Need Math grade 10! Help. Complement and Synthesis.

cluelessinmath · 2010-01-11 16:06:58

1. Solve the following system of equations.
Round off to the nearest tenth. Show work in algebraic solution.

y = - x2(squared) - 6x - 5

y = 3/4x + 6.5

2. A parabolic mirror is represented in the system, where the units are measured in centimetres.
The parabola passes through point(10 , 9.625) and its vertex is point(25,4).

At what distance from the y axis does the light ray strike the parabolic mirror?
Round off to the nearest unit. Show Work!

http://i206.photobucket.com/albums/bb308/missy_me420/math02.jpg

The links are pictures or in this case (drawings) of the problems in accordance to the number(just copy and paste in new tab).

These are the pre-test questions I received. I can honestly tell you any help and answer would help out alot. I do not know where I made my mistakes as our teacher does not show us our results. So in this case I failed horribly as to the mark I received. I have in total 13 questions, in order to prep my self for the exam properly. So if there is any enthusiasts out there who can solve these problems and take on the challenge to answer the other 11 questions. Then you will save my life since this is my last book in order to finish sec 4 math or grade 10 math in this case.

The book is called Complement and Synthesis 1. It is a mixture of Parabolas, functions, geometry. Basically a summary of grade 10 math. In case if you never heard of it, it is only given out in adult education.

Thank you all in advance! Hope I can get some help out there.

bobbym · 2010-01-11 16:20:07

Hi cluelessinmath;

y = - x2(squared) - 6x - 5
y = 3/4x + 6.5

For number 1:

Now use the quadratic formula from here. This will give you the 2 x values. Then just plug them into the original equations to get the y's.

cluelessinmath wrote:

I do not know where I made my mistakes

If you would provide some of what you did, then I could maybe get you on the right track.

cluelessinmath · 2010-01-12 02:18:54

1.Thank you. I now know where I made my mistake with this number. I mixed up the positive with the negatives.

2. I was lost on this one. I didn't get the chance to do it because I couldn't figure it out. Could you please help with that one as well?

Thank you again Bobbym it is very nice of you to answer so quickly, much appreciated.

bobbym · 2010-01-12 04:30:56

Hi;

cluelessinmath wrote:

2. A parabolic mirror is represented in the system, where the units are measured in centimetres.
The parabola passes through point(10 , 9.625) and its vertex is point(25,4).
At what distance from the y axis does the light ray strike the parabolic mirror?

I can get the equation of the parabola. But what is so special about that light ray that determines that point the drawing shows? Have you left something out or am I missing something?

cluelessinmath · 2010-01-12 05:48:44

I'm not sure but I think there was a dot on the ray on the opposite side of the ? mark. Basically the total length of this: <---?---> on the opposite side there was a dot I presume, and that was all to the best of my knowledge. That's why I had a bit of confusion going on there as well I suppose there is something missing in that drawing if not for the dot.

If you figure that out then can you help me with the next following lovely questions?

7. Calculate the area of the parallelogram shown below.
Round off to the nearest unit if necessary. Show Work!

http://i206.photobucket.com/albums/bb308/missy_me420/math07.jpg

My Answer:

distances length=d= √(x2-x1)2(squared) + (y2-y1)2(squared) <===(This whole part is square rooted)

BD=(1,4), (4,-3)
√(4,-1)2(quared) + (-3,-4)2(squared) <===(This whole part is square rooted) = √9+49= √58= 7.62

AC=(0,0), (5,1)
√(5,-0)2(squared) + (1,-0)2(squared) <===(This whole part is square rooted) = √25+1= √26= 5.1

bxh= 7.62*5.1= 38.86 cm2(square) =(Rounded off to) 38.9 cm2(square)

If this is correct then please do say if it is, because a second opinion is always great,
if not then what would the right answer be?

8. Triangle ABC is formed by joining the following points:

A(-3 , 2) , B(6 , 3) , and C(-1 , -1).

What is the equation of the median drawn from vertex C? Show Work!

http://i206.photobucket.com/albums/bb308/missy_me420/math08.jpg

My Answer:

a. slope of AB= m= -3-2/6-(-3)= -5/9

b. slope of m2(squared)= (-1)/-5/9= 9/5

9/5= (y-(-1))/x-(-1)= 5y+5= 9x+9= y=(9x+4)/5

If this is correct then please do say if it is, because a second opinion is always great,
if not then what would the right answer be?

9. A quadrilateral is formed by joining the following points:

A(3 , 5) , B(7 , -5) , C(2 , -10) , and D(-8 , -6).

