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vladimir1956 [14]
2 years ago
13

Which expression best represents the product of two consecutive integers? CLEAR CHECK x?(2+x) x?(x+1) 2?(x+1) 2x+2

Mathematics
1 answer:
Stella [2.4K]2 years ago
4 0

Answer:

<h2>The product of two consecutive integers:</h2><h2>x · (x+1) = x(x + 1)</h2>

Step-by-step explanation:

Consecutive integer:

... -2, -1, 0, 1, 2, 3, ...

Difference between two consecutive integers is equal to 1.

Therefore two consecutive integers is x and x + 1.

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Conjugate/Rational Number?
hram777 [196]

Answer:

1)  \dfrac{2}{\sqrt{5} }  = \dfrac{2 \cdot \sqrt{5} }{5}

2)  -\dfrac{5}{\sqrt{3} } = -\dfrac{5 \cdot \sqrt{3} }{3}

3)  \dfrac{\sqrt{2} + \sqrt{5}  }{\sqrt{10} } =\dfrac{\sqrt{5}  }{5} + \dfrac{ \sqrt{2}  }{2}

4)  \dfrac{3 + \sqrt{2} }{\sqrt{3} } \times \dfrac{\sqrt{3} }{\sqrt{3} } = \sqrt{3} + \dfrac{\sqrt{6} }{3}

5)  \dfrac{\sqrt{3} }{\sqrt{5} + \sqrt{2}  }= \dfrac{\sqrt{15} - \sqrt{6} }{3}

Step-by-step explanation:

The rationalization of the denominator of the surds are found as follows;

1) \dfrac{2}{\sqrt{5} }

\dfrac{2}{\sqrt{5} } \times \dfrac{\sqrt{5} }{\sqrt{5} } = \dfrac{2 \cdot \sqrt{5} }{5}

\dfrac{2}{\sqrt{5} }  = \dfrac{2 \cdot \sqrt{5} }{5}

2) -\dfrac{5}{\sqrt{3} }

-\dfrac{5}{\sqrt{3} } \times \dfrac{\sqrt{3} }{\sqrt{3} } = -\dfrac{5 \cdot \sqrt{3} }{3}

-\dfrac{5}{\sqrt{3} } = -\dfrac{5 \cdot \sqrt{3} }{3}

3) \dfrac{\sqrt{2} + \sqrt{5}  }{\sqrt{10} }

\dfrac{\sqrt{2} + \sqrt{5}  }{\sqrt{10} } \times \dfrac{ \sqrt{10}  }{\sqrt{10} } = \dfrac{\sqrt{20} + \sqrt{50}  }{10 } = \dfrac{2\cdot \sqrt{5} + 5 \cdot \sqrt{2}  }{10} = \dfrac{\sqrt{5}  }{5} + \dfrac{ \sqrt{2}  }{2}

\dfrac{\sqrt{2} + \sqrt{5}  }{\sqrt{10} } =\dfrac{\sqrt{5}  }{5} + \dfrac{ \sqrt{2}  }{2}

4) \dfrac{3 + \sqrt{2} }{\sqrt{3} }

\dfrac{3 + \sqrt{2} }{\sqrt{3} } \times \dfrac{\sqrt{3} }{\sqrt{3} } = \dfrac{3 \cdot \sqrt{3}+\sqrt{6}  }{3 } = \sqrt{3} + \dfrac{\sqrt{6} }{3}

\dfrac{3 + \sqrt{2} }{\sqrt{3} } \times \dfrac{\sqrt{3} }{\sqrt{3} } = \sqrt{3} + \dfrac{\sqrt{6} }{3}

5) \dfrac{\sqrt{3} }{\sqrt{5} + \sqrt{2}  }

\dfrac{\sqrt{3} }{\sqrt{5} + \sqrt{2}  } = \dfrac{\sqrt{5} - \sqrt{2} }{\sqrt{5} - \sqrt{2} }  = \dfrac{\sqrt{15} -\sqrt{6} }{5 - 2} = \dfrac{\sqrt{15} - \sqrt{6} }{3}

\dfrac{\sqrt{3} }{\sqrt{5} + \sqrt{2}  }= \dfrac{\sqrt{15} - \sqrt{6} }{3}

6) \dfrac{\sqrt{7} }{\sqrt{3} - \sqrt{5}  }

\dfrac{\sqrt{7} }{\sqrt{3} - \sqrt{5}  } \times \dfrac{\sqrt{3} + \sqrt{5}}{\sqrt{3} + \sqrt{5}}  = \dfrac{\sqrt{21} + \sqrt{35}}{{3} + {5}} = \dfrac{\sqrt{21} + \sqrt{35}}{8}

\dfrac{\sqrt{7} }{\sqrt{3} - \sqrt{5}  } \times \dfrac{\sqrt{3} + \sqrt{5}}{\sqrt{3} + \sqrt{5}}  =\dfrac{\sqrt{21} + \sqrt{35}}{8}

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2 years ago
Find the missing side of each triangle.
Bogdan [553]
They answer is 12.t obeys
6 0
3 years ago
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Whats thr answer to this? 3( -2d + 1) (pre alg)
sineoko [7]

Answer:

here

Step-by-step explanation:

if all you're doing is distributing it, the answer is -6d + 3

8 0
2 years ago
Choose the best decimal to represent 5 3/7<br><br> 2.3<br><br> 5.428571<br><br> 2.3<br><br> 5.428571
NemiM [27]

Answer:

5.428571

Step-by-step explanation:

5\frac{3}{7}

take the fraction and divide that:

\frac{3}{7} =0.428571

then just add 5:

5 + 0.428571 = 5.428571

or...

convert the mixed fraction to improper fraction:

5\frac{3}{7} = \frac{38}{7}

divide like normal:

\frac{38}{7} = 5.428571

4 0
2 years ago
Read 2 more answers
In the graph below, figure I undergoes a sequence of rotations, reflections, translations, and dilations to transform to figure
Aleksandr-060686 [28]

The answer for the first one is <em><u>Congruent</u></em> and for the second for the second is <em><u>No</u></em>

8 0
3 years ago
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