Melody

Please post only one question per post.

Is it a triangle?

You need more brackets to make your meaning clear.

A function f has domain [0, 2] and range [0, 1]. (The notation [a, b] denotes {x : a ≤ x ≤ b}.)

Define the function g as g(x) = 1 − f(x + 1).

If [p, q] is the domain of g and [r,s] is the range of g, then determine p + q + r + s.

I am not really sure but,

f(x) has a domain of  [0,2]

so

\(For\;\;f(x)\quad0\le x\le2\\ For\;\;f(x+1)\\ 0\le x+1 \le2\\ -1\le x \le1\)

So the domain of g is [-1,1]      p=-1,  q=1

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\(0\le f(x+1) \le 1\\ \text{seperates to}\\ 0\le f(x+1) \qquad \qquad f(x+1) \le 1\\ 0\ge -f(x+1) \quad \qquad -f(x+1) \ge -1\\ 1\ge 1-f(x+1) \qquad 1-f(x+1) \ge 0\\ 1-f(x+1)\le 1 \qquad 0\le1-f(x+1)\\ 0\le1-f(x+1)\le 1\\ 0\le g \le 1\qquad \qquad \\\text{The range of g is [0,1]} \)

-1+1+0+1= 1

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Here is a graph that fits the description to help you understand what I have done

I chose f to be the top half of a circle, radius 1 and centre (1,0)

Here is the direct link to the Desmos graph if you want it.

I got 6 degrees

360-179-145-30 = 6

In the figure, if MR = MK, the measure of arc MK is 130 degrees, and measure of arc MQ is 23 degrees, then what is angle RPK, in degrees?

Let X be the centre

Mz understanding of the question is that   

and you want 

When two angles stand on the same arc, the angle at the centre is twice the angle on the circumference,

so

None of the other info is relevant.

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For some reason this is not displaying properly, so hee is a picture of it

Let f(x) = x^3+bx+c  where b and c are integers. If f(5+\sqrt 2)=0 determine b+c

\((5+\sqrt 2)^3+(5+\sqrt 2)b+c=0\\ \text{If a+b= a constant then I can let one of them be b=0 maybe}\\ If\;\;b=0\;\;then (5+\sqrt 2)^3+c=0\\ c=-(5+\sqrt 2)^3\\ b+c=-(5+\sqrt 2)^3\approx -264 \)

\(However\\ If\;\;c=0\\ (5+\sqrt2)^3+(5+\sqrt2)b=0\\ (5+\sqrt2)b=(5+\sqrt2)^3\\ b=(5+\sqrt2)^2\\ so\\ b+c=(5+\sqrt2)^2\)

The answers are different so b+c does not equal a constant.

I expect you did not copy the question properly.

LaTex:

(5+\sqrt 2)^3+(5+\sqrt 2)b+c=0\\ 
\text{If a+b= a constant then I can let one of them be b=0 maybe}\\
If\;\;b=0\;\;then
(5+\sqrt 2)^3+c=0\\ 
c=-(5+\sqrt 2)^3\\
b+c=-(5+\sqrt 2)^3\approx -264

Thanks Alan, that sure made it easy 

11 definites, 3 uncertain.  only 1 seat available.

P(a person will show)=0.45  

P(a person won't show)=0.55

\(\text{P(no one shows)} \qquad \qquad= \binom{3}{0} * 0.45^0 * 0.55^3\\ \text{P(only one person shows)} = \binom{3}{1} * 0.45^1 * 0.55^2\\ etc\)

You should be able to take it from there.

Yes that is good.

Now in the same amount of time they have both completed 135 degrees.

So that means that in any given period of time they both have covered the same number of degrees.

So who will finish first?