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https://web2.0calc.com/questions/please-help-asap_99#r2

Post the real image please.

But how

Answer is 2

All 1 <= x < 3 work, so the answer is [1,3).

k = 7/3

There are 20 pairs of integers.

(x+2)^2 is always positive or zero, so it cannot make the answer <0

so either x+1   or x   (but not BOTH) has to be less than zero for this equation to be true

x<0       or     x+1<0

x<0       or     x<-1           <======    so the only interval ONE of these is less than zero is   (-1,0)

Yeah, thats correct.

This is my answer:

Either the (x-2)^2  or the (x+1)  needs to be negative (but not both) for this equation to be true

    However, (x-2)^2  is always POSITIVE (or zero)

      so the (x+1) portion must be negative

            (x+1) <0

              x <-1

(-inf, -1)

Disregard this answer.....  I didn't see the leading 'x' of the equation !!!!!

Sorry, but you can't post AoPS problems on the forum. It breaks their code of conduct.

Well, since Rayna is a name with 5 letters, and the question is asking for the probability for R, and that's only 1 letter. 

So the answer must be 1/5.

(Correct me if I'm wrong.)

All negative x satisfy the inequality, so the solution is (-infty,0).

3x = 6

3x/3 = 6/3

x = 2

Between 1 and 99 = 9 zeros
Between 100 and 999 = 180 zeros
Between 1000 and 2999 = 600 zeros
Between 3000 and 3333 = 174 zeros
Total =9 + 180 + 600 + 174 = 963 zeros.

3/x + 2/y = (3y + 2x)/xy, so wrong at line 3

Correct answer is x = 5/4  y = 5/6, giving a minimum of 4.8.

Drop a line from the apex of the triangle to form 2 triangles then use law of sines:

Sin30 / height    = sin 90 / 4         

4 sin 30 = height  = 2

sin 60 / base = sin 90 / 4

4 sin 60 = base  = 2 sqrt 3

area of each triangle = 1/2 base * height

1/2 (2) * 2 sqrt 3 = 2 sqrt 3        for each triangle (remember, there are two)         Area = 4 sqrt 3

Brad has a cylindrical barrel with radius 10 inches and height 15 inches. He wants to fill it from a well, using a bucket in the shape of a hemisphere with a radius of 10 inches. How many trips must Brad make to the well in order to fill the barrel?

See here. Does it agree with your answer?   https://web2.0calc.com/questions/alice-and-bob-both-go-to-a-party-which-starts-at-5-00-each-of-them-arrives-at-a-random-time-between-5-00-and-6-00-what-is-the-probability

I don't know.

Omi's solution might be even simpler using trig!

What is the area of the shaded region?

MY IQ IS sooo low.

I just realized that the solution DOES NOT match your problem!
 

However, they use different numbers but ask the same question, so you should get the correct answer using Omi's or AoPs's method.

Satisfying solution by Melody here!

You have to make sure it satisfies 2x + 3y = 5

How can you be sure xy is equal to 5?