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What is the value of c?

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\(0.5x^2 + 99x + c=0\)

\(x = {-99 \pm \sqrt{99^2-4\cdot 0.5\cdot c} \over 2\cdot 0.5}\)

\(99^2-4\cdot 0.5\cdot c=7801\\c=-\dfrac{7801-99^2}{2}\)

\(c=1000\)

The value of c is 1000.

  !
 

Yes, that is true.    

GCD should have AT MOST 6 digits.

238 - ( - 34) ==272

272 / 17  +  1 ==17 multiples of 17 between -50 and 200

There are 200 such 3-digit numbers as follows:

102  103  104  105  106  107  108  109  112  113  114  115  116  117  118  119  122  123  124  125  126  127  128  129  132  133  134  135  136  137  138  139  142  143  144  145  146  147  148  149  152  153  154  155  156  157  158  159  162  163  164  165  166  167  168  169  172  173  174  175  176  177  178  179  182  183  184  185  186  187  188  189  192  193  194  195  196  197  198  199  204  205  206  207  208  209  214  215  216  217  218  219  224  225  226  227  228  229  234  235  236  237  238  239  244  245  246  247  248  249  254  255  256  257  258  259  264  265  266  267  268  269  274  275  276  277  278  279  284  285  286  287  288  289  294  295  296  297  298  299  306  307  308  309  316  317  318  319  326  327  328  329  336  337  338  339  346  347  348  349  356  357  358  359  366  367  368  369  376  377  378  379  386  387  388  389  396  397  398  399  408  409  418  419  428  429  438  439  448  449  458  459  468  469  478  479  488  489  498  499  Total =  200 such integers.

Note: A short code in C++ found these integers.

The probability is: 3/6  x  3/6 ==9 / 36 ==1 / 4

m==256   and    m==768

Note: A short code in C++ found the 2 numbers.

Find the smallest value of x such that x^2 + 10x + 25 = 16.    

Subtract 16 from each side to get       x² + 10x + 9 = 0  

Factor the quadratic                           (x + 9)(x + 1) = 0  

Set each factor equal to zero              (x + 9) = 0           x = –9  

                                                            (x + 1) = 0           x = –1  

The smaller value is x = –9   

_.

2 , 4 , 5 , 7 , 8 , 10 , 14 , 16 , 20 , 25 , 28 , 32 , 35 , 40 , 50 , 56 , 64 , 70 , 80 , 100 , 112 , 125 , 128 , 140 , 160 , 175 , 200 , 224 , 250 , 256 , 280 , 320 , 350 , 400 , 448 , 500 , 512 , 560 , 625 , 640 , 700 , 800 , 875 , 896 , 1000 , 1024 , 1120 , 1250 , 1280 , 1400 , 1600 , 1750 , 1792 , 2000 , 2048 , 2240 , 2500 , 2560 , 2800 , 3125 , 3200 , 3500 , 3584 , 4000 , 4096 , 4375 , 4480 , 5000 , 5120 , 5600 , 6250 , 6400 , 7000 , 7168 , 8000 , 8192 , 8750 , 8960 , Total ==  78 such integers.

Note: A short code in C++ found all these integers.

xz/yz=zy/xy=1/2  Incorrect!!!  

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

1/       XZ/XY = YZ/XY = 1/2    Correct!!!       X(-5, -13) 

2/      XZ/YZ = XY/YZ = 1/2     Correct!!!       X(-1/2, 2) 

3/      XY/XZ = YZ/XZ = 1/2     Correct!!!       X(4, 17) 

All three above cases are correct but, as you can see, the coordinates of X are not the same!

You need to pick one. 

.89 - .81 = 0. 08  gm left

Given:    G = 1.6 N

In ONE hour Grady rides 7.5 miles MORE than Noah

         G = N + 7.5          sub in the red equation

        1.6 N = N + 7.5

           N = 12.5 m/hr

0-99 is 100 numbers

odd      odd       25

even    odd       25

odd      even     25

even    even     25       so 75 have at least one odd digit

26 letters x 26 lettes x 75 numbers = 50700 plates

Say there are 24 boards         1/4 = 6 red boards

     so 2/3 of the scooters are red  = 6 also            then total  scooters = 9      *** edited *** (for clarity-- answer does not change)

24 + 9 = 33 total items            12 of the total (6+6)  are red 

                                 33 f = 12      f = fracton of total        f = 12/33 = 4/11 of the total are red

r=1                  <<<<<<<<<

1/a+1/b - 2ab = -4/3.

The possible remainders are 2, 3, and 4.

r = 25/4.

The number is 4 - 3*sqrt(5), so a + b + c = 4 + 3 + 5 = 12.

The probability is:552 / 10,000==5.52%

ha same lol

The FIRST 37 is prime !!

There are:  10^4 ==10,000 4-digit permutations with repeats.

Since there are only 4 prime numbers < 10, then you have:

6 choices for the first place

4 choices for the 3rd place

3 choices for the 2nd place

2 choices for the 1st place.

6 x 4   x  3  x  2 ==144. Then the 4 primes taken 3 at a time gives us:

4 C 3 ==4 and: 144 x 4 ==576 permutations with at least 3 primes. But, there are:4! permutations which have 4 primes, and since we want EXACTLY 3 primes, then we have:

576 - 4! ==576 - 24 ==552 permutations with exactly 3 primes.

Say there are 24 boards      1/4 = 6 red boards

     so 2/3 of the scooters = 6 also           then red scooters = 9

24 + 9 = 33 total items            12 are red       33 f = 12      f = fracton of total        f = 12/33 = 4/11 of the total are red

Convert to acommon denominator

5 1/4   =42/8       and   1 5/8  = 13/8

(42-13)/8 = 29/8    then simplify to  3 5/8