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I agree with Hectictar :)

There are points of inflection at x=1 and at x=-1 

The "reciprocal" of a number is just 1 divided by that number.

The reciprocal of   \(x\)   is   \(\frac1x\) .     The reciprocal of   \(\frac{a}{b}\)   is   \(\frac{b}{a}\) .

But the slopes of perpendicular lines are not just reciprocals of each other.

The slopes of perpendicular lines are negative reciprocals of each other. To find the slope of a line perpendicular to one with a given slope, we must take the negative reciprocal of the given slope. That means take the reciprocal of the slope and also multiply it by -1 .

For example...

If a line has a slope of  \(\frac34\) ,  the slope of a line perpendicuar  =  -\(\frac43\)

For a shape to be inscribed in a circle, all the vertices have to be on the circle.

A square can be inscribed in a circle, like this:

Since a square is a rectangle, and a square can be inscribed in a circle, a rectangle can be inscribed in a circle. And since a square is a parallelogram, and a square can be inscribed in a circle, a parallelogram can be inscribed in a circle.

Note that a rectangle with different side lengths could also be inscribed in a circle. However, a parallelogram with non-right angles could not be inscribed in a circle.

An isosceles trapezoid can also be inscribed in a circle, like this:

All of the options could be inscribed in a circle.

The central angle is 5pi over 7

\pi ^{\circ }\left(23^{\circ }3.143^{\circ }\left(23^{\circ }5\div \left(53\div 4\right)^'\right)^'\right)^'

James please do not give answers without explanation, they are useless for learning and only encourage cheating.

x2+14x+48 = (x+_)(x+_)

You need to look for two numbers 

that multiply to 48

and add to 14

Since everything is positive the numbers will both be positive.

lets see, look at the muliply first, 

   12*4 =48 but 12+4=16, that is no good.

    6*8=48  and  6+8=14  wonderful

so tha answer is

(x+6)(x+8)

Hi James, it is really good that you took a shot at this but our guest is correct.    

See solution #3 here:

https://web2.0calc.com/questions/need-help-asap_18

Ok, Thanks, Melody I think I got it now!!

There are 5 children left who will get a something for the Christmas party.

They are  Trey, Sarah, Emily, Daniel and Mitchel

Only Sarah and Emily are girls.

So P(of chosing a girl next) = 2/5

The others are just as easy.  Give them a go :)

ummmm...

There are 5 students left and 2 of them are girls so

P(girl) = 2/5

You can do the others.

well done B)

\(x^a\cdot x^b\,=\,x^{a+b}\)

So....

\(\sqrt3^\sqrt2\cdot\sqrt3^{-\sqrt2}\,=\,\sqrt3^{\sqrt2+-\sqrt2}\\~\\ \phantom{\sqrt3^\sqrt2\cdot\sqrt3^{-\sqrt2}}\,=\,\sqrt3^{\sqrt2-\sqrt2}\\~\\ \phantom{\sqrt3^\sqrt2\cdot\sqrt3^{-\sqrt2}}\,=\,\sqrt3^0\\~\\ \phantom{\sqrt3^\sqrt2\cdot\sqrt3^{-\sqrt2}}\,=\,1\)

could you give an algebreaic solution and explain it pelase?

the answer is 26³, because the first letter and the last letter are the same.

This means that picking a four letter word that follows this rule is just like picking any 3 letter word (pick a 3 letter word, and then add a "copy" of the first letter as a fourth letter)

for example- \(Dye\Rightarrow Dyed\)

so there's a total of 26³ =17,576 combinations- 26 options for the first letter, 26 options for the second letter, and 26 options for the third letter. 

He would have to look a 26⁴ combinations.

This is because:

2 letter words =

AA to ZZ

AA to AZ is 26 combinations, then you repeat with BA to BZ, CA to CZ etc.

As you repeat this 26 combo thingamajig 26 times,

This means that there are 26² combinations for two letter words.

3 letter words =

AAA to ZZZ

AAA to AAZ is 26 combinations, AAA to AAZ is 26 combinations.

then you repeat with ABA to ABZ, etc.

This means that there are 26³ combinations for three letter words.

Therefore..

4 letter words =

AAAA to ZZZZ

AAAA to AAAZ is 26 combinations, then you repeat with AABA to AABZ, AACA to AACZ etc.

This means that there are 26⁴ combinations for four letter words.

Not sure about the answer though...

lol its been awhile! I joined in November

I THINK the graph of  y = f(x)  looks something like this.....

f’(0)  =  0  so  when  x = 0  the slope of f(x) is  0

f’(1)  =  3  so  when  x = 1  the slope of f(x) is  3

f’(3)  =  1  so  when  x = 3  the slope of f(x) is  1

When  x  is between 0  and  1  the slope is smaller, closer to zero, than it is when  x = 1 .

Notice that there is a value between  0  and  1  that also makes the slope be  1 .

When  x  is greater than  1  the slope is closer to zero than it is when  x = 1 .

f’(-1)  =  -3  so  when  x = -1  the slope of f(x) is  -3

f’(-3)  =  -1  so  when  x = -3  the slope of f(x) is  -1

When  x  is between  0  and  -1  the slope is closer to zero than it is when  x = -1 .

When  x  is less than  -1  the slope is closer to zero than it is when  x = -1 .

May 27th, 2015?

Wow.

Almost three years.

Good Good.