 = 4 , x2 = 6 and y1 = 5 , y2 = 4

∴ $\frac{y-5}{x-4}=\frac{4-5}{6-4}$

∴ $\frac{y-5}{x-4}=\frac{-1}{2}$

- By using cross multiplication

∴ 2(y - 5) = -1(x - 4) ⇒ simplify

∴ 2y - 10 = -x + 4 ⇒ add x and 10 for two sides

∴ x + 2y = 14 ⇒ (2)

# (x1 , y1) = (2 , 8) and (x2 , y2) = (8 , 5)

∵ x1 = 2 , x2 = 8 and y1 = 8 , y2 = 5

∴ $\frac{y-8}{x-2}=\frac{5-8}{8-2}$

∴ $\frac{y-8}{x-2}=\frac{-3}{6}=====\frac{y-8}{x-2}=\frac{-1}{2}$

- By using cross multiplication

∴ 2(y - 8) = -1(x - 2) ⇒ simplify

∴ 2y - 16 = -x + 2 ⇒ add x and 16 for two sides

∴ x + 2y = 18 ⇒ (3)

# (x1 , y1) = (2 , 10) and (x2 , y2) = (6 , 14)

∵ x1 = 2 , x2 = 6 and y1 = 10 , y2 = 14

∴ $\frac{y-10}{x-2}=\frac{14-10}{6-2}$

∴ $\frac{y-10}{x-2}=\frac{4}{4}======\frac{y-10}{x-2}=1$

- By using cross multiplication

∴ (y - 10) = (x - 2)

∴ y - 10 = x - 2 ⇒ add 2 and subtract y in the two sides

∴ -8 = x - y ⇒ switch the two sides

∴ x - y = -8 ⇒ (4)

# (x1 , y1) = (2 , 9) and (x2 , y2) = (8 , 6)

∵ x1 = 2 , x2 = 8 and y1 = 9 , y2 = 6

∴ $\frac{y-9}{x-2}=\frac{6-9}{8-2}$

∴ $\frac{y-9}{x-2}=\frac{-3}{6}======\frac{y-9}{x-2}=\frac{-1}{2}$

- By using cross multiplication

∴ 2(y - 9) = -1(x - 2) ⇒ simplify

∴ 2y - 18 = -x + 2 ⇒ add x and 18 for two sides

∴ x + 2y = 20 ⇒ (5)

- Equations (1) and (5) are the same

∴ The 1st and the 5th tables represent the same function

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3 years ago

E^2x -2e^x -8=0<br><img src="https://tex.z-dn.net/?f=%20%7Be%7D%5E%7B2x%7D%20-%20%20%7B2e%7D%5E%7Bx%7D%20-%208%20%3D%200" id="Te

vovikov84 [41]

E^2x -2e^x -8=0 => e<span>^(2x) -2e^x -8=0

Temporarily replace e^x with y.

Then (y)^2 - 2y - 8 = 0. Factors are (y-4) and (y+2).

Roots are y = 4 and y= -2.

Now remembering that we temporarily replaced e^x with y, we let
y=4 = e^x. We need to solve for x. Taking the natural log of both sides, we get:

ln 4 = x (answer)

We have to discard the other root (y= -2), because we cannot take the ln of a negative number.

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8 0

3 years ago

During a sale at the bookstore, books sold for $4 and magazines sold for $3.50. Jan spent $22 and bought a total of 6 books

Vinvika [58]

Answer:

four magazines and two books

Step-by-step explanation:

3.50*4= 14

4*2= 8

14+8= 22

8 0

3 years ago