5

6) Find the equation of the line passing through (2,0) and (-1,1).7) Given: y = f(x) = 3x + 6 Find the following a) 5 f(-2) +7 b) Slope c) y-intercept d) x-intercep...

Question

6) Find the equation of the line passing through (2,0) and (-1,1).7) Given: y = f(x) = 3x + 6 Find the following a) 5 f(-2) +7 b) Slope c) y-intercept d) x-intercept e) The graph8) Express the number 5 + V-3asa complex number.9) Write the answer in interval notation x+42-2(x+2)10) The projected per capita (per person) health care expenditures in the Bahrain are given by the equation y = [Ox? + 200where y is projected per capita health expenditures in Bahraini Dinar (BD) and X is years after 201(

6) Find the equation of the line passing through (2,0) and (-1,1). 7) Given: y = f(x) = 3x + 6 Find the following a) 5 f(-2) +7 b) Slope c) y-intercept d) x-intercept e) The graph 8) Express the number 5 + V-3asa complex number. 9) Write the answer in interval notation x+42-2(x+2) 10) The projected per capita (per person) health care expenditures in the Bahrain are given by the equation y = [Ox? + 200 where y is projected per capita health expenditures in Bahraini Dinar (BD) and X is years after 201 (a)What will be the per capita health care expenditures in the year 20242 (6) In what year will the per capita expenditures reach BD 4502



Answers

Solve each problem. In part ( a), give equations in slope-intercept form. (Round the slope to the nearest tenth.) See Example $8 .$
Expenditures for home health care in the United States are shown in the graph.
(GRAPH NOT COPY)
A. Use the information given for the years 2003 and 2007 , letting $x=3$ represent 2003 $x=7$ represent $2007,$ and $y$ represent the amount (in billions of dollars) to write an equation that models home health care spending.
B. Use the equation from part (a) to approximate the amount spent on home health care in $2005 .$ How does your result compare with the actual value, $\$ 48.1$ billion?

We're told to let X equal three when it's 2003 and let X equal seven represent 2007 Well, in 2003 were told that they spent 38.0 $1,000,000,000. So that's a coordinate 0.3 representing this 2003 comma 38.0. Same with 2007. Then they've also given us the coordinate point of seven representing the 2007 comma 59 because it shows us that there was $59 billion spent in 2007 on home health care. So now it wants us to write an equation using those two points. What we know how to do that. We need to find a slope between those two points and then plug stuff into the point slope form. So this would be X one y one Then this would be except to y siptu, which means if we're finding the slope, we would be taking our Weiss up to a 59 minus R y sub one of 38 divided by our except two of seven minus R x of one of three 59 minus 38 would be 21 seven minus three, but before well, 21 does not divide by four evenly, but we'll just use the decimal. It gives us 5.25 Doesn't give us any rules on a rounding, so we really can't just leave. It is 5.25 So now we can use our excellent R Y sub one and R M value that we just found for Point Slope form We would have. Why minus r y sub one value of 38 equals are in value of 5.25 times the quantity of X minus rxa born value of three. Solving that down, we first want to distribute the 5.25 so I'll just rewrite the Y minus 38. That's really bad There, 5.25 Times X would just be 5.25 x 5.25 times negative three would be a negative 15.75 To get this into slope intercept form. All we have left to do is get why by itself, which means we simply need toe add 38 to the other side of the equation. Now why is by itself is equal to 5.25 x and then negative. 15.75 plus 38. I would give us a positive 22.25 last part of this period. That's last answer party. Sorry that that's your party right there. That's your equation. Last part of this, then, is asking you to approximate the amount spent on home healthcare in 2005. So if we were plugging in three to represent 2003 and we were using seven for our X value to represent 2007 well, then, that would mean for part B. We're gonna be using five for X value to represent 2005. So we just need to plug five into that equation. That would give us why is equal to 5.25 times five plus 22.25 out of five There. Order of Operations says multiplication comes first, so we're taking 5.25 times five. That gives us 26.25 and then we just need to add that to 22.25 If we add that to 22.25 we get 48.5 remember that were being our that we're told that this is representing billions. So make sure you do label this, that this is 48.5 $1,000,000,000 that we're talking about. Okay? Final question is, this is how does the result compare with the actual value? 48.1 billion? Well, we got 48.5 only approximated. And we can see that it should have been 48.1 on the actual graph. So we were a little bit greater. Our prediction was slightly greater, but it wasn't too far off. But you do want to say somewhere that we were we were greater than the value.

