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Aktiwiteit 4

Om uitdrukkings en vergelykings te onderskei

[lu 2.1, 2.6]

  • Uitdrukkings is kombinasies van letters ( a , b , х , y , ens.), bewerkings (+, –, ×, ) en getalle (1, –5, π, ½ , ens.), asook hakies en ander tekens. Dit sluit nie gelykaantekens in nie.
  • ‘n Uitdrukking is nogal soos ‘n woord of ‘n frase – dit het nie ‘n werkwoord nie.
  • ‘n Paar voorbeelde: х , х 3 , 5½ , 2πr, 5( ab bc ), 5 a 3 – 3 a 2 + a – 3, 2 a + b size 12{ sqrt {2 left (a+b right )} } {} , 5a 4 2a 2 size 12{ { {5a - 4} over {2a rSup { size 8{2} } } } } {} , ens.
  • ‘n Uitdrukking kan slegs gemanipuleer word, gewoonlik om dit te vereenvoudig. Dit kan nie opgelos word nie; dit het nie ‘n oplossing nie. Jy kan jou werk slegs kontroleer deur agteruit te werk om te sien of jy by die begin uitkom.
  • ‘n Vergelyking is doodgewoon twee uitdrukkings met ‘n gelykaanteken tussenin!
  • Dit is soos ‘n sin met ‘n werkwoord; dit maak ‘n stelling. Byvoorbeeld 2 х – 3 = 45 sê dubbel ‘n sekere getal, met drie verminder, is gelyk aan 45. Dis ons werk om daardie getal te bepaal.
  • Vergelykings word opgelos; hulle het oplossings wat bevestig kan word.
  • Ons vereenvoudig heelwat tydens die oplos van vergelykings, maar ons doen meer – ons word toegelaat om meer te doen. Onthou dat ons terme kan bytel of aftrek, as ons dit net aan beide kante doen! Ons kan met faktore deel of vermenigvuldig, as ons dit net aan beide kante doen. Omdat ‘n uitdrukking nie twee kante het nie, kan ons hierdie bewerkings nie op uitdrukkings toepas nie. Moenie uitdrukkings en vergelykings verwar nie, en oefen totdat jy instinktief weet wat om te doen.

Aktiwiteit 5

Om twee vergelykings gelyktydig op te los

[lu 2.4, 2.9]

1. Die lyn in diagram 1 het definisie-vergelyking y = 2.

Vraag: Lê die punt (1 ; 1) op die lyn?

Antwoord: Ons kan die antwoord grafies (deur die grafiek te bekyk) oplos. Dis duidelik dat die punt nie op die lyn lê nie, en dus is die antwoord nee .

Ons kan die antwoord algebraïes oplos, soos volg: Substitueer die punt (1 ; 1) vir ( х ; y ) in die vergelyking. Doen LK en RK apart soos voorheen.

LK: y = ( 1 ) = 2 RK: 2 LK ≠ RK – die punt (1 ; 1) lê nie op y = 2 nie.

Vraag: Lê die punt (–2 ; 2) op die lyn?

Grafies : Ja.

Algebraïes : LK: y = ( 2 ) = 2 RK: 2 LK = RK; Ja.

Vraag: Lê die punt (1½ ; 2) op die lyn? Bepaal die antwoord beide grafies en algebraïes .

2. Die lyn in diagram 2 word gedefinieer deur die vergelyking y = 2 х – 1.

Vrae: Lê die punt (0 ; 0) op die lyn?

Lê die punt (1 ; 1) op y = 2 х – 1?

Lê die punt (1½ ; 2) op die lyn?

3. In diagram 3 is dieselfde twee lyne saam op een stel asse getrek.

Bepaal grafies: Watter punt lê op beide lyne? Die antwoorde op vrae 1 en 2 hierbo sal help.

Dit is ooglopend uit diagram 3 dat die enigste punt op beide lyne (1½ ; 2) is.

