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 Functions/152933: This question is from textbook glencoe mcgraw-hill what is the range for the function {(1,3),(5,7),(9,11)}1 solutions Answer 112382 by jim_thompson5910(28711)   on 2008-08-21 17:15:51 (Show Source): You can put this solution on YOUR website!Range: All y values that are possible So in this case, the range is {3,7,11}
Rational-functions/152928: Another graphing a function question! I can't figure the graphing part out.
Graph the function f(x)= -3x squared + x-5
1 solutions

Answer 112379 by jim_thompson5910(28711)   on 2008-08-21 16:50:51 (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 .

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 .

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 .

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 .

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 .

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-2-19
-1-9
0-5
1-7
2-15



Now let's plot the points:

#### Graph:

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

Graph of

 Rational-functions/152926: Please help me solve this problem on functions: 1. Graph the function f(x)= -3x+7. Label the axes and the line with its equation. Thank you so much!1 solutions Answer 112378 by jim_thompson5910(28711)   on 2008-08-21 16:46:41 (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 -3 and the run is 1. This means that to go from point to point, we can go down 3 and over 1 So starting at , go down 3 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
 Expressions-with-variables/152904: Write the equation 5x-2y=3 in slope intercept form I need the answer and steps to this thanks :)1 solutions Answer 112373 by jim_thompson5910(28711)   on 2008-08-21 16:01:42 (Show Source): You can put this solution on YOUR website! Start with the given equation. Subtract from both sides. Rearrange the terms. Divide both sides by to isolate y. Break up the fraction. Reduce. So the equation is now in slope intercept form where the slope is and the y-intercept is note: the y-intercept is the point
 Expressions-with-variables/152903: Write a verbal phrase for the algebraic expression 10 + x/4 I need the steps for this thanks :)1 solutions Answer 112369 by jim_thompson5910(28711)   on 2008-08-21 15:52:47 (Show Source): You can put this solution on YOUR website!Is the expression ??? If so, then the expression can be verbally described as "the sum of 10 and the quotient of x and 4"
 Equations/152905: 720-2=1/6 5280+1760+63360=1 This is my 6th graders homework assignment. Please help!!!1 solutions Answer 112367 by jim_thompson5910(28711)   on 2008-08-21 15:50:44 (Show Source): You can put this solution on YOUR website!Where are the variables? In other words, where are the letters "x", "y", "z", etc. that represent the unknown numbers?
 Expressions-with-variables/152914: You have $40.00. You wish to buy a T-Shirt costing$14.50 and a pair of jeans costing \$23.95. There is a 4% sales tax on clothing.Do you have enough money to pay for both?1 solutions Answer 112364 by jim_thompson5910(28711)   on 2008-08-21 15:44:36 (Show Source): You can put this solution on YOUR website!Cost (without tax) = 14.50 + 23.95 = 38.45 Tax = 0.04 * 38.45 = 1.54 Total Cost (with tax) = 38.45 + 1.54 = 39.99 So you have enough money
 Expressions-with-variables/152915: Write an algebraic expression for "three times the difference of a number x and 5"1 solutions Answer 112363 by jim_thompson5910(28711)   on 2008-08-21 15:41:48 (Show Source): You can put this solution on YOUR website!"three times the difference of a number x and 5" --->
 Expressions-with-variables/152911: Model the following situation with an equation by determining the slope and y intercept. A candle is 8 inches tall and burns at a rate of 1.5 inches per hour. Im doing a summer math packet and this question stumped me1 solutions Answer 112361 by jim_thompson5910(28711)   on 2008-08-21 15:38:06 (Show Source): You can put this solution on YOUR website! Since the candle starts at 8 inches, this means that the constant is . Also, because the candle burns at a rate of 1.5 inches per hour, this means that the slope is (note: the rate is negative since the length of the candle is decreasing). So the equation that models the candle is
Expressions-with-variables/152912: Find both intercepts of the line 3x+4y=-12
1 solutions

Answer 112360 by jim_thompson5910(28711)   on 2008-08-21 15:35:09 (Show Source):
You can put this solution on YOUR website!

#### x-intercept

To find the x-intercept, plug in and solve for x

Plug in .

Multiply and 0 to get 0.

Simplify.

Divide both sides by to isolate .

Reduce.

So the x-intercept is .

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

#### y-intercept

To find the y-intercept, plug in and solve for y

Plug in .

Multiply and 0 to get 0.

Simplify.

Divide both sides by to isolate .

Reduce.

So the y-intercept is .

