A negative number raised to an odd power ______ negative

Mathematics

2 answers:

Fiesta28 [93]3 years ago

3 0

A negative number raised to an odd power IS negative

love history [14]3 years ago

3 0

Answer:

A negative number raised to an odd power is always negative.

Step-by-step explanation:

To complete the statement - A negative number raised to an odd power ______ negative.

Solution :

We know that,

A negative number raised to an odd power is always negative.

1) When a negative number is raised to an even power, the pairs of negatives will cancel out.

For example - $(-1)^2=(-1)\times (-1)=1$

2) When it is raised to an odd power, after pairs of the negative sign have canceled each other out, there will still be one minus sign left unpaired, which will not cancel out.

For example - $(-1)^3=(-1)\times (-1)\times (-1)=1\times (-1)=-1$

Therefore, The required blank is 'always'.

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A third-grade class is told to send a valentine to every single one of their classmates. On Valentine’s Day, the class ends up w

FinnZ [79.3K]

306 is the total cards sent by all the students in the class. Lets say x is the number of students in class, therefore each student needs to send x-1 cards (since they do not send themselves a card). So depending on your level of math, you could either take the complex way to solve it using quadratic equations, or just find the number that if multiplied by itself then subtracted, gives you 306.
$(x \times x) - x = 306 \\ lets \: try \: 18 \\ (18 \times 18) - 18 = 306 \\ so \: x = 18$
===============
Complex way
$(x \times x) - x = 306 \\ {x}^{2} - x - 306 = 0$
So a = 1, b = -1, c=-306
using the quadratic equation:
$x = \frac{ - b + \sqrt{ {b}^{2} - 4ac } }{2a}$
$x = \frac{1 + \sqrt{1 - (4 \times 1 \times - 306)} }{2} \\ x = \frac{1 + \sqrt{1 - ( - 1224)} }{2} \\ x = \frac{1 + \sqrt{1225} }{2} \\ x = \frac{1 + 35}{2} \\ x = \frac{36}{2} \\ x = 18$