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irina [24]
2 years ago
13

Identify the constant of proportionality (k) 8Y = 16x k=

Mathematics
1 answer:
RUDIKE [14]2 years ago
6 0

Answer:

JUST WRITE THIS AS YOUR ANSWER

Step-by-step explanation:

Step 1: Put together the general equation.

Step 2: Solve for the constant of proportionality.

Step 3: Plugging the constant into the equation, solve for the unknown variable.

Let's solve a few problems to see how this works, shall we?

Example 1: Y is directly proportional to x. When x = 5, y = 8. What does y equal when x = 9?

First, we set up our general equation. Because y is directly proportional to x, we have:

y = cx

where c is the constant of proportionality. In other words, when x goes up, y goes up, and when x goes down, y goes down.

The next thing we do is plug our values for x and y into the equation so we can solve for c:

8 = (c)(5)

Solving for c, we get c = 8/5 = 1.6 and we plug this into our equation:

y = 1.6x

Now, we can plug x = 9 into the equation to find out what y equals:

y = (1.6)(9)

y = 14.4

So, our answer is 14.4

Example 2: Y is directly proportional to the square of x. When x = 2, y = 32. What does y equal when x = 5?

This time, our general equation is slightly more complicated because x is squared:

y = cx2

Like before, we solve for our constant:

32 = (c)(22)

32 = (c)(4)

We get c = 8:

y = 8x2

Solving for y when x = 5, we get y = (8)(52) = (8)(25) = 200

Example 3: Y is inversely proportional to x. When x = 2, y = 8. What does y equal when x = 24?

This time, because y is inversely proportional to x, our general equation is different:

xy = c

so when x goes up, y goes down, and vise versa. But, other than that, we solve these kinds of problems the same way as direct proportion problems. Solving for the constant, we get:

(2)(8) = c

So c = 16 and our equation is now:

xy = 16

Solving for y when x = 24 we get y = 16/24 = 2/3

Example 4: Y is inversely proportional to the square root of x. When x = 36, y = 2. What does y equal when x = 64?

As before, we set up our equation:

eq001

Since the square root of 36 is 6, it is easy to solve for c:

(6)(2) = c

We get c = 12 and our equation is now:

eq002

Solving for y when x = 64 we get 8y = 12 or y = 12/8 = 1.5 because the square root of 64 is 8.

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Please help! .........
stira [4]

Answer:

1) When x is 1, y is 4, and vice versa

2) When x is -6, y is 42, and when x is 7, y is 114

3) When x is -2, y is 2, and when x is 8, y is 42

Step-by-step explanation:

1)

y=x^2-6x+9

y+x=5 which can be rearranged as y=5-x.

Substituting this lone y into the first equation, you get:

5-x=x^2-6x+9

Move everything to one side:

x^2-5x+4=0

Factor:

(x-4)(x-1)=0

x=1, 4

y=4, 1

2)

y-30=12x which can be rearranged as y=12x+30.

y=x^2+11x-12

Let's use elimination this time and subtract the first equation from the second:

0=x^2-x-42

Factor:

(x-7)(x+6)=0

x=-6, 7

y= -42, 114

3)

y=x^2-2x+6

y=4x+10

Let's set the two equations equal to each other through substitution:

x^2-2x-6=4x+10

Move everything to one side:

x^2-6x-16=0

Factor:

(x-8)(x+2)=0

x=-2, 8

y= 2, 42

Hope this helps!

6 0
2 years ago
I know you probably don’t see this but i forgot to do my homework it’s due tomorrow and it’s the called “Volume Unit Study Guide
saw5 [17]

Answer: Make sure all words are spelled correctly.

Try different keywords.

Try more general keywords.

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Step-by-step explanation:

6 0
2 years ago
Find the area of each shape, please help and I will give a lot points
Alex73 [517]

Answer:

15. Area of parallelogram = bh

    b = 9m

    h = 4m

    a = 9*4 = 36m^2

   You can also use the rectangle property here.

    a = l*b

    l = 9

    b = 6

    a = 9*6 = 54 m^2

    Though I would prefer the first one better.

16. Area of triangle = 1/2*bh

    b = 17m

    h = 3

    a = 17*3/2 = 51/2 = 25.5m^2

18. Area of a trapezium = a+b/2*h (a and b are two parallel sides and h the            height)

a = 15

b = 7

h = 15

a = 15+7/2*15 = 22/2*15 = 11*15 = 165m^2

19. Area of triangle = 1/2*bh

    b = 24

    h = 7

    a = 24*7/2 = 168/2 = 84

Hope u understood

Please mark as brainliest

Thank You

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2 years ago
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The graph shows the relationship between the number of pounds of pears purchase and the total cost of the pears.
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