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 Functions/153209: Can someone help me out, please? Thank you! The owners of a parking garage have determined that their weekly revenue and cost in dollars are given by the following: R(x) = 56x - 2x^2 C(x) = 24x + 101 find the break even point.1 solutions Answer 112727 by jim_thompson5910(28595)   on 2008-08-24 14:00:55 (Show Source): You can put this solution on YOUR website!Remember, Profit = Revenue - Cost which is symbolically: Plug in and Distribute the negative. Combine like terms Now the break even point occurs when you neither gain money nor lose money. In other words, break even point happens when the profit is zero. So this means that the break even point occurs when Plug in Notice we have a quadratic equation in the form of where , , and Let's use the quadratic formula to solve for x Start with the quadratic formula Plug in , , and Square to get . Multiply to get Subtract from to get Multiply and to get . Simplify the square root (note: If you need help with simplifying square roots, check out this solver) or Break up the expression. So the answers are or which approximate to or So the break even points occur when the price is either $4.33 or$11.67
 Graphs/153204: Graph f(x)=10x-3 I did i went down three than up 10/11 solutions Answer 112724 by jim_thompson5910(28595)   on 2008-08-24 13:45:13 (Show Source): You can put this solution on YOUR website! Looking at we can see that the equation is in slope-intercept form where the slope is and the y-intercept is Since this tells us that the y-intercept is .Remember the y-intercept is the point where the graph intersects with the y-axis So we have one point Now since the slope is comprised of the "rise" over the "run" this means Also, because the slope is , this means: which shows us that the rise is 10 and the run is 1. This means that to go from point to point, we can go up 10 and over 1 So starting at , go up 10 units and to the right 1 unit to get to the next point Now draw a line through these points to graph So this is the graph of through the points and
 Graphs/153205: Graph f(x)=10x-3 I did i went down three than up 10/11 solutions Answer 112723 by jim_thompson5910(28595)   on 2008-08-24 13:44:54 (Show Source): You can put this solution on YOUR website! Looking at we can see that the equation is in slope-intercept form where the slope is and the y-intercept is Since this tells us that the y-intercept is .Remember the y-intercept is the point where the graph intersects with the y-axis So we have one point Now since the slope is comprised of the "rise" over the "run" this means Also, because the slope is , this means: which shows us that the rise is 10 and the run is 1. This means that to go from point to point, we can go up 10 and over 1 So starting at , go up 10 units and to the right 1 unit to get to the next point Now draw a line through these points to graph So this is the graph of through the points and
 Graphs/153206: Graph f(x)=10x-3 I did i went down three than up 10/11 solutions Answer 112722 by jim_thompson5910(28595)   on 2008-08-24 13:44:40 (Show Source): You can put this solution on YOUR website! Looking at we can see that the equation is in slope-intercept form where the slope is and the y-intercept is Since this tells us that the y-intercept is .Remember the y-intercept is the point where the graph intersects with the y-axis So we have one point Now since the slope is comprised of the "rise" over the "run" this means Also, because the slope is , this means: which shows us that the rise is 10 and the run is 1. This means that to go from point to point, we can go up 10 and over 1 So starting at , go up 10 units and to the right 1 unit to get to the next point Now draw a line through these points to graph So this is the graph of through the points and
Polynomials-and-rational-expressions/153200: factor completly:
10x^3-31x+15
1 solutions

Answer 112721 by jim_thompson5910(28595)   on 2008-08-24 13:44:04 (Show Source):
You can put this solution on YOUR website!
Are you sure that the expression is not ???

Looking at the expression , we can see that the first coefficient is , the second coefficient is , and the last term is .

Now multiply the first coefficient by the last term to get .

Now the question is: what two whole numbers multiply to (the previous product) and add to the second coefficient ?

To find these two numbers, we need to list all of the factors of (the previous product).

Factors of :
1,2,3,5,6,10,15,25,30,50,75,150
-1,-2,-3,-5,-6,-10,-15,-25,-30,-50,-75,-150

Note: list the negative of each factor. This will allow us to find all possible combinations.

These factors pair up and multiply to .
1*150
2*75
3*50
5*30
6*25
10*15
(-1)*(-150)
(-2)*(-75)
(-3)*(-50)
(-5)*(-30)
(-6)*(-25)
(-10)*(-15)

Now let's add up each pair of factors to see if one pair adds to the middle coefficient :

First NumberSecond NumberSum
11501+150=151
2752+75=77
3503+50=53
5305+30=35
6256+25=31
101510+15=25
-1-150-1+(-150)=-151
-2-75-2+(-75)=-77
-3-50-3+(-50)=-53
-5-30-5+(-30)=-35
-6-25-6+(-25)=-31
-10-15-10+(-15)=-25

From the table, we can see that the two numbers and add to (the middle coefficient).