Using the formulas and principles related to the slopes and measures of the line segments
show that this quadrilateral is an isosceles trapezoid. Show Work!

http://i206.photobucket.com/albums/bb308/missy_me420/math09.jpg

My Answer:

slope of AB= (3,5), (7,-5)
m= (-5-5)/7-3= -10/4= -5/2

slope of BC= (7,-5), (2,-10)
m= (-10-(-5))/2-7= -5/-5= 1

slope of CD= (2,-10), (-8,-6)
m= (-6-(-10))/-8-2= 4/-10= -2/5

slope of DA= (-8,-6), (3,5)
m= (5-(-6))/3-(-8)= 11/11= 1

distances= AB/CD= √(7-3)2(squared) + (-5-5)= √16+100= 10.77
√(-8-2)2(squared) + (-6-(-10))2(squared)= √100+16= 10.77

The segment AB, CD are the same in length and segment BC, DA are parallel.

If this is correct then please do say if it is, because a second opinion is always great,
if not then what would the right answer be?

Thank you in advance, and I appreciate the effort and time you put in to helping out.

bobbym · 2010-01-12 09:00:04

Hi;

For #7 I am not getting your answer.

cluelessinmath · 2010-01-12 09:36:12

So is #2 solvable?

#7 it's pretty simple I calculated the area of the parallelogram. which in the end I rounded it off to 38.9 cm2(squared)

for #8 is my answer correct?

for #9 is my answer correct?

Thank you, I will be waiting for your reply.

bobbym · 2010-01-12 10:00:36

Hi;

I would need a bit more for #2, but maybe someone else can get it. I might be missing something.

Let's look at #7 first, Your answer is not correct. Let's start there.

cluelessinmath · 2010-01-12 10:36:08

OK! So let's start at #7 then. Well since your saying that it's incorrect, then I guess I'm as lost as ever. So hopefully you can come up with a proper and detailed answer. Take your time, and thanks again.

bobbym · 2010-01-12 10:58:35

Hi;

Do it like this; The Quadrilateral is labeled ABCD , treat it as two triangles, ABC and ADC

The formula for the area of a triangle when 3 points are given is:

So lets work this out for ΔABC

(x1, y1) = (0,0)
(x2, y2) = (1,4)
(x3, y3) = (5,1)

So 19 / 2 is the area of the first triangle. Can you find the area of Δ ADC ?

cluelessinmath · 2010-01-12 11:23:10

To be honest I never seen this formula in my textbooks. And I'm pretty sure they wanted me to use the distance formula to solve this equation. Isn't the formula for a parallelogram b(Base)*(multiplied)by h(Height)?

bobbym · 2010-01-12 11:30:00

And you know that this quadrilateral is a parallelogram?

cluelessinmath · 2010-01-12 11:35:09

Yes, it's even stated in the problem.

bobbym · 2010-01-12 11:39:25

Yes, it is, but you made some kind of error in your calculations there, when you add up the 2 triangles by this method you would see the correct answer and know you made some mistake. One method checks the other.

cluelessinmath · 2010-01-12 14:08:54

Ok, I sort of get it, your formula is quite useful! From what I understand the area of the parallelogram is 19, since the area of one triangle is 19/2 all I have to is multiply it by two for the area of the parallelogram.
Thank you for the help!

cluelessinmath · 2010-01-12 14:13:07

OK! So #7 is complete.

So now I'm ready to move onto #8.

8. Triangle ABC is formed by joining the following points:

A(-3 , 2) , B(6 , 3) , and C(-1 , -1).

What is the equation of the median drawn from vertex C? Show Work!

http://i206.photobucket.com/albums/bb308/missy_me420/math08.jpg

My Answer:

a. slope of AB= m= -3-2/6-(-3)= -5/9

b. slope of m2(squared)= (-1)/-5/9= 9/5

9/5= (y-(-1))/x-(-1)= 5y+5= 9x+9= y=(9x+4)/5

If this is correct then please do say if it is, because a second opinion is always great,
if not then what would the right answer be?

bobbym · 2010-01-12 14:25:07

Hi cluelessinmath;

Just one second, did you figure out what mistake you made on #7? Can you tell me why your #7 did not work? Do that now while I work on #8.

cluelessinmath · 2010-01-12 14:42:38

Well to be honest the formula I used for somewhat reason did not give me the right answer and I used yours and it gave me a more simple and logical answer. There is only one thing that only puzzles me about #7 , because it says in the problem to round it off to the nearest tenth and with your formula it comes out to a full number? Usually they would wright that down in the problem.

cluelessinmath · 2010-01-12 14:48:16

Usually they *wouldn't wright that down in the problem.

bobbym · 2010-01-12 14:48:55

Actually for #7 you didn't take the right sides, instead of BD you were supposed to use BC.

On this #8 you have an error. the diagram shows B as (6 , -3) but your problem above says B is (6,3)

cluelessinmath · 2010-01-12 14:54:16

I'm very sorry I made a mistake it is (6,-3) I must of forgot to input the -(minus)

bobbym · 2010-01-12 14:56:00

Do you know what a median is?

