Hi cleanncrazi and thank you for asking to Google Answers!!
1)evaluate the expression if a = 9 and b = 5
6a+2b
6*a + 2*b = 6*9 + 2*5 =
= 54 + 10 =
= 64
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2) 4*(5+2)*6 = 4*(7)*6 =
= 28*6 =
= 168
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3)add
5/15+10/20
15 = 3*5
20 = 2*2*5
Least Common Denominator (LCD) = 2*2*3*5 = 60
60/15 = 4, then:
5/15 = (5*4)/60 = 20/60
60/20 = 3, then:
10/20 = (10*3)/60 = 30/60
5/15 + 10/20 = 20/60 + 30/60 = (20+30)/60 = 50/60,
simplifying:
5/15 + 10/20 = 5/6
See for reference:
"Adding Fractions with the same Denominator"
http://www.aaamath.com/B/fra57ax2.htm
"Adding Fractions with Different Denominators"
http://www.aaamath.com/fra66k-addfracud.html
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4)true or false
3*(6+2)=3*(2+8)
FALSE:
3*(6+2) = 3 *(8) = 24
3*(2+8) = 3*(10) = 30
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5)1 3/9 + 2 2/6 =
1 3/9 = 1 + 3/9 = 9/9 + 3/9 = 12/9 = 4/3
2 2/6 = 2 + 2/6 = 12/6 + 2/6 = 14/6 = 7/3
1 3/9 + 2 2/6 = 4/3 + 7/3 = (4 + 7)/3 = 11/3
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6)
-4 -(-10) - 1 = -4 + 10 -1 =
= 10 - 4 - 1 =
= 10 - (4+1) =
= 10 - 5 =
= 5
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7)r = c - 8s/5d for c
r = c - (8*s/5*d)
==> r + (8*s/5*d) = c - (8*s/5*d) + (8*s/5*d) =
= c
Then:
c = r + (8*s/5*d)
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8)a = 8*r*s - 3*k for r;
a = (8*r*s) - (3*k)
==> a + (3*k) = (8*r*s) - (3*k) + (3*k) =
= 8*r*s
==> [a + (3*k)] / 8*s = 8*r*s / 8*s =
= r
Then r = [a + (3*k)] / 8*s
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9)graph x>8
If this line represents the Real numbers:
<-------------------------I-------I-------------------->
-oo 0 8 +oo
The set of numbers x that x > 8 is represented by this line:
I (-------------------->
-oo 0 8 +oo
For additional reference see:
"Solving Inequalities":
http://www.purplemath.com/modules/ineqsolv.htm
-------------------------------------------------------------
10)graph x <= 3
If this line represents the Real numbers:
<-------------------------I--I------------------------->
-oo 0 3 +oo
The set of numbers x that x <= 3 is represented by this line:
<----------------------------]
-oo 3 +oo
------------------------------------------------------------
11)graph x>5
If this line represents the Real numbers:
<-------------------------I----I----------------------->
-oo 0 5 +oo
The set of numbers x that x > 5 is represented by this line:
(----------------------->
-oo 0 5 +oo
-------------------------------------------------------------
12)solve the inequality:
5 - 3*x > 14 ==> - 3*x > 14 - 5 = 9 ==>
==> (-3)*x > 9 ==> x < 9/(-3) = -3 ==>
==> x < -3
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13)solve for x
|x-1| = 4 ==> (x-1) = 4 or (x-1) = -4
Case 1:
x-1 = 4 ==> x = 4+1 = 5
Case 2:
x-1 = -4 ==> x = -4+1 = -3
Solution:
x=5 or x=-3
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14)true or false
-5<5
TRUE:
-5<5 <==> 0 < 5 + 5 = 10
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15)find the intercepts of the line
2*x - 3*y = 6
Recall the intercepts of a graph are where it crosses the x- and y-axes.
See for reference "x- and y-Intercepts":
http://www.purplemath.com/modules/intrcept.htm
x-intercept (y = 0):
2*x - 3*0 = 6
Then:
2*x = 6 ==> x = 6/2 = 3
==> x=3
Then the x-intercept is the point (x,y) = (3,0)
y-intercept (x = 0)
2*0 - 3*y = 6
Then:
3*y = 6 ==> y = 6/3 = 2
==> y=2
Then the y-intercept is the point (x,y) = (0,2)
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16)what does the graph looks like for
2x+2y<=6
3x-y>=3
This is a system of linear inequalities, we must solve each inequality
separately and graph wich half plane each one defines, then we must
find the overlaped area.
