Patrick's 8 questions

Question 1: Find 3 Consecutive numbers such that the sum of the second and three times the first is four more that three times the third.



x + 1 + 3(x) = 3(x + 2) + 4
x + 1 + 3x = 3x + 6 + 4
4x + 1 = 3x + 10
4x - 3x = 10 - 1
x = 9


Question 2: Jim is 4 times as old as Harry, and Harry is 8 years younger than Bill. The sum of the ages of Jim and Harry decreased by Bill's age, is 12. Find their present ages.



4(x - 8) + x - 8 - x = 12
4x - 32 + x - 8 - x = 12
4x + x - x - 32 - 8 = 12
4x - 40 = 12
4x = 12 + 40
4x/4 = 52/4
x = 13

Question 3: The sum of the angles of a triangle is 180 degrees. If the fist angle of a triangle is three times as large as the second, and the third angle is 5 degrees larger than the first, how many degrees are there in each angle ?




3x + x + 3x + 5 = 180
7x + 5 = 180
7x = 180 - 5
7x/7 = 175/7
x = 25


Question 4: The proceeds of a Junior High School dance amounted to $37.25. If the students paid 35 cents per couple, and non-students paid 50 cents per couple, how many of the 82 couples at the dance were students ?



35x + 50(82 - x) = 3725
35x + 4100 - 50x = 3725
35x - 20x = 3725 - 4100
15x/15 = 375/15
x = 25


Question 5: At what price per kilogram should a merchant sell a mixture of 50 kilograms of nuts if it contains 30 kilograms of almonds worth 40 cents per kilogram, and 20 kilograms of Brazil nuts worth 50 cents per kilogram ?



30(40) + 20(50) = 50x
1200 + 1000 = 50x
2200/50 = 50x/50
44 = x


Question 6: Mr. Jones withdraws $10 000 from a bank where it was earning 2% interest. He then invests part of the $10 000 in bonds paying 3%, and the remainder in stocks yielding 4% interest. By investing his $10 000 in this manner, he increases his yearly income by $140. How much has he invested in bonds ?



0.03x + 0.04(10 000 - x) = 0.02(10 000) + 140
0.03x + 400 - 0.04x = 200 + 140
0.03x - 0.04x = 340 - 400
- 0.01x/- 0.01 = - 60/- 0.01
x = 6000

Question 7: If pump A and pump B operate together, it takes 12 minutes to empty a swimming pool. By itself, Pump A can empty the pool in 20 minutes. How long would it take to empty the pool of only pump B was working ?



1/20 + 1/R = 1/12
(20)(R)(12)1/20 + (20)(R)(12)1/R = (20)(R)(12)1/12
12R + 240 = 20R
12R - 20R = - 240
- 8R/- 8 = - 240/- 8
R = 30


Question 8: For the Jones family, the trip from home to the cottage and back takes 3 hours. Going to the cottage they travel 50 km/h and coming back they travel 70 km/h. How far away from home is the cottage ?



D1 = D2
ST = ST
50x = 70(3 - x)
50x = 210 - 70x
50x + 70x = 210
120x/120 = 210/120
x = 1.75

D1 = D2
ST = ST
50(1.75) = 70(3 - 1.75)
87.5 = 70(1.25)
87.5 = 87.5

Tianna Blog Post

The train question..

What we need to know
- .75km

- 50km/ 60mins
- 1.5min

6(x + o.75) = 6(5/6) 1.5
6x + 4.5 = 7.5
6x/6 = 3/6
x = .5km

Then you have to convert km into m

(.5)(1000) = 500m
The train is 500m

Then we did some stuff like this....

3(x + 4) = 20

First you expand the brackets..

3x + 12 = 20

Then...

3x + 12 - 12 = 20 - 12

so..

3x = 8

Then you divide both sides by the coefficient

3x/3 = 8/3

The answer is x = 8/3



The next question

4y - 8 = 15
4y - 8 +8 = 15 + 8

4 y/4 = 23/4

y = 23/4

HOMEWORK 8.3
read pp. 314 -318
CYU #1,4
Practise, Apply: ALL
Extend: only 4
and 28
8.3 Homework Book.

