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 Quadratic_Equations/128744: (x+7)^2=811 solutions Answer 94182 by jim_thompson5910(28595)   on 2008-02-24 12:47:38 (Show Source): You can put this solution on YOUR website! Start with the given equation Take the square root of both sides Simplify the square root (note: If you need help with simplifying the square root, check out this solver) Subtract 7 from both sides to isolate x. Break down the expression into two parts:  or  Now combine like terms for each expression:  or  ----------------------------------- Answer: So our solution is  or  Notice when we graph the equations and we get: graph of (red) and (green) Here we can see that the two equations intersect at x values of and , so this verifies our answer.
 Systems-of-equations/128655: If f(x)=2x^2 -7x+3 find Part A f(2) Part B f(-3) I have tried to solve this by plugging the 2 in for x and for part A came up with -3 and for part B came up with 42. am I doing this correctly1 solutions Answer 94125 by jim_thompson5910(28595)   on 2008-02-23 22:10:30 (Show Source): You can put this solution on YOUR website!a) Let's find f(2) Start with the given function Plug in Raise 2 to the 2nd power to get 4 Multiply 2 and 4 to get 8 Multiply 7 and 2 to get 14 Subtract 14 from 8 to get -6 Add -6 and 3 to get -3 ---------------------------------- b) Let's find f(-3) Start with the given function Plug in Raise -3 to the 2nd power to get 9 Multiply 2 and 9 to get 18 Multiply 7 and -3 to get -21 Subtract -21 from 18 to get 39 Add 39 and 3 to get 42 So you are correct.
 Systems-of-equations/128657: ok this one I really do not understand becuase they do not give me a value for x or anything. Part A) Calculate the value of the discriminant of x^2+x+3=0 Part B) by examining teh sign of the discriminant in part a, how many x-intercepts would the graph of y = x^2+x+3 have? Why? I know that to get the discrimant the equation is b^2 - 4ac, and that if the discriminant is positive the the solutions will be real numbers, and if it is a negative you will have two complex solutions. but how do I solve this if I do not know what the value of b is or the value of A and C1 solutions Answer 94123 by jim_thompson5910(28595)   on 2008-02-23 22:06:57 (Show Source): You can put this solution on YOUR website! From the quadratic formula the discriminant consists of all of the terms in the square root. So the discriminant is the discriminant tells us how many solutions (and what type of solutions) we can expect for any quadratic. Now let's find the discriminant for (notice how , and ): Start with the given equation Plug in a=1, b=1, c=3 Square 1 to get 1 Multiply -4*1*3 to get -12 Combine 1 and -12 to get -11 Since the discriminant equals -11 (which is less than zero) , this means there are two complex solutions. Notice if we graph , we get and we can see that there are two complex solutions. So this visually verifies our answer.
 absolute-value/128605: find the y-intercept -x+3y=241 solutions Answer 94093 by jim_thompson5910(28595)   on 2008-02-23 16:35:31 (Show Source): You can put this solution on YOUR website! Start with the given equation To find the y-intercept, let x=0 and solve for y: Plug in Simplify Divide both sides by 3 to isolate y Reduce So the y-intercept is (note: the y-intercept will always have a x-coordinate equal to zero)
 Functions/128612: Make a table of at least 7 ordered pairs that satisfy the equation . Then use your table to graph the function.1 solutions Answer 94091 by jim_thompson5910(28595)   on 2008-02-23 16:22:43 (Show Source): You can put this solution on YOUR website!In order to generate ordered pairs, we need to plot evaluate some x values to get some y values to get the points. So let's find the first point: Start with the given function Plug in Raise -5 to the 2nd power to get 25 Multiply 1 and 25 to get 25 Subtract 3 from 25 to get 22 So when , we have So our 1st point is (-5,22) -------------- Let's find another point -------------- Start with the given function Plug in Raise -4 to the 2nd power to get 16 Multiply 1 and 16 to get 16 Subtract 3 from 16 to get 13 So when , we have So our 2nd point is (-4,13) -------------- Let's find another point -------------- Start with the given function Plug in Raise -3 to the 2nd power to get 9 Multiply 1 and 9 to get 9 Subtract 3 from 9 to get 6 So when , we have So our 3rd point is (-3,6) -------------- Let's find another point -------------- Start with the given function Plug in Raise -2 to the 2nd power to get 4 Multiply 1 and 4 to get 4 Subtract 3 from 4 to get 1 So when , we have So our 4th point is (-2,1) -------------- Let's find another point -------------- Start with the given function Plug in Raise -1 to the 2nd power to get 1 Multiply 1 and 1 to get 1 Subtract 3 from 1 to get -2 So when , we have So our 5th point is (-1,-2) -------------- Let's find another point -------------- Start with the given function Plug in Raise 0 to the 2nd power to get 0 Multiply 1 and 0 to get 0 Subtract 3 from 0 to get -3 So when , we have So our 6th point is (0,-3) -------------- Let's find another point -------------- Start with the given function Plug in Raise 1 to the 2nd power to get 1 Multiply 1 and 1 to get 1 Subtract 3 from 1 to get -2 So when , we have So our 7th point is (1,-2) -------------- Let's find another point -------------- Start with the given function Plug in Raise 2 to the 2nd power to get 4 Multiply 1 and 4 to get 4 Subtract 3 from 4 to get 1 So when , we have So our 8th point is (2,1) -------------- Let's find another point -------------- Start with the given function Plug in Raise 3 to the 2nd power to get 9 Multiply 1 and 9 to get 9 Subtract 3 from 9 to get 6 So when , we have So our 9th point is (3,6) -------------- Let's find another point -------------- Start with the given function Plug in Raise 4 to the 2nd power to get 16 Multiply 1 and 16 to get 16 Subtract 3 from 16 to get 13 So when , we have So our 10th point is (4,13) -------------- Let's find another point -------------- Start with the given function Plug in Raise 5 to the 2nd power to get 25 Multiply 1 and 25 to get 25 Subtract 3 from 25 to get 22 So when , we have So our 11th point is (5,22) Now lets make a table of the values we have calculated  xy -522 -413 -36 -21 -1-2 0-3 1-2 21 36 413 522  Now plot the points. Note: you need to use Firefox to see the next two graphs. Now connect the points to graph (note: the more points you plot, the easier it is to draw the graph)
Functions/128610: Let , and

