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Wiskunde

Graad 8

Heelgetalle, vergelykings en meetkunde

Module 7

Vergelykings

Die “wonderwêreld” rondom VERGELYKINGS

KLASOPDRAG 1

  • Kom ontdek stap vir stap meer omtrent ... wat is ’n vergelyking, en hoe om dit op te los.

1. Wat verstaan jy onder die term: “vergelyking” ?

2. Wat verstaan jy onder die term: “inspeksie”?

3. Wat beteken dit as ons sê “los die vergelyking op” ?

4. Gee ’n voorbeeld van ’n vergelyking.

5. Los nou die vergelyking in (4) op.

(Laat jou onderwyser jou help).

6. Los nou elk van die volgende vergelykings deur inspeksie, op.(m.a.w. bepaal die waarde van a)

6.1 1 - a = 7

6.2 5 a = 50

6.3 a /7 = 6

6.4 66/ a = 6

6.5 - a /2 = 15

6.6 5 a - 4 = 26

7. Hoe los jy ’n vergelyking op (nie deur inspeksie nie)

7.1 Hier is ’n paar wenke:

2a + 6 = -5 a - 9

Stap 1: Kry al die onbekendes (in die geval “ a ”) aan die linkerkant van die “=” teken.

Stap 2: Kry al die konstantes aan die regterkant van die “=” teken.

Stap 3: Tel gelyksoortige terme bymekaar.

Stap 4: Kry onbekende alleen (deur te × of te ÷ met koëffisiënt van onbekende)

Stap 1:

+5 a (moet aan anderkant dieselfde doen) +5 a (om van “ a ’s” ontslae te raak)

2 a + 6 = -5 a - 9

Nou lyk dit so: 2 a + 5 a + 6 = -9

Stap 2:

-6 (om van +6 ontslae te raak) -6 (moet aan anderkant dieselfde doen)

2 a + 5 a + 6 = -9

Nou lyk dit so: 2 a + 5 a = -9 - 6

Stap 3: Tel die soorte bymekaar

7 a = -15

Stap 4: Kry “ a ” alleen: ÷ 7 links en regs van “=” teken

7a 7 size 12{ { {"7a"} over {7} } } {} = -15 7 size 12{ { {"-15"} over {7} } } {}

a = 2 1 7 size 12{ - 2 { { size 8{1} } over { size 8{7} } } } {}

7.2 Wat van ?: a / 3 = 7

a / 3 = 7 / 1 (vermenigvuldig nou oorkruis)

a x 1 = 7 x 3

a = 21

7.3 Onthou indien hakies voorkom, moet die hakies eers verwyder word.bv.

2(2 a - 6) + 7 = 9 a - 3( a - 2)

4 a - 12 + 7 = 9 a - 3 a + 6

4 a - 3 a - 9 a = 6 - 7 + 12

-8 a = 11

a = 11 / -8

a = - 1 3 / 8

8. Doen jy nou die volgende: Los die volgende vergelykings op.

8.1 5 - 3(4 - a ) = 5( a + 1) + 2

8.2 2 a - 24 = 3 a

8.3 a / 4 + 5 = 10 (wenk: breuke en oorkruisvermenigvuldiging)

8.4 5 a - 3 a - 7 = 9

8.5 -8 a = 72

8.6 3² + 3 a + 3 = 2 3 + 4(-2 a )

8.7 -12 / a = -24

8.8 5(2 a + 1) = 4(2 a + 3)

8.9 -2(3 a - 3) = 6 a + 24

8.10 Stel enige vergelyking van jou keuse op en los dit dan op.

Voorwaardes: dit moet hakies bevat, breuke en negatiewe getalle.

KLASOPDRAG 2

  • Kom ontdek stap vir stap meer omtrent ... die oplos van woordprobleme, wat ’n fees word as jy dit as ’n vergelyking kan weergee.

Om in hierdie fees te kan deel, het jy die volgende basiese kennis nodig ......

1. Woorde soos ... meer (beteken +), minder (beteken -) en keer (beteken ×), opeenvolgende getalle (eerste getal: x , tweede getal: x + 1 en derde getal: x + 2)

1.1 Hoe sal jy drie opeenvolgende ewe getalle voorstel?

Eerste getal: …………… Tweede getal: …………… Derde getal: ……………

1.2 Hoe sal jy ’n tweesyfergetal voorstel indien die syfers onbekend is?

  • Wel, hoe sal jy 24 in uitgebreide notasie skryf: (2 x 10) + (4 x 1)
  • As daar gesê word die tiene syfer is die helfte van die ene syfer, sal jy as volg te werk gaan:

tiene ene

a 2 a (tiene syfer is helfte van ene syfer)

Dus: ( a x 10) + (2 a x 1) = 10 a + 2 a = 12 a (12 a is dan die getal)

2. Jou eerste vraag moet altyd wees: “Van watter een weet ek niks nie?”- dit word dan as (bv. x ) voorgestel, en die ander onbekendes in terme van ( x ).

3. Skryf dan ’n vergelyking neer .

Questions & Answers

anyone know any internet site where one can find nanotechnology papers?
Damian Reply
research.net
kanaga
Introduction about quantum dots in nanotechnology
Praveena Reply
what does nano mean?
Anassong Reply
nano basically means 10^(-9). nanometer is a unit to measure length.
Bharti
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
Damian Reply
absolutely yes
Daniel
how to know photocatalytic properties of tio2 nanoparticles...what to do now
Akash Reply
it is a goid question and i want to know the answer as well
Maciej
characteristics of micro business
Abigail
for teaching engĺish at school how nano technology help us
Anassong
Do somebody tell me a best nano engineering book for beginners?
s. Reply
there is no specific books for beginners but there is book called principle of nanotechnology
NANO
what is fullerene does it is used to make bukky balls
Devang Reply
are you nano engineer ?
s.
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
Tarell
what is the actual application of fullerenes nowadays?
Damian
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
Tarell
what is the Synthesis, properties,and applications of carbon nano chemistry
Abhijith Reply
Mostly, they use nano carbon for electronics and for materials to be strengthened.
Virgil
is Bucky paper clear?
CYNTHIA
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
NANO
so some one know about replacing silicon atom with phosphorous in semiconductors device?
s. Reply
Yeah, it is a pain to say the least. You basically have to heat the substarte up to around 1000 degrees celcius then pass phosphene gas over top of it, which is explosive and toxic by the way, under very low pressure.
Harper
Do you know which machine is used to that process?
s.
how to fabricate graphene ink ?
SUYASH Reply
for screen printed electrodes ?
SUYASH
What is lattice structure?
s. Reply
of graphene you mean?
Ebrahim
or in general
Ebrahim
in general
s.
Graphene has a hexagonal structure
tahir
On having this app for quite a bit time, Haven't realised there's a chat room in it.
Cied
what is biological synthesis of nanoparticles
Sanket Reply
what's the easiest and fastest way to the synthesize AgNP?
Damian Reply
China
Cied
types of nano material
abeetha Reply
I start with an easy one. carbon nanotubes woven into a long filament like a string
Porter
many many of nanotubes
Porter
what is the k.e before it land
Yasmin
what is the function of carbon nanotubes?
Cesar
I'm interested in nanotube
Uday
what is nanomaterials​ and their applications of sensors.
Ramkumar Reply
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
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Source:  OpenStax, Wiskunde graad 8. OpenStax CNX. Sep 11, 2009 Download for free at http://cnx.org/content/col11033/1.1
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