  • So bepaal ons dit algebraïes:

Die vergelyking y = 2 gee y die waarde 2. Substitueer nou hierdie waarde in y = 2 х – 1.

As ons dan die vergelyking oplos, kry ons die waarde van х . So:

Substitueer: ( 2 ) = 2 х – 1 en los op vir х :

2 = 2 х – 1 х - terme na links

–2 х + 2 = –1 konstante terme na regs

–2 х = –2 – 1 vereenvoudig

–2 х = –3 deel beide kante deur –2

х = –3  –2 vereenvoudig

х = 1½

Dit toon die punt waar die lyne mekaar sny: ( х ; y ) = (1½ ; 2).

  • In hierdie metode het ons die twee vergelykings gelyktydig opgelos om die waardes van beide veranderlikes te vind wat beide vergelykings waar maak. As ‘n vergelyking slegs een veranderlike het, benodig ons slegs een vergelyking om daardie waarde van die veranderlike te vind wat die vergelyking waar maak. As ons twee veranderlikes het, benodig ons twee vergelykings om op te los vir die twee veranderlikes.


1 Los algebraïes op vir a en b : 2 a – 3 b = 0 en a = 6

2 Waar sny die lyne y = – х + 5 en y = –1? Bepaal die antwoord algebraïes.

3 Lê die punt (3 ; 4) op beide lyn y = 4 en lyn y = – х + 1? Doen algebraïes.

4 Sny die lyne y = –2 en y = 2? Bepaal die antwoord algebraïes.

Aktiwiteit 6

Om eenvoudige eksponiensiële vergelykings op te los

[lu 2.4, 2.8]

Probleme en sommige antwoorde.

1 Ek dink aan ‘n getal waarvan die kwadraat 100 is. Wat is die getal?

Die getal kan 10 wees, want 10 2 = 100. Maar is –10 nie ook ‘n korrekte antwoord nie?

Ja, hierdie probleem het twee geldige antwoorde!

Maak ‘n vergelyking uit hierdie stelling: Gestel die getal is х .

х 2 = 100

х 2 = 10 2 of х 2 = (–10) 2 Die hakies is noodsaaklik – sien jy dit?

х = 10 of х = –10 Beide antwoorde is geldig.

2 Ek dink aan ‘n negatiewe getal waarvan die kwadraat 25 is. Wat is dit?

Laat die getal y wees

y 2 = 25

y 2 = (5) 2 of y 2 = (–5) 2

y = 5 of y = –5 is die twee oplossings verskaf deur die vergelyking.

Die probleemstelling bevestig egter dat y = –5 die enigste geldige antwoord is.

3 Vind daardie getal wat ‘n derdemag van 27 het.

Laat die getal х wees

х 3 = 27  х 3 = 3 3 х = 3.

Hoekom kan х nie –3 wees nie?