So the two numbers and both multiply to and add to

Now replace the middle term with . Remember, and add to . So this shows us that .

Replace the second term with .

Group the terms into two pairs.

Factor out the GCF from the first group.

Factor out from the second group. The goal of this step is to make the terms in the second parenthesis equal to the terms in the first parenthesis.

Combine like terms. Or factor out the common term

---------------------------------------------

So factors to .

Note: you can check the answer by FOILing to get or by graphing the original expression and the answer (the two graphs should be identical).

Polynomials-and-rational-expressions/153201: factor completly:
4m^2-12m+9
1 solutions

Answer 112720 by jim_thompson5910(28595)   on 2008-08-24 13:42:06 (Show Source):
You can put this solution on YOUR website!

Looking at the expression , we can see that the first coefficient is , the second coefficient is , and the last term is .

Now multiply the first coefficient by the last term to get .

Now the question is: what two whole numbers multiply to (the previous product) and add to the second coefficient ?

To find these two numbers, we need to list all of the factors of (the previous product).

Factors of :
1,2,3,4,6,9,12,18,36
-1,-2,-3,-4,-6,-9,-12,-18,-36

Note: list the negative of each factor. This will allow us to find all possible combinations.

These factors pair up and multiply to .
1*36
2*18
3*12
4*9
6*6
(-1)*(-36)
(-2)*(-18)
(-3)*(-12)
(-4)*(-9)
(-6)*(-6)

Now let's add up each pair of factors to see if one pair adds to the middle coefficient :

First NumberSecond NumberSum
1361+36=37
2182+18=20
3123+12=15
494+9=13
666+6=12
-1-36-1+(-36)=-37
-2-18-2+(-18)=-20
-3-12-3+(-12)=-15
-4-9-4+(-9)=-13
-6-6-6+(-6)=-12

From the table, we can see that the two numbers and add to (the middle coefficient).

So the two numbers and both multiply to and add to

Now replace the middle term with . Remember, and add to . So this shows us that .

Replace the second term with .

Group the terms into two pairs.

Factor out the GCF from the first group.

Factor out from the second group. The goal of this step is to make the terms in the second parenthesis equal to the terms in the first parenthesis.

Combine like terms. Or factor out the common term

Condense the terms

---------------------------------------------

So factors to .

Note: you can check the answer by FOILing to get or by graphing the original expression and the answer (the two graphs should be identical).

 Inequalities/153193: I have a word problem that is from a worksheet that I do not understand how to write in order to solve. Could someone show me how this problem should be written. Thank you. Four more than the quotient of a number and 3 is at least that number.1 solutions Answer 112717 by jim_thompson5910(28595)   on 2008-08-24 12:57:36 (Show Source): You can put this solution on YOUR website!The sentence "Four more than the quotient of a number and 3 is at least that number" translates to Start with the given inequality. Multiply both sides by the LCD to clear any fractions. Distribute and multiply. Subtract from both sides. Subtract from both sides. Combine like terms on the left side. Divide both sides by to isolate . note: Remember, the inequality sign flips when we divide both sides by a negative number. Reduce. ---------------------------------------------------------------------- Answer: So the answer is
 Inequalities/153192: I have have an inequality word problem from a worksheet, could someone show me how the problem should be written so I can solve it thanks... The sum of a number and 81 is greater than the product of 3 and that number.1 solutions Answer 112716 by jim_thompson5910(28595)   on 2008-08-24 12:56:16 (Show Source): You can put this solution on YOUR website!The sentence "The sum of a number and 81 is greater than the product of 3 and that number" translates to Start with the given inequality. Subtract from both sides. Subtract from both sides. Combine like terms on the left side. Divide both sides by to isolate . note: Remember, the inequality sign flips when we divide both sides by a negative number. Reduce. ---------------------------------------------------------------------- Answer: So the answer is Which approximates to
Quadratic-relations-and-conic-sections/153191: I am trying to graph y=-x^2 -8x +9, I am not sure how to solve and graph
1 solutions

Answer 112715 by jim_thompson5910(28595)   on 2008-08-24 12:47:39 (Show Source):
You can put this solution on YOUR website!

In order to graph , we need to plot some points.

Let's find y when

Plug in .

Square to get .

Multiply and to get .

Multiply and to get .

Combine like terms.

So when , then .

So we have the point .

----------------------------------------------------

Let's find y when :

Plug in .

Square to get .

Multiply and to get .

Multiply and to get .

Combine like terms.

