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3(2x-3)-6x=10
3(2x)+3(-3)-6x=10
6x-9-6x=10
(6-6)x-9=10
0x-9=10
0-9=10
-9=10
You're not crazy, this problem has no solution. When your variables are eliminated, and the two sides of the equation are not equal, there is no solution.
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simplify the following as completly as possible








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Find the slope of the line passing through the points (–8, –3) and (–2, 2).
The formula for finding the slope when given two points is:
(x1,y1)=(-8,-3) and (x2,y2)=(-2,2)



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The problem is:
x-2y=4
It's great that you're thinking, but you're thinking too hard. Pick an easy number to deal with and substitute it into the equation and solve for the other variable. There are an infinite number of choices.
:
If x=0, then:
(0)-2y=4
-2y=4
-2y/-2=4/-2
y=-2 The ordered pair (x,y)=(0,-2)
Check: 0-2(-2)=4
4=4
:
If y=0, then:
x-2(0)=4
x-0=4
x=4 The ordered pair is (x,y)=(4,0)
Check: 4-2(0)=4
4=4
:
If x=2, then:
2-2y=4
-2+2-2y=-2+4
-2y=2
-2y/-2=2/-2
y=-1 The ordered pair is (x,y)=(2,-1)
Check: 2-2(-1)=4
2+2=4
4=4
:
You really can pick an infinite number of possibilities. A person could lose a brain cell doing that in their head!!!
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solve the following equations and express the answer as an ordered pair if possible
L1) 2x-4y=8
L2) x-2y=4
Multiply L2 by -2 and add it to L1 in order to eliminate one of the variables.
-2(x-2y=4) --->> -2x+4y=-8
:
2x-4y=8
-2x+4y-8
___________
0x+0y=0
0=0
:
This is a special case, our variables are both eliminated and our constants are =. Graphically, they are the same line and have all points in common.
This means there are an infinite number of solutions. Some teachers and books are happy to get that answer or "all real numbers."
:
Others want you to solve either equation for y and write your answer like this:
x-2y=4
-2y=-x+4
-2y/-2=-x/-2+4/-2
y=(1/2)x-2
The answer is: (x,(1/2)x-2)
You don't have to do this last part unless your teacher or book requires it.
:
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Ernie has $.65 in nickels and dimes. He has 13 more nickels than dimes. how many coins does he have?
:
Let the number of dimes be: x
then the number of nickles is: x+13
Then the amount of money in dimes he has is: .10x
The amount of money in nickles is: .05(x+13)
The total amount of money is: $3.65
:
The problem to solve is:
.10x+.05(x+13)=3.65
.10x+.05x+.65=3.65
.15x+.65=3.65
.15x+.65-.65=3.65-.65
.15x=3.00
.15x/.15=3.00/.15
x=20
The amount of dimes: x=20
The amount of nickles: x+13=20+13=33
The total amount of coins are:20+33=53
:
Check does 20 dimes and 33 nickles = $3.65?
.10(20)+.05(33)=$3.65
2.00+1.65=$3.65
$3.65=$3.65 Cool beans, we're right!!!
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Given y=(x-2)/(x+5) find the inverse function (switch x&y and solve for Y)








This is the inverse.
Some books and teachers don't like having all of those negative signs. If that's the case, multiply the numerator and denominator by -1:


Might be the answer in the back of your book. It's the same thing.
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Divide 2-7x^2+x^4-2x-x^3 by x+2
Put your polynomials in descending order.
divided by x+2
You didn't specify that I had to use long division which is very difficult to me to illustrate because I don't know all the java commands to allow for spaces and lines. I'm using synthetic division.
Change the sign of 2 in x+2, that's on the outside. Put the coefficients on the inside:
-2|1 -1 -7 -2 2
::|
--------------- Bring down the 1
:: 1
:
-2|1 -1 -7 -2 2
::|0 -2
---------------- Multiply -2 by 1 and put it under -1
:: 1
:
-2|1 -1 -7 -2 2
::|0 -2
----------------- add -1 and -2 and put the answer under them
:: 1 -3
:
-2|1 -1 -7 -2 2
::|0 -2 6 2 0
------------------ Repeat the steps until you have this.
:: 1 -3 -1 0 2
These are the coefficients of your polynomial starting 1 degree less than what you started with. The last number is the remainder.
r=2
r=2 Sometimes you write the remainder as the numerator and the divisor as the denominator.