2*x + 2*y =< 6
Since 2*x + 2*y = 2*(x+y), then
2*(x+y) =< 6 , then
x+y =< 6 , then
y =< -x + 6
That means the graph #1 is all the area below the straigh line y = -x
+ 6 , including such line.
3*x - y >= 3 , then
3*x - 3 >= y or y =< 3x - 3
That means the graph #2 is all the area below the straigh line y = 3x
- 3 , including such line.
For additional reference and some samples to see how this solutions
looks like visit the following pages:
"Graphing Linear Inequalities":
http://www.purplemath.com/modules/ineqgrph.htm
"Systems of Linear Inequalities":
http://www.purplemath.com/modules/syslneq.htm
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17)what does the graph look like for
y>-3
x<2
Use the method described in the previous problem to solve this easier
problem (the graph looks like an "infinite rectangle" defined by the
straight lines y=-3 and x=2, more exactly these lines divides the
plane in four parts (quadrants) -each line is parallel to one main
axis- and the "infinite rectangle" is the upper left part or quadrant
defined by these lines).
Feel free to request for a clarification if the answer to this problem
does not satisfy you.
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18) 2 3/18 + 3 2/9 =
2 3/18 = 2 + 3/18 =
= 36/18 + 3/18 =
= 39/18 = 13/6
3 2/9 = 3 + 2/9 =
= 27/9 + 2/9 =
= 29/9
6 = 2*3
9 = 3*3
Least Common Denominator (LCD) = 2*3*3 = 18
Then:
2 3/18 + 3 2/9 = 13/6 + 29/9 =
= (39 + 58)/18 =
= 97/18
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19)evaluate
|6-9 to the 2nd power| = |6 - 9^2| =
= |6 - 9*9| =
= |6 - 81| =
= |-75| =
= 75
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20) on tuesday the tempature high was -9F. that night the temp dropped
another 12 degree. during the day the temp rose 14 degrees to reach
the high what was it?
Initial temp T0 = -9ºF
Then dropped 12ºF, so T1 = -9ºF - 12ºF = -21ºF;
During the day temp rose 14ºF to reach the high
T2 = -21ºF + 14ºF = -7ºF
Friday high temperature was -7ºF.
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21)If the selling price of the house, x, less the sales commission of
4% must be at least 90,000, the .96x>= 90,000
true or false?
If x is the selling price, then the 4% sales commission is:
0.04*x .
Then Selling price less sales commission is:
x - 0.04*x = 0.96*x
According to the problem statement this value is at least 90,000, so:
0.96*x >= 90,000 , so the statement is TRUE.
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22)solve 10x+[6x-(6x+3)] = -9(x-8)
10*x + [6*x -(6*x+3)] = -9*(x-8)
Then:
10*x + [6*x - 6*x - 3] = -9*x + 72
Then:
10*x + [- 3] = -9*x + 72
Then:
10*x - 3 = -9*x + 72
Then:
10*x + 9*x = 72 +3
Then:
(10+9)*x = 19*x = 75
Then:
x = 75/19
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23)solve for x
2y-2(x+3)=y-x :
2*y - 2*(x+3) = y - x
Then:
2*y - (2*x + 2*3) = y - x
Then:
2*y - (2*x +6) = y -x
Then:
2*y - 2*x - 6 = y - x
Then:
2*y - 2*x - 6 + 2*x - y = y - x + 2*x - y
Then:
2*y - y - 6 = -x + 2*x
Then:
y - 6 = x
Answer:
x = y - 6
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24)p=10rt-tk/17g for g
p = 10*r*t - t*k/17*g
Then:
p - 10*r*t = 10*r*t - t*k/17*g - 10*r*t
Then:
p - 10*r*t = - t*k/17*g
Then:
(p - 10*r*t)*g = -(t*k/17*g)*g
Then:
(p - 10*r*t)*g = -(t*k/17)
Then:
(p - 10*r*t)*g/(p - 10*r*t) = -(t*k/17)/(p - 10*r*t)
Then:
g = -(t*k/17)/(p - 10*r*t)
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25)carrie is pratcing for her SAT's. her first two pratice scores are
1250 and 1380. if she wants her average score to be between 1300 and
1400 what must the range of her third score be?
The average score of the 3 practices is:
(1250 + 1380 + x)/3 where x is the third score.
