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Recent problems solved by 'kkasko'

kkasko answered: 46 problems
Jump to solutions: 0..29 , 30..59, >>Next

logarithm/598898: Evaluate f(x)=e^x for given x values:
(a) x=2, f(x)=
(b) x=-2, f(x)=
(c) x+3.5, f(x)=
(d) x=5/3, f(x)=
(Round to 4 decimals)
1 solutions

Answer 378716 by kkasko(46) About Me  on 2012-04-14 16:27:49 (Show Source):
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Evaluate f(x)=e^x for given x values:
press 2nd/ on the calculator to get e then press ^2=7.3891
(a) x=2, f(x)=7.3891
(b) x=-2, f(x)=.1353
(c) x+3.5, f(x)=x+3.5=0
x=-3.5
e^-3.5=.0302
(d) x=5/3, f(x)=5.2945
(Round to 4 decimals)


Quadratic_Equations/560369: please solve this equation 64k^2+112k+49=0, thank you
1 solutions

Answer 363905 by kkasko(46) About Me  on 2012-01-21 20:00:49 (Show Source):
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please solve this equation 64k^2+112k+49=0, thank you
Plug into the quadratic formula x=%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac%29%29%2F%282%2Aa%29
k=-112+%2B-+sqrt%28+112%5E2-4%2A64%2A49%29%2F%282%2A64%29
k=-112+%2B-+sqrt%28+12544-12544%29%2F%28128%29
k=-112+%2B-+sqrt%280%29%2F%28128%29
Simplify -112/128 by dividing the numerator -112 and denominator 128 by 16
k=%28-7+%2B-+sqrt%280%29%2F%288
Since the discriminant is zero. The equation will have 2 equal roots. Where only one root shows.
k=%28-7+%2B-+sqrt%280%29%2F%288
k=-.875 Math Fract =-7/8
k=-7/8 k=-7/8



Expressions-with-variables/560403: 6(x-2)=8(2x+3)
1 solutions

Answer 363892 by kkasko(46) About Me  on 2012-01-21 19:37:02 (Show Source):
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6(x-2)=8(2x+3)
Step 1:multiply what is out of the brackets by what is in the brackets.
6(x-2)=8(2x+3)
6x-12=16x+24
Step 2: get x one one side and the integers on the other by doing the inverse of the interger or the variable.
6x-12=16x+24
-6x -24. -6x. -24
-12-24=16x-6x
Step: 3 subtract -12-24=-36 and 16x-6x =10x
Step 4: isolate the variable by dividing by the integer for instance 10 in this case
-36=10x
/10./10
x=-3.6


Linear-systems/560397: 3x+5=x+15
1 solutions

Answer 363864 by kkasko(46) About Me  on 2012-01-21 16:00:22 (Show Source):
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3x+5=x+15
move the x values and the numbers to opposite sides. by subtracting x on both sides of the equation
Step 2: subract the x values
Step 3: subtract the numbers
Step 4: Divide
3x+5=x+15-5
-x-5 -x
3x-x=15-5
2x=10
/2 /2
x=5


Sequences-and-series/560377: what is the next number in the arithmetic sequence 3, 11, 19, 29
1 solutions

Answer 363863 by kkasko(46) About Me  on 2012-01-21 15:50:44 (Show Source):
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what is the next number in the arithmetic sequence 3, 11, 19, 29...
Are you sure the 29 is not supposed to be 27?
3+8=11+8=19+8=27
To solve you should first find the common difference.
d=t4-t3
d=27-19
d=8
plug it into the formula tn=t1+(n-1)d
t5=3+(5-1)8
t5=3+4(8)
t5=3+32
t5=32
3,11,19,27,32...


expressions/560365: 2(x+2y)-(x+3y)
1 solutions

Answer 363861 by kkasko(46) About Me  on 2012-01-21 15:32:46 (Show Source):
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2(x+2y)-(x+3y)
2x+4y-x-3y
x-y


Quadratic_Equations/560000: what is the table of values for the following equation 12x + -2y = -34
1 solutions

Answer 363647 by kkasko(46) About Me  on 2012-01-20 13:07:31 (Show Source):
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what is the table of values for the following equation 12x + -2y = -34?
Step 1: Solve for y
12x+-2y=-34
-12x -12x
-2y=-12x-34
/-2 /-2 /-2
y=6x+17
step 2: Create a chart x|y
put possible x values such as 0,1,2,3,4,5,6... in for x for instance
y=6(0)+17
y=0+17
y=17
y=6(1)+17
y=6+17
y=23
y=6(2)+17
y=12+17
y=29
x|y
0|17
1|23
2|29
3|35
4|41
5|47
6|53