JOMER, YOU'RE DOING THE NEXT BLOG

Trisha's Blog Post

In class we...

Did Chapter 8.2 in the textbook.

3x + 2 = 5

5x - 2 = -4

That answer will be a fraction because Mr. Backe said to make it easier on us but decimal is optional.

x/3 + 4 = 6

x = 6

x/4 - 3 = - 5

Homework:

Read pg. 304 - 310

Do the Show You Know

Check Your Understanding

Practice, Apply - ALL

Extend - Any 2 and #32

Chapter 8.2 in the Homework Book

AND the Yellow Sheet is due tomorrow.

You need to show cross multiply, divide by coefficient, multiply by the reciprocal and find the common denominator.

Mr. Backe won't take it if it's late so don't forget to do your homework.

The next person I choose is ...Tianna.

Shane's Blog Post

Solving Equations

Isolate variable on left side.

HOMEWORK:

Read pp. 292-300

Do SYK

CYU no.3

Practise- All

Apply- All

Extend- 3 of 5

Homework Book 8.1

MANGA HIGH !! 

I pick TRISHA to do the next blog !

Binomial by Binomial Mutiplication

while solving these problems remember to look at the signs

and always remember that x multiplied by x is x^2 (squared) not 2x

Here are some problems we did using F.O.I.L.

DIVISION OF POLYNOMIALS

You can solve these by thinking of it like this

Here are a couple of more difficult ones....

Homework

Read pgs. 272-274

CYU #2,3

Practice odd/even

Apply ALL

Extend 2 of three

Homework book 7.3

Green sheet 7.10 #1-7

and I pick Shane to do the next blog!!!!

Nils' Blog Post

Multiplying Polynomials by Monomials

Greetings ladies and germs! Today in class we learned about multiplying polynomials by monomials. Let's start off with a little explanation.

Usually we add the numbers in the bracket together than multiply the bracket by the constant.

4 (2 + 4) = 4 (6)

= 24

Is there another way we can do this?

What about multiplying each part of the bracket by 4?

4 (2 + 4) = 4(2) + 4(4)

= 8 + 16

= 24

The answer is the same.

Here's another example.

5 (6-3) = 5(3)

= 15

Once again let's use our method.

5 (6 -3) = 5(6) -3(5)

= 30 - 15

= 15

The answer is the same.

How about something more complex?

2x (3x + 4)

We can still do the same thing as before.

2x (3x + 4) = 2x(3x) +2x(4)

= 2(3)(x)(x) + 2(4)(x)

= 6 x^2 + 8x

It's the same concept. It just takes a bit more time to do.

Can we represent this with a picture? We sure can!

5 x (-2x +y -2)

Let's do a multiplication diagram for this.

The solution is -10x^2 + 5xy - 10x

Now I'll show you how to do the reverse. Finding the equation when you have the diagram.

Remember that the first part of the polynomial is on the left side of the diagram.

In this case -2x is the first part. 3x -4 is the other part.

So the formula is -2x (3x - 4)

Now we solve!

-2x (3x -4) = -2x (3x) - 4 (-2x)

= -6x^2 + 8x
Some common mistakes people make when multiplying polynomials by monomials is...

1. Forgetting to look at the signs. Instead of making a number negative, you make it positive and vice versa

2. You forget to multiply all the terms in a polynomial. This one is kind of self-explanatory. REMEMBER TO MULTIPLY ALL THE TERMS!

Okay people! Here's the homework.

1. Read Pages 264 -268



2. Check your Understanding 2 and 3



3. Practise 0dd or even



4. Apply All



5. Extend 2 of 3



6. And the 7.4 Green sheet we got ages ago.



7. And last but certaionly not least... MANGAHIGH!!! We are in a Fai-To!!!

If you have questions please ask. If not, then I bid you adieu.