So this is actually five problems in once of each of these five parts A, B, C, D and E don't relate to one another. They're just asking the same sort of question, but their lives are totally different. So let's start with part A. We're going to be working in the form while you close MX plus B, and we know our slope is four so we can write. Why equals four X plus B? Then we need to find R B and were given the point. Negative three common negative one. So we'll plug in this point for X and Y so we have negative one equals four times negative three plus B. So negative one equals negative 12 plus B and adding 12 to both sides. We get B equals 11. So our final equation is five equals four X plus 11. So we'll do a quick sketch, so we'll call this 11 and then we know it rises four for every one running so 15 years or so. So it's a pretty steep line positive, and the Y intercept is 11. So here we go. This is a sketch. All right, so now is going to the next part. So for Part B, we know we have the soap 1/2 So why equals 1/2 x plus B? And then we need to find the B. Again. Cell will be using the point five halves comma, zero said, plugging in. We get zero in close 1/2 kinds. Five has plus B so zero equals 5/4 plus b. So be because negative 5/4. So our equation iss Why? Because 1/2 X minus five points and so will sketch it over here. And so are my intercept is negative and that our slope is really gentles positive, but it's positive one. So here is a nice sketch. So there we go. And now let's do part c So we're told the X and Y intercepts. So our X intercept is six. So we know we have the 60.6 comma zero and our Y intercept is five. So we have the 50.0 comma five. So let's find this slope. So our m will be the change and why over change in X. So I changed and why here is going from 0 to 5. So five and our change in X is 6 to 0. Also negative. Six. So negative 56 is our m, And then we already know our y intercept were told that it is five. So we're ready to write our line. Why equals negative 56 X plus five. So this is our equation. And then just sketch are why intercept is at five and we're going negative. Not quite negative one, but nearly so here is our negative. So all right, and to now will dio parte de so we know our slope is 3/4 so we can start with writing line equals 3/4 x plus b And then we have an X intercept at negative two. So negative two comma zero is a point. So a plug it in. So zero equals 3/4 times negative too. Plus B zero equals negative three halves plus B and adding three halves. We get B equals three house. So our line here is why equals 3/4 x plus three house. So this is our equation and then we'll do our sketch over here. So are my intercepts up in about 1.5 and our slope is positive. Not quite one between what happened. Well, so there we go and finally will do party. We have two points, one common to and to common six. So let's begin by finding the slope. So we're gonna do change and why over change in X our change and why we're going from 2 to 6. So that is a positive change of four on our changing acts. Going from 1 to 2 is one. So our slope here is for So why equals four x plus b. So to find B will plug in one of our points. Let's plug in one comment to just cause it's smaller, so we'll plug it in a four x and y. So we have two equals four times one and plus beep. So subtracting for we yet B equals negative, too. So our equation is why equals four X minus two and our sketch. We'll start at negative two, and we'll have a steep slope of positive one. So there we go. We aren't done

