Questions on Algebra: Graphs, graphing equations and inequalities answered by real tutors!

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Question 994548: For the equation 9 x ^3 - 9 y ^2 = -6 answer the following questions.
Is the equation symmetric with respect to the y-axis? ( yes or no)
Is the equation symmetric with respect to the x-axis? ( yes or no)
Is the equation symmetric with respect to the origin? ( yes or no)
I have substitute both axis and the origin with the corresponding transformation of -x and -y. However, I couldn't find the right answer and I would like to know what I did wrong.
For example,
x axis: 9x^3-9(-y)^2=-6
9x^3-9y^2=-6 <-- same equation as original therefore Yes
Y axis: 9(-x)^3-9y^2=-6
-9x^3-9y^2=-6 <--- not the same equation as original therefore No
Origin: 9(-x)^3-9(-y)^2=-6
-9x^3-9y^2=-6 <--- not the same equation as original therefore No

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Looks symmetric to the horizontal axis to me. And it certainly is not symmetric to either the vertical axis or the origin.

So I don't know what you mean by "couldn't find the right answer" because the right answer is right there in your post.

John

My calculator said it, I believe it, that settles it

Question 994416: 3x + 23 = 23
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3x + 23 = 23
3x = 0
x = 0

Question 994433: The sum of two numbers is 48, and one number is twice the other. Find the numbers
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Hi there,
The sum of two numbers is 48,
and one number is twice the other
x + 2x = 48
3x = 48
x = 48/3
x = 16
First number = 16
Second number = 32
Hope this helps :-)

Question 994381: system of linear equations using elimination for -x-6y=11 and 5x-6y=-19
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-x-6y= 11
5x-6y=-19
--------------- Subtract

Question 994374: system of linear equations using substitution y=5x-11, y=-3x+5
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system of linear equations using substitution y=5x-11, y=-3x+5
----
y=5x-11
y=-3x+5
---
sub for y
5x-11 = -3x+5
8x = 16
etc

Question 994298: Determine whether the function is an odd or even function:

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.
This function is odd.

Change  x  for  -x,  and you will see that the function will change the sign.

Question 994299: Determine whether the function is an odd or even function:

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.
Neither odd nor even.
See the plot in the Figure:
 Plot of =

Question 994306: If 4 < a ≤ 8 and 1/4 < b < 1/2, then what are the possible values of ab?
A. 1 ≤ ab ≤ 4
B. None of these
C. 1 ≤ ab < 4
D. 1 < ab ≤ 4
E. 1 < ab < 4

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.
Correct answer is E. 1 < ab < 4

Question 994086: Write equations for the vertical and horizontal lines passing through the point (-1,-5)
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Write equations for the vertical and horizontal lines passing through the point (-1,-5)
-----
Vertical:: x = -1
Horizontal:: y = -5
-----
Cheers,
Stan H.
-----------

Question 994085: How do you do h-(-2) is greater than or equal to 10?
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h-(-2) > or = 10
- time - is a +
h + 2 > = 10
subtract 2 from both sides of inequality
h > = 8

Question 994024: Find the equation of the line that contains the given point and has the given slope. Express the equation in the form Ax + By = C, where A, B and C are integers.
(5, 6), m = 5/6

____=-11

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Find the equation of the line that contains the given point and has the given slope. Express the equation in the form Ax + By = C, where A, B and C are integers.
(5, 6), m = 5/6
____=-11
m=∆y/∆x=(y-6)/(x-5)=5/6
6y-36=5x-25
5x-6y=-9 (equation of the line)

Question 994036: Which equation represent the line with slope -2 that passes through the point (4,-1)
Y= -2x-9
Y= -2x-7
Y= -2x+2
Y= -2x+7

Found 2 solutions by vleith, josgarithmetic:
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they all have a slope of -2.
You need to see which equation has the point (4,-1) on it. Just substitute 4 for x and -1 for y in each equation. Then find the equation that ends up being a "true" result.
It's D since

which is true

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Two ways to solve.

Plug-in the coordinate values and see which equation is true.

OR

Plug slope and given point into point-slope formula and simplify into general form.

