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3 years ago

Graph the function and find the range

Mathematics

1 answer:

kramer3 years ago

6 0

The answer for the graph would be C. While x is less than or equal to 0, there is the graph of -4x. While x is greater than x, there is the graph of -5 (horizontal line). Furthermore, the closed dot at the end of the -4x represents the less than or EQUAL TO. The dot at the end of the -5 is open because it is only true when x > 0.

The range (y-values where the graph exists) is [-5]∪[0, infinity)

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What is the sum? StartFraction 3 y Over y squared + 7 y + 10 EndFraction + StartFraction 2 Over y + 2 EndFraction

katovenus [111]

Answer:

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Step-by-step explanation:

Here, we have to find the sum of 2 fractions:

1st fraction: $\dfrac{3y}{y^{2}+7y+10}$

2nd fraction: $\dfrac{2}{y+2}$

Considering the denominator of 1st fraction:

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Using factorization method:

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Taking 5 common from $5y+10$ and y common from $y^{2}+2y$ : $\Rightarrow y(y+2)+5(y+2)$

Now taking $(y+2)$ common:

$\Rightarrow (y+5)(y+2)$

$\dfrac{3y}{y^{2}+7y+10}$ can be written as $\dfrac{3y}{(y+5)(y+2)}$

Now, calculating the sum:

$\dfrac{2y}{(y+5)(y+2)} + \dfrac{2}{y+2}$

Taking LCM and solving:

$\Rightarrow \dfrac{3y+2(y+5)}{(y+5)(y+2)}\\\Rightarrow \dfrac{5y+10}{(y+5)(y+2)}\\\Rightarrow \dfrac{5(y+2)}{(y+5)(y+2)}\\\Rightarrow \dfrac{5}{(y+5)}$

Hence, answer is $\dfrac{5}{y+5}$ .

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Tpy6a [65]

Answer:

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Step-by-step explanation:

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3 years ago

Read 2 more answers