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Start with the column of B's 

The only number that when multiplied by 3 ends with itself is 5       

So B = 5  

Then the column of G's  

G times 3 has to end with 4 because you carry 1 from the units column. 

The only number that when multipled by 3 ends with 4 is 8  

So G = 8  

The column of R's 

You carry 2 from the tens column so R times 3 has to end with 3   

The only number that will work is 1   

So R = 1 

Test it -- 

                        1  8  5 

                        1  8  5 

                        1  8  5 

                      ————    

                        5  5  5 

_.

b=5

g=8

r=1  is what I see

Whatever b is....when you add three of them you get b plus a carry digit.....only 5 will work for this   5 + 5 + 5 = 15   carry 1

    then   1 +  g +g + g    must also end in a 5       8 is the only digit that works....with a carry of 2

       then   2 + r + r + r  must equal 5 also     1   is the onlt digit that works

6 years after Jacob is three times,his current age,he will be the same age as his dad is now.His dad is 39 years old now.How old is Jacob now? 

Multiply Jacob's age by three, then add six.  This will equal dad's age. 

                                                         3J + 6 = 39   

subtract 6 from both sides                3J       = 39 – 6  

                                                         3J       = 33 

divide both sides by 3                         J      = 11 

_.

What is the total area in blue knowing that the area of the large triangle is 1? 

I'm not sure there's enough information provided to make the following assumption, but here goes. 

The dimensions of each smaller triangle appear to be half the height and half the base of the previous. 

I haven't a formal proof for this assumption, but I did try to measure with a ruler against my computer screen. 

So, basing the following on the preceding... 

If the assumption is correct, then the area of the largest blue triangle is one-fourth.

Then, the area of each smaller blue triangle is one-fourth the area of the previous, 

I don't know how to write this in mathematical notation, but 1/4 + 1/16 + 1/64 + 1/256 and so on. 

The total of (1/4)ⁿ where n=1, 2, 3, 4, and continuing forever. 

d = daughter age now

m = mom age now

difference in ages =   m-d

roll back daughters age by the difference in ages    d - (m-d) = 10  or      2d-m=10 

advance moms age by age difference   m + (m-d) = 88                  or       2m-d=88     

  solve for   m = 62   d = 36 y/o 

Find cubic feet of water missing

36 ft x 18 ft x  15/12 ft = 810 ft³

^{810 ft^3 x 7.48 gal/ ft^3 = ~~6059 gallons}

6059 gal / 1500 gal/load = ~~ 4 trips

The greatest possible product is when the displayed numbers are:3 and 4. Opposite 3 is 4 and 3 x 4 =12.

Opposite 4 is 3 and 4 x 3 =12. And 12 x 12 = 144 - which is greatest product possible.

LOOKs like  1/3

d, just plug the numbers in and yull get it

You do not need a calculator, plot them by hand.

You can plot them here I guess.  I have done the first one for you.

Yes, although I would go for 5:45 (I mean 45 minutes) myself

You are very welcome. 

I come here to help people learn and I think I have done that here so I am happy.   

thanks! ill take a look at it!

The midpoint of (7,9) and (10,2) is located at the average of x- and y-coordinates of both vertices.

\(M=(x,\frac{9+2}{2})\\ M=(x,\frac{11}{2})\)

This midpoint is the same for the other two vertices of the square. Let's let the y-coordinates of the first unknown vertex be \(y_1\) and the second unknown vertex one be \(y_2\). Then, we would calculate the average of those vertices as follows:

\(\frac{y_1+y_2}{2}=\frac{11}{2}\\ y_1+y_2=11\)

Therefore, the sum of the y-coordinates of the other two vertices is 11.

Oh I see, I thought they asked for an actual calculation. The pace is the same at 5.5 hours! Thank you for the help Melody!

What is the complex number z=−4√3+4i represented in polar form?

Get t in terms of x, I mean make t the subject, then substitute it into the second equation so that the t disappears.

Yes that is right. Initially the gradient of A is less than B, and then about half way along it gets stepper which means it is going faster.

About 2 and half hours from the start the gradient is about equal (parallel) 

So they have about the same pace at 2.5 hours then again when?

So from 0 to 2.5 hours A is walking more slowly than B,     then from 2.5 to how many hours is A walking faster than B?  

Part a is only asking for a comparison. It is asking which one is faster or slower and when that is happening.

In the first four hours A moves at a slower pace and then he speeds up? I'm not quite sure how to convert this into an 1 km/h format though

Speed= distance travelled / time taken.

Since A and B have both travelled 8km (vertical axis) in 8 hours (horizontal axis) there average speed over the 8 hours is identical.

However

Since at any given moment in time, velocity = distance/ time where the unit of time is approaching zero.

This means that velocity at any given point is given by the GRADIENT of the tangent to the curve at that point.

Your B curve is linear so the gradient is always the same. Velocity=speed= 8/8 = 1km/hour

The A pace changes.

Perhaps you can tell me what is happening. When is the gradient of the A curve equal, less, or greater  than that of the B curve ?

See 3D graph:

Oops!  I was careless in looking at the graph and misled myself (and you!).   The point where the two functions meet at a single point is at x = 48, not 50.  Plug this into the first function to get y (= 114).  Then use this value of y in the second function, together with x = 48 to get k ( =  18).

I answered this yesterday - see: https://web2.0calc.com/questions/please-help-how-do-you-graph-parametric-equations#r1 

I have not managed to prove it algebraically but here is a graphical demonstration where it certainly appears to be true.

O is the center of a circle

M is a midpoint of a diagonal BD

tan(BDC) = 3/4        angle BDC = 36.86989765º

Angles  BDC, BNM, and CNO are congruent

BN = MB / sin(BNM)  = 4.166666666

CN = BN - BC  =  1.1666666666

OC = sin(CNO) * CN  = 0.7   or   7/10   

A circle passes through two diagonally opposite vertices of a 3-inch by 4-inch rectangle. What is the least possible distance between the center of the circle and a vertex of the rectangle? Express your answer as a common fraction.

 The least possible distance between the center of the circle and a vertex of the rectangle is  7/10