Question 993987: Find the slope if possible of the line passing through the points, (1,2) and (1,-1) and describe the line.
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Find the slope if possible of the line passing through the points, (1,2) and (1,-1) and describe the line.
slope of given line is undefined. It can be described as a vertical line passing thru x=1

Question 993287: For what values of "a" is the distance between P(a, 3) and Q(6, 2a) greater than 29?

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Distance between P(a,3) and Q(6,2a) is

=
=
For this distance to be greater than 29;

=>
=>
Solving the quadratic we get roots as -10.44 and 15.24
Since coefficient of a^2 is positive, the graph is opening upwards
So the value of this quadratic is negative between these two roots.
So the required value of a for the quadratic to be positive, is
All values of a except [-10.44,15.24] range.

Question 993988: The equation, in general form, of the line that passes through the point (3,5) and is parallel to the line 6x-9y+2=0 is Ax+By+C=0 where A,B and C are what?
Found 2 solutions by anand429, josgarithmetic:
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For parallel lines:
A1/A2 = B1/B2
So,
=> -3A=2B ----------------------------(i)
Now it passes through (3,5) so,
A*3 +B*5 +C=0
=> 3A+5B + C=0
=> 3B = -C (using (i))-----------(ii)
Simplfying given equation in terms of single variable we get,
Ax+By+C=0
=>
=>

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A study about that STANDARD form equation format would help you to understand or be able to determine that the slope is . Your given line accordingly has a slope . You find the value for C using the point (3,5) which must be on the line parallel to the given line.

Be careful. The original given line is 6x-9y+2=0, and using this, the slope is also , so you might want to stay with the less simplified form just to avoid complicating mistakes if you want.

Parallel lines in the plane has equal slopes, so the line you are trying to find will also have slope .

Staying in STANDARD FORM, the equation you want will be .

.

Values for A and B were already explained and shown.

Your description mentioned "general form" at the beginning. If you want that, then solve for y from . Notice that if you simplify this standard form equation it is . Using this simplified form of the standard form equation, you have .

Question 993873: whats the slope of (5,8) (-5,8)
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Slope is

Points: (x1, y1) --> (5, 8) and (x2, y2) --> (-5,8)

Question 993863: what is y=3/4x-2 when you graph it

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what is y=3/4x-2 when you graph it
--------------
Depends.
Is it (3/4)x - 2 ?
or (3/4x) - 2 ?
or 3/(4x - 2) ?

Question 993828: how do you transform y=3x+18 into a standard form

Found 2 solutions by MathTherapy, josgarithmetic:
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how do you transform y=3x+18 into a standard form
3x + 18 = y ----------- Reversing sides
3x - y + 18 = 0 ------- Subtracting y to get variables on left-hand side
--------- Subtracting 18 to get the constant on the right-hand side
DONE!!



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Done, now shown fully in the previous question.

If you have any slope intercept line equation , in which the slope is , converting into standard form is a matter of very simple algebra.

This result matches the form . Carefully note how the coefficients A and B are used in forming the slope. Slope is.

Question 993823: how do you transform y=3x+18 into a slope intercept form

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Converting into STANDARD FORM?
You want a form like .
The equation as you have is almost like what you need, only requiring ONE SIMPLE STEP.

, I am using more than just one step;

or you can use the equivalent equation, . Do you understand how?

Question 993714: plase help me solve this. Rearrange this equation into that form that can be plotted as a straight line graph y=10ex. the x is a power.Thank you.
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http://slc.umd.umich.edu/slconline/TRANSF/

generally speaking, you are transforming y = 10 * e^x into the equation ln(y) = x + ln(10)

that's done in the following manner:

take natural log of both sides to get:

ln(y) = ln(10 * e^x)

this becomes:

ln(y) = ln(10) + x * ln(e) which becomes:

ln(y) = ln(10) + x

rearrange the terms to get:

ln(y) = x + ln(10) which is in the form of a linear equation.

i don't pretend to understand what they doing or why they're doing it, but the reference i found on the web should be helpful.