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Factor the algebraic expressions completely:
There are other method you can use for the first polynomial. I am grouping or using the ac method or using the arch method it's got a lot of names.
First factor out the GCF, 2.
2 factors that multiply to give you ac=3*8=24, but add to give you b=-14 are -12 and -2 (-12*-2=24 and -2-12=-14) Replace the middle term with -12x-2x
Group the first two and last two terms
Factor out the GCF in each parenthesis.
Factor out the x-4

:
and
:
You have to facto by grouping.
Group the first two terms and the last two terms.
Factor the GCF out of each.
Factor (x+2) out of each.

:
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These are kind of cool because you get to pick the points to solve for. You get to make this as easy as you can.
:
2x+y=10
Let x=0 and solve for y: (0 is easy!)
2(0)+y=10
0+y=10
y=10 This ordered pair (x,y)=(0,10)
:
Now let's let y=0 and solve for x:
2x+0=10
2x=10
2x/2=10/2
x=5 This ordered pair (x,y)=(5,0)
:
Let x=1 and solve for y: (1 is easy too!)
2(1)+y=10
2+y=10
-2+2+y=10-2
0+y=8
y=8 This ordered pair is (1,8)
:
What easy numbers do you want x to be? There are an infinite number of points to choose, make it as easy as you can on yourself.
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The slope-intercept form of a line is , m=slope, and (0,b)=y-intercept.
write the equation of each line given the slope and y-intercept.
4. m=3/4;y-intercept=-1


:
5.m=-4;y-intercept=8

:
6.m=-1/4;y-intercept=0


:
write the equation of each line given a point on the line and the slope.
7. (0,7), m=-3

:
Just put the parts where they belong in the slope intercept form of a line.
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Determine which two equations represent parallel lines.(a) y = x + 3 (b) y = x – 6 (c) y = 2x + 10 (d) y = 2x – 3
These equations are in slope intercept form:, m=slope, and b=y-intercept.
Parallel lines have the same slopes.
(a)y=(1)x+3
(b)y=(1)x-6
(a) and (b) both have a slope of 1 and are parallel.
:
(c) y=(2)x+10
(d y=(2)x-3
(c) and (d) both have a slope of 2 and are parallel.
:
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Dear A Student,
L1) x-y=7
L2) 3x-11y=-1
L3) x+y+1=0
You found the intersection of L1 and L2 (9.75,2.75)
You found the intersection of L1 and L3 (3,-4)
Now you have to find the intersection of L2 and L3:
3x-11y=-1
x+y+1=0--->x=-y-1
:
3(-y-1)-11y=-1
-3y-3-11y=-1
-14y-3=-1
-14y=2


:




The third vertex is (-6/7,-1/7)
It helps to graph the lines so you can see which lines you need to use for each vertex.
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Hi ac,
The base of a ladder is 3 feet away from the wall. The top of the ladder is 14 feet from the floor. Find the length of the ladder to the nearest thousandth.
:
The ladder, floor and wall form a right triangle in which the wall and floor are the legs and the ladder is the hypotenuse.
The pythagorean theorem can be used to solve this kind of problem: c=hypotenuse, a=one leg, and b=other leg.
Let the ladder=c.






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It says simplify:

You kind of know what to do.



That's all that you can do.
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54 divided by negative one half
54 divided by Flip the fraction over and multiply.
Remember -2/1=-2
When multiplying numbers of opposite signs, multiply as usual and the answer is -.

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Two dice are rolled. What are the number of ways an 8 can appear from the throw of the dice?
A die has 1-6 dots possible.
Below you see the ways you can roll 8 with 2 dice.
(2,6),(3,5),(4,4),(5,3),(6,2)
There are 5 ways to roll an two dice with the sum of 8.

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We need you to type in your problem and directions. We don't have your book. Tell me your problem and directions and I'll send you the problem worked out.

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Find the slope of the line passing through the points (3, 2) and (3, -3).
Notice that both the x's are the same. If you connected the two points, you'd have a vertical line. Vertical lines have undefined slopes.
If you did try to find the slope between these two points using the slope fomula: With the points (x1,y1)=(3,2) and (x2,y2)=(3,-3), you'd get:

A 0 in the denominator of a fraction is undefined.
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Find the slope and the y-intercept. y = 6x – 6
The slope intercept form of a line is , m=slope and (0,b)=y-intercept.
slope:
y-intercept: or (0,-6)
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Exponential Functions
It is known that fourth of all aluminum cans distributed will be recycled each year. A company distributes 1,9000 cans.
The number of cans still in use after time t, in years, is given by the following function.