Complete the table
xf(x)g(x)h(x)
-1-3
-2
12

1 solutions

Answer 94090 by jim_thompson5910(28595)   on 2008-02-23 16:11:10 (Show Source):
You can put this solution on YOUR website!
xf(x)g(x)h(x)
-1-3
-2
12

Let's find the first entry of g(x)

Plug in

Multiply

Subtract

So our table becomes

xf(x)g(x)h(x)
-1-3-6
-2
12

Let's find the second entry of f(x)

Plug in

Multiply

Reduce

xf(x)g(x)h(x)
-1-3-6
1-2
12

Let's find the third entry of x

Plug in

Divide both sides by 3 to isolate x

Now plug this value into the last row of the x column

xf(x)g(x)h(x)
-1-3-6
1-2
412

Let's find the third entry of g(x)

Plug in

Multiply

Subtract

Now plug this into the last entry of the g(x) column

xf(x)g(x)h(x)
-1-3-6
1-2
4129

Now let's find the first entry of h(x)

Break up the function

Plug in

Plug in , (these values are from the table)

Multiply

xf(x)g(x)h(x)
-1-3-6
1-2
4129

Now let's find the first entry of h(x)

Break up the function

Plug in

Plug in , (these values are from the table)

Multiply and reduce

Combine the fractions

xf(x)g(x)h(x)
-1-3-6
1-2
4129

 Linear-equations/128597: find the slope of the line containing the pair of points (9,0) and (10,6). Simplify your answer, type an integer or a fraction.1 solutions Answer 94089 by jim_thompson5910(28595)   on 2008-02-23 15:41:51 (Show Source): You can put this solution on YOUR website! Let's denote the first point (9,0) as . In other words, and Now let's denote the second point (10,6) as . In other words, and ------------------------- Start with the slope formula Plug in ,,, Subtract the terms in the numerator to get . Subtract the terms in the denominator to get Reduce --------------------- Answer: So the slope of the line through the points (9,0) and (10,6) is
 Expressions-with-variables/128583: Simplify 3(2r - 5) + 8(r + 2) Simplify to make easier please thanks!1 solutions Answer 94085 by jim_thompson5910(28595)   on 2008-02-23 14:20:47 (Show Source): You can put this solution on YOUR website! Start with the given expression Distribute Group like terms Combine like terms So simplifies to In other words,
 Inequalities/128582: Solve the inequality. y - 6 < 9 Any help please! Thanks1 solutions Answer 94084 by jim_thompson5910(28595)   on 2008-02-23 14:17:42 (Show Source): You can put this solution on YOUR website! Start with the given inequality Add 6 to both sides Combine like terms on the right side -------------------------------------------------------------- Answer: So our answer is
 Equations/128592: Solve: 9x – 10 = 3x - 1 1 solutions Answer 94083 by jim_thompson5910(28595)   on 2008-02-23 14:16:57 (Show Source): You can put this solution on YOUR website! Start with the given equation Add 10 to both sides Subtract 3x from both sides Combine like terms on the left side Combine like terms on the right side Divide both sides by 6 to isolate x Reduce -------------------------------------------------------------- Answer: So our answer is (which is approximately in decimal form)
 Functions/128591: Graph the inverse function 1 solutions Answer 94082 by jim_thompson5910(28595)   on 2008-02-23 14:15:06 (Show Source): You can put this solution on YOUR website! Start with the original graph In order to graph the inverse function, simply reflect the original graph over the line (the dashed line) (note: for some reason, the following image does not display correctly in Internet Explorer. So I recommend the use of Firefox to see this image.) Graph of the original function (red line) and the inverse function (blue line)
 Functions/128590: The given function is Find 1 solutions Answer 94079 by jim_thompson5910(28595)   on 2008-02-23 13:55:24 (Show Source): You can put this solution on YOUR website! Start with the given function To find , simply swap x and f(x) to get Add 15f(x) to both sides Subtract x from both sides Divide both sides by 15 to isolate f(x) So the inverse function is Now plug in Subtract Divide
 Functions/128579: Find the domain and range of the following: 1 solutions Answer 94078 by jim_thompson5910(28595)   on 2008-02-23 13:06:45 (Show Source): You can put this solution on YOUR website! Looking at the graph, notice how the graph extends to infinity in both directions in the x direction. So this shows us that there are no restrictions on the domain. Since we don't have any restrictions on the domain, this shows us that the domain is all real numbers. In other words, we can plug in any in for x So the domain of the function in set-builder notation is: In plain English, this reads: x is the set of all real numbers (In other words, x can be any number) Also, in interval notation, the domain is: --------------------------------------------------- From the graph, we can see that the lowest point is (0,-3). So the smallest that y can be is -3 So the range of the function in set-builder notation is: In plain English, this reads: y is the set of all real numbers that are greater than or equal to -3 Also, in interval notation, the range is: [-3,)