Oh yeah I almost forgot. The next blog person is......... ANA LOPENA

Multiplying and Dividing Monomials

The signs to see if it should be a negative or a positive.




We started off the class by doing simple multiplication.

(3)(2)=6

(-4)(3)=-12

(-2)(-2)=4

(6)(-2)=-12



Then we started working on something more harder.


Tip: First number goes on the left side.
Second number goes on the top.

Here's another question.





Another question.

The last multiplication question

We then started dividing numbers.

6/3=2

-8/4=-2

16/-4=-4

-12/-4=3

Tip: The big number goes inside.

The divisor goes to the left.
Quotient goes on top.




Another question,







Another question,





Some questions you can solve, but can't model.
Examples:





Here is a video that may help you understand.

HOMEWORK:

7.1 READ pg. 254-259
CYU- 2
PRACTISE ODD/EVEN
APPLY: ALL
EXTEND 24, 26, 27
HOMEWORKBOOK 7.1

Don't forget to check MANGAHIGH!!

I Pick Nils to do the next blog

Roemer's Blog Post

Interpolation - Within the graph.
ex.




















Extrapolation - Outside of the graph.





















Read 220-225
Key Ideas
CYU #1
Practice (odd or even)
Apply(even or odd)

Surprise, Surprise, I pick ɐuuɐǝɹq.

Cathlene's Linear Relation Blog Post

Unit 5 Linear Equations

Ordered Pairs on Cartesian Plane or also known as the Coordinate Grid

Ordered Pairs have orders and it is always x and y

A Cartesian Plane or Coordinate Grid

Example #1

In this example the tables are the independent and the chairs are the dependent.

You can also use the horizontal table, but it's good to know both ways.

Example #2

Example #3

Homework

6.1 read page 210 - 116

CYU #2, 3

Practice Odd or Even

Apply all questions

Extend 17, 15, or 16

Manga High

For the next blog I choose Roemer.

STUDY FOR TOMORROWS TEST ON POLYNOMIALS.

Homework.

Homework
-Mangahigh
-Read page 190-195
-CYU #1-3
-Practise #5-15
-Apply odd or even
-Extend any 3
-5.3 extra practise
-5.3 homework book
-Definition decoder
-Green sheet 7.3

Test on Monday or Tuesday

I choose Cathlene to do the next blog.

Anabelle's Blog Post: Equivelant Expressions

Combining Integers
Positive + positive= always positive | ex. 3 + 5= 8
Negative + Negative= always negative | ex. -4 -6= -10
Negative + Positive= will always keep the sign of the greatest absolute value | ex. -5 + 7= 12
Positive + Negative= same as negative + positive | 5 - 7= -2
________

Multiplying Integers
Positive x Positive= Positive | ex. (5)(2)=10
Negative x Negative= Positive | ex. (-2)(-3)= 6
Negative x Positive= Negative | ex. (3)(-5)= 15
Positive x Negative= Negative | ex. (-2)(4)= 8

________
Combining Like Terms


Step 1: Collect terms in order of alphabet and degree (in that order) from left to right.


Step 2: Combine and Simplify


When we combine the terms we show our work on the side like this:


________

Removing Brackets while collecting like terms
Step 1: Look at the signs in front of each bracket. If positive simply remove the bracket and keep the terms the same. (Drop the + sign.)



Step 2: Collect like terms.


Step 3: Simplify.


Here is another example:


_______

Step 1: If it is negative multiply out each term by negative and rewrite. (Like switching signs.)


Step 2: Combine like terms.


Step 3: Simplify.


Here is another example:

________

Homework:

★ Manga high
★★ Read pg. 183-186
★★ CYU #2,#4
★★ Practice odd or even
★★ Apply #13-22
★★ Extend #23-35
1/2★ pg 2 of interaction sheet
5.2 Extra Practice= If needed
5.2 homework book= If needed
★ Why did the donkey get a passport?
★Why is it good to play cards in a graveyard?

I choose Tianna to do the next blog post.