So this problem is actually five problems in one. So all of these lines are completely different. They had nothing to do with each other. So we have to do each piece separately. So let's begin with the first piece part. So we're going to be working in y equals MX plus B format. So let's begin by finding our slope. So we have the points. Negative seven Negative too. Yeah, zero Syria. So to find the slope M, we dio change. And why? Over a change of X between our two pumps. So I changed it. Why here we went from negative 2 to 0. So that's two on our change in X went from negative 7 to 0. So positive seven. So the 2/7 is our slip. We already have our by intercept because we have the 0.0 So zero is our y intercept so we can write our equation. Why equals 2/7 X and we can write plus zero. But we don't really have Teoh. We know that this means we have a lie intercepted of zero. So then we'll do a sketch over here and so we'll be passing through the origin and then we have a positive slope. But gentle, positive slope to seventh is not very steep. So here is our sketch. All right, now we'll do a part B. So we're told that our Y intercept RB value it's eight just great. So we already know that. And so we also know that this corresponds to the point zero comma eight. So I intercepted eight means that the X value is zero when the Y value is eight. And then we're also given the 0.6 negative for me. And so we'll use thes two points here to find our slope. So our delta y here, let's go from 0826 Negative three. You can go either way. You just have to be consistent. So going from eight to negative three, that is a why Change of negative 11 on going from 0 to 6 is an exchange of positive at six. So this is our smoke negative. 11 6 Almost negative to, but not quite so Why equals negative 11 6 x on then plus each. Since we know RB value, it's given to us awesome. And then we'll do a sketch over here, so we'll start up at eight. You call us eight. This will be our my intercept. And then our slope is pretty steep. It isn't, but it is actually negative. So we're going negative. Almost two down said, this is our sketch. So negative direction Negative. 11 6 with this one and accept appear at gate. All right, so part c. So we have the same slope as three x plus for Why equals 12. So let's solve for why here? So we can actually find the slip. So subtracting three x, we have four y equals negative three x lost well and dividing by four we have y equals naked of 3/4 x plus three. So our slope here is negative. 3/4 unsaid says it has the same slope. So we'll be using this look. And then we also have the point zero comment. Negative. So this tells us that negative one is RB. Valka. So we have everything we need. We just need to put it together. So why equals negative Three forks, X minus one R b. So this is our equation. And then we'll do our sketch right next to it. Let's do that a little bit. Okay, so we have negative one here as our intercept, and then we have a negative 3/4 slope, So not quite a negative one slip. Here we go. Now, this is just a sketch. If your teacher needs you to label points, do that. But the book just has to give a sketch. So that is what we will do. Courage. Next. We'll move on. She's part Indian. So we have the point six common to and the same X intercept as the line negative two x plus y equals one. So the ex ministers are what I generate that correctly. So the X intercept occurs when y equals zero. So let's plug and y equals zero here to get the X intercept. So negative two x plus zero Nichols one. So dividing by two, we got X equals negative 1/2. All right, so we have this X intercept. And so now we have the point. Negative 1/2 comma zero. So this is our X intercept is the same x intercept as this line. So now we have these two points that we're going to use for this new line. So first, let's find a slope between them. So Delta. Why over Delta X So are adults a lot going from 6 to 2 negative. 1/2 0 is a change of naked too. And going from six to negative. 1/2 is negative. 6.5. And so we'll call that negative 13 Hafs. All right. And so this becomes negative Two times negative to over 13. So for over 13 is our slope. And so now we need to find our value. Our Y intercept regards lip. So we have y equals for 13th X Class B and so will play in one of our points to find be, um, let's plug in negative 1/2 comma zero zero equals 4/13. So I am this negative 1/2 plus B when we could plug in either point. Either way is fun. All right, so this becomes negative to 13 speed and so adding negative to 13. So both sides, we get b equals positive. Teoh over 13. All right, so we have our pieces now it's right out. Why equals for 13 x plus to 13th? All right, So let's sketch nous s o brien, except is pretty small, but it's positive do thirteen's, and then our slope is also small, but positive. So we'll get something that looks like that said. There we go. We're done at this part. All right. And then finally, we have party. So we have X intercept. Negative six. And why intercept went to All right, So this means that we have the point. Negative six. Common zero. This means that we have the point zero comma route to All right, so our slope is going to be change in. Why? Over change in X, and we're going to leave the room in it. We're going to have a radical. If you want to use a catheter to get a decimal approximation, that's totally fine. But keeping the radical keeps actually, um, or exact answer. So we'll keep it from so are changing. Why? We're going from zero to root to sober, too, and are changing X negative 6 to 0 iss six. All right, so this is our slope, and we'll keep as this and then we're actually already told our right intercept. It is. So we're ready to write this. So why Equals grew to over six x plus route to I know it looks a little bit weird. This is the most exact way of writing it. But you can use a decile approximation to help you, especially with Graphing s over two is about 1.4. So this helps us know that we have our point here about 1.4. And so then our slope is about one point for over six. So about 60.7 so positive, but less than one. So here is our sketch. All right, so we have all five parts done, so we are now done.

