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Recent problems solved by 'philline_palana'

philline_palana answered: 20 problems

Quadratic-relations-and-conic-sections/242289: Graph each conic section and state the desired information?
Parabola
x= y^2 + 8y + 20
1 solutions

Answer 177553 by philline_palana(20) on 2009-11-24 19:00:11 (Show Source):

You can put this solution on YOUR website!

Solved by pluggable solver: SOLVE quadratic equation with variable

Quadratic equation ay%5E2%2Bby%2Bc=0

(in our case 1y%5E2%2B8y%2B20+=+0

) has the following solutons:

y%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac

should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac

.

The discriminant -16 is less than zero. That means that there are no solutions among real numbers.

If you are a student of advanced school algebra and are aware about imaginary numbers, read on.

In the field of imaginary numbers, the square root of -16 is + or - sqrt%28+16%29+=+4

.

The solution is y%5B12%5D+=+%28-8%2B-+i%2Asqrt%28+-16+%29%29%2F2%5C1+=++%28-8%2B-+i%2A4%29%2F2%5C1+

Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B8%2Ax%2B20+%29

Linear-systems/242469: how would you graph and solve 3y>4x?
1 solutions

Answer 177548 by philline_palana(20) on 2009-11-24 18:48:56 (Show Source):

You can put this solution on YOUR website!
3y>4x

3y=4x
if x = -1
3y=4(-1)
3y/3=-4/3
y=-4/3
Point 1: (-1, -4/3)

if x = -2
3y=4(-2)
3y/3=-8/3
y=-8/3
Point 2: (-2, -8/3)

if x = -3
3y=4(-3)
3y/3=-12/3
y=-4
Point 3: (-3, -4)

if x = 1
3y=4(1)
3y/3=4/3
y=4/3
Point 4: (1, 4/3)

if x = 2
3y=4(2)
3y/3=8/3
y=8/3
Point 5: (2, 8/3)

if x = 3
3y=4(3)
3y/3=12/3
y=4
Point 5: (3, 4)

connect the points.
Shade the upper part of the line because y>x

Linear-equations/242505: i need to plot at least three points for each graph for 3x-2y=6
1 solutions

Answer 177542 by philline_palana(20) on 2009-11-24 18:33:29 (Show Source):

You can put this solution on YOUR website!
3x-2y=6

if x=0
3(0)-2y=6
-2y=6 >>divide by -2
-2y/-2=6/-2
y=-3
point 1: (0,-3)

if x=1
3(1)-2y=6
3-2y=6 >>transpose 6
3-6-2y=0 >>transpose -2y
3-6=2y
-3=2y >>divide by 2
-3/2=2y/2
y=-3/2
point 2: (1,-3/2)

if y=0
3x-2(0)=6
3x=6 >>divide by 3
3x/3 = 6/3
x=2
point 3: (2,0)

Triangles/242502: If a triangle has two short sides that are each three and four inches in length,how long is the longest side?
1 solutions

Answer 177538 by philline_palana(20) on 2009-11-24 18:23:40 (Show Source):

You can put this solution on YOUR website!
use pythagorean theorem:
side a: 3 inches
side b: 4 inches
c = sqrt(3^2+4^2)
c = sqrt(9+16)
c = sqrt(25)
c = 5 >> the longest side

Triangles/242349: How do you know if a triangle is an isosceles or an equiangular etc, in simpler terms?

1 solutions

Answer 177535 by philline_palana(20) on 2009-11-24 18:18:58 (Show Source):

You can put this solution on YOUR website!
Sometimes it would be stated in the problem and if it would not be stated literally, its up to you to analyze the whole problem carefully.

Linear-systems/242499: y+4=-5x
y=3x+2
1 solutions

Answer 177532 by philline_palana(20) on 2009-11-24 18:08:14 (Show Source):

You can put this solution on YOUR website!
y+4=-5x >> Equation 1
y=3x+2 >> Equation 2
First is to transpose all variables in one side.
for Equation 1:
y+4=-5x
5x+y+4=0 >> Our new Equation 1
for Equation 2:
y=3x+2
3x-y+2=0 >> Our new Equation 2
I'll be using the method of eliminating a variable by addition/subtraction:
I'll be eliminating the variable "y" by addition:
5x+y+4=0
+ 3x-y+2=0
-----------
8x +6=0 >> transpose
8x = -6 >> divide the equation by 8
8x/8 = -6/8
x = -3/4 >> we have now a value for x, now we will substitute it to Equation 2.
3x-y+2=0
3(-3/4)-y+2=0 >> transpose y
3(-3/4) + 2 = y >> solve
-9/4 + 2 = y
y = -1/4 >> we have now a value for y
our solution are: x = -3/4 and y = -1/4

Complex_Numbers/242415: 2vsquared-5v-25=0
1 solutions

Answer 177523 by philline_palana(20) on 2009-11-24 17:49:34 (Show Source):

You can put this solution on YOUR website!