 Functions/128578: Find the domain and range of the following: 1 solutions Answer 94077 by jim_thompson5910(28595)   on 2008-02-23 12:59:56 (Show Source): You can put this solution on YOUR website! Looking at the graph, notice how the line extends to infinity in all four directions. So this shows us that there are no restrictions on the domain. Since we don't have any restrictions on the domain, this shows us that the domain is all real numbers. In other words, we can plug in any in for x So the domain of the function in set-builder notation is: In plain English, this reads: x is the set of all real numbers (In other words, x can be any number) Also, in interval notation, the domain is: --------------------------------------------------- Also, since there are no restrictions on the range, this means that the range is all real numbers. So the range of the function in set-builder notation is: In plain English reads: y is the set of all real numbers (In other words, y can be any number) Also, in interval notation, the range is:
 Functions/128577: Find the domain and range of the following: 1 solutions Answer 94076 by jim_thompson5910(28595)   on 2008-02-23 12:53:07 (Show Source): You can put this solution on YOUR website! Looking at the graph, notice how both the x-values and y-values are restricted. In other words, we cannot plug in x=10 (as it does not fall on the curve). So we can only plug in x-values from -4 to 4. So the domain is which in set-builder notation is In plain English, this reads: x is the set of all real numbers that are in between -4 and 4 Also, in interval notation, the domain is: [-4,4] ------------------------------- This also applies to the range. The range is also . Which in set-builder notation is In plain English, this reads: y is the set of all real numbers that are in between -4 and 4 Also, in interval notation, the range is: [-4,4] -------------------------- Summary: So the domain and range are both [-4,4]
 Functions/128576: Find the domain and range of the following: b) 1 solutions Answer 94075 by jim_thompson5910(28595)   on 2008-02-23 12:44:32 (Show Source): You can put this solution on YOUR website! Looking at , we can see that there are no square roots, logs, and other functions where there are restrictions on the domain. Also, we can see that the function does not have a division by x (or any combination of variables and constants). So we don't have to worry about division by zero. Since we don't have any restrictions on the domain, this shows us that the domain is all real numbers. In other words, we can plug in any in for x So the domain of the function in set-builder notation is: In plain English reads: x is the set of all real numbers (In other words, x can be any number) Also, in interval notation, the domain is: Now to find the range, simply graph the function to get From the graph, we can see that the lowest point is (2,0). So the smallest that y can be is 0 So the range of the function in set-builder notation is: In plain English reads: y is the set of all real numbers that are greater than or equal to 0 Also, in interval notation, the range is: [0,)
 Functions/128575: Find the domain and range of the following: a) 1 solutions Answer 94074 by jim_thompson5910(28595)   on 2008-02-23 12:40:08 (Show Source): You can put this solution on YOUR website! Looking at , we can see that there are no square roots, logs, and other functions where there are restrictions on the domain. Also, we can see that the function does not have a division by x (or any combination of variables and constants). So we don't have to worry about division by zero. Since we don't have any restrictions on the domain, this shows us that the domain is all real numbers. In other words, we can plug in any in for x So the domain of the function in set-builder notation is: In plain English reads: x is the set of all real numbers (In other words, x can be any number) Also, in interval notation, the domain is: Now to find the range, simply graph the function to get From the graph, we can see that the lowest point is (0,-2). So the smallest that y can be is -2 So the range of the function in set-builder notation is: In plain English reads: y is the set of all real numbers that are greater than or equal to -2 Also, in interval notation, the range is: [-2,)
