chronicle
│x – 5│ = 3
a. x = 8 and x = 2
b. x = 8 and x = –2
c. x = 8
d. x = 2
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seidi.yamauti
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if |x-5| >0 , then x-5=3
if |x-5| <0, then -x-(-5)=3;
-x+5=3
seidi.yamauti
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since x is a variable, you can't say |x-5| is > or < than 0, so you must consider both cases
(unless the question tells you if it is < or >)
chronicle
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d?
seidi.yamauti
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not d
chronicle
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ohh a?
seidi.yamauti
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haha right. It's a
chronicle
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seidi.yamauti
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linear function means the graph will be a straight line
so, if you take the same deltax for diferent x's, there should be the same deltay in both cases
I guess it's a bit confuse - sorry I can't explain the right way cause my english is poor...
seidi.yamauti
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like if you pick up x1=1, y1=1 & x2=2, y2=-3
for any other deltax = x2-x1 = 1, there should be the same deltay = y2=y1 = -4
chronicle
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i suppose its not ?
seidi.yamauti
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it is!
plot the graph and you will see. Every point (x,y) is in an unique line
chronicle
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oooh haha thanks
seidi.yamauti
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|dw:1358481474606:dw|
chronicle
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Tell whether the sequence is arithmetic. If it is, what is the common difference?
–12, –7, –2, 3, . . . (1 point)
yes; 5
yes; 8
yes; 3
no
seidi.yamauti
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and you can even write the function, which is y=5-4x
chronicle
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that one is yes; 5 ?
seidi.yamauti
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right
chronicle
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For the data in the table, does y vary directly with x? If it does, write an equation for the direct variation.
x y
3 6
6 18
8 24
(1 point)
yes; y = 2x
yes; y = 3x
yes; y = 4x
no; y does not vary directly with x
chronicle
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d?
seidi.yamauti
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in this case, any member of the sequence is given by An= -12 + 5n
seidi.yamauti
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hahaha, calm down!
chronicle
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haha mybad
seidi.yamauti
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well, that's the same as the other
seidi.yamauti
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actually, it is yes
chronicle
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The table shows the height of a tree as it grows. What equation in slope-intercept form gives the tree's height at any time?
Time
(months) Height
(inches)
2 14
4 23
6 32
8 41
y = 9x + 2
y = 9/2x + 5
y = 9/2x
y = 5x + 9/2
seidi.yamauti
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(by the way, the previous one is d, sorry)
chronicle
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i know, thank you
seidi.yamauti
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you need to find the slope
which is deltay/deltax
seidi.yamauti
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y=ax+b
a is the slope
once you find it, just put any value for y from the tableand you get b
chronicle
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Write y = –2/5x – 3 in standard form using integers.
2x + 5y = –15
2x + y = –3
2x + 5y = –3
x + y = –15
seidi.yamauti
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it is (-2/5)x , right?
chronicle
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yep
seidi.yamauti
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just multiply everything by 5
chronicle
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c?
chronicle
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no a ! haha
seidi.yamauti
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yes
chronicle
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thanks your helping so much
chronicle
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Write the equation of a line that is perpendicular to the given line and that passes through the given point.
y = –1/3x + 5; (4, 3)
y = –3x + 15
y = 3x – 9
y = –4x + 3
y = –1/3x – 11
seidi.yamauti
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you're welcome :)
seidi.yamauti
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aaaaaa, I forgot the rule
seidi.yamauti
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to be perpendicular, the multiplication of the slopes' values must be -1, is it right?
seidi.yamauti
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the equation you need to find is y=ax+b
a.(-1/3) = ?
then substitute (4;3)
seidi.yamauti
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ah, the slope2 of a perpendicular line is -1/slope1
seidi.yamauti
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a1 the slope of a line
a2 the slope of a perpendicular line
then a2= -1/a1
or a1.a2=-1
chronicle
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hmm C?
seidi.yamauti
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yes
chronicle
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What is the solution of the system?
