April 5, AIM: How do we solve algebraic fractions?
MIDTERM ON MONDAY APRIL 10
Homework:
Todays lesson: Read pp 715-716
Do: pg. 716 #'s 13, 15, 16, 17, 20, 21
Midterm preparation sheet: pp 1, and 2 all problems
Extra Credit: 3 points. Post correct assigned midterm prep sheet problem to todays comment section on this post or on the board tomorrow. All steps in arriving at a solution must be shown for credit.
Todays lesson review:
http://www.regentsprep.org/Regents/math/fractions/Fequations.htm
Todays practice enrichment exercises: http://www.regentsprep.org/Regents/math/fractions/Penrich.htm
posted by Mr.Napoli @ 1:06 PM
26 Comments:
3x(x+1)+4(x-1)
3x*x=3x2
3x*1=3x
4*x=4x
4*-1=-4
3x2+3x+4x-4
3x2+7x-4
EXTRA CREDIT!!!!!
1. Factor: 4x2-9
this problem is the difference between perfect squares so when we factor the answer is:
(x-3)(x+3)
:D!!!
28) First you see if there is an sad smiley or happy one. When this is done you now know for this problem that the graph has a negative in it. The only 2 options that are left is number 2 and 4. At this point you find the turning point using the formula x=-b . THe final step is 2a
is to see which turning point matches the one on the graph. The solution is number 2
Hi Mr. Napoli is scheilla; you assigned me today to do problem #4, so here it is:
FACTOR: X2+5X-24X
(X+8)(X-3)
THE FIRST THING I DID HERE WAS TO FIND TERMS OF c(24X) THAT ADDING WOULD GIVE ME +5(POSITIVE FIVE) SO THE NUMBERS WERE +8 AND -3, SO WHEN WE ADD THEM GIVE US +5:
+8-3=+5.
I HOPE THE ANSWER IS RIGHT, SEE YOU TOMORROW Mr. Napoli.
Tiffany Abreu, period 8
36. Perform the indicated operations and express the result as a trinomial:
3x(x+1)+4(x-1)
When you distribute, and combine like terms, your answer 3xsquared+7x-4
#2) Factor x-squared - y- squared
It's the difference of prefect squares.
(x-y) (x+y)
Midterm Review Sheet
#2) Factor x(squared)- y(squared)
It's the difference between perfect squares.
Answer: ( x-y ) ( x+y )
Hi Mr. Napoli !!
So Im doing.. number... 30 ?
(x^2 -2x -3)
(x-3)(x+1)
-------------
+3 | -1
Answer : 1. 3,-1
By: Karina Khafizova
Period 8
Oksana Khafizova # 31
x^2-2x-15
(x-3)(x+5)
+3 | -5
24. Which is the solution for the following system of equations?
y=x^2
y=-2x+15
(1). (-3,9) (3). (3,9)
(2). (5,25) (4). (-5,3)
y=x^2
y=-2x+15
-2x+15=x^2
+2x-15=x^2= x^2+2x-15
(x+5)|(x-3)
-5 | +3
Answer: (4).(5-,3)
16) 5a 4a
___ - ___
6 9
5a(3) 4a(2)
___ - ____ LCD=18
6(3) 9(2)
15a 8a 7a
____ - ____ = ___
18 18 18
By: Wendy Reyes M$2 PERIOD 8
Answer to Problem #17:
Y = -(X*X) + 6X
When X = 0; Y = -(0*0) + 6*0 = 0
X = 1; Y = -(1*1) + 6*1 = 5
X = 2; Y = -(2*2) + 6*2 = 8
X = 3; Y = -(3*3) + 6*3 = 9
X = 4; Y = -(4*4) + 6*4 = 8
X = 5; Y = -(5*5) + 6*5 = 5
X = 6; Y = -(6*6) + 6*6 = 0
(b) No. Because 3 units from the origin the height of the ball is 9 units. If there is a wall there that is 9 units tall, then, the ball does not get over the wall.