And we want that it be between 1300 and 1400, so we want:
1300 < (1250 + 1380 + x)/3 < 1400
We need to find x, we have:
1300 < (1250 + 1380 + x)/3 < 1400
Then:
1300 < (2630 + x)/3 < 1400
Then:
1300*3 = 3900 < 2630 + x < 1400*3 = 4200
Then:
3900 - 2630 < x < 4200 - 2630
Then:
1270 < x < 1570
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26)solve 14x-6=13x
14*x - 6 = 13*x
Then:
14*x - 6 - 13*x = 13*x -13*x = 0
Then:
(14*x - 13*x) - 6 = 0
Then:
x - 6 = 0
Then
x = 6 .
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27)solve for x 12(x-12)-9x=-36+3(x-36)
12*(x-12)- 9*x = -36 + 3*(x-36)
Then:
12*x - 144 - 9*x = -36 + 3*x - 3*36
Then:
(12-9)*x -144 = 3*x - 144
3*x - 144 = 3*x - 144
We have the same expression at each side of the equation, that means
the solution is valid for any value of x.
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28) A taxi charges 4.00 for the first mile and 2.00 for each
additional mile. wirte an inequality representing the number of miles
a passenger could travel if they could not spend more then 10.00.
First mile charge (fixed value): 4
From mile two to x: 2 per mile = 2*(x-1)
Total charge: y = 4 + 2*(x-1)
You want that the total charge does not be more than 10 or, in other
words, to be less or equal than 10; in symbols you want total charge y
to be:
y =< 10 , then the answer is:
4 + 2*(x-1) =< 10
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29)solve the inequality
|2x+3|<=2
|2x+3| =< 2 is thae same of:
-2 =< 2x+3 =< 2
then:
-2 - 3 =< 2x =< 2-3
then:
-5 =< 2x =< -1
then:
-5/2 =< x =< -1/2
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30)the rice town library carries 27 diffrent magazines. let L
represent the number at the lakesville library and B represent those
at the brownsville library. Write an inequality showing the
relationship between the three libraries if brownsville carries more
than 6 times the number of magazines handled by both of the other
libaries combined.
Let R represent the number at the rice town library, then:
R = 27
According to the statement:
B > 6*(R+L) = 6*(27+L) = 162 + 6*L
Then:
B > 6*(R+L)
or (because we know that R = 27)
B > 162 + 6*L
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31)find the slope and y-intercept
2x+2y = 3
To solve this problem we must know that if the linear equation is:
ax + by = c , with b different to zero,
then the slope is -(a/b) and the y-intercept is the point (0,c/b).
In this case a = b = 2 and c = 3.
Then the y-intercept is the point (x,y) = (0,3/2) ;
and the slop is -(2/2) = -1.
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32)find the slope
(-9,-6) and (-8,-9)
Given two points of a line we know that:
Slope of line = Changes Vertical/Changes Horizontal
Then:
Slope of line = [-6 - (-9)] / [-9 - (-8)]
= [-6 + 9] / [-9 + 8]
= (+3)/(-1)
= -3
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33)graph the point and slope
(2,1), m=1/2
What you need here is to find the point (2,1) in the coordinate plane,
to do that just remember that the first value of the pair is the
x-value and the second is the y-value.
From this point and using the slope value, you must find a different
point of the line to graph it.
Remember the previous problem:
m = Slope = Changes Vertical/Changes Horizontal = 1/2 ;
Yes, as you are guessing the value m = 1/2 means that for each change
of 1 in the vertical direction there is a change of 2 in the
horizontal direction, so another point is easy to find by "moving"
from the point (2,1) one unit in the positive vertical direction and
two units in the positive horizontal direction, that is from (2,1) to
(2+2,1+1) = (4,2).
Now we have two points, then a straight line can by draw.
Other way is using the "slope-intercept" equation form:
We have the point (2,1), and we know that the linear equation is:
y = mx + b .
We know m and we know a pair of values for x and y that satisfies the equation:
x = 2 and y = 1 ; then we have:
1 = 1/2 * 2 + b , solving for b we have:
b = 0
So y = (1/2)*x + 0
To find another point to draw the line just give a value to x
different to the known point and use it to find the respective value
for y.
For example using 4 for x you will find y = 2, so you have found the
point (4,2) on the line, using it together with the one given in the
statement you can graph the line.
See for reference:
"Slope of a Straight Line":
http://www.purplemath.com/modules/slope.htm
"Slope-Intercept Form":
http://www.purplemath.com/modules/strtlneq.htm
"Straight-Line Equations":
http://www.purplemath.com/modules/strtlneq2.htm
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34)what is the slope intercept?