y = x – 14
y = –4x + 11
(5, –9)
1 over 5 and – (69 over 5)
5 over 3 and – (37 over 3)
– (3 over 5) and – (73 over 5)
seidi.yamauti
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subtracting the first by the second, you have 0=5x-25
this gives you x=5
seidi.yamauti
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substitue x in any of the equations and you find y
chronicle
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im confused
chronicle
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idk where 0=5x-25 is from :/
seidi.yamauti
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y=x-14
y=-4x+11 (minus)
_____________
0=x-(-4x)-14-11
seidi.yamauti
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or
since y=y, then x-14=-4x+11
chronicle
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d?
seidi.yamauti
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no, it's a, the simplest
chronicle
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ohh lol
seidi.yamauti
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haha
chronicle
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Bradley and Ryan are having a contest to see who can collect the most bumper stickers. Bradley started with 23 bumper stickers and plans to add 4 each month. Ryan has 9 bumper stickers and plans to add 6 each month. After how many months will they have the same number of bumper stickers? (1 point)
10 months
2 months
7 months
51 months
seidi.yamauti
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a way to solve it is writing the equations of stickers collected by each of them
seidi.yamauti
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being m = months, then
Bradley: Stickers=23+4m
Ryan: Stickers=9+6m
seidi.yamauti
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it means BRadley has 23 stickers and owns 4more each month
and Ryan has 9 stickers and owns 6 more each month
chronicle
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b.2 months?
seidi.yamauti
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it is the same as the previous, and you can just write
y=23+4x
y=9+6x
you want to know x
seidi.yamauti
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not b
chronicle
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hmm
seidi.yamauti
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in this case, you don't want to know y
seidi.yamauti
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either, you could substitute the options in the formulas and see if they give the same number
chronicle
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i dont know :(
seidi.yamauti
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Sure you know!
Bradley: [number of stickers]=23+4x
Ryan: [number of stickers]=9+6x
seidi.yamauti
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if you call number of stickers as 'y'
then you see that y MUST be the same in both equations
seidi.yamauti
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and so the right hand sides of the equations
seidi.yamauti
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so 23+4x=9+6x
and you just need to find x
seidi.yamauti
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the secret in this question is to transform words in equations, once you done that, you solve matematicaly (?)
chronicle
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7months!
seidi.yamauti
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yes! haha
chronicle
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haha thank you thank you
seidi.yamauti
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oh well, there's any other problem?
I must go soon :P
chronicle
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k last one How many solutions does the system have?
12y = –3x + 20
y = –1/4x + 5/3 (1 point)
one
two
infinite
none
i think its infinite?
seidi.yamauti
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let's see
seidi.yamauti
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You are right
seidi.yamauti
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but look at the system and you will see one is the same as the other
seidi.yamauti
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one equation is the same as the other
seidi.yamauti
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so you can't find just one value for (x,y)
any x value gives an right y value
seidi.yamauti
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multiply the second by 12, and you will end up with 2 equal equations
chronicle
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oohh so its B?
seidi.yamauti
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no, it is infinite, as you said
chronicle
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i see
seidi.yamauti
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you have 1 equation and 2 variables
seidi.yamauti
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any given value of x will result in a y
or any y will result in a x
seidi.yamauti
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all of then right
chronicle
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What is the slope of the line that passes through the pair of points?
(5, 7), (2, 1)
8/7
2
–8/7
1/2
seidi.yamauti
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deltay/deltax
chronicle
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i still have to graph some questions but i will let you know
seidi.yamauti
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if you are not in a hurry, i can answer as soon as i come back
chronicle
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k im not in a hurry
seidi.yamauti
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(7-1)/(2-5) or (1-7)/(5-2)
You just need to use the correspondent positions to x's and y's values
seidi.yamauti
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like (y2-y1)/(x2-x1) or (y1-y2)/(x1-x2)
but not (y2-y1)/(x1-x2) or (y1-y2)/(x2-x1)
seidi.yamauti
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any other question, message me :)
bye!
chronicle
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thank u