Answer to problem number 29:
Turning point of y=x^2-6x+2
a=1 b=-6 c=2
X=
-b
___=
2a
-(-6)
=_____=
2(1)
6
=__=
2
=3
___________________________
y=(3)^2-6(3)+2=9-18+2=-7
The turning point is: (3,-7)
Mr. Napoli I'm doing #25:
The turning pt of the graph of the function of y=2x(squared)+4x+3 is..
First you need to find the axis of symmetry by the formula x=-b over 2a. Figure out what a, b, and c equal from the quadratic equation. By looking at it, you can see that a=+2,b=+4,and c=+3. Then you plug in the numbers and get..X=-(4)over 2(2). Then you come up with -4 over 4, which when divided give you a -1. so now you are aware that x=-1. Now take that -1 and plug it into the original equation which now looks like..y=2(-1)squared+4(-1)+3.
2(-1)squared=2..+4(-1)=-4..and what is left over is +3. Now one must combine like terms:
2-4+3=1..
so y=1
Answer: (-1;1)
-liana isakova
4) x2+5x-24
by factoring the answer is
(x+8)(x-3)
4)x2+5x-24
by factoring the answer is
(x+8)x-3)
by:Joseph Lobo
#33 Michael Kaziyev
extra credit
0.62*10^3= 620
6.2*10^2= 620
They are equivalent
Answer= #4
16)Express 5a/6 - 4a/9 as a single fraction in simplest form.
1st you have to see if the denominators are common, 6&9 are not so you have to find the LCD. In this problem the LCD is 18. You multiply 6(3) and 5a(3). Then you multiply 9(2) and 4a(2. What ever you do to the denominator you have to do to the numerator. 5a(3)=15a and 6(3)=18. Next fraction is 4a(2)= 8a and 9(2)= 18.Then you forget about the denominater b/c they are common. Next you subtract 15a -8a= 7a. The solution is 7a/18. This is in simplest form.
ENDRI BRAHIMAJ PERIOD 7
Factor: 4x^2-9
(x-3)(x+3)
Gurminder K.
period 11
32) x² + 2x - 15 = 0
first you have to find two # that when multiplied together equal -15 and when added equal +2. they are -3 and +5. so you put them in the brackets (x - 3) (x + 5) and thats it... the answer is # 2
This wonderful message has been posted by Boris (period 7)
Paola Uzhca
Pd 7
# 31
x^2-2x-15=0
(x-5)(x+3)=0
x-5= 0 x+3= 0
+5 +5 -3 -3
------ --------
x=5 x=-3
Solution Set {5,-3}
First thing I did was factor
Then when I got the factors I set it equal to zero and solve for x.
this iz 4 the extra credit!!!
i chose number 30
30. x^2-2x-3=0
i factored the numer 3 which is
(x-3) (x+1)
then i got the solution set which is -3,1
Nicholas Go
15)Express the sum of 4x^2-3x+2 and
-2x^2+7x+3 as a trinomial.
First step:
(4x^2-3x+2)
+(-2x^2+7x+3)
Second step:combine liketerm
4x^2+(-2x^2)=2x^2
-3x+7x=4x
2+3=5
Third step:put them in standard form
Ans:2x^2+4x+5
23. The larger of two positive integers is five more than twice the smaller integer. The product of the integers is 52. Find the integers.
First you have to substitute the integers with X. Then create an algebraic equation to solve.
smaller integer=x
larger integer=5+2x
x(5+2x)=52
5x+2x(squared)=52
2x(squared)+5x-52=0
(2x+13)(x-4)
2x+13/x=4
reject!
x=4
5+2x=13
By:Oksana Avizova
hi mr. napoli i hope that i get the 3 extra points on my midterm exam. Did i get the operation right?
aqsa asif
EXTRA CREDIT
6. x3+5x2+6x
to solve this problem first look for gcf which is x and then solve it like a quadratic expression WHEN A=1
x(x2+5x+6)
x(x-3)(x+2)
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