Notice that if we graph the equation , we can see that the graph has the x-intercept and the y-intercept

Graph of

 Radicals/152886: Ok this is my problem. Since I don't have a "radical" key on my computer, I'm going to type it the way it would be said. Its 81x to the 4th, y to the 20th, all under a radical, raised to the 4th power. Help would be greatly appreciated ...I can't remember how to do these kinds of problems at all. thank you, sarah.1 solutions Answer 112355 by jim_thompson5910(28711)   on 2008-08-21 13:59:59 (Show Source): You can put this solution on YOUR website! Start with the given expression. Rewrite the radical expression into exponential form. Rewrite as . Multiply the outer exponent by each of the inner exponents. Multiply the exponents. Reduce. Convert back to radical notation. Take the fourth root of to get So where every variable is positive.
 logarithm/152883: log(2x-1) = log(x+3) + log31 solutions Answer 112350 by jim_thompson5910(28711)   on 2008-08-21 13:17:06 (Show Source): You can put this solution on YOUR website! Start with the given equation. Combine the logs using the identity Set the inner arguments equal to one another. Distribute. Add to both sides. Subtract from both sides. Combine like terms on the left side. Combine like terms on the right side. Divide both sides by to isolate . Reduce. So the possible answer is ; however, we must check it. Start with the given equation. Plug in Simplify. Since you cannot take the log of negative number, this means that is not a solution. So there are no solutions.
 Rate-of-work-word-problems/152882: A man can construct a wall in 20 hrs. With the help of his apprentice assistant the task would take 12 hrs. How long would it take the apprentice, working alone, to construct the wall? 1 solutions Answer 112349 by jim_thompson5910(28711)   on 2008-08-21 13:11:53 (Show Source): You can put this solution on YOUR website!Let x=# of hours apprentice can complete the job Start with the work done formula. Since the "man can construct a wall in 20 hrs", this means that T=20 Plug in (for 1 job) and Divide both sides by 20. So the man's rate is of a wall per hour Go back to the first formula Plug in and Divide both sides by x. So the apprentice's rate is of a wall per hour Now add the two rates to get So together, their rate is Go back to the first formula Plug in , , and (this is the time for them if they work together) Multiply both sides by . Distribute Subtract from both sides. Combine like terms on the left side. Divide both sides by to isolate . Reduce. ---------------------------------------------------------------------- Answer: So the answer is which means that it'll take 30 hours for the apprentice to do it alone.
 Equations/152871: How many positive real solutions are there in f(x) = x^4 + 4x^3 + 6x^2 + 4x – 1 Apply Descartes' Rule of Signs. a. 1 b. 1 or 2 c. 4 or 2 d. 2 or 01 solutions Answer 112348 by jim_thompson5910(28711)   on 2008-08-21 13:02:28 (Show Source): You can put this solution on YOUR website! Count the sign changes of From to , there is no change in sign From to , there is no change in sign From to , there is no change in sign From to , there is a sign change from positive to negative So there is 1 sign change for the expression . So there are 1 positive zeros So the answer is a) 1
 Equations/152872: Whose theorem is used to determine how many real zeroes are likely in this function, f(x) = 16x^4 – 3x^3 – 2x^2 + 8x? Apply Descartes' Rule of Signs. a. Pascal’s b. Einstein’s c. Penrose’s d. Descartes’1 solutions Answer 112347 by jim_thompson5910(28711)   on 2008-08-21 13:00:38 (Show Source): You can put this solution on YOUR website!Descartes’ rule of signs is used to determine how many real zeroes are likely in any function. So the answer is d. Descartes’
 Trigonometry-basics/152881: I HAVE BEEN GIVEN A TABLE WHICH SHOWS THE MEDIAN "B.M.I" (BODY MASS INDEX) FOR FEMALES OF DIFFERENT AGES IN THE U.S IN THE YEAR 2000 . THE QUESTION IS USE TECHNOLOGY TO PLOT THE DATA POINTS ON A GRAPH?? . DEFINE ALL VARIABLES USED AND STATE ANY PARAMETERS CLEARLY??what type of function ,models the behavior of the graph? explain why one chose this function? AGE B.M.I 2 16.40 3 15.70 4 15.30 5 15.20 6 15.21 7 15.40 8 15.80 9 16.30 10 16.80 11 17.50 12 18.18 13 18.70 14 19.36 15 19.88 16 20.40 17 20.85 18 21.22 19 21.60 20 21.65 1 solutions Answer 112346 by jim_thompson5910(28711)   on 2008-08-21 12:57:38 (Show Source): You can put this solution on YOUR website!Let x=age and y=BMI If we plot the points, we get Notice that the data is periodically rising and falling. So a trigonometric function like or would fit this data. Here is my attempt to fit a function to the data. It's not perfect, but it gets pretty close
 Equations/152874: Let Q(x) = x+1/x-1. If W(x) = Q(x) – 1, then W(x) = a. W(x) = x/x+1 b. W(x) = x/x-1 c. W(x) = 2/x-1 d. W(x) = 2x/x-11 solutions Answer 112345 by jim_thompson5910(28711)   on 2008-08-21 12:49:15 (Show Source): You can put this solution on YOUR website! Start with the given equation. Plug in . Multiply 1 by Combine the fractions. Distribute Combine like terms So the answer is C)
