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Using the formula:  t_n  =  t₁ + (n - 1)d

          94  =  t₁ + (27 - 1)d                    46  =  t₁ + (94 - 1)d

          94  =  t₁ + 26d                            46  =  t₁ + 93d

Combining these two formulas:

                 94  =  t₁ + 26d 

                 46  =  t₁ + 93d

Subtracting down:

                 48  =  - 67d     --->     d  =  -48/67     and     t₁  =  112 42/67

Take 5,6, and 7 

Now you can add  0 more, or 1 more or 2 more etc right up to all of them.

1 more   7C1 ways

2 more   7C2 ways

etc.

Now if you have any idea what I'm talking about you can finish it easily. 

Wu rolls two fair, six-sided dice. You are not told what the rolls were, but you are told that the sum of the two rolls is a prime. What is the probability that the sum of the two rolls is $2$?  

There are 36 possible rolls, but only one of them totals 2. 

Therefore the probability is 1/36.  

Here is a table showing all 36 possible rolls. 

As you can see, there's only one way to get a 2.  

1,1   1,2   1,3   1,4   1,5   1,6  

2,1   2,2   2,3   2,4   2,5   2,6  

3,1   3,2   3,3   3,4   3,5   3,6  

4,1   4,2   4,3   4,4   4,5   4,6  

5,1   5,2   5,3   5,4   5,5   5,6  

6,1   6,2   6,3   6,4   6,5   6,6  

The sum of the internal angles of an n-sided polygon is given by 180^o • (n – 2)  

So for an octagon (8 sides) the sum of its internal angles equals 180^o • (8 – 2)  

Doing the arithmetic, this sum is 1,080^o    

Since it is a regular octagon, all internal angles are equal, so each one is 135^o  

x is a supplementary angle of one of those 135^o angles, so it equals 180^o – 135^o  

Thus, x = 45^o  

_.

The units digit of 16^17 is 6, the units digit of 17^18 is 3, and the units digit of 18^19 is 2, so the units digit of 16^17*17^18*18^19 is the same as the units digit of 6*3*2, which is 6.

Similar question:       https://web2.0calc.com/questions/geometry-question_69#r2

You got it !!  

NM = 1/2(AB + CD)

PQ = 1/2(AB + NM)

This was very difficult.

Your answer is correct!!! 

I'm sorry, but this is wrong

The only triple that works is (x,y,z) = (2,2,4), so the sum of all possibe values of z is 4.

[ACD] = 290.547

A rhombus with an area of 840 has a diagonal of length 42. What is its side length?

840 / 42 = 20

Side = sqrt(21² + 20²)

Find another point that must lie on the graph of y = f(x).

Hello Guest!

The other point is (3, -8).

  !

There are 3586 ways.

The area is 45.

The vertex is (3,-5).

the answer is 38 

The question is about the "SUM" of the digits that are divisible by 10 !! Example: 1,000,000,009, 1,000,000,o18, 1,000,000,027.......Just add up the digits: [1 + 9], [1 + 1 + 8], [1 + 2 + 7]....and so on.

Okay, I got it. it is -1, therefore \(-(4)^{50}\)

Thanks Alan,

I always forget how this is done   

These are usually best done by using polar coordinates. e.g.

Like so:

find dy/dx e^ysinx=x+xy

Hello Guest!

\( \frac{dy}{dx}(e^ysinx)=\frac{dy}{dx}(x+xy )\)

\(y'\cdot e^y\cdot sin\ x+e^y\cdot cos\ x=1+y+x\cdot y'\)

   u'           v           u       v'                u'v      u   v'

  !

x - (5x/15 + 4x/15 + 1.5x/15 + 0.75x/15) = 15

x = 60

Ivan had $60

book = $20

game = $16

CD = $6

candy bar = $3