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YZ = 32/5.

I do not think this is possible with the numbers given,    Please check your post .   Need 103 dogs in school to make the other numbers work.

36 possible rolls

to produce product 3 , possible rolls are    1,3    and    3,1

   for 12      6,2   2,6    3,4    4,3 

       6 rolls out of 36   = 1/6 probability

PQ = 35.

QR = 28.

 x^2 + 10x + 25 = 8 + 17

[x  +  5]^2 = 25

Use the quadratic formula to get:

x = 0

x = - 10 - which is the smallest value of x.

 2x * (3x + 12)(x + 4) = (4x^2 + 8x + 8x^2)

6x^3 + 48x^2 + 96x=12x^2 + 8x

6x^3 + 36x^2  + 88x=0

x [3x^2 + 18x + 44] = 0, solve for x

[3x^2 + 18x + 44] = 0 - use the quadratic formula to get:

x = 0
x = -3 - i sqrt(17/3)
x = -3 + i sqrt(17/3)

You have posted this question about a dozen times in the last two weeks or so! Have you looked under one of these question such as this one:  https://web2.0calc.com/questions/counting_36934

Note: if you think the answer is wrong, then let us know. Or even better, tell us what the right answer is.

[100 + C] / [60 + C] = [160 + C] / [100 + C], solve for C

Cross Multiply

[100 + C]^2 = [60 + C) * [160 + C] 

C^2 + 200 C + 10000 = C^2 + 220 C + 9600

C^2 - C^2 + 200C - 220C ==9600 - 10000

- 20C =- 400

C == - 400 / - 20 = 20

So, the GS would look like this:

[60 + 20], [100 + 20], [160 + 20] = 80,  120,  180

First term = 80  and  Common ratio = 120 / 80 = 1.5

Let the constant be x:

By the definition of a geometric sequence, then:  (60 + x)/(100 + x)  =  (100 + x)/(150+ x)

Cross multiplying:  (60 + x)(150 + x)  =  (100 + x)(100 + x)

--->   9000 + 210x + x²  =  10000 + 200x + x²

--->   10x  =   1000

--->   x = 100 

(3x+12)(x+4)=(

=3x²+12x+12x+12

= 3x²+24x+12

=x²+8x+4

BCDAE

set x^2 = y, or find deritative of function regarding x^3

:)

have you tried complemetary counting? Otherwise a wise person once said use the binomial theorem

Use the binomial theorem

Just use vieta's formula and quadratic factoring and you should find that the answer is 70