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Westkost [7]
3 years ago
13

How can knowing how to represent proportional relationships in different ways be useful to solving problems

Mathematics
1 answer:
Anna35 [415]3 years ago
8 0

Answer:

  appropriately writing the proportion can reduce or eliminate steps required to solve it

Step-by-step explanation:

The proportion ...

  \dfrac{A}{B}=\dfrac{C}{D}

is equivalent to the equation obtained by "cross-multiplying:"

  AD = BC

This equation can be written as proportions in 3 other ways:

  \dfrac{B}{A}=\dfrac{D}{C}\qquad\dfrac{A}{C}=\dfrac{B}{D}\qquad\dfrac{C}{A}=\dfrac{D}{B}

  Effectively, the proportion can be written upside-down and sideways, as long as the corresponding parts are kept in the same order.

I find this most useful to ...

  a) put the unknown quantity in the numerator

  b) give that unknown quantity a denominator of 1, if possible.

__

The usual method recommended for solving proportions is to form the cross-product, as above, then divide by the coefficient of the variable. If the variable is already in the numerator, you can simply multiply the proportion by its denominator.

<u>Example</u>:

  x/4 = 3/2

Usual method:

  2x = 4·3

  x = 12/2 = 6

Multiplying by the denominator:

  x = 4(3/2) = 12/2 = 6 . . . . . . saves the "cross product" step

__

<u>Example 2</u>:

  x/4 = 1/2 . . . . we note that "1" is "sideways" from x, so we can rewrite the proportion as ...

  x/1 = 4/2 . . . . . . written with 1 in the denominator

  x = 2 . . . . simplify

Of course, this is the same answer you would get by multiplying by the denominator, 4.

The point here is that if you have a choice when you write the initial proportion, you can make the choice to write it with x in the numerator and 1 in the denominator.

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Andrews [41]

Answer:

Step-by-step explanation:

let f(x)=ab^x

when x=1,f(x)=6

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when x=2,f(x)=18

18=ab^2

divide

\frac{ab^2}{ab}=\frac{18}{6}\\b=3\\ab=6\\3a=6\\a=2\\f(x)=2(3)^x

4 0
3 years ago
Help please, I will give brainliest to whoever answers correctly​
Temka [501]
Answer: X=5/2, Y= 15, T=4
3 0
2 years ago
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Points E, F, and G are collinear. If EF = 8 and EG = 12, which point cannot lie between the other two?
Dima020 [189]
Point G can not be between
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3 years ago
Ten raised to what power equals ten thousand?
ArbitrLikvidat [17]

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Hope this helps. - M
4 0
3 years ago
If y = 6 when x = 24, what is the value of x when y =7
sladkih [1.3K]
Y = 6 when x = 24

direct variation y = kx

the given numbers from one ratio is expressed as y/x = 6/24

to find x, when y = 7

we set up a new ratio that is y/x = 7/x

by the definition both ratios are equal 6/24 = 7/x

6/24 = 7/x
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x = 7 × 4
x = 28

the value of x is 28 when y = 7

hope this helped, God bless!
6 0
3 years ago
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