Checking equations

When checking the equation, all you have to do is take the answer you get after solving the equation and substitute the X with the answer you got and resolve the equation from the beginning.

example: -3x - 5 = -20 ~original equation
+5 +5
---------------
-3x = -15
-- --
-3 -3
---------------
1x = 5 Check~ -3(5) - 5 = -20
-15 - 5 = -20
-20 = -20

Today in class we learned how to solve equations.

An equation states that two quantities are equal.

*Make sure that when you write a equation you define the variables.*

An example of an equation is:

D=5T

D= distance in miles

T= time or number of hours

So if you traveled for 3 hours you would have traveled 15 miles because t=3 and 3*5 equals 15 so you would have traveled for 15 miles in 2 hours.

There is also another kind of equation.

When solving this equation think of maintaining equality, which means keeping something balanced on both sides.

For example if the equation was 85=70+15 and you wanted to make both side 70 you would subtract 15 from 85 and another 15 from 85 (because 70+15= 85-15=70). They now equal 70 on both sides of the equal sign.

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today we started working on 4.2 I think and we did a,b and d we did c yestarday

1 teaspoon X teaspoons
________ _________
10 pounds 7 pounds

7 pounds/10 pounds= .7 teaspoons

how to do it ? : well you divide 10 and 7 and you get 0.7 so you would do the same for the top but opposite. so you would multiply 1 and 0.7 and get 0.7 . so as you see x=0.7.
its very easy once you know how to do them.

^

from Victoria

this is how to solve proportions

Making Sense of Proportions

In class today we did Investigation 4 on pg.48.
The problems help you understand proportions.
PROPORTION- an equation that states two ratios are equal.

• Calculators(money)- You can buy 20 calculators for $1,000. How many can be purchased for $1,250? To answer this you would... take the $1,000 and divide it by the 20 calculators. In turn you would get $50 as the price for 1 calculator. Then you would take the $1,250 and divide it by $50 (the price for one calculator) to find out how many calculators you can buy with the $1,250.
• Similar Figures(shape length)- The scale factor between two similar figures is 2. One side of the larger figure is 10cm. long. How long is the corresponding side of the smaller figure? To answer this you would... make two shapes, one big one small. On the larger shape write 10cm. and on the smaller shape write Xcm. You know, by the information given in the question, that the scale from Xcm. to 10cm. is 2. So you just have to find the scale from 10cm. to Xcm. to find the length of X.
• Country Music(percent)- Country music makes up 20% of American radio stations. There are about 10,600 radio stations in the United States. About how many stations focus on country music? To answer this you would... make the 20.% into a decimal by carrying the decimal place two places over to the left(.20). Then you would take 10,600 radio stations and multiply it by .20 and get 2,120(the number of radio stations that focus on country music).
• Doctors(ratio)- Among American doctors, males outnumber females by a ratio of 15 to 4. If about 450,000 doctors are males, about how many are females? To answer this you would... take the 15 male doctors from the ratio and divide them by the 450,000 male doctors from the question. In turn you would get 30,000(the scale factor between the ratio number and the question number). Then you would take the 4 female doctors from the ratio and multiply them by the scale factor of 30,000, to get the answering number of female doctors which is 120,000.

Each of these problems can be solved in several ways.

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Today in class we worked on problems that was all about rates and rate tables. The content of the problem was calculators and comparing their prices and also how many calculators you could but with a certain amount of money. There was three different types of calculators each with different jobs and prices. The table had: fraction calculator 1calculator = $6

scientific calculator 1calculator = $16

graphing calculator 1calculator = $80

The chart however did not tell us how much each calculator coast. What the chart read numbers 1,2,3,4,5,10,15,20. The price for every 20 calculators was $120, when you divide 120 by 20 you get 6, so 1 calculator = $6. For every calculator you must go through the same process. The scientific calculator gave the information for every 15 calculators you have it coasts $240, 240/15=16 so for each calculator its coasts $16. Finally for the graphing calculator for every 10 calculators you but it coasts $800, 800/15=53.333 repeating which you must round down to 50 calculators.

For the rest of the problems B-F you use the same exact methods you use as before in the chart.

Shapes

Today we used a bunch of different shapes and made the larger shapes out of the smaller shape. We found the perimeter and the area of each shape. Every group had a different shape to figure put the area and the perimeter. So all of our shapes in the end will have different areas, perimeters, scale factor, and side lengths. And also for some shapes you cant make the 1st larger or even the 2nd larger shape depending on the actual shape.

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Today in class we wrapped up the rubber stretch by having a dicussion on what stays the same and what is different. Then we talked about corrosponding angles and sides and learned that they must be the same to be corrosponding. We put the vocab definition of corrosponding in the vocabulary section of our binders.

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What we did was use the gemotres sketch pad to do the rubber band trace. if you move the ancor down the figure gets bigger. without adjusting just traceing it than it is 2x the size same angles and shape.

Today we learned how to find the area and the perimeter of a rectangle. To find the perimeter it is b+hx2. Another way you could do this is b+b+h+h. Then you will get the answer for perimeter but have to label it with the unit.

To find the area of the rectangle all you need to for is b x h. This will tell you the cubed space. To label this you need to put a 2 to show squared at the end of your answer.

Notes 12-1-09

Prime numbers are only divisable by one and itself.
Composite nimbers are divisable by more than two factors.

Prim Factorization= A composite number written as the product of its prim factors.

An easy way to find the (GCF) is to use the latter method. All you do is divid a prime factor by two until you get to a prime number. Then you take the same numbers on each latter and multiply them together to get the (GCF).

You can also use a vendiagram. You put one of the prime factors on one saide and the other on the other side. Then u use the latter method to find numbers that both prime factors have in common. Then you multiply the numbers that are the same to get the (GCF).