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2 years ago

1 decigram (dg) = ______ grams (g)?

Mathematics

1 answer:

AleksandrR [38]2 years ago

6 0

Answer:

B) 0.1

Step-by-step explanation:

The prefix "deci-" means "tenth", so a decigram would be one-tenth of a gram (or 0.1 grams). Therefore, option B is correct.

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4) The quantities x and y are in proportion x 4 30 8 __b__ a) b) c) y 6 45 __a__ 15 Find the value of a and b. Find the constant

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Question:

The quantities x and y are in proportion

x y

4 6

30 45

8 b

a 15

(a) Find the values of a and b.

(b) Find the constant of variation. Is it direct variation or inverse variation?

Answer:

$a = 10$ and $b = 12$

Constant of variation is 1.5

Direct Variation

Step-by-step explanation:

Solving (a): The values of a and b

First, we determine the equation that relates x and y

From the table, we have:

$(x_1,y_1) = (4,6)$

$(x_2,y_2) = (30,45)$

The slope (m) is:

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

$m = \frac{45 - 6}{30 -4}$

$m = \frac{39}{26}$

$m = 1.5$

The equation is then calculated using:

$y - y_1 = m(x - x_1)$

This gives:

$y - 6 = 1.5(x - 4)$

$y - 6 = 1.5x - 6$

$y = 1.5x$

Solving for the value of b

From the table: x = 8, y = b

Substitute these values in $y = 1.5x$

$b = 1.5 * 8$

$b = 12$

Solving for the value of a

From the table: x = a, y = 15

Substitute these values in $y = 1.5x$

$15 = 1.5 * a$

Solve for a

$a = \frac{15}{1.5}$

$a = 10$

Solving (b): The constant of variation.

This has been solved in (a) above as:

$m = 1.5$

Direct or Inverse?

From the given table, we notice that y increases as x increases and y decreases as x decreases.

<em>This shows direct variation</em>

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