 Equations/152875: The Richter Scale is an example of the application of: a. Logarithmic functions b. Rational functions c. Polynomial functions d. All of the above1 solutions Answer 112344 by jim_thompson5910(28711)   on 2008-08-21 12:46:02 (Show Source): You can put this solution on YOUR website!Since the Richter Scale is logarithmic scale, this means that the answer is a) Logarithmic functions
 Equations/152878: The best base to determine the solution to 2^2x + 1 = 4^x is: @ Since 4 is a multiple power of 2, 2 is the best base. a. b = 10 b. b = 2 c. b = e d. None of the above, there is no solution to the problem1 solutions Answer 112343 by jim_thompson5910(28711)   on 2008-08-21 12:44:11 (Show Source): You can put this solution on YOUR website!I'm assuming that you answered "Since 4 is a multiple power of 2, 2 is the best base. " ? Since , you are correct. So the answer is b)
 Equations/152879: logbM = logaM/logaB is an expression of the change of base property. a. ‘a’ b. M over b c. M – b d. None of the above; you have to know what b, M, and ‘a’ are first1 solutions Answer 112342 by jim_thompson5910(28711)   on 2008-08-21 12:43:13 (Show Source): You can put this solution on YOUR website!What is the question? What do you want to do with the change of base property?
 logarithm/152880: 10 log .55 = ? 10 log .30 = ? thank you1 solutions Answer 112341 by jim_thompson5910(28711)   on 2008-08-21 12:42:03 (Show Source): You can put this solution on YOUR website! Note: Solutions are approximate solutions.
 Equations/152876: What is the range of standard exponential functions? also, exponential functions are asymptotic to the x-axis. a. f(x) ∈ (0, ∞) b. f(x) ∈ (-∞, ∞) c. f(x) ∈ [0, ∞) d. f(x) ∈ [1, ∞)1 solutions Answer 112340 by jim_thompson5910(28711)   on 2008-08-21 12:34:36 (Show Source): You can put this solution on YOUR website!If you graph something like , you get Graph of From the graph, notice that x doesn't cross the x-axis. So this means that the range of any standard exponential function in the form of is
 Percentage-and-ratio-word-problems/152848: Please Help Me Figure This Out!!!!!!!! Question- A baseball park has 40,000 seats of which 13,040 are box seats and 18,200 are reserved seats. What percent of the seats are box seats? What percent of the seats are reserved seats?1 solutions Answer 112329 by jim_thompson5910(28711)   on 2008-08-21 11:14:12 (Show Source): You can put this solution on YOUR website! # of box seats Percent of Box Seats = ----------------- * 100 total # of seats # of reserved seats Percent of Reserved Seats = ----------------------- * 100 total # of seats  Percent of Box Seats = = 32.6 % Percent of Reserved Seats = = 45.5 % Note: the percentages normally add to 100%, but in this case, there are more seats that are not considered.
 Quadratic_Equations/152851: This question is from textbook Intermediate Algebra I have a problem solving this problem Can someone help me? The problem is solve using the sqrt property: 2x^2-35=151 solutions Answer 112326 by jim_thompson5910(28711)   on 2008-08-21 11:05:18 (Show Source): You can put this solution on YOUR website! Start with the given equation. Add to both sides. Combine like terms on the right side. Divide both sides by to isolate . Reduce. Take the square root of both sides or Break up the expression or Take the square root of 25 to get 5 So the solutions are or
 Quadratic-relations-and-conic-sections/152793: how do i turn -5, 4, and 6 into polynomial funtions with rational coeffients in standard form?1 solutions Answer 112305 by jim_thompson5910(28711)   on 2008-08-20 23:47:46 (Show Source): You can put this solution on YOUR website! Since , , and are given zeros this means that: , , and Get all terms to the left side in each case , , and Now use the zero product property in reverse to join the factors. FOIL Distribute Distribute again Combine like terms ------------------------------------------- Answer: So the polynomial with roots of , , and is Notice how if we graph , we can visually verify our answer Graph of with roots of , , and
 Quadratic-relations-and-conic-sections/152795: This question is from textbook Algebra 2 Texas Put in the form 1 solutions Answer 112304 by jim_thompson5910(28711)   on 2008-08-20 23:41:19 (Show Source): You can put this solution on YOUR website! Start with the given expression. Factor out the coefficient . This step is very important: the coefficient must be equal to 1. Take half of the coefficient to get . In other words, . Now square to get . In other words, Now add and subtract inside the parenthesis. Make sure to place this after the "y" term. Notice how . So the expression is not changed. Group the first three terms. Factor to get . Combine like terms. Distribute. Multiply. So after completing the square, transforms to . So . So is equivalent to . This means that the equation is in the form where , , and
 Vectors/152748: Insert grouping symbols in each expression to make a true equation. 7-2x5-3+2=121 solutions Answer 112298 by jim_thompson5910(28711)   on 2008-08-20 21:14:33 (Show Source): You can put this solution on YOUR website!(7-2)x(5-3)+2=12 5x2+2=12 10+2=12 12=12
 Expressions-with-variables/152738: what is the sum of 5 and a1 solutions Answer 112263 by jim_thompson5910(28711)   on 2008-08-20 16:19:02 (Show Source): You can put this solution on YOUR website!"the sum of 5 and a" translates to or