4 Die derdemag van ‘n sekere getal is –8. Wat is die getal?

5 Los op vir х , en bevestig jou antwoord met die LK/RK metode:

a) х 2 = 64

b) х 2 = 36

c) х 2 = –100

d) х 2 – 49 = 0

e) х 2 = 12,25

f) 3 х 2 = 12

g) 2 х 2 – 10,58 = 0

6 Los op vir a en kontroleer jou antwoord:

a) a 3 = 64

b) a 3 + 1 = 0

c) 2 a 2 = 16

d) a 4 = 81

Questions & Answers

how did psychology begin?
Valerie Reply
of psychologys commencement, the traces can be seen in the work of Aristotle, where he talk about soul and body, likewise work in durrant, de anima, all these were somewhere supporting dualism, in which soul could exist separately from body
but if you talk about the moder psychology, Gustav fechner, is credited with performing scientific experiments, basis of his experiments in psychology with his studies perception.
does psychology deal with love?
Mohammed Reply
Maybe, i think
I definitely would say yes
how so
there are so many different reasons why you can fall in love with someone, many of them develope subconsciously -> psychology
love messes with the brain, a lot, ergo I believe that Psychology does indeed deal with love
what is synapse
Katie Reply
In the central nervous system, a synapse is a small gap at the end of a neuron that allows a signal to pass from one neuron to the next. synapse are found where nerve cells connect with other nerve cells
can you do auto book auto
Mariah Reply
WHT u mean?
heyy, may i join the conversation please?
edem Reply
who is the father of psychology
Richy Reply
and please, how would you guys, describe the study of psychology at college ?
psychologist student?
i mean not yet but am about to start college so wanna know how is it(college in general and psychology course) please
Psychology is the study of mind and behaviour. So if you will take psychology as a subject so you will get to know how your everything (physical, mental, social, spiritual aspects) effects your behaviour
With this brief knowledge you can help people to cope up with their problems and only you can guide them correctly
And if you go for further specialisations you can study hypnosis, face reading, body language etc
Thanks a lot🙏🏾 And ik some of the stuffs u said but i am also going to write thesis, right ?
ok no prob, thanks a lot🙏🏾✨
hae everyone, hope you are well this evning my question is what is the difference between drive and motivation
good question
drive is more like an impulse or urge and i think they both go together (drive and motivation) even if there is a slight difference
@ Michael Drive is delivered to be innate without the use of an external stimuli, motivation normally evolves an outside stimuli which may include praise, appreciate, or reward.
*believed...sorry for typo
@Reginald, can't the motivation come from the inner self?
Good question, please give an example.
can we say desire of success for example
Wilhelm Wundt is the father of psychology
Wilhem Wundt thank you for the road that you opened.
You mean who is the father of having a great educated argumentative guess? nothing is more wrong than this question. The question is you should ask yourselfs is, how sure are you abour their scientific studying? one's percieved assimilated approach to judging another person and saying they are
the biggest problem with scientific research and data is that ya you could get the same result 1000 times then it could go the other way 1000 times, but we would never know that and we did, we would still say ya but the proof is there. The only thing science proves is that humanity has
no facts about human behavior in the scientific context, but more in the trial and error.. sorry to tell you, but so far no one has proven Father of anything, thats up to you and i, judgement is bias, science is good enough lazy
cognitive development is the growing and development of the brain.
Jessy Reply
Anyone knows about Techno-fascism?
Hussein Reply
Ecofascism is a theoretical political model in which an authoritarian government would require individuals to sacrifice their own interests to the "organic whole of nature". The term is also used as a rhetorical pejorative to undermine the environmental movement.
what's the big difference between prejudice and discrimination?
Danice Reply
A prejudiced person may not act on their attitude.  Therefore, someone can be prejudiced towards a certain group but not discriminate against them.  Also, prejudice includes all three components of an attitude (affective, behavioral and cognitive), whereas discrimination just involves behavior
Nancy Lee
what is all about cognitive development?
cognitive development is the growing and development of the brain
how do you control a variable when using spss whilst running a pearsons correlation analysis?
Jessie Reply
it dependa on your study. according to what you want to say and explain your result
why does it say her and she
Jayla Reply
stages of cognitive development
brivia Reply
sensory preoperatinal concrete formal
what is psychology
Chethani Reply
the study of insecurities and the effect on the host .
Psychology is the scientific study of behavior & mental processes
psychology is science about learning human behaviour
In thinking about the case of Candace described earlier, do you think that Candace benefitted or suffered as a result of consistently being passed on to the next grade?
Nene Reply
what is reward
Angeles Reply
reward is a technique to change behaviour
Reward is a way to promote a specific behaviour or to teach someone/ something to behave a specific way or perform a specific task.
a reward is something that is usually associated with desirable behavior. The child got a reward for winning the game. A reinforcer is different in that a reinforcer is anything that increases behavior, even if it is increasing an undesirable behavior.
reward is earned effort realized
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Source:  OpenStax, Wiskunde graad 9. OpenStax CNX. Sep 14, 2009 Download for free at http://cnx.org/content/col11055/1.1
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