 Equations/128569: Hi Can I have some help with the following function? A function f is given. f(x) = √6x - 8 (a) Find f -1.1 solutions Answer 94073 by jim_thompson5910(28595)   on 2008-02-23 12:37:04 (Show Source): You can put this solution on YOUR website!Is this what the function looks like: ? Start with the given equation Plug in Multiply Subtract If you have not learned about imaginary numbers, then this is where you would stop. If you have, then... Simplify the square root ------------------------------------------------- OR Is this what the function looks like: ? Start with the given equation Plug in Multiply Simplify the square root Rearrange the terms
 Functions/128568: Find the domain and range of the following: c) d) 1 solutions Answer 94072 by jim_thompson5910(28595)   on 2008-02-23 12:31:03 (Show Source): You can put this solution on YOUR website!c) Looking at , we can see that there are no square roots, logs, and other functions where there are restrictions on the domain. Also, we can see that the function does not have a division by x (or any combination of variables and constants). So we don't have to worry about division by zero. Since we don't have any restrictions on the domain, this shows us that the domain is all real numbers. In other words, we can plug in any in for x So the domain of the function in set-builder notation is: In plain English reads: x is the set of all real numbers (In other words, x can be any number) Also, in interval notation, the domain is: Now to find the range, simply graph the function to get From the graph, we can see that the lowest point is (0,0). So the smallest that y can be is 0 So the range of the function in set-builder notation is: In plain English reads: y is the set of all real numbers that are greater than or equal to 0 Also, in interval notation, the range is: [0,) d) Looking at , we can see that there are no square roots, logs, and other functions where there are restrictions on the domain. Also, we can see that the function does not have a division by x (or any combination of variables and constants). So we don't have to worry about division by zero. Since we don't have any restrictions on the domain, this shows us that the domain is all real numbers. In other words, we can plug in any in for x So the domain of the function in set-builder notation is: In plain English reads: x is the set of all real numbers (In other words, x can be any number) Also, in interval notation, the domain is: Now to find the range, simply graph the function to get From the graph, we can see that the lowest point is (-2,0). So the smallest that y can be is 0 So the range of the function in set-builder notation is: In plain English reads: y is the set of all real numbers that are greater than or equal to 0 Also, in interval notation, the range is: [0,)
 Functions/128565: Find the domain and range of the following: a) b) 1 solutions Answer 94071 by jim_thompson5910(28595)   on 2008-02-23 12:25:16 (Show Source): You can put this solution on YOUR website!a) Looking at , we can see that there are no square roots, logs, and other functions where there are restrictions on the domain. Also, we can see that the function does not have a division by x (or any combination of variables and constants). So we don't have to worry about division by zero. Since we don't have any restrictions on the domain, this shows us that the domain is all real numbers. In other words, we can plug in any in for x So the domain of the function in set-builder notation is: In plain English reads: x is the set of all real numbers (In other words, x can be any number) Also, in interval notation, the domain is: Now to find the range, simply graph the function to get From the graph, we can see that the lowest point is (0,3). So the smallest that y can be is 3 So the range of the function in set-builder notation is: In plain English reads: y is the set of all real numbers that are greater than 3 Also, in interval notation, the range is: [3,) b) Looking at , we can see that there are no square roots, logs, and other functions where there are restrictions on the domain. Also, we can see that the function does not have a division by x (or any combination of variables and constants). So we don't have to worry about division by zero. Since we don't have any restrictions on the domain, this shows us that the domain is all real numbers. In other words, we can plug in any in for x So the domain of the function in set-builder notation is: In plain English reads: x is the set of all real numbers (In other words, x can be any number) Also, in interval notation, the domain is: Now to find the range, simply graph the function to get From the graph, we can see that the lowest point is (0,-5). So the smallest that y can be is -5 So the range of the function in set-builder notation is: In plain English reads: y is the set of all real numbers that are greater than -5 Also, in interval notation, the range is: [-5,)