So when , then .

So we have the point .

----------------------------------------------------

Let's find y when :

Plug in .

Square to get .

Multiply and to get .

Multiply and to get .

Combine like terms.

So when , then .

So we have the point .

----------------------------------------------------

Let's find y when :

Plug in .

Square to get .

Multiply and to get .

Multiply and to get .

Combine like terms.

So when , then .

So we have the point .

----------------------------------------------------

Let's find y when :

Plug in .

Square to get .

Multiply and to get .

Multiply and to get .

Combine like terms.

So when , then .

So we have the point .

----------------------------------------------------

Let's find y when :

Plug in .

Square to get .

Multiply and to get .

Multiply and to get .

Combine like terms.

So when , then .

So we have the point .

----------------------------------------------------

Let's find y when :

Plug in .

Square to get .

Multiply and to get .

Multiply and to get .

Combine like terms.

So when , then .

So we have the point .

----------------------------------------------------

Let's find y when :

Plug in .

Square to get .

Multiply and to get .

Multiply and to get .

Combine like terms.

So when , then .

So we have the point .

----------------------------------------------------

Let's find y when :

Plug in .

Square to get .

Multiply and to get .

Multiply and to get .

Combine like terms.

So when , then .

So we have the point .

----------------------------------------------------

Let's find y when :

Plug in .

Square to get .

Multiply and to get .

Multiply and to get .

Combine like terms.

So when , then .

So we have the point .

----------------------------------------------------

Let's find y when :

Plug in .

Square to get .

Multiply and to get .

Multiply and to get .

Combine like terms.

So when , then .

So we have the point .

----------------------------------------------------

Now let's make a table of the values we just found.

#### Table of Values:



xy-90
-89
-716
-621
-524
-425
-324
-221
-116
09
10



Now let's plot the points:

#### Graph:

Now draw a curve through all of the points to graph :

