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3 years ago

Will make bianleast no picture

Mathematics

1 answer:

natita [175]3 years ago

7 0

Answer: 24, 24, 47

<u>Step-by-step explanation:</u>

In order to form a triangle, the sum of two sides must be GREATER than the third side for all combinations.

a + b > c & a + c > b & b + c > a

23 + 28 = 51 which is NOT greater than 55

15 + 30 = 45 which is NOT greater than 45

8 + 17 = 25 which is NOT greater than 25

24 + 24 > 47 & 24 + 47 > 24 & 24 + 24 > 27

all combinations are true so these side lengths can form a triangle

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For what value of X-1/3x=12

vovangra [49]

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Step-by-step explanation:

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4 years ago

Please help! Will mark the brainliest!

JulsSmile [24]

The domain is the set of all possible x-values which will make the function valid.
$f(x) = \frac{6}{x+3} \ \ \ \ , \ g(x) = \frac{1}{4-x}$
For the given function The denominator of a fraction cannot be zero

(a)

(1) The domain of f ⇒⇒⇒ R - {-3}

Because ⇒⇒⇒ x+3 = 0 ⇒⇒⇒ x =-3

(2) The domain of g ⇒⇒⇒ R - {4}
Because: 4 - x = 0 ⇒⇒⇒ x = 4

(3) $f + g = \frac{6}{x+3} + \frac{1}{4-x} = \frac{6(4-x)+(x+3)}{(x+3)(4-x)}$
The domain of (f+g) ⇒⇒⇒ R - {-3,4}
because: x+3 = 0 ⇒⇒⇒ x = -3   and    4 - x = 0 ⇒⇒⇒ x = 4

(4) $f - g = \frac{6}{x+3} - \frac{1}{4-x} = \frac{6(4-x)-(x+3)}{(x+3)(4-x)}$
The domain of (f-g) ⇒⇒⇒ R - {-3,4}
because: x+3 = 0 ⇒⇒⇒ x = -3   and    4 - x = 0 ⇒⇒⇒ x = 4

(5) $f * g = \frac{6}{x+3} * \frac{1}{4-x} = \frac{6}{(x+3)(4-x)}$
The domain of (f*g) ⇒⇒⇒ R - {-3,4}
because: x+3 = 0 ⇒⇒⇒ x = -3   and    4 - x = 0 ⇒⇒⇒ x = 4

(6) $f * f = \frac{6}{x+3} * \frac{6}{x+3} = \frac{36}{(x+3)^2}$
The domain of ff ⇒⇒⇒ R - {-3}

Because ⇒⇒⇒ x+3 = 0 ⇒⇒⇒ x =-3

(7) $\frac{f}{g} = \frac{\frac{6}{x+3} }{ \frac{1}{4-x} } = \frac{6(4-x)}{x+3}$
The domain of (f/g) ⇒⇒⇒ R - {-3,4}

because: x+3 = 0 ⇒⇒⇒ x = -3   and    4 - x = 0 ⇒⇒⇒ x = 4
(8) $\frac{g}{f} = \frac{ \frac{1}{4-x} }{ \frac{6}{x+3} } = \frac{x+3}{6(4-x)}$
The domain of (g/f) ⇒⇒⇒ R - {-3,4}

because: x+3 = 0 ⇒⇒⇒ x = -3   and    4 - x = 0 ⇒⇒⇒ x = 4
===================================================
(b)

(9) $(f+g)(x) = \frac{6}{x+3} + \frac{1}{4-x} = \frac{6(4-x)+(x+3)}{(x+3)(4-x)}$

∴ $(f + g)(x) = \frac{24-6x+x+3}{(x+3)(4-x)} = \frac{27-5x}{(x+3)(4-x)}$

(10) $(f - g)(x) = \frac{6}{x+3} - \frac{1}{4-x} = \frac{6(4-x)-(x+3)}{(x+3)(4-x)}$

∴ $(f - g)(x) = \frac{24-6x-x-3}{(x+3)(4-x)} = \frac{21 - 7x}{(x+3)(4-x)}$

(11) $(f * g)(x) = \frac{6}{x+3} * \frac{1}{4-x} = \frac{6}{(x+3)(4-x)}$

(12) $(f * f)(x) = \frac{6}{x+3} * \frac{6}{x+3} = \frac{36}{(x+3)^2}$

(13) $(\frac{f}{g})(x) = \frac{\frac{6}{x+3} }{ \frac{1}{4-x} } = \frac{6(4-x)}{x+3}$

(14) $(\frac{g}{f})(x) = \frac{ \frac{1}{4-x} }{ \frac{6}{x+3} } = \frac{x+3}{6(4-x)}$

===================================================

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Step-by-step explanation:

.6 is in the tenth place and it does not need to be rounded up but the number in the hundreths place is not above 4

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3 years ago

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yulyashka [42]

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3 years ago

Determine the range of the following graph:

Allisa [31]

Answer:

Range: -8 ≤ y ≤ 7.

Step-by-step explanation:

The range is the possible set of all the y-values of the function represented on the graph.

To get the set of all y-values, find the least possible y-value of the function represented on the graph on the y-axis, and the highest y-value on the y-axis.

Taking a look at the given graph, the least possible value of y is equal to or less than -8, while the highest possible y-value is equal to or less than 7.

Therefore, range is [-8, 7]. This can be represented also as: -8 ≤ y ≤ 7.

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3 years ago