All Answers 358087 Answers

(961, 1147, 1271, 1333, 1369, 1457, 1517, 1591, 1643, 1681, 1739, 1763, 1829, 1849, 1891, 1927, 1961, 2021, 2077, 2173, 2183, 2201, 2209, 2257, 2263, 2279, 2419, 2449, 2479, 2491, 2501, 2537, 2573, 2623, 2627, 2701, 2747, 2759, 2773, 2809, 2867, 2881, 2911, 2923, 2993, 3007, 3053, 3071, 3127, 3131, 3139, 3149, 3193, 3233, 3239, 3293, 3317, 3337, 3379, 3397, 3403, 3431, 3481, 3503, 3551, 3569, 3589, 3599, 3649, 3713, 3721, 3737, 3763, 3811, 3827, 3869, 3901, 3953, 3977, 4087, 4141, 4171, 4181, 4183, 4187, 4189, 4307, 4331, 4343, 4399, 4453, 4489, 4559, 4661, 4717, 4747, 4757, 4819, 4891, 4897, 5041, 5063, 5141, 5143, 5183, 5251, 5293, 5329, 5353, 5429, 5561, 5609, 5723, 5767, 5893, 5917, 5959, 5963, 6059, 6161, 6241, 6319, 6497, 6499, 6557, 6767, 6887, 6889, 7031, 7171, 7081, 7387, 7373, 7663, 7921, 7979, 8051, 8383, 8633, 8927, 8989, 9379, 9409, 9797, 9991, 10201, 10403, 10609, 11021, 11227, 11449, 11881, 19321) - 164 such numbers,

They all fall between the numbers 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137 & 139.

11 years give or take

3431 = 47 x 73

Wrong!

Prime Factors of 3431 = 3431 is a prime number and cannot be factorize

The only factors of 3431 are 1 and 3431

- Unknown guest

To see if that is prime or not, you could check its divisibility rules.

If it is divisible by 2, then it is an even number---51 is odd.

If it is divisible by 3, then the digits sum to a number divisible by 3, 5 + 1 = 6, and 6 is divisible by 3.

Thus, 51 is divisible by 3.

Remember the divisibility rules Guest!

yw

I would like to give the problem a shot:

First I would like to draw an altitute from T to FG and from T to EF. The points of intersection are A and B respectively. 

Intuitively, you can see that triangle FAT is a 30-60-90 triangle, and TAG is a 45-45-90 triangle, and you could find that angle ETF = 105 degrees. 

To give a serious go, we can use the fact that putting a rectangle with 2 sides on the sides of a 45-45-90 triangle will create 2 similar triangles that are 45-45-90 and a rectangle: 

Since BT = FA because it is a rectangle, and TG = 3sqrt(2), then AG = 3, and FA = sqrt(3). 

Tan TFA = 3 / sqrt(3) = sqrt(3), thus angle TFA = 60 degrees. Angle FAT is also 90 degrees. Angle FTB is congruent to angle TFA, so angle BTF = 60 degrees. 

Since angle ETB is 45 degrees, and angle ETB + angle BTF = angle ETF, then 60 + 45 = angle ETF.

Thus, angle ETF = 105 degrees.

< Where did I make my mistake? >   

At   2y = 132    =>>    y = 61    simple arithmetic error   

actually, half of 132 is 66  

_.

If |z| = 1, then z could be 1 and -1. 

We can see there are multiple possible values of z. 

First plugging in 1 to the quadratic, we end up with |1 + 1 - 1| = 1

Plugging in -1 to the quadratic, we end up with |1 - 1 - 1| = 1 

As you can see, the only value of |z^2 + z - 1| is 1.

Thus,

The largest possible value of \(|z^2 + z - 1|\) is 1.

In the equation 2y = f(2x)/2 + 2, try plugging x as 4.5 and see what happens.

=^._.^=

ok thanks for responding.  Did you get anything from it?

I quit 3/4 of the way through because I already know that stuff.

It was not the most exciting presentation but the content was good.

Thanks for your response.

I am still interested in your question. 

I would have liked you to explain it.  So I at least understood the question.

Thanks.  I did watch it, and I know why you quit 3/4 of the way through, LOL.  :-)  

_.

Thank you sir!

EXACTLY!

Nvm i got it.

x + y + z  =  180

      y + z  =  4x

            z  =  12 + y

Combining the first and second equations:  x + 4x  =  180     --->     5x  =  180     --->     x  =  36

Replacing this value into the second equation:  y + z  =  4(36)     --->     y + z  = 144

Combining this with the third equation:

                y + z  =  144

                      z  =  12 + y

     --->     y + 12 + y  =  144

                            2y  =  132

                              y  =  61

--->     z  =  12 + y  =  12 + 61  =  73

But, this is impossible!  Where did I make my mistake?

For the first problem:  slope = -1     y-intercept = -2     shaded below     dashed line

                        y  <  -1x - 2

For the second problem:  slope = -1/3     y-intercept = -8/3     shaded below     solid line

                       y  <=  (-1/3)x - 8/3

Can you get these inequalities into the correct form?

nice dickk size

why are you answering all day

I'm not a moderator, but I answer here because I have a passion to help other people. 

The moderators undoubtedly have the same motive.  I know they've helped me a lot.    

You can write this as an equation, where n is the number of weeks. 

\({2n \over 12+3n} = {1 \over 2}\)

Solve for n, and round up to get your answer. 

The question is incomplete...