Solved by pluggable solver: SOLVE quadratic equation with variable

Quadratic equation av%5E2%2Bbv%2Bc=0

(in our case 2v%5E2%2B-5v%2B-25+=+0

) has the following solutons:

v%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac

should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac

.

Discriminant d=225 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--5%2B-sqrt%28+225+%29%29%2F2%5Ca

v%5B1%5D+=+%28-%28-5%29%2Bsqrt%28+225+%29%29%2F2%5C2+=+5

v%5B2%5D+=+%28-%28-5%29-sqrt%28+225+%29%29%2F2%5C2+=+-2.5

Quadratic expression 2v%5E2%2B-5v%2B-25

can be factored:
2v%5E2%2B-5v%2B-25+=+2%28v-5%29%2A%28v--2.5%29

Again, the answer is: 5, -2.5. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+2%2Ax%5E2%2B-5%2Ax%2B-25+%29

absolute-value/242419: What is the solution of |2x - 1| = 5 ?
2x-1=5
2x=5+1
2x=6
2/2=6/2
X=3
|2x-1|=-5
2x=5+1
2x=-4
2/2=-4/2
x=-2
so (x=3 and -2)

1 solutions

Answer 177519 by philline_palana(20) on 2009-11-24 17:44:42 (Show Source):

You can put this solution on YOUR website!
We have two answers for your problem because it is an absolute value,
|2x - 1| = 5
first solution:
|2x - 1| = 5 >>remove the absolute value sign
2x - 1 = 5 >>transpose
2x = 5 + 1 >>add
2x = 6 >>divide the equation by two
2x/2 = 6/2
x = 3 >>we are not yet done
second solution:
|2x - 1| = 5 >>remove the absolute value sign and change the sign of 5 into negative
2x - 1 = -5 >>transpose
2x = -5 + 1 >>add
2x = -4 >>divide the equation by two
2x/2 = -4/2
x = -2 >>we are done.
so for this problem, our two solutions are: x=3 and x=-2

Quadratic_Equations/239701: use the discriminate to find the number and type of solutions to the following quadratic equation x^2+2x+6=0 i got the answer of -20 i just don't know if it's 2 real solutions, 2 imaginary solutions or 1 real solution.
1 solutions

Answer 176059 by philline_palana(20) on 2009-11-17 22:26:05 (Show Source):

You can put this solution on YOUR website!

Solved by pluggable solver: SOLVE quadratic equation with variable

Quadratic equation ax%5E2%2Bbx%2Bc=0

(in our case 1x%5E2%2B2x%2B6+=+0

) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac

should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac

.

The discriminant -20 is less than zero. That means that there are no solutions among real numbers.

If you are a student of advanced school algebra and are aware about imaginary numbers, read on.

In the field of imaginary numbers, the square root of -20 is + or - sqrt%28+20%29+=+4.47213595499958

.

The solution is

Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B2%2Ax%2B6+%29

Quadratic_Equations/240082: 3x^2=2x+2

1 solutions

Answer 176057 by philline_palana(20) on 2009-11-17 22:23:40 (Show Source):

You can put this solution on YOUR website!
3x^2=2x+2 >>Transpose 2x+2 to the left side
3x^2-2x-2=0 >>We now have a quadratic equation

Solved by pluggable solver: SOLVE quadratic equation with variable

Quadratic equation ax%5E2%2Bbx%2Bc=0

(in our case 3x%5E2%2B-2x%2B-2+=+0

) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac

should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac

.

Discriminant d=28 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--2%2B-sqrt%28+28+%29%29%2F2%5Ca

x%5B1%5D+=+%28-%28-2%29%2Bsqrt%28+28+%29%29%2F2%5C3+=+1.21525043702153

x%5B2%5D+=+%28-%28-2%29-sqrt%28+28+%29%29%2F2%5C3+=+-0.548583770354864

Quadratic expression 3x%5E2%2B-2x%2B-2

can be factored:
3x%5E2%2B-2x%2B-2+=+3%28x-1.21525043702153%29%2A%28x--0.548583770354864%29

Again, the answer is: 1.21525043702153, -0.548583770354864. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+3%2Ax%5E2%2B-2%2Ax%2B-2+%29

Quadratic_Equations/240118: 3x^2-14x+8=0
1 solutions

Answer 176056 by philline_palana(20) on 2009-11-17 22:21:29 (Show Source):

You can put this solution on YOUR website!

Solved by pluggable solver: SOLVE quadratic equation with variable

Quadratic equation ax%5E2%2Bbx%2Bc=0

(in our case 3x%5E2%2B-14x%2B8+=+0

) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac

should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac

.

