Turn the sentence into an expression 5.three times the sum of two consecutive integers

Mathematics

1 answer:

ryzh [129]3 years ago

8 0

3(x+x+1)

hope this helps

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Tpy6a [65]

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Step-by-step explanation:

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3 years ago

<img src="https://tex.z-dn.net/?f=y%2B%20%20%5Cfrac%7B13%7D%7B4%7D%20%20%3D%20%28x%5E2-%20%5Cfrac%7B1%7D%7B2%7D%20%29%5E2" id="T

zhenek [66]

Answer: $\bold{y=\dfrac{1\pm \sqrt{4x+13}}{2}}$

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

Inverse is when you swap the x's and y's and solve for y:

$y+\dfrac{13}{4}=\bigg(x-\dfrac{1}{2}\bigg)^2\\\\\\x+\dfrac{13}{4}=\bigg(y-\dfrac{1}{2}\bigg)^2\rightarrow \text{(swapped the x's and y's)}\\\\\\\sqrt{x+\dfrac{13}{4}}=\sqrt{\bigg(y-\dfrac{1}{2}\bigg)^2}\rightarrow \text{(took square root of both sides)}\\\\\\\sqrt{\dfrac{4x+13}{4}}=\pm \bigg(y-\dfrac{1}{2}\bigg)}\rightarrow \text{(created common denominator in radical)}\\\\\\ \dfrac{\sqrt{4x+13}}{2}=\pm \bigg(y-\dfrac{1}{2}\bigg)}\rightarrow \text{(simplified radical)}$

$\pm \dfrac{\sqrt{4x+13}}{2}=y-\dfrac{1}{2}}\rightarrow \text{(divided both sides by}\ \pm )\\\\\\\dfrac{1}{2}\pm \dfrac{\sqrt{4x+13}}{2}=y\quad \rightarrow \text{(added}\ \dfrac{1}{2}\ \text{to both sides)}\\\\\\\dfrac{1\pm \sqrt{4x+13}}{2}=y\quad \rightarrow \text{(combined numerators)}$