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What's the question?

What's the question?

Can you explain how?

The parabola  is graphed below. Find abc. (The grid lines are one unit apart.)

https://latex.artofproblemsolving.com/3/d/c/3dcbfd37344accf75039423aaee0e135a89dc16a.png

Many people have said the answer is 30, but it has to be a fraction. Can someone PLEASE give me the correct answer?

First we want to count the number cases without any restriction which is 9! Then we count the number we don't want which is 5*4*4*3*3*2*2*1*1 = 2880. 9!-2880 = 360000.

Let  P  = cost of one pencil

Let  E  =  cost of one eraser

2P + 3E  =  1.45      --->     multiply by 5     --->     10P + 15E  =  7.25

5P + 1E  =  2.65     --->     multiply by -2     --->    -10P -   2E  =  -5.30

    Add down the columns:                                               13E  =  1.95

    Divide by 13:                                                                    E  =  0.15

arc(TA)  =  2·41^o  =  82^o

arc(AU)  =  2·63^o  =  126^o

arc(TAU)  =  82^o + 126^o  =  208^o

arc(TU)  =  360^o - 208^o  =  152^o

angle(QPR)  =  ½·(208^o - 152^o)  =  28^o

More than I thought:  3, 5, 8, 9, 11, 13, and 14.

x² - 15 <  2x     --->     x² - 2x - 15  <  0     --->     (x +3)(x - 5)  <  0     --->     -3  <  x  <  5

The value of  a  is  -2  and the value of  b  is  4     --->     b - a  =  4 - -2  =  4 + 2  =  6

Using the quadratic formula:

x² + bx + c  =  0     --->     x  =  [ -b +/- sqrt(b² - 4c) ] / 2

Difference of the roots:  | [ (-b + sqrt(b² - 4c) / 2 ] - [ (-b - sqrt(b² - 4c) / 2 ] |  =  | 2sqrt(b² - 4c) / 2 |  =  sqrt(b² - 4c)

But:  sqrt(b² - 4c)  =  | b - 2c |

squaring both sides:  b² - 4c  =  (b - 2c)²

                                  b² - 4c  =  b² - 4bc + 4c²

                                        -4c  =  -4bc + 4c² 

                                           0  =  4c² + 4c - 4bc

                                           0  =  c² + c - bc

                                           0  =  c(c + 1 - b)

Either  c = 0  or  c + 1 - b  =  0

Since  c is not equal to 0,  c = b - 1

Anyone?

cos(2x)  =  1 - sin²(x)

cos(2x)  =  1 - (15/17)²

Now, finish ...

All multiples of 7 between 7 and 343:

[343 - 7] / 7 + 1 =49 such numbers.

Thank you! Can you explain a little more? I am not very familiar with Arithmetic Sequences. Thanks!

The answer is C. 

Written as decimal fractions, the values listed in C are –3.333, –2.000, +0.200, +1.900 

_.

The answer for one of them, or the answer for two of them. For both answers to be correct, there is a 1 in 9 chance because 1/3*1/3 = 1/9.

But if you want to find the probability that one answer is right and the other is wrong is 1/3*2/3 which is 2/9. But, you have to multiply that by two because you can have the first right and the second wrong or the second right and the first wrong, so it is actually 4/9. Both answers right: 1/9, one answer right one answer wrong:4/9, Both right or one right one wrong:5/9