BD in the above drawing is a median.

Whomever did your drawing does not know what a median is. The way you solved #8 also shows that you do not know what a median is. You solved it by saying that the slope of the median is the negative reciprocal of line AB. This is not true as my picture shows.

cluelessinmath · 2010-01-12 15:31:50

Thank you very much I just noticed the big mistake that I have made. So since it's a median I have to find the bisector of AB and connect it with vertex C ? Once this is done could I use the formula, slope= (y2-y1)/(x2-x1) and from there on proceeding to find the equation? Unless you have a faster method or better technique.

bobbym · 2010-01-12 15:36:51

Hi;

You won't need the slope, once you find the midpoint of AB, you will have point C and the the midpoint of AB that is all you need to get the equation of the median. Remember 2 points determine a straight line.

cluelessinmath · 2010-01-12 15:57:48

Thank you. I understand it now, I will re-do it tomorrow morning, and once I get the chance I will post my answer so that you can verify it.

Before I leave I just want to find out if #9 is as awful as #8 that I failed to do because of minor mistake that I did not take into consideration.

9. A quadrilateral is formed by joining the following points:

A(3 , 5) , B(7 , -5) , C(2 , -10) , and D(-8 , -6).

Using the formulas and principles related to the slopes and measures of the line segments
show that this quadrilateral is an isosceles trapezoid. Show Work!

http://i206.photobucket.com/albums/bb308/missy_me420/math09.jpg

My Answer:

slope of AB= (3,5), (7,-5)
m= (-5-5)/7-3= -10/4= -5/2

slope of BC= (7,-5), (2,-10)
m= (-10-(-5))/2-7= -5/-5= 1

slope of CD= (2,-10), (-8,-6)
m= (-6-(-10))/-8-2= 4/-10= -2/5

slope of DA= (-8,-6), (3,5)
m= (5-(-6))/3-(-8)= 11/11= 1

distances= AB/CD= √(7-3)2(squared) + (-5-5)= √16+100= 10.77
√(-8-2)2(squared) + (-6-(-10))2(squared)= √100+16= 10.77

The segment AB, CD are the same in length and segment BC, DA are parallel.

If this is correct then please do say if it is, because a second opinion is always great,
if not then what would the right answer be?

After this # I will leave you alone for tonight, since you helped me out a lot for today. And start fresh off tomorrow with some more numbers for you to verify. And then I guess I should be ready to ace this puppy afterwords once I get your insight and finalize this horrendous test that I failed at.

Math Is Fun Forum

#1 2010-01-11 16:06:58

Need Math grade 10! Help. Complement and Synthesis.

#2 2010-01-11 16:20:07

Re: Need Math grade 10! Help. Complement and Synthesis.

#3 2010-01-12 02:18:54

Re: Need Math grade 10! Help. Complement and Synthesis.

#4 2010-01-12 04:30:56

Re: Need Math grade 10! Help. Complement and Synthesis.

#5 2010-01-12 05:48:44

Re: Need Math grade 10! Help. Complement and Synthesis.

#6 2010-01-12 09:00:04

Re: Need Math grade 10! Help. Complement and Synthesis.

#7 2010-01-12 09:36:12

Re: Need Math grade 10! Help. Complement and Synthesis.

#8 2010-01-12 10:00:36

Re: Need Math grade 10! Help. Complement and Synthesis.

#9 2010-01-12 10:36:08

Re: Need Math grade 10! Help. Complement and Synthesis.

#10 2010-01-12 10:58:35

Re: Need Math grade 10! Help. Complement and Synthesis.

#11 2010-01-12 11:23:10

Re: Need Math grade 10! Help. Complement and Synthesis.

#12 2010-01-12 11:30:00

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#13 2010-01-12 11:35:09

Re: Need Math grade 10! Help. Complement and Synthesis.

#14 2010-01-12 11:39:25

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#15 2010-01-12 14:08:54

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#16 2010-01-12 14:13:07

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#17 2010-01-12 14:25:07

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#18 2010-01-12 14:42:38

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#19 2010-01-12 14:48:16

Re: Need Math grade 10! Help. Complement and Synthesis.

#20 2010-01-12 14:48:55

Re: Need Math grade 10! Help. Complement and Synthesis.

#21 2010-01-12 14:54:16

Re: Need Math grade 10! Help. Complement and Synthesis.

#22 2010-01-12 14:56:00

Re: Need Math grade 10! Help. Complement and Synthesis.

#23 2010-01-12 15:31:50

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#24 2010-01-12 15:36:51

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#25 2010-01-12 15:57:48

Re: Need Math grade 10! Help. Complement and Synthesis.

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