Graph of

 Graphs/153190: This question is from textbook Algebra 2 I am so bad with math and they only way that im going to be able to pass this year is to get help. When a question is asking...Find the slope of each line. Then Graph. 54. y=8 57. x=9 60. x=-1/3 63. y=2/3 i dont understand how i am suppose to do that.1 solutions Answer 112714 by jim_thompson5910(28595)   on 2008-08-24 11:59:59 (Show Source): You can put this solution on YOUR website!I'll do the first two to get you started The slope of any line in the form of y=k where k is any number is 0 since the equation is a horizontal line. So the slope of is 0 So the graph of is: Graph of --------------------------------------- The slope of any line in the form of x=k where k is any number is undefined since the equation is a vertical line. So the slope of is undefined. So the graph of is: Graph of
 Graphs/153188: I have a graphing question. I am new to using graphing calculators. I have worked out the super basic understanding of how to use the function portion of my TI-84 Plus. However, when I key in y1 for f(x)=x2+x=-9, and I try to graph it and/or calculate it -- I never get the correct vertex -- which is suppose to be the ordered pair of (0.5,-9.25). I've tried working this so much, I am now completely confused. I know that my parabola opens upward because of the 1 co-effient. I know that it is to be a minimum. I've tried going into where I choose to calcuate the minimum. Yet I am missing something. I have to get this, otherwise, I am not able to proceed to continue my class. This is all online.1 solutions Answer 112713 by jim_thompson5910(28595)   on 2008-08-24 11:50:24 (Show Source): You can put this solution on YOUR website!I'm not too familiar with the TI 84 plus, but this page might be able to help.
 Unit_Conversion_Word_Problems/153128: I am the dad here and frustrated I can't help my son with this problem. It reads: If 1.0 km cubed of air has mass 1,200,000,000 kg, what is the density of air in g/cm cubed? The answer is given as 1.2x10 to the negative 3 g/cm cubed. We know the equation is density equals mass/volume but we obviously are missing something in the "power of" and the ending up with a negative power in the answer. I think we got the conversions correct, but am not even sure of that now. My son and I have worked on this (what appears to be a) simple math problem for over an hour and cannot explain the steps on getting to the answer given. I'm ashamed to admit we're both snowed. Any help would be appreciated. This is from a worksheet and I have no idea if it is from a textbook.1 solutions Answer 112629 by jim_thompson5910(28595)   on 2008-08-23 18:31:30 (Show Source): You can put this solution on YOUR website!Remember, 1 kg = 1000 g or 1 kg = 1*10^3 g and 1 km = 1000 m = 100,000 cm or 1 km = 1*10^3 m = 1*10^5 cm So 1,200,000,000 kg = 1,200,000,000,000 g or 1,200,000,000 kg = 1.2*10^12 g and 1 km^3 = (100,000)*(100,000)*(100,000) cm^3 = 1,000,000,000,000,000 cm^3 = 1*10^15 cm^3 ----------------------------- So 1,200,000,000 kg = 1.2*10^12 g and 1 km^3 = 1*10^15 cm^3 ---------------------------------- Also, remember that  Mass Density = --------- Volume  which is symbolically Start with the given equation. Plug in the given mass M=1.2*10^12 g and the given volume V=1*10^15 cm^3 Divide 1.2 by 1 to get 1.2. Divide by by subtracting Subtract the exponents. So the density is g/cm^3
 Linear-systems/153084: For a school play, 340 tickets with a total value of $810 were sold. Some tickets cost$2 and some cost $3. How many of each type were sold?1 solutions Answer 112568 by jim_thompson5910(28595) on 2008-08-22 21:11:55 (Show Source): You can put this solution on YOUR website!Let x=# of$2 tickets and y=# of $3 tickets First translate the word problem into the system of equations: Let's use substitution to solve the system Now in order to solve this system by using substitution, we need to solve (or isolate) one variable. I'm going to solve for y. So let's isolate y in the first equation Start with the first equation Subtract from both sides Rearrange the equation --------------------- Since , we can now replace each in the second equation with to solve for Plug in into the first equation. In other words, replace each with . Notice we've eliminated the variables. So we now have a simple equation with one unknown. Distribute to Multiply Combine like terms on the left side Subtract 1020 from both sides Combine like terms on the right side Divide both sides by -1 to isolate x Divide -----------------First Answer------------------------------ So the first part of our answer is: Since we know that we can plug it into the equation (remember we previously solved for in the first equation). Start with the equation where was previously isolated. Plug in Multiply Combine like terms -----------------Second Answer------------------------------ So the second part of our answer is: -----------------Summary------------------------------ So our answers are: and which means that 210$2 tickets and 130 $3 tickets were sold  Polynomials-and-rational-expressions/153076: How do you add this hard rational expression: x^2+3x+2/x^2-16 + 3x+6/x^2-16?wats the answer?1 solutions Answer 112554 by jim_thompson5910(28595) on 2008-08-22 19:08:23 (Show Source): You can put this solution on YOUR website! So where or  Polynomials-and-rational-expressions/153077: How do you subtract this rational expression: 7/x-5 - 2+x/x-5? whats the answer?1 solutions Answer 112553 by jim_thompson5910(28595) on 2008-08-22 19:05:35 (Show Source): You can put this solution on YOUR website! So where  Polynomials-and-rational-expressions/153075: How do you subtract this rational expression 4x+y/2x+3y - 2x-2y/2x+3y?1 solutions Answer 112552 by jim_thompson5910(28595) on 2008-08-22 19:03:02 (Show Source): You can put this solution on YOUR website! note:  Square-cubic-other-roots/153065: √-1=?1 solutions Answer 112523 by jim_thompson5910(28595) on 2008-08-22 16:04:43 (Show Source): You can put this solution on YOUR website!Since you cannot take the square root of -1 and get a real number, by convention where "i" is an imaginary number  Linear_Equations_And_Systems_Word_Problems/153060: Tickets to a local movie were sold at$6 for adults and $4.50 for students. If 63 tickets were sold for a total of$358.50, how many adult tickets were sold?1 solutions Answer 112517 by jim_thompson5910(28595)   on 2008-08-22 15:18:35 (Show Source): You can put this solution on YOUR website!Let x=# of adults and y=# of students Since the "63 tickets were sold", this means that the first equation is Also, because the tickets "were sold at $6 for adults and$4.50 for students" and they collected a "total of \$358.50", this means that the second equation is Multiply every term in the second equation by 10 to move the decimal point one spot to the right So we have the system of equations: Now in order to solve this system by using substitution, we need to solve (or isolate) one variable. I'm going to solve for y. So let's isolate y in the first equation Start with the first equation Subtract from both sides Rearrange the equation --------------------- Since , we can now replace each in the second equation with to solve for Plug in into the first equation. In other words, replace each with . Notice we've eliminated the variables. So we now have a simple equation with one unknown. Distribute to Multiply Combine like terms on the left side Subtract 2835 from both sides Combine like terms on the right side Divide both sides by 15 to isolate x Divide -----------------First Answer------------------------------ So the first part of our answer is: Since we know that we can plug it into the equation (remember we previously solved for in the first equation). Start with the equation where was previously isolated. Plug in Multiply Combine like terms -----------------Second Answer------------------------------ So the second part of our answer is: -----------------Summary------------------------------ So our answers are: and So there were 50 adults and 13 students