Question 993775: If there is an improper fraction such as -17 over 3 how would u change it into a mixed fraction to graph it?
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If there is an improper fraction such as -17 over 3 how would u change it into a mixed number to graph it?
----
Divide -17 by 3 to get:
Ans: -(5 2/3)
------------
Cheers,
Stan H.
-------

Question 993679: What is the slope of the line through the points (2,-3) and (6,5)?
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Slope is found by
m = (y2 - y1)/(x2 - x1)
m = (5-(-3)) / (6 - 2)
m = 8 / 4 = 2

Question 993563: If I have -(x+3)^2+5 how do I make a vertical compression that restricts to 20% of the original? I'm thinking a would need to equal 20, but I'm not sure.
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20% is 1/5. For vertical compression, you need a "less than 1" lead coefficient.

John

My calculator said it, I believe it, that settles it

Question 993532: How do you solve 4x+5y=25 and 8x-5y=35 when using substitution

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.
How do you solve  4x+5y=25  and  8x-5y=35 when using substitution.
----------------------------------------------------------------

.

You can express  4x  from the first equation,  4x = 25-5y,  and then substitute it into the second equation.  You will get

2*(25-5y) - 5y = 35.

Simplify and solve:

50 - 10y - 5y = 35,
15y = 30 - 35,
15y = 15,
y = 1.

Now substitute the found value of  y=1  into the first equation to find  x.  You will get

4x + 5*1 = 25,
4x = 20,
x = 5.

Answer.  x = 5, y = 1.

Question 993524: m:3/2,(4,6)
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Slope and included point of a line?

Learn to understand and use Point-Slope formula.
Line with slope m and point on the line, (h,k)
has an equation .

Question 993522: How to find the slope thru a pair of points
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Imagine one point is (a,b), and another point is (c,d) on a graph (these letters represent x and y values).
Slope: rise/run= (d-b) divided by (c-a)

Question 993481: Given the function
y = ( x+3 ) ( x^2+3 x−3 )
find the coordinates of the points of intersection with the x-axis and y-axis.
Please enter your answer as a set of coordinate pairs, where a single coordinate pair (a, b)
constants should all be given exactly, using the sqrt function and fractions as necessary
THANK YOU

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intersection with the x-axis occurs where
and
intersection with the y-axis occurs where
so set and find intersection with the x-axis
...will be true for or , or both
if =>

solutions: exact solutions

or

approximate solutions:

or

so, ordered pairs are:
(,)
(,)
(,)
or
(,)
(,)
(,)

now find y-intercept:

the y-axis occurs where , so set

ordered pair is:
(,)

see it on the graph:

Question 993482: Given the function
y = ( x - 4 ) ( x^2 + 3x + 2 )
find the coordinates of the two stationary points and the point of inflection.
Note. A stationary point is a critical point at which the derivative is 0.
Please enter your answer as a list of coordinate pairs, where a single coordinate pair (a, b)
THANK YOU

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In order to find the stationary points, you need to find the zeros of the first derivative. In order to find the point of inflection you will need to find the zero of the second derivative. None of this is very rigorous, but will work just fine for a polynomial function.

You have two choices for finding the first derivative. Since you have the product of two functions, you can use the product rule:

Or you can just perform the indicated multiplication and take the derivative by repeated applications of the power rule.

Either way, after you have the first derivative, set the quadratic equal to zero and solve. You will get the values of the two stationary points.

The second derivative is just the derivative of the first derivative quadratic polynomial

Set the second derivative equal to zero and solve for the value of the coordinate of the inflection point.

John

My calculator said it, I believe it, that settles it

Question 993404: The perimeter of a rectangle is 32in. If the length of the rectangle is 1 more than twice the width. Find the dimensions of the rectangle .

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Hi there,
Make the width = 'x'
Length = 1 + 2x
Perimeter = 2 x Width + 2 x Length
32 = 2(x) + 2(1 + 2x)
32 = 2x + 2 + 4x
Collect like terms.
2x + 4x = 32 - 2
6x = 30
x = 5
Width = 5 in
Length = 11 in
Hope this helps :-)

Question 993369: NEEDING HELP WITH THIS QUESTION PLEASE.
f(x) = 3x2 − 12x + 8
INCREASING=?
DECREASING=?
HOW DO I FIND/WHAT FORMULA DO I USE TO FIND THIS?
THANK YOU!

