All posts by mathconfidence

August 2017 Brain Teaser Solution

Q: With one straight cut a cake can be sliced into two pieces. A second cut that crosses the first one will make four pieces, and a third cut can produce as many as seven pieces. What is the largest number of pieces that you can get with six straight cuts?

A: 22
With 0 cuts, you get 1 big cake
With 1 cut, 2 pieces
With 2 cuts, 4 pieces
For the 3rd cut, if you cut cleverly you can get 7 pieces
click here for more info and nice graphics thanks to the Guardian
http://bit.ly/CuttingthePieGardner

 

 

 

Get the Math and Points June 2017 CC Alg I Regents #8

June 2017 CC Alg I 8

Using substitution, we can rewrite the second equation as
3(-2x + 2x + 8) = 12
3(8) = 12
24 = 12
huh?  NO solution

If we were to solve the second equation for Y=, we would get:
by distributing the 3
-6x + 3y = 12
add 6x to each side
3y = 6x + 12
Divide both sides by 3
y = 2x + 4 this is parallel to the first line y = 2x + 8 and therefore the lines will never meet
making the answer “No solution”

 

 

 

 

 

 

 

Get the Math and Points June 2017 CC Alg I #7

June 2017 CC Alg I 7
First look at the graph — looks super nonlinear and pretty exponential
Use the point (0,4).
We can eliminate answers (2) and (3), as if we substitute h=0,  the output would be 6/5 and 4.2 as opposed to the 4 for the y value we are looking for.
Now we can use the point (1,8) to see if y = 8 when x = 1
For answer (4), if we substitute in x = 1, we get 2/3(1)^3 – 1^2 + 3(1) + 4 = 2/3 – 1 + 3 + 4≠ 8
Try answer (1): using order of operations: 4(2)^1 = 4(2) = 8
4(2)^2 = 16 and 4(2)^3 = 32.  That’s it –2 points
You can also use Y= and check the table for a match: