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45√3

I don't understand the question.

I can't read that.

The point of intersection is (2, -5, 0).

The angle is 45 degrees.

By the prime number theorem, the nth prime is like n*log n.  This is not a polynomial, so there must be an n such that p(n) is composite.

There are 3525 pairs that work.

The answer is 75.

The probability is 71/180.

Sam Read 32 pages from page 12 to 43 inclusive =880

Delilah also read 32 pages from page 16 to 47 inclusive =1008

Point P or Point X is on side BC.

are the triangles equilateral?

I've looked at this problem; are you given any idea where the point P is?

I would draw this in the first quadrant on a sheet of graph paper.

I would place the right angle (C) at the origin.

I would have the "4" side on the horizontal axis, with the point B being at (4,0).

I would have the "3" side on the vertical axis, with the point A being (0,3).

The circumcenter of a right triangle is the midpoint of the hypotenuse.

The coordinates of the midpoint of AB are (2, 1.5).

To find the incenter (which is found at the point of intersection of the angle bisectors:

-- the angle bisector of angle(C) is on the line y = x. 

-- to find the angle bisector of B, I'll find the size of angle(B), divide that in two, and find its tangent.

     -- to find the size of angle(B), find the tangent(B)  =  3/4

     -- turn that into degrees.

    -- divide those degrees by 2

    -- find the tangent of that angle; which is 1/3.

-- use this slope to count back from B three steps and up one step, giving you the point (1, 1) 

     -- this point is on the line y = x, so this point is the incenter.

Circumcenter  =  (2, 1.5)

Incenter  =  (1, 1)

Use the distance formula ...

To find the average (mean) add up all the individual amounts and divide by 7 (because there are 7 numbers).

f(x)  =  ax² + bx + c

f(1)  =  0     --->     a(1)² + b(1) + c  =  0     --->     a + b + c  =  0                     (equation #1)

f(2)  =  1     --->     a(2)² + b(2) + c  =  1     --->     4a + 2b + c  =  1                 (#2)

f(3)  =  8     --->     a(3)² + b(3) + c  =  8     --->     9a + 3b + c  =  8                 (#3)

Subtracting #1 from #2:     4a + 2b + c  =  1

                                      - (    a +  b + c  =  0  )

                             --->         3a +  b       =  1              (#4)

Subtracting #2 from #3:     9a + 3b + c  =  8

                                      - ( 4a + 2b + c  =  1  )

                             --->        5a +  b        =  7              (#5)

Subtracting #4 from #5:     5a + b  =  7

                                      - ( 3a + b  =  1  )

                            --->         2a        =  6

                            --->                 a  =  3

Using #4:     3a + b  = 1     --->   3(3) + b  =  1     --->     9 + b  =  1     --->     b  =  -8

Using #1:     a + b + c  =  0     --->     3 + -8 + c  =  0     --->     c  =  5

Answer:  f(x)  =  3x² - 8x + 5     

Never mind

3x² - 12x + 16  is a quadratic (parablola) that has a minimum of 4  (which occurs when  x = 2 ).

2y² + 6y + 9  is a quadratic that has a minimum of 4.5  (which occurs when  y = -1.5).

Since  4 x 4.5  =  18, the pair of real numbers is  (2, -1.5)

Isn't APB and APC ACB and AXC?

Thanks for the recognition :)

The probability is 43/288.

An arithmetic sequence is a sequence of numbers where the difference between consecutive terms is constant. 

The sum of n terms of an arithmetic sequence can be found with the formula \(S_n=n*\frac{a_1+a_n}{2}\).

The term \(a_n\) can be found with the following formula \(a_n=a_1+d(n-1)\). When we put these formulas together, we can solve for d.

\(S_{7}=7*\frac{a_1+a_7}{2}\\ a_7=a_1+6d\\ 63=\frac{7(2a_1+6d)}{2}\\ 9=a_1+3d\\ 9=3+3d\\ 3=1+d\\ d=2\)

Hi! The first one would be pointing to 365, the second, 700, and the third, 76.5.

Hope this helped!