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Graphed it looks like a triangle     base = 6       height =  1  2/3 

   area = 1/2 b * h        you should be able to calculate that.....

When a flask in the shape of an upside-down cone is put on its circular base, the water lies 10 units from the vertex. When flipped, the water lies 3 units away from the base. What is the height of the flask? Express your answer in simplest radical form.

Since 67 is a prime number, there are only 2 integer results we can have: 1 and 67.

To get 67, the denominator should be 1.

2x - 23 = 1 

2x = 24

x=12

To get 1 as the integer result, the denominator should be 67.

2x - 23 = 67

2x = 90

x = 45

12 + 45 = 57

https://web2.0calc.com/questions/pls-help_99

The values of n where the quadratic has no real root are 5, 6, 7, 8, 9, 10, so the probability is 6/10 = 3/5.

There are a total of 22 black or white socks out of a total of 26 socks.

The probability of pulling out either a black or white sock is 22/26.

Since this sock is replaced, the probability of then pulling out a brown sock is 4/26.

To find the total probability, multiply these together:  (22/26) x (4/26)  =  answer

Since the first term of  9x² + 10x + c  is  9, in factored form it must look like:  (3x + a)².

Expanding  (3x + a)²  =  9x² + 6ax + a²

This means that  10x = 6ax   --->   6a  =  10   --->   a  =  10/6   --->   a  =  5/3

Placing this value of  a  into  (3x + a)²    --->   (3x + 5/3)²   --->   9x² + 10x + 25/9

So:  c = 25/9.

Reflection matrix for y = 1/2*x + 5 applied to (6,2):

\(\begin{pmatrix} 3/5 & 4/5 \\ 4/5 & -3/5 \end{pmatrix} \begin{pmatrix} 6 \\ 2 \end{pmatrix} = \begin{pmatrix} 26/5 \\ 18/5 \end{pmatrix}\)

So the relfection is B = (26/5,18/5).

Completing the square, we get (3x + 5/6)^2, so c = 25/36.

Let  X  represent your expression.

Since the expression is infinite in length, we can write:  X  =  sqrt( 2 - X)

Square both sides:  X²  =  2 - X

Rewrite:        X² + X - 2  =  0

Solve for X (toss away the negative value)

thanks!

The probability that the first card is a heart is 13/52.

The probability that the second card is a spade is 13/51.         (only 51 cards remain)

The probability that the third card is another heart is 12/50.     (only 50 cards remain, only 12 hearts remain)

Since these are independent events, the total probability is found by multiplying these three numbers together.

The center is the point where the perpendicular bisectors of two chords intersect.

Plan:  to find the equations of the two perpendicular bisectors and then find what point they have in common.

The first chord has endpoints (-2,0) and (2,0). This chord is horizontal and has a midpoint of (0,0).

The perpendicular bisector will be the y-axis and the y-axis has an equation of x = 0.

The second chord has endpoints (2,0) and (3,2). This chord has its midpoint at (2.5,1).

The slope of this chord is:  (2 - 0)/(3 -2 )  =  2. Therefore, the slope of the perpendicular bisector is -1/2.

The equation of the perpendicular bisector is:  y - 1  =  -0.5(x - 2.5)

Simplifying this equation gives:  2x + 4y  =  9.

The point where  x = 0  and  2x + 3y = 9  intersect is:  (0, 2.25)

For the mean score of 3 games to be 51 points, they must have scored 3 x 51  =  153 points.

After two games, they have already scored 60 + 50 = 110 points.

Therefore, they need to score 153 - 110 = 43 points.

thank you i figured it out with your help thank you

1)  Replace each range of values in column 1 with the middle value; for example, replace 5 <= t < 10 with 7.5

2)  After you have done this, create a third column that is found by multiplying the value in the time column with its 

     corresponding value in the frequency column; for example, for the first row, the value in the third column is 15.0.

3)  Sum this third column and divide this value by the sum of the frequency column. This is your answer to part a.

4)  To find the answer to part b:  add up the number of persons who have finished in fewer than 20 minutes and

      divide this number by the sum of the frequency column.

Start with:  x(2x - 7)  =  3

Solve:          2x² -7x  =  3

              2x² - 7x - 3  =  0   

Use the quadratic formula with a = 2, b = -7, and c = -3:

      x  =  [7 +/- sqrt(73) ] / 4

From this answer, pick out m, n, and p and use these values to get the answer.

List equations:

6x-2(x-2)=152

6x-2x+4=152

4x=148

x=37

x-2=35

35, 37 are the numbers

@EP hello!

Final Amount  =  Initial Amount · (1 + yearly perecentage)^{number of years}

                 72000  =  24000(1 + 0.13)ⁿ

                 72000  =  24000(1.13)ⁿ                              simplify

                         3  =  1.13ⁿ                                           divide both sides by 24000 

                  log(3)  =  log(1.13ⁿ)                                    find the log of both sides

                  log(3)  =  n·log(1.13)                                  property of logs

 log(3) / log(1.13)  =  n                                                 divide both sides by log(1.13)

                         n  =  9.0 years                                     calculator time!

24 000 * (1.13)^t  = 72000    solve for t in years  

Area of lareger rectangle = L   x     W

                                            (x+7)   *   (x+5)   =    x^2 + 12x + 35       Now subtract the area of the hole

Hole area   (2x-3)(x-2)  = 2x^2 -7x+6

(x^2 + 12x+35 )    -    (2x^2 -7x +6)    = area without including hole......simplify  

- x^2 + 19x + 29

1  Complete the square   

      x^2 - 5x + c        take 1/2 of the x coefficient and square it ...this will be 'c' = 6.25

        (x -2.5)^2                           

2    the final term 4 is divided by 4 to get '1'

       divide the whole thing by 4

           1/4 x^2 + 2x + 1      Then add A   and B

3 if not real solutions , the discriminant must be < 0       b^2 - 4ac <0

                                                                                         m^2 - 4 (5)(8) <0

                                                                                          m^2 - 160 <0                 - 4 sqrt10    <   m <  + 4 sqrt10        m = 12 is greatest integer

ok thanks!!!!!

The net Aamount of widgets PER DAY is    2x+1      -  (3-x)   =  3x-2 w/d

started with  9-2x      and added three days

9-2x          + 3  *  (3x-2)   =     widgets after three days  ....expand and simplify