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Flura [38]
2 years ago
9

Given radical a and radical b are in simplest radical form and radical a timed radical b equals c radical d and c radical d is i

n simplest form. Explain in words how c and d are related to a and b. Then give an example to support your solution.

Mathematics
1 answer:
lawyer [7]2 years ago
6 0

Answer:

See below.

Step-by-step explanation:

Since sqrt(a) and sqrt(b) are in simplest radical form, that means a and b have no perfect square factors. When sqrt(a) and sqrt(b) are multiplied giving c * sqrt(d), the fact that c came out of the root means that there was c^2 inside the product sqrt(ab). This means that a and b have at least one common factor.

ab = c^2d

Example:

Let a = 6 and let b = 10.

sqrt(6) and sqrt(10) are in simplest radical form.

Now we multiply the radicals.

sqrt(a) * sqrt(b) = sqrt(6) * sqrt(10) = sqrt(60) = sqrt(4 * 15) = 2sqrt(15)

We have c = 2 and d = 15.

ab = c^2d

6 * 10 = 2^2 * 15

60 = 60

Our relationship between a, b and c, d works.

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Valentin [98]

ANSWER

y = 3x - 3

EXPLANATION

Let

y = mx + c

be the equation.

We can choose any two ordered pairs to determine the equation of the relation.

(6,15) \: and \:  (8,21)

We find m using the formula;

m =  \frac{y_2-y_1}{x_2-x_1}

m =  \frac{21 - 15}{8 - 6}  =  \frac{6}{2}  = 3

The equation becomes

y = 3x + c

When x=6, y=15.

This implies that,

15 = 3(6) + c

15= 18 + c

15 - 18= c

c =  -3

The equation of the relation is therefore,

y = 3x -3

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Step-by-step explanation:

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