Discriminant d=100 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--14%2B-sqrt%28+100+%29%29%2F2%5Ca

x%5B1%5D+=+%28-%28-14%29%2Bsqrt%28+100+%29%29%2F2%5C3+=+4

x%5B2%5D+=+%28-%28-14%29-sqrt%28+100+%29%29%2F2%5C3+=+0.666666666666667

Quadratic expression 3x%5E2%2B-14x%2B8

can be factored:
3x%5E2%2B-14x%2B8+=+3%28x-4%29%2A%28x-0.666666666666667%29

Again, the answer is: 4, 0.666666666666667. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+3%2Ax%5E2%2B-14%2Ax%2B8+%29

Quadratic_Equations/240171: determine how long the cannon ball was in the air.
using h=-5t(squared)+ 40t+ 3

1 solutions

Answer 176055 by philline_palana(20) on 2009-11-17 22:17:27 (Show Source):

You can put this solution on YOUR website!

Solved by pluggable solver: SOLVE quadratic equation with variable

Quadratic equation at%5E2%2Bbt%2Bc=0

(in our case -5t%5E2%2B40t%2B3+=+0

) has the following solutons:

t%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac

should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac

.

Discriminant d=1660 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-40%2B-sqrt%28+1660+%29%29%2F2%5Ca

t%5B1%5D+=+%28-%2840%29%2Bsqrt%28+1660+%29%29%2F2%5C-5+=+-0.0743097574926722

t%5B2%5D+=+%28-%2840%29-sqrt%28+1660+%29%29%2F2%5C-5+=+8.07430975749267

Quadratic expression -5t%5E2%2B40t%2B3

can be factored:
-5t%5E2%2B40t%2B3+=+-5%28t--0.0743097574926722%29%2A%28t-8.07430975749267%29

Again, the answer is: -0.0743097574926722, 8.07430975749267. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-5%2Ax%5E2%2B40%2Ax%2B3+%29

Quadratic_Equations/236090: I must use the discriminant to determine the number of solutions of the quadratic equation and whether the solutions are real or complex. I am having trouble understanding how to find the discriminant and then find the solutions.
I do not need to find the roots.
3z^2 + z - 1 = 0
1 solutions

Answer 173828 by philline_palana(20) on 2009-11-07 03:39:13 (Show Source):

You can put this solution on YOUR website!

Solved by pluggable solver: SOLVE quadratic equation with variable

Quadratic equation az%5E2%2Bbz%2Bc=0

(in our case 3z%5E2%2B1z%2B-1+=+0

) has the following solutons:

z%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac

should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac

.

Discriminant d=13 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-1%2B-sqrt%28+13+%29%29%2F2%5Ca

z%5B1%5D+=+%28-%281%29%2Bsqrt%28+13+%29%29%2F2%5C3+=+0.434258545910665

z%5B2%5D+=+%28-%281%29-sqrt%28+13+%29%29%2F2%5C3+=+-0.767591879243998

Quadratic expression 3z%5E2%2B1z%2B-1

can be factored:
3z%5E2%2B1z%2B-1+=+3%28z-0.434258545910665%29%2A%28z--0.767591879243998%29

Again, the answer is: 0.434258545910665, -0.767591879243998. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+3%2Ax%5E2%2B1%2Ax%2B-1+%29

Quadratic_Equations/234852: For this problem I need to use the discriminate to determine the number of solutions of the quadratic equation, and whether the solutions are real or complex. It is not necessary to find the roots; just determine the number and types of solutions
2x^2 - 10x + 25 = 0
1 solutions

Answer 173158 by philline_palana(20) on 2009-11-04 06:03:48 (Show Source):

You can put this solution on YOUR website!

Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)

Quadratic equation ax%5E2%2Bbx%2Bc=0

(in our case 2x%5E2%2B-10x%2B25+=+0

) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac

should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac

.

The discriminant -100 is less than zero. That means that there are no solutions among real numbers.

If you are a student of advanced school algebra and are aware about imaginary numbers, read on.

In the field of imaginary numbers, the square root of -100 is + or - sqrt%28+100%29+=+10

.

The solution is x%5B12%5D+=+%28--10%2B-i%2Asqrt%28+-100+%29%29%2F2%5C2+=++%28--10%2B-i%2A10%29%2F2%5C2+

, or
Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+2%2Ax%5E2%2B-10%2Ax%2B25+%29

Quadratic_Equations/234854: For this problem I need to use the discriminate to determine the number of solutions of the quadratic equation, and whether the solutions are real or complex. It is not necessary to find the roots; just determine the number and types of solutions
2x^2-6x+5=0
1 solutions

Answer 173156 by philline_palana(20) on 2009-11-04 06:00:20 (Show Source):

You can put this solution on YOUR website!

Solved by pluggable solver: SOLVE quadratic equation with variable

Quadratic equation ax%5E2%2Bbx%2Bc=0

(in our case 2x%5E2%2B-6x%2B5+=+0

) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac

should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac

.