Here in the support a problem number 15 we are given this set of X and Y values and has been asked to grow up scatter diagram. Now with the elbow photographing. We're going to look at this point. Money condition for your play. And our fast quiet is -20 or 100 strong teeth. The Second Point is -71 20 70 from one plate it and start fighting's minus 15. Uh huh. 118. The 4th White Piece -14 or more walt is going to settle. The 5th point is Which is the it's the last one is like a stemmed mola 14 people. So this is a scattered paragraph. But we of the problems is to select any two random wives from the documents state of X and Y. Bangles and find the equation of the line. So for that we choose the clark then the last once could be coming there discussion on the line passing through this twice. Well as well the equation of the line that puzzles too. No points there. Still on the White one. Right? Its students. Why? Please? Yeah Y -Y. one by X- Excellent. Was why want mine us like to related by excellent by us. Yes I do. Excellent. Why you want this minus you teen for what? 101 eight. So X one is minus two in And while -11 eight. And police station X two. Why tool is the blank Buying a Skin Probleble 1 40. So excluding this. Mine in spain I mean why do this one. So our Equation of the light the degree of the four. Why minus white one. So why not? This 11 thing 118 divided by it's minus its one so minus 50 which was y one minus like enjoy one again I guess so. I don't want it. And Like this one or simple and uh excellent minus X. Place one his miners from in thank it's been this lightness. Think that's related to the situation in the next stretch farther. Why -1182 118 divided by its fighters. Oh well minus 15. That was 11 Think -140. You know I don't like blindness in lighter sort minus then. Or why minus only one page reminder to buy minus minus becomes plus. Oh it's plus pimp. That was 118 -140. to become minus critical minus 15 plus. And within the record again minus so this will become plus so minus scripting a stent. This becomes -22 minus five or 1 -11 eight divided by x plus four pin. It was the minus council south from both in America. And in America side without scrunching through bike five or Y -118. This it was 2255 by the place where explosive 16 or Why? guns. Bye. Yeah plus 15 in full 22 People don't like five and We'll divide both. The numerator and denominator by five. To get Yeah three that one or Y -11 age people. Us. 22 white flight It's Yeah or Y -118 was 22 x five eggs plus 66. Or Yes like find us so why? Because 22 x five X. Lost 60 suits +11. Hey or like close clicking through plates. Life it's flus speech sleep. I won't be fooled. Yeah Sorry it's not 24. Yeah. Sorry smart question went before. Yeah. Peace what we do. So so this is the prepared equation of the line and our answer took part B. Part C. Of the motion. Lots who? Lord the light that we operate in party people. And the question of the line is the zone why cause credited by the virus plus white board. So with the empire calculator with a stay cation of the length. Forget it start. So this is the like that requires us equation no party of the question. Als we'll find that line of best fit of the scatter of God for that we use an inbuilt function and use the points of the scattered blood. Really. Uh huh. The red line here we possess that line up the street of the scattered light. Party of the question asks to find that coalition cook she ate it all this kind of look for that. You can use that. Built in functions for elation proficient. You said points of this better dog week. See you. Thank you. Mhm. So The correlation coefficient is sort of .96 party from the question, asks grandfather lying on best week. And also, let's get our thought, which we already have offered.