(6,24) and (10,20)
m = Changes Vertical/Changes Horizontal =
= (24-20)/(6-10) =
= 4/(-4) =
= -1
y = mx + b = -x + b
Using one of the points as data:
20 = -10 + b , solving for b:
b = 30
then y = -x + 30 is the slope intercept form of this linear equation.
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35)The graph of y=x:
a)the x axis
b)splits quadrents 1 and 3
c)is the y axis
d)splits quadrents 2 and 4
Here I guess that you need to know wich of the statements is correct.
The correct statement is b).
In the first and third quadrents x and y have the same sign, that does
not happen in the second and fourth quadrents, so in these last
quadrents the equation x=y cannot be satisfied.
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36)give the equation of the line through (-2,6) with the slope of -3/4
m = -3/4 and the pair x=-2 and y=6 satisfy the equation, then:
y = mx + b = -3/4 x + b
For x=-2 and y=6 we have:
6 = -3/4 * (-2) + b =
= 3/2 + b
Solving for b:
b = 6 - 3/2 = 12/2 - 3/2 = (12-3)/2 = 9/2
Then the equation of the line through (-2,6) with the slope of -3/4 is:
y = -3/4 x + 9/2
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37)solution set
y=9-2x and 2x-5y=15
2x-5y = 15 , since by the other equation we have that y = 9-2x , then:
15 = 2x-5y = 2x-5(9-2x) = 2x - 45 + 10x =
= 12x -45
Then:
12x = 15 + 45 = 60
Then x = 5
we had:
y = 9 - 2x = 9 - 2*5 = 9 - 10 = -1
Solution:
x = 5
y = -1
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38)solution set
3x+2y=3 and 63x-36y=11
63x-36y = 11
3x+2y = 3
From the second equation we have, solving for x:
3x + 2y = 3
Then:
3x = 3 - 2y
Then
x = (3 - 2y)/3 =
= 1 - 2/3 y
Replacing in the first equation:
11 = 63x - 36y = 63*(1 - 2/3 y) - 36y =
= 63 - 42y -36y =
= 63 - 78y
Now, solving for y:
11 = 63 - 78y
Then:
78y = 63 - 11 = 52
Then:
y = 52/78 = 26/39
then:
x = 1 - 2/3 y =
= 1 - 2/3 * 26/39 =
= 1 - 52/117 =
= 117/117 - 52/117 =
= 65/117
Solution:
x = 65/117
y = 26/39
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39)solve by substitution
x+y=2
x=4y+5
By the second equation we have:
x = 4y + 5
Replacing in the first equation:
2 = x + y = (4y + 5) + y =
= 5y + 5
Solving this for y:
5y + 5 = 2
then:
5y = 2-5 = -3
Then:
y = -3/5
Then:
x = 4y + 5
= 4 (-3/5) + 5 =
= -12/5 + 5 =
= -12/5 + 25/5 =
= (-12+25)/5 =
= 13/5
Solution:
x = 13/5
y = -3/5
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40)solve by addition
x+y=-3
x-2y=-5
Rewrite the first equation with the similar (multiplying it by 2):
2x + 2y = -6
Now we can add the second equation to the first:
2x + 2y = -6
+
x - 2y = -5
----------------
3x = -11
then x = -11/3
Replacing in the second equation:
x - 2y = -5
Then:
-11/3 - 2y = -5
then:
-2y = -5 + 11/3 = -15/3 + 11/3 = -4/3
then:
y = (-4/3)/(-2) = 2/3
Solution:
x = -11/3
y = 2/3
Additional reference for System of Linear Equations can be found at these pages:
"SYSTEMS OF EQUATIONS in TWO VARIABLES":
http://www.sosmath.com/soe/SE2001/SE2001.html
"Solving Systems of Linear Equations":
http://www.math.csusb.edu/math110/src/systems/solving.html
"Linear Algebra - System of Equations":
http://library.thinkquest.org/10030/10lsoeq.htm?tqskip1=1
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I hope this helps you. If you find something unclear or incomplete,
please request for an answer clarification before rate this answer,
due the extent of this question some typos or other little mistakes
(like misunderstanding of one problem)could happened. Also feel free
to request for further assistance is needed on graphs questions,
because is to difficult, and will give more confusion to try to draw
the graphs here. I would appreciate it if you give me a chance to
respond your requests before rate this answer if it is necessary.
Best regards.
livioflores-ga |