N(t)=1900(1/4)^t
N(5)=1900(1/4)^(5)
N(5)=1900(1/1024)
N(5)=1.85546875
You can round it off to whatever your asked for. Please double check the formula you typed in, and the question to be sure I gave you what you really wanted.
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f(x)= x(x-6)
State wheather the function is a polynomial function or not. If it is,give its degree. If it is not,tell why not.
:

<---it is a polynomial (it has 2 terms).
<---it's degree is 2.
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Write the slope of a line parallel to the given line.
-5x + y = 12
:
Put the equation of the line in slope intercept form:, m=slope, and b=yintercept.
:
-5x+y=12
5x-5x+y=5x+12
slope m=5
Parallel lines have equal slopes so any line parallel to this one has a slope of
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The width of a rectangle is 3/4 of its length. If the perimeter of the rectangle is 140 feet, what are the dimensions of the rectangle?
:
The formula for perimeter of a rectangle is:
Let the length (L) be:x
Then width (W) is: (3/4)x
Perimeter (P) is: 140 ft
: Plug those values into your formula and solve for x:
140=2(x)+2(3/4)x
140=2x+6/4x
140=2x+3/2x
140=(4/2)x+(3/2)x
140=(7/2)x
2(140)=2(7/2)x
280=7x
280/7=7x/7
40=x
Length: x=40 ft.
Width:(3/4)(40)=3(10)=30 ft.
:
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THE RANDOLPHS USED 12 MORE GALLONS OF FUEL OIL IN OCTOBER THAN IN SEPTEMBER AND TWICE AS MUCH OIL IN NOVEMBER AS IN SEPTEMBER. IF THEY USED 132 GALLONS FOR THE THREE MONTHS, HOW MUCH WAS USED DURING EACH MONTH?
:
Let the amount used in Sept.=x
Then the amount used in Oct.=x+12
Then the amount used in Nov.=2x
Add the months together=132
:
Equation to solve:
(x)+(x+12)+(2x)=132
4x+12=132
4x+12-12=132-12
4x=120
4x/4=120/4
x=30
:
Sept: x=30 gal
Oct:x+12=30+12=42 gal
Nov:2x=2(30)=60 gal
:
Check, if you add all three months do you get 132 gal?
30+42+60=132
132=132 Yes it does!!!
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solving inequalities:
5x - 14 < 6
5x-14+14<6+14
5x<20

x<4
This is read x is less than 4, if you need to graph this on a number line, put either a o ar a ) over 4 (that depends on your book and teacher) and shade over the numbers that are less than 4.
<<========o--------->
-1,0,1,2,3,4,5,6,7,8,9
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Let C = 64/27. Then find C with exponent -2/3.
Flip the fraction and change the sign of the exponent.
Notice that 27=3^3 and 64=4^3
Multiply the inner exponents by the outer exponents.
Cancel the 3's
Apply the squares
Pat yourself on the back your done.
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State the degree of the following polynomial:
8x^3+6x^2y+4xy^3-2y^4
The degree of a polynomial is the degree of it's highest degreed term.
8x^3 <--degree 2
6x^2y <--degree 2+1=3
4xy^3 <--degree 1+3=4
2y^4 <--degree 4
The two highest degreed terms have a degree of 4, so the degree of the polynomial is
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Parallel to y-1=0 with y-intercept (0,-1)
y-1=0
y-1+1=0+1
y=1
This is a special case. Any time you have y=k, where k is a real number and there's no x, you have a horizontal line going through k. In this case y=1 is a horizontal line going through y=1. Horizontal lines have slopes of 0 because y never changes.
A line parallel to a horizontal line would also be parallel. Horizontal lines have the same y value for every point.
The equation of a horizontal line going through (0,-1) is
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Question says to simplify...
Distribute the 3x^2 and -2


You can only combine numbers without variables and numbers with the same exact variables raised to the same exact powers.

You're done.
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Multiply and simplify.
Distribute 6x^2 to every term in the parenthesis.
When multiplying terms add the exponents of like bases.
None of these are like terms, so your done.
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