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If I give my brother 5  dollars, then we will have the same amount of money. If instead he gives me 25 dollars, then I'll have twice as much money as he will have. How much money does my brother currently have (in dollars)?  

If I give my brother 5 dollars, then we will      

have the same amount of money.                       Me – 5  =  Bro + 5  

If instead he gives me 25 dollars, then I'll   

have twice as much money as he will have.        Me + 25  =  2 * (Bro – 25)  

By equation 1                           Me  =  (Bro + 10)  

Substitute that value  

for Me into equation 2              (Bro + 10) + 25  =  2Bro – 50  

                                                           Bro + 35  =  2Bro – 50  

                                                                     85  =  Bro   

That's the answer that was asked for; i.e., my brother has 85.  

But continuing, just to be thorough, that means that I have 95. 

If my brother gives me 25, then I'll have 120 and he'll have 60.   

_.

The perimeter of rectangle OSTQ is 34.

The perimeter of rectangle OSTQ is 50.

My brother has 48 dollars.

Find m + b

Hello Guest!

\(P_1(-3,1)\\ P_2(5,3)\\ {\color{blue}P(1,2)}\ middle\ of\ the\ route\\ m_{1,2}=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{3-1}{5-(-3)}\\ m_{1,2}=\dfrac{1}{4}\\ m=-\dfrac{1}{m_{1,2}}=-\dfrac{1}{\frac{1}{4}}\\ \color{blue}m=-4\)

Point-direction equation of straight lines

\(y=m(x-x_P)+y_P\\ y=-4(x-1)+2\\ y=-4x+4+2\\ \color{blue}y=-4x+6\\ \color{blue}m=-4,\ b=6\\ \color{blue}m+b=2\)

  !

The perimeter of rectangle OSTQ is 36.

The answer is 15.

The midpoint of the segment connecting the two points is the point on the line of reflection. This point has coordinates ((−3+5)/2​,(−1+3)/2​)=(1,1). Therefore, the equation of the line of reflection is y=x+1. We can then plug in one of the points to find m+b. Since (5,3) lies on the line, we have 3=5+1 ⇒ m+b=4​.

I Cans It would be helpful if you could provide more information or attach an image of the diagram so that I can provide a solution.

q(4) = 3*4 - b  or  q(4) = 12 - b

p(q(4)) = 2*q(4) - 7   or  p(q(4)) = 2*(12-b) - 7  or  p(q(4)) = 24 - 2b - 7   or  p(q(4)) = 17 - 2b

But p(q(4)) = 7, so  17 - 2b = 7   or 17 - 7 = 2b    or  10 = 2b   or  b = 5

Your example is not an equation (it's an identity).  An equation contains one or more unknowns. For example 12x - 4 = 8 is a linear equation in a single unknown.  You add or subtract terms to both sides so that similar types are together.  In the above you would add 4 to both sides to get the constants together:    12x - 4 + 4 = 8 + 4  or 12x = 12.  Now you divide both sides by 12 to isolate the unknown:  12x/12 = 12/12  or x = 1.  Now you have solved for what was originally unknown.  

Has this helped?

incorrect answer sir/ma'am 

sorry but that is wrong

We have that p(q(4))=7. Substituting in the definitions of p and q, we get:

p(q(4)) = 2(3(4) - b) - 7

12 - 2b - 7 = 7

-2b = -8

b = 4

There are only two such functions: f(x) = x and f(x) = -x.

Notice that the number of ways to get to point C is the sum of the number of ways to get to point A and point B. We can then use this logic on all the other points until we get to point I. 

There is 1 way to get to point A and 1 way to get to point B, so there are 2 ways to get to point C. 

There are 2 ways to get to point C and 1 way to get to point B so there are 3 ways to get to point D. 

There are 3 ways to get to point D and 2 ways to get to point C so there are 5 ways to get to point E. 

There are 5 ways to get to point E and 3 ways to get to point D so there are 8 ways to get to point F. 

There are 8 ways to get to point F and 5 ways to get to point E so there are 13 ways to get to point G. 

There are 13 ways to get to point G and 8 ways to get to point F so there are 21 ways to get to point H. 

There are 21 ways to get to point H and 13 ways to get to point G so there are \(\color{brown}\boxed{34}\) ways to get to point D.