Similar Solved Questions

5 answers
Complele each ordered pair s0 lhat it iS solution of the given linear equation Ay = - 3 ( 1J, (13,The first ordered pair iSThe second ordered pair iS (13[enet VOuI tEach 0l the answet boxe
Complele each ordered pair s0 lhat it iS solution of the given linear equation Ay = - 3 ( 1J, (13, The first ordered pair iS The second ordered pair iS (13[ enet VOuI t Each 0l the answet boxe...
3 answers
The WI 0 E pe 9aconadence mean size company salary shown information regarding interval for Jbetowo the 128 Male difference independent random between the samples eans 8 8 8 ema two and femal populations emplove
The WI 0 E pe 9aconadence mean size company salary shown information regarding interval for Jbetowo the 128 Male difference independent random between the samples eans 8 8 8 ema two and femal populations emplove...
5 answers
+OW many electrons can be described by the quantum numbers n = 7,1= 1? A) 0 B) 2 C) 6 D) 7 E) 14
+OW many electrons can be described by the quantum numbers n = 7,1= 1? A) 0 B) 2 C) 6 D) 7 E) 14...
5 answers
#2) Create the piecewise function (with conditions) for the graph below_
#2) Create the piecewise function (with conditions) for the graph below_...
5 answers
25.23 The following function exhibits both flat and steep regions over a relatively short x region:fx)0.3)2 + 0.010.9)2 + 0.04Determine the value of the definite integral of this function between T= 0 and using an adaptive RK method:
25.23 The following function exhibits both flat and steep regions over a relatively short x region: fx) 0.3)2 + 0.01 0.9)2 + 0.04 Determine the value of the definite integral of this function between T= 0 and using an adaptive RK method:...
5 answers
(a) The rootsthe quadratic equation 2x2 Sx+4 = are and B Find quadratic equation whose roots are and (5](b) The roots of a quadratic equation ax bx +c = 0 are and Prove that 3b2 16ac
(a) The roots the quadratic equation 2x2 Sx+4 = are and B Find quadratic equation whose roots are and (5] (b) The roots of a quadratic equation ax bx +c = 0 are and Prove that 3b2 16ac...
5 answers
Tir all Jeks ST,a W, (-T)-W 4s-(T-H ) then XGl-T) and X4W kxt x6 (S-T)-w =xej,X4t,X4h Xes, Xe(t-w an Yo4 go from xCt, xew AIn thlj ster hov t xfct-+) ?
Tir all Jeks ST,a W, (-T)-W 4s-(T-H ) then XGl-T) and X4W kxt x6 (S-T)-w =xej,X4t,X4h Xes, Xe(t-w an Yo4 go from xCt, xew AIn thlj ster hov t xfct-+) ?...
5 answers
Fec eac ( proble~ calev late + ftnty 4 slt Llicl 74lv Aoy{ #rsten 1ar;+2041
Fec eac ( proble~ calev late + ftnty 4 slt Llicl 74lv Aoy{ #rsten 1ar;+204 1...
5 answers
In the Bohr model, what happens when an electron makes a transition between orbits?
In the Bohr model, what happens when an electron makes a transition between orbits?...
5 answers
Mataete molar sotubility of A80. Ksp for Ag = 10-10 For Youranster type In thc base 10 number th an exponent Do nD: try f0 sosctitize the LunDncnt eele M the answer I$ 10-15,then ju* tpe 10-15 clr thetoolbar, press ALTFIO (PC) &* ALTAFN-FIO (Mac) Perogroph priol 14pxWnto wrhout sputc0 words POMRLD dy
Mataete molar sotubility of A80. Ksp for Ag = 10-10 For Youranster type In thc base 10 number th an exponent Do nD: try f0 sosctitize the LunDncnt eele M the answer I$ 10-15,then ju* tpe 10-15 clr thetoolbar, press ALTFIO (PC) &* ALTAFN-FIO (Mac) Perogroph priol 14px Wnto wrhout sputc 0 words PO...
5 answers
Solve for the indicated variable.$$5 p+6(p+7)=3(p+2)$$
Solve for the indicated variable. $$5 p+6(p+7)=3(p+2)$$...
5 answers
A bottle of reagent grade hydrochloric acid has the following information in the label: 0 % HCl by weight; Density: 1.19 g/mL. (a) determine the molarity of the acid solution; (b) How many milliliters of the solution are needed to prepare 100 mL of 0.30 M solution by dilution?
A bottle of reagent grade hydrochloric acid has the following information in the label: 0 % HCl by weight; Density: 1.19 g/mL. (a) determine the molarity of the acid solution; (b) How many milliliters of the solution are needed to prepare 100 mL of 0.30 M solution by dilution?...
5 answers
Questlon 3: (4 polnts)Consider the vector fieldgzy f(z,y) = 12eFind the direction which the directional derivative of f (z,y) , at the point (€,y) = (0,6), has value of 1. Please input your answer as column vector.Identify one point at which the gradient of Ihe functionf(z,y) = 822 + 6y2is i+j Give your answer in the form (T,y) .
Questlon 3: (4 polnts) Consider the vector field gzy f(z,y) = 12e Find the direction which the directional derivative of f (z,y) , at the point (€,y) = (0,6), has value of 1. Please input your answer as column vector. Identify one point at which the gradient of Ihe function f(z,y) = 822 + 6y2 ...
5 answers
In the periodic table, how many elements are found in each of the following?a. Group 2Ab. the oxygen familyc. the nickel groupd. Group 8A
In the periodic table, how many elements are found in each of the following? a. Group 2A b. the oxygen family c. the nickel group d. Group 8A...
5 answers
Galvanic cell at a temperature of 25.0 *€ is powered by the following redox reaction:MnOz (s)+4Ht (aq) + 2Cr? (aq) Mn? (aq)+2H,0 (0)+2Cr3+ (aq)Suppose the cell is prepared with 6.97 M H and 0.133 MCr?- in one half-cell and 4.70 M Mn?+ ad 5.27 M Cr' in the other.Calculate the cell voltage under these conditions_ Round your answer to 3 significant digits_DxoD.04
galvanic cell at a temperature of 25.0 *€ is powered by the following redox reaction: MnOz (s)+4Ht (aq) + 2Cr? (aq) Mn? (aq)+2H,0 (0)+2Cr3+ (aq) Suppose the cell is prepared with 6.97 M H and 0.133 MCr?- in one half-cell and 4.70 M Mn?+ ad 5.27 M Cr' in the other. Calculate the cell volta...

-- 0.022505--