Linear_Algebra/558769: -4x+4y=12 solve for y
1 solutions

Answer 363175 by kkasko(46) About Me  on 2012-01-17 22:26:10 (Show Source):
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-4x+4y=12 solve for y
+4x. +4x
4y=4x+12
/4. /4. /4
y=x+3


Quadratic_Equations/558776: My example for the class to solve with an exact answer.
x^2 + 2x - 8
1 solutions

Answer 363172 by kkasko(46) About Me  on 2012-01-17 22:21:10 (Show Source):
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My example for the class to solve with an exact answer.
x^2 + 2x - 8. _+_=2 _x_=-8
x^2+4x-2x-8
x(x+4)-2(x+4)
(x-2)(x+4)
x-2=0 x+4
x=2. x=-4


Expressions-with-variables/558779: I cannot figure this out at all! I have tried and tried. Please help! Thanks!!
When a number is decreased by 20% of itself the result is 32. What is the number???
1 solutions

Answer 363166 by kkasko(46) About Me  on 2012-01-17 22:13:12 (Show Source):


Graphs/557727: find the slope of y=+5-7
1 solutions

Answer 362744 by kkasko(46) About Me  on 2012-01-15 22:52:47 (Show Source):
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Do u mean y=5x-7
The slope is 5


Money_Word_Problems/556680: an item is $55 with a 20% discount and 5% sales tax,what is the total cost
1 solutions

Answer 362210 by kkasko(46) About Me  on 2012-01-12 21:28:04 (Show Source):
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an item is $55 with a 20% discount and 5% sales tax,what is the total cost
$55x0.20=11
$55-$11=44x0.05=$2.20
$44+$2.20=$46.20


Expressions-with-variables/556670: x+y=11
x-y=7
1 solutions

Answer 362205 by kkasko(46) About Me  on 2012-01-12 21:21:03 (Show Source):
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Step 1: Isolate for variable y
x+y=11
-x. -x
y=-x+11
x-y=7
-x. -x
-y=-x+7
Cannot have a -1 so divide by -1
y=-x/-1+7/-1
y=x-7
Step 2: draw a x and y axis
Plot the first equation at (0,11) and go down 1 right one till you have gone as far right as possible. Then from (0,11) go up 1 left 1 and go as far left as possible.
Plot the second equation at (0,-7) go up 1 right one until you have gone as far right as possible. Then from the point (0,-7) go down one left one until you have gone as far left as possible.
Step 3: the points should now connect at (9,2)


Linear-systems/555497: I need to name the slope and name one point on the line that each point-slope equation represents. This is the problem: y = 3+4(x-5)
1 solutions

Answer 361794 by kkasko(46) About Me  on 2012-01-10 21:24:25 (Show Source):
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I need to name the slope and name one point on the line that each point-slope equation represents. This is the problem: y = 3+4(x-5)
Y=3+4(x-5)
Y=3+4x-20
Y=4/1x-17
Slope= 4/1x or 4x and the point on the line or b that each equation represents is (0,-17)


Linear-systems/555475: 4x+3y=33
6x+y=25
1 solutions

Answer 361790 by kkasko(46) About Me  on 2012-01-10 21:15:41 (Show Source):
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4x+3y=33
6x+y=25
4x+3y=33
-4x. -4x
3y=-4x+33
/3. /3. /3
Y=-4/3x+11
6x+y=25
-6x. -6x
y=-6x+25
You can now create a graph by the starting y intercepts and the slope of each line. For instance the first equation starts at (0,11) and goes down 4 right 3. Then once you have gone to the edge of the graphing paper. Start again at (0,11) and go down 4 left 3.
The second equation starts at (0,25) and has a slope of -6/1 which means it goes down 6 and right one. Then after goes as far right as possible. The two lines should connect at (3,7). This is the solution to the problem.