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you look at what the highest order exponent term is doing.
it's 3x^2
when x is negative, x^2 is positive, so this function should be increasing on the left and on the right.
here's what the graph looks like:

here's a good reference on figuring out how to analyze these.

Question 993358: I know how to find increasing and decreasing but I am having trouble finding this one:
f(x) = −2(x + 1)2 + 4
Increasing:?

Decreasing:?

Found 2 solutions by stanbon, Fombitz:
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f(x) = −2(x + 1)^2 + 4
f(x) = -2(x^2+2x+1) + 4
f(x) = -2x^2-4x+2
-------------------

----------------------
Take the derivative to get:
f'(x) = -4x-4
---
Increasing:?
Solve: -4x-4 > 0
-4x > 4
x < -1
Increasing on (-oo,-1)
-----------------------------
Decreasing:?
Solve: -4x-4 < 0
-4x < 4
x > -1
Decreasing on (-1,+oo)
===========
Cheers,
Stan H.

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This equation is in vertex form.
The vertex of the parabola is (,).
Since the multiplier for the quadratic term is negative ,, the parabola opens downwards and the maximum value occurs at the vertex.
So for x values before the vertex the y values are increasing and for x values after the vertex, the y values are decreasing.
Increasing :
Decreasing :
.
.
.
.

Question 993204: A line has a slope of - 3/4. What is the slope of the line parallel to it? What is the line perpendicular to it?
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A line has a slope of - 3/4.
What is the slope of the line parallel to it?
Ans: -3/4
--------------
What is the slope of the line perpendicular to it?
Ans: 4/3
-------------
Cheers,
Stan H.
=========

Question 993150: I am doing homework and part of it deals with graphs and I just don't understand how to come up with the solution. The problem is -2x+y=6
Thank you! :)

Found 2 solutions by ikleyn, Alan3354:
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The plot is here
 Plot y = 2x + 6.

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I am doing homework and part of it deals with graphs and I just don't understand how to come up with the solution. The problem is -2x+y=6
===========================
There is no unique solution to the equation.
---
If you mean how to graph it:
It's a straight line so you need 2 points.
You can use the 2 intercepts.
At the y-intercept x = 0 --> y = 6 --> point (0,6)
At the x-intercept y = 0 --> x = -3 --> point (-3,0)
----------
Plot the 2 points, draw a line thru them.

Question 993132: How would I graph a slope 1/3 and (-4,-1)
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First plot the point (-4,-1).
Slope is change in y over change in x.
So in this case a change in x of 3 units gives you a change in y of 1 unit.
So another point on the line would be,
(-4,-1)+(3,1)=(-1,0)
Plot that point.
Then draw the line connecting the points.
.
.
.
.

Question 993060: x + y = 10 is this a function or not

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yes it is. it is a non-vertical line.So it passes the vertical line test for being a function

Question 992932: How could I use the point-slope form to find the equation of the line? The answer has to be in slope-intercept form.
One point on the line is (−2, −6). The slope is 2. Thank you!

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Just plug your givens into point-slope format and do the algebra steps you need.

Question 992858: all reals greater than or equal to -3 and less than 6 what is the interval representation
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interval notation:
[,)

Question 992304: Find the point of intersection of the two lines to 2x+y=5 and y=x-1
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.
You need to solve this system of two equations with two unknowns:

.

Substitute  y  from the second equation to the first one.  You will get an equation for the single unknown x only.

Then solve it.

Then substitute the found value of  x  into either equation of the original system to find  y.

Is it clear?

Good luck!

Question 992378: Suppose admission to the fair is $3. a) Write an equation slope-intercept form for the total cost of admission and any number of tickets at the rate of 6 tickets for$5.
b) Write an equation in slope-intercept form for the total cost of admission and any number of tickets at the rate of 12 tickets for $8. Answer by solver91311(20879) (Show Source): You can put this solution on YOUR website!$3 is a fixed cost and is therefore the -coordinate of the -intercept. For a) you get 6 tickets for \$5, therefore you get 1 ticket for . The rate per independent variable unit is the slope.

John

My calculator said it, I believe it, that settles it

Question 992349: Graph f(x)=x^2 and show f(1), f(2), f(3)