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3 years ago

Find a common denominator for the pair of fractions 3/4 and 1/3 then write equivalent fractions with the common denominator.

Mathematics

2 answers:

andrew11 [14]3 years ago

8 0

Answer:

common denominator = 12

3 x 3 9/12

4 x 3

1 x 4 4/12

3 x 4

so 9/12 and 4/12

Margaret [11]3 years ago

3 0

Answer:

Common denominator: 12; Equivalent fractions: 9/12, 4/12

Step-by-step explanation:

The two denominators in question are:

3/4: 4

1/3: 3

In order to find the common denominator, find the LEAST COMMON MULTIPLE of these two numbers, which is in this case, 12.

4, 8, 12

3, 6, 9, 12

Now that we know the common denominator is 12, we can make equivalent fractions, which are fractions with different denominators that have the same value when simplified.

For 3/4, you multiplied the denominator, 4, by 3 to get to your common denominator (12). So multiply the numerator, 3, by 3 in order to get your equivalent fraction. 3 * 3 = 9. Meaning your equivalent fraction will be 9/12.

For 1/3, repeat the same steps. You multiplied the denominator, 3, by 4 to get the common denominator (12), so you must do the same to the numerator, 1, to get the equivalent fraction. 1 * 4 = 4. Meaning this equivalent fraction will be 4/12

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Find the value for x

d1i1m1o1n [39]

Answer:

Value of x --> 15°

Step-by-step explanation:

(2x + 60°) and 6x lie on a straight line. So, they form a linear pair. Their sum gives 180°.

---> (2x + 60°) + 6x = 180°

2x + 60° + 6x = 180°

8x + 60° = 180°

8x = 180°- 60°

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x = $\frac{120}{8}$

<h3>x equals 15°</h3>

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3 years ago

1. (5pts) Find the derivatives of the function using the definition of derivative.

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We have

$f(x+h) = \dfrac4{\sqrt{3-(x+h)}}$

and

$f(x+h)-f(x) = \dfrac4{\sqrt{3-(x+h)}} - \dfrac4{\sqrt{3-x}}$

Combine these fractions into one with a common denominator:

$f(x+h)-f(x) = \dfrac{4\sqrt{3-x} - 4\sqrt{3-(x+h)}}{\sqrt{3-x}\sqrt{3-(x+h)}}$

Rationalize the numerator by multiplying uniformly by the conjugate of the numerator, and simplify the result:

$f(x+h) - f(x) = \dfrac{\left(4\sqrt{3-x} - 4\sqrt{3-(x+h)}\right)\left(4\sqrt{3-x} + 4\sqrt{3-(x+h)}\right)}{\sqrt{3-x}\sqrt{3-(x+h)}\left(4\sqrt{3-x} + 4\sqrt{3-(x+h)}\right)} \\\\ f(x+h) - f(x) = \dfrac{\left(4\sqrt{3-x}\right)^2 - \left(4\sqrt{3-(x+h)}\right)^2}{\sqrt{3-x}\sqrt{3-(x+h)}\left(4\sqrt{3-x} + 4\sqrt{3-(x+h)}\right)} \\\\ f(x+h) - f(x) = \dfrac{16(3-x) - 16(3-(x+h))}{\sqrt{3-x}\sqrt{3-(x+h)}\left(4\sqrt{3-x} + 4\sqrt{3-(x+h)}\right)} \\\\ f(x+h) - f(x) = \dfrac{16h}{\sqrt{3-x}\sqrt{3-(x+h)}\left(4\sqrt{3-x} + 4\sqrt{3-(x+h)}\right)}$

Now divide this by h and take the limit as h approaches 0 :

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• power rule

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