Linear-equations/555040: What is the answer in x+y-6=0 of y =mx+b
1 solutions

Answer 361703 by kkasko(46) About Me  on 2012-01-10 16:17:24 (Show Source):
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What is the answer in x+y-6=0 if =mx+b
X+y-6=0
-x. +6
Y=-x+6


Expressions-with-variables/555235: how do u solve
y=5x-10
y=3x+8
1 solutions

Answer 361699 by kkasko(46) About Me  on 2012-01-10 16:05:40 (Show Source):
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how do u solve
y=5x-10
y=3x+8
This is solved by graphing as it is already in y=mx+b form.
The point you should start at for the first equation is (0,-10) which is on the y-axis and from that point go up 5 and right 1. And then from (0,-10) go down 5 and left 1.
The point you should start at for the second equation is (0,8) also on the y axis from that point go up 3 and right 1. Then from that point you should go down 3 and left 1. The points should now connect and that is your solution.
You could also do this problem with a graphing calculator by putting both equations into y=. Equation one in Y1 and equation 2 in Y 2. Then enter correct window settings which are { -10,10,1,-60,40,1,1}. Or you could press zoom fit which shows where they intersect on the screen. And changes the window settings. It's still good to know how to change window settings manually though. As zoom fit does not show an accurate graph. Then press 2nd calc. Intersect. Enter, enter, enter.
The equations intersect at (9,35)


Equations/555224: -7x-3y=21 step by step

1 solutions

Answer 361694 by kkasko(46) About Me  on 2012-01-10 15:52:21 (Show Source):
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-7x-3y=21 step by step
+7x. +7x
-3y=7x+21
/-3. /-3 /-3
y= -7/3x-7
Draw a x and y axis Plot (0,-7) , from that point go down 7 and right 3.


Expressions-with-variables/555081: For the following system, use the second equation to make a substitution for x in the first equation.
3x + 2y = 7
x - y + 3 = 0
What is the resulting equation?
1 solutions

Answer 361637 by kkasko(46) About Me  on 2012-01-10 10:28:08 (Show Source):
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For the following system, use the second equation to make a substitution for x in the first equation.
3x + 2y = 7
x - y + 3 = 0
What is the resulting equation?
x-y+3=0
+y-3. +y-3
X=y-3
3x+2y=7
3(y-3)+2y=7
3y-9+2y=7
5y-9=7


Equations/555096: 4n + 3 = 5(2 – 2n)
1 solutions

Answer 361636 by kkasko(46) About Me  on 2012-01-10 10:20:10 (Show Source):
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4n + 3 = 5(2 – 2n)
4n+3=10-10n
move -10 to the left side and move 3 to the right side by doing the opposite
4n+3=10-10n
+10n -3. -3.
14n=7
/14. /14
n=7/14
Reduce
7/14=1/2
n=1/2


Expressions-with-variables/555082: Based on the lesson, which of the following would be the best approach for solving this system by substitution?
5x = y + 6
2x - 3y = 4
1 solutions

Answer 361633 by kkasko(46) About Me  on 2012-01-10 10:11:26 (Show Source):
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Based on the lesson, which of the following would be the best approach for solving this system by substitution?
5x = y + 6
2x - 3y = 4
Isolating the x value from the 5 by dividing it like this
5x=y+6
/5. /5. /5
x=1/5y+6/5
2x-3y=4
2(1/5y+6/5)-3y=4
2/5y+12/5-3y=4
Now collect like terms -3y+2/5y
-13/5y+12/5=4
-12/5. -12/5
-13/5y=8/5
Isolate the y
-13/5y=8/5
/(-13/5). /(-13/5)
y=-.6153846151. However we need to convert this into a fraction to get x so Math Fract
Y=-8/13
Now substitute it into the original equation
2x-3y=4
2x-3(-8/13)=4
Again can't have a decimal so math Fract
2x+24/13=4
Isolate 2x from -24/13 by adding 24/13 to 4
2x+24/13=4
-24/13. -24/13
Again math Fract
2x=28/13
Divide by 2
2x=(28/13)
/2. /2
Math Fract
x=14/13
CHECK
2x-3y=4
2(14/13)-3(-8/13)=4
4=4
Left hand side = Right hand side
Solution=(14/13,-8/13)


Expressions-with-variables/555083: Solve the following system of equations.
2x + y = 3
x = 2y - 1
Make sure there are NO SPACES in your answer. Include a comma in your answer.