 Equations/128537: This question is from textbook Pre-Algebra I can't figure this out at all. Problem #44 states: Suppose , and a,b,c and d are all positive integers. Find the value of . I don't even know how to begin. I understood this chapter up to this question. Thanks.1 solutions Answer 94070 by jim_thompson5910(28595)   on 2008-02-23 12:17:23 (Show Source): You can put this solution on YOUR website!Remember, the number 24,130 can be broken up like this: So this shows us that which means . Also, which means . This continues until you run out of variables. So we have the values , , , and So becomes
 Polynomials-and-rational-expressions/128560: Can you please help me understand the rules and format for this type of math? (6x^2-4x+7)+(2x^2-3x-9)= I tried this one,but i cant figured it out? 6x-(4x-5)=13 6x+(4x+5)=13 1 solutions Answer 94069 by jim_thompson5910(28595)   on 2008-02-23 11:53:44 (Show Source): You can put this solution on YOUR website! Start with the given expression Group like terms Combine like terms
 Polynomials-and-rational-expressions/128558: This question is from textbook Introductory Algebra I think I came up with the right answer, but would love for someone to double-check my work! The problem reads: Solve 3a-5/a^2+4a+3 + 2a+2/a+3 = a-3/a+1 I came up with a = -6 or -11 solutions Answer 94068 by jim_thompson5910(28595)   on 2008-02-23 11:51:57 (Show Source): You can put this solution on YOUR website! Let's verify the solution Start with the given equation Plug in . In other words, replace each with Square and multiply Combine like terms Combine the fractions on the right side and reduce Since the two sides of the equation are equal, this verifies our answer. ------------------------------------------------------------------------- Let's verify the solution Start with the given equation Plug in . In other words, replace each with Square and multiply Combine like terms Notice how there are denominators of zero. Since division by zero is undefined, is not a solution of the equation. So our only solution is
 Functions/128507: Find the domain and range of the following d) e) 1 solutions Answer 94022 by jim_thompson5910(28595)   on 2008-02-22 19:29:32 (Show Source): You can put this solution on YOUR website!# 1 d) Start with the given function Set the denominator equal to zero. Remember, dividing by 0 is undefined. So if we find values of x that make the denominator zero, then we must exclude them from the domain. Subtract 9 from both sides Combine like terms on the right side Since makes the denominator equal to zero, this means we must exclude from our domain So our domain is: which in plain English reads: x is the set of all real numbers except So our domain looks like this in interval notation note: remember, the parenthesis excludes -9 from the domain --------------------------------------------------------- Now to find the range, simply graph the function to get note: ignore the vertical lines, they are not part of the graph and are asymptotes Looking at the graph, we can see that y can be any number except 0. So . So our range is: which in plain English reads: y is the set of all real numbers except So our range looks like this in interval notation note: remember, the parenthesis excludes 0 from the range e) Start with the given function Set the denominator equal to zero. Remember, dividing by 0 is undefined. So if we find values of x that make the denominator zero, then we must exclude them from the domain. Factor the left side (note: if you need help with factoring, check out this solver) Now set each factor equal to zero: or or Now solve for x in each case So our solutions are or Since and make the denominator equal to zero, this means we must exclude and from our domain So our domain is: which in plain English reads: x is the set of all real numbers except or So our domain looks like this in interval notation note: remember, the parenthesis excludes -2 and 2 from the domain --------------------------------------------------------- Now to find the range, simply graph the function to get note: ignore the vertical lines, they are not part of the graph and are asymptotes Looking at the graph, we can see that y can be any number except 0. So . So our range is: which in plain English reads: y is the set of all real numbers except So our range looks like this in interval notation note: remember, the parenthesis excludes 0 from the range