Bosco

@IQantCorrectAnser    Indeed, there might be something wrong with the question, but there's nothing wrong with my answer to the problem stated in this thread.  Maybe the problem on the Staar test says something different and the OP copied it incorrectly.  OP means Original Poster.  

_.

They didn't sell the same number of cookies.    

The problem says Max sold half as many as Jessica.  

_.

Normally, I wouldn't bother with an unsubstantiated claim like this,   

but there isn't anything good on television right now, so why not.  

The problem gives four answers to choose from.    

Let's try all of them.    

72 – 18 = 54     36 –   9 = 27      Same number left over?  No.

72 – 36 = 36     36 – 18 = 18      Same number left over?  No.  

72 – 24 = 48     38 – 12 = 26      Same number left over?  No.   

72 – 72 =   0     36 – 36 =   0      Same number left over?  Yes   

_.

Find the area of the equiangular octagon below.     

I think the dimensions don't work.  

If a side is 4, then the distance from the center to a side     

would be 2 + (4 / sqrt(2) ) which is 2 + 2.828 = 4.828, not 3.               

_.

Jessica baked 72 cookies and sold x cookies. Max baked 36 cookies and sold half as many cookies as Jessica did. How many cookies did Jessica sell if they each had the same number of cookies left over?    

Call "n" the number of cookies they each had left over.    

                                                                72 – x  =  n         (1)     

                                                                36 – x/2  =  n      (2)     

Subtract (2) from (1)                                36 – x/2  =  0             

                                                                        x/2  =  36   

                                                                           x  =  72   

So                                                        Jessica sold 72 cookies    

                                                             Max        sold 36 cookies     

                                                             and neither had any cookies left over (i.e., n = 0).    

_.

There are 60 pencils in 4 pencil boxes. How many pencils are in 7 boxes?     

There are 60 pencils in 4 pencil boxes.  That's 60 / 4 = 15 pencils in each box.    

How many pencils are in 7 boxes?          Then 7 x 15 = 105 pencils total.    

_.

Two circles of radius $1$ are centered at $(4,0)$ and $(-4,0).$ How many circles are tangent to both of the given circles and have radius $3$?    

Picture the circles on the x-axis.  Better yet, get some paper and draw them.      

Centers on –4 and 4 and radius 1, their edges reach to –3 and 3.  

Note that –3 and 3 are 6 units apart.    

Note that radius 3 equals diameter 6.   

So there's only 1 circle of radius 3 that will fit between them and be tangent.    

_.

For what value of $h$ does the quadratic $7x^2 + 5x = h + 6x^2 - 3x$ have exactly one real solution in $x$?    

                                                      7x^2 + 5x = h + 6x^2 - 3x

                                                      7x² – 6x² + 5x + 3x – h  =  0

Combine units.                                  x² + 8x – h  =  0     

This is in the form                             ax² + bx + c

To have only one solution means  

that the expression is a square.  

For it to be a square, then                b² – 4ac has to equal zero.       

                                                          8² – (4)(1)(–h)  =  0    

                                                           64 + 4h  =  0  

                                                                   4h  =  –64    

                                                                     h  =  –16   

Check Answer   

Substitute –16 into the   

quadratic equation.                  x² + 8x –(–16)   

                                                x² + 8x + 16   

Will this factor?  Yes.               (x + 4)(x +  4)   

_.