1 solutions

Answer 361628 by kkasko(46) About Me  on 2012-01-10 09:44:17 (Show Source):
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Solve the following system of equations.
2x + y = 3
x = 2y - 1
Make sure there are NO SPACES in your answer. Include a comma in your answer.
It looks like I could substitute the x=2y-1. Into 2x+y=3
2(2y-1)+y=3
4y-2+y=3
5y=5
y=1
x=2(1)-1
x=1
(1,1)
CHECK
2x+y=3
2(1)+(1)=3
2+1=3
3=3
Left hand side=Right hand side
Check other equation
x=2y-1
1=2(1)-1
1=1
Therefore the solution is (1,1). Since the left hand side= right hand side in each equation


Graphs/554829: 15x+5>10

1 solutions

Answer 361534 by kkasko(46) About Me  on 2012-01-09 20:41:34 (Show Source):
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15x+5>10
-5. -5
15x > 5
/15. /15
x > 5/15
x=1/3
Start at (0,0) and go up 1 and right 3
then from (0,0) do the opposite and go down 1 left 3. This equation also has a dashed or broken line.


Equations/554884: what is n+2=3times12
1 solutions

Answer 361529 by kkasko(46) About Me  on 2012-01-09 20:30:28 (Show Source):
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what is n+2=3times12
n+2=36
-2. -2
n=34


Pythagorean-theorem/554848: If the side of a triangle are 7,6,and 9 the triangle is an
1 solutions

Answer 361525 by kkasko(46) About Me  on 2012-01-09 20:27:10 (Show Source):
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If the side of a triangle are 7,6,and 9 the triangle is an scalene triangle since no sides are equal.


Number-Line/554592: where is the number 0 located in the number line?
1 solutions

Answer 361408 by kkasko(46) About Me  on 2012-01-09 15:20:18 (Show Source):
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the number 0 is located in the middle of the number line. This is because it separates the negative numbers from the positive numbers.
for instance,
-4,-3,-2,-1,0,1,2,3,4


Graphs/554543: Good Afternoon,
Can you graph the following inequality for me?
3x -2y < -6
and explain the points to me.
Hope to hear from someone soon.
Sincerely,
TH.

1 solutions

Answer 361405 by kkasko(46) About Me  on 2012-01-09 15:12:37 (Show Source):
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3x -2y < -6
solve the inequality in terms of x
3x -2y <-3x-6
-3x
-2y<-3x-6
flip the < sign since you are dividing by a negative number.
/-2>/-2 /-2
y > 3/2x+3
I am not sure how to do a graph on this software yet however the inequality is in y=mx+b form.
so draw a y axis and an x axis. Plot the (0,3) on the y axis. go up 3 and left 2 and then go down 3 left 2 from (0,3). Connect the points and draw arrows on each end of the line. Since y is greater than 3/2x+3 the line is a broken or dashed line.


real-numbers/554569: What is the difference between rational, irrational, etc.?
1 solutions

Answer 361399 by kkasko(46) About Me  on 2012-01-09 14:52:13 (Show Source):
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What is the difference between rational, irrational, etc.?
Rational and irrational are the exact opposite of each other. A rational number is one that can be wrote as a fraction. Irrational numbers cannot be written as fractions.


Inequalities/554558: Solve the inequality for u
-2/3u+7>7u-9
1 solutions

Answer 361394 by kkasko(46) About Me  on 2012-01-09 14:42:57 (Show Source):
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Solve the inequality for u
First get u on its own side and the integers on their own side by doing the inverse of the variables and the intergers. Then divide the u value by the interger on the other side.
-2/3u+7>7u-9
+2/3u. +2/3u
7>7.666666667u-9
+9. +9
16>7.666666667u
2.086956522>u
Math Frac enter= 48/23


Inequalities/554574: 7x + 2 > 30
1 solutions

Answer 361385 by kkasko(46) About Me  on 2012-01-09 14:32:58 (Show Source):
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7x + 2 > 30
-2. -2
7x >28
/7. /7
X>4


test/554546: Factor the trinomial (can you please show & tell me how to do this)
5tsquared -22t-15
1 solutions

Answer 361381 by kkasko(46) About Me  on 2012-01-09 14:22:25 (Show Source):
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Factor the trinomial (can you please show & tell me how to do this)
The first step is to find _x_= 5x-15=-75
_+_=-22

5t^2 -22t-15. -25+3=-22. -25x3=-75
Now put the -25t+3t into the equation where -22t was so.
5t^2-25t+3t-15
Now break the trinomial into two factors by 5x_=-25 and after the bracket put a 3 and then another bracket( t and 3x_=-15
5t(t-5)3(t-5)
(5t+3)(t-5)
These are the factors to the trinomial