The discriminant -4 is less than zero. That means that there are no solutions among real numbers.

If you are a student of advanced school algebra and are aware about imaginary numbers, read on.

In the field of imaginary numbers, the square root of -4 is + or - sqrt%28+4%29+=+2

.

The solution is x%5B12%5D+=+%28--6%2B-+i%2Asqrt%28+-4+%29%29%2F2%5C2+=++%28--6%2B-+i%2A2%29%2F2%5C2+

Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+2%2Ax%5E2%2B-6%2Ax%2B5+%29

Inequalities/234882: I need help on solving -5w+8>=13 and the steps to solving it.
1 solutions

Answer 173149 by philline_palana(20) on 2009-11-04 04:05:05 (Show Source):

You can put this solution on YOUR website!
-5w+8>=13
-5w>=13-8
-5w>=5
-5w/-5>=5/-5
*we should change the sign into "<=" because we divide the equation by a negative number so our answer is:
w<=-1

Quadratic_Equations/234935: For this problem I must apply the quadratic formula to find the roots of the given function and then graph the function.
f(x)=x^2+4
1 solutions

Answer 173148 by philline_palana(20) on 2009-11-04 03:50:22 (Show Source):

You can put this solution on YOUR website!

Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)

Quadratic equation ax%5E2%2Bbx%2Bc=0

(in our case 1x%5E2%2B0x%2B4+=+0

) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac

should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac

.

The solution is x%5B12%5D+=+%28-0%2B-i%2Asqrt%28+-16+%29%29%2F2%5C1+=++%28-0%2B-i%2A4%29%2F2%5C1+

, or
Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B0%2Ax%2B4+%29

Quadratic_Equations/234936: For this problem I must apply the quadratic formula to find the roots of the given function and then graph the function.

g(x)=x^2+x+12
1 solutions

Answer 173147 by philline_palana(20) on 2009-11-04 03:49:08 (Show Source):

You can put this solution on YOUR website!

Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)

Quadratic equation ax%5E2%2Bbx%2Bc=0

(in our case 1x%5E2%2B1x%2B12+=+0

) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac

should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac

.

The discriminant -47 is less than zero. That means that there are no solutions among real numbers.

If you are a student of advanced school algebra and are aware about imaginary numbers, read on.

In the field of imaginary numbers, the square root of -47 is + or - sqrt%28+47%29+=+6.85565460040104

.

The solution is

, or
Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B1%2Ax%2B12+%29

Quadratic_Equations/234937: This problem I must factor the quadratic expression completely, and find the roots of the expression.
135x^2 - 222x + 91
1 solutions

Answer 173146 by philline_palana(20) on 2009-11-04 03:47:22 (Show Source):

You can put this solution on YOUR website!

Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)

Quadratic equation ax%5E2%2Bbx%2Bc=0

(in our case 135x%5E2%2B-222x%2B91+=+0

) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac

should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac

b%5E2-4ac=%28-222%29%5E2-4%2A135%2A91=144

.

Discriminant d=144 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--222%2B-sqrt%28+144+%29%29%2F2%5Ca

x%5B1%5D+=+%28-%28-222%29%2Bsqrt%28+144+%29%29%2F2%5C135+=+0.866666666666667

x%5B2%5D+=+%28-%28-222%29-sqrt%28+144+%29%29%2F2%5C135+=+0.777777777777778

Quadratic expression 135x%5E2%2B-222x%2B91

can be factored:
135x%5E2%2B-222x%2B91+=+%28x-0.866666666666667%29%2A%28x-0.777777777777778%29

Again, the answer is: 0.866666666666667, 0.777777777777778. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+135%2Ax%5E2%2B-222%2Ax%2B91+%29

Quadratic_Equations/234938: This problem I must factor the quadratic expression completely, and find the roots of the expression.

6x^2 - 42x + 72
1 solutions

Answer 173145 by philline_palana(20) on 2009-11-04 03:42:43 (Show Source):

You can put this solution on YOUR website!

Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)

Quadratic equation ax%5E2%2Bbx%2Bc=0

(in our case 6x%5E2%2B-42x%2B72+=+0

) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac

should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac

.

Discriminant d=36 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--42%2B-sqrt%28+36+%29%29%2F2%5Ca

x%5B1%5D+=+%28-%28-42%29%2Bsqrt%28+36+%29%29%2F2%5C6+=+4

x%5B2%5D+=+%28-%28-42%29-sqrt%28+36+%29%29%2F2%5C6+=+3

Quadratic expression 6x%5E2%2B-42x%2B72

can be factored:
6x%5E2%2B-42x%2B72+=+%28x-4%29%2A%28x-3%29

Again, the answer is: 4, 3. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+6%2Ax%5E2%2B-42%2Ax%2B72+%29

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