Depaitic J UCdCvCiie0 GradesCourse HelpHw18-Obj-C3: Problem 14Problem Value; point(s) Problem Score; 8696 . Attempts Remaining: attemptspoint) For each of the follo...

Solve each problem by using a system of three linear equations in three variables. Quizzes The Rabbit had an average (mean) score of 7 on the first three College Algcbra 101 quizzes. His second quiz score was one point higher than the first quiz score and the third was 4 points higher than the second. What were the three scores? Witul Mean is the total of the scores divided by the number of scores.

We have about 33. This piece wise function, which is being given as affects Equal toe X plus three if minus two less than equal to works less than 15 if X equal to run and the minus X plus two. If X is greater than one Onda well defined certain things. First days find the domain off each function. After that, The range. Okay, so he is the domain domain of the function. Okay, so we see that if we combine all these three values effects so X becomes greater than or equal to minus two, so domain will be minus two to infinity. Okay, so, uh, we have to now locate any intercepts. So for any intercept, but be this is the line. So why Culture X plus three is the line. Why call to X plus three the line between minus two to when minus one. So if we have any jump any intercept. So for the x intercept, let us black and white called zero X plus three. It's actually be equal toe minus tree. Okay, X will be equal to minus three Now. This minus three is not included in this graph. Sorry, in this domain. So this cannot be the intercept for y intercept. Why intercept? We have to plug in Mexico to zero X equal to zero. So I called to three. Yes, X equal to zero is in this interval. So there is a why intercept, which is zero comma. Three for this, For this line I'm concerned about. Okay, so it will not have an intercept because it is a point function now for this Minus why? Culture minus X plus two for why? Equal to minus X plus two for X. Greater than one. Okay for X intercept y zero minus X plus two. So x will be equal toe to yes, which is included in this domain. So yes, it has ax intercept toe comma zero now for y intercept minus access to be put. Zero but zero is not included here. So it will be having only acts intercept. And it will be having only y intercept. So there are two intercept. This is the Y Intercept. This is the acts intercept. Okay, Now we have to draw the graph off each of the function. So part C first is why call toe express three. That is often X equal to zero or I call 23 When Why call to zero X equal toe minus three. So we can draw the graph very easily. Okay, No second is but that we have to restrict the graph from minus two to one. Only second is viable to five when x equal to one. So there is no problem because it is a point function. Okay, Thurday's 30 days vai call to minus X plus two. So when x equal to zero. How I called to when exit when Weichel +20 execute toe to so these air two points. But we have rescued this line for executed than when. Now let us draw the graph. Oh, Okay, this is X. This is why minus three. Okay, Okay. Minus one minus two minus 30 minus 412 34 12 three. And for this is off course. Zero. So for this lion, we have toe plot. Zero comma three and minus three comma zero zero geometry and minus three comma zero zero comma tree and minus three, comma zero. Okay, so this will be the line. But we have to restrict this line from minus two to one. Only from minus 2 to 1 only. So let us draw the daughter line. Okay. And minus 2 to 1. This is minus two. This is one up to here. Okay, so from and, um, one is not included, toe. So let us right. Let us draw like this here, minus toe the value of y at minus trade included. And here it is not included. So this will be the graph. Let us It is this. Okay, this is a graph off the graph of the line. Why? I called you X plus three, while contracts plus three within the stipulated in travel. No, B is now. Second is when x equal to one where I call to five. So when x equal toe one, why will be equal to five. So let us just right. Five year. Okay, so this is fire. That is one come of five. Okay, no, third graf for this we have to plug the 0.0 comma two and two comma, zero zero comma to and two comma. Zero. And the graph will be from, uh, for X greater than one. So, like this, let us first draw the daughter the graph, then we'll be moving forward. Okay, this is the doctor Graph off the straight line. But we have to just put Is that clear? And the graph must look like this. Okay, so this is a graph for why call toe minus X plus two minus X plus tau. Now it is all these. Okay, so we can Very much so. This is a graph An answer of party. This is the answer of part C. But the is based on the graph. Find the range so her range will be from minus infinity. That is, from this minus. Infinity minus 10. 52. Minus infinity to we should say, uh, at at X equal to one x at X equal toe one. It is five. Okay, so we will be having our range 24 And why I called to five. That in minus and fainted. 24 Union five. Okay. Ok. Minus. Invented to full. Yes, my has infringed 24 for his excluded in the Union five union. We're adding five okay, for is for this is for due to the fact that when x equal to one, uh, I will become equal to from here while become equal to four. That's why. But we have to exclude for that's where the small bracket. So this is the range. But e his half continues on his domain. No, If it's not continuous in its domain, as it is discontinuous at X equal to one as graph is broken as at X equal to one. We don't have any graph in between from here to here and here to here. So the graph are broken at two points at one point. Execute toe one. So this it is continuous. Thank you.

So we're trying to figure out what our bases here, that's be variable given that there's a 0.3 comma 64 on our graph, which is just wise equal to be raised the X power, that's the function in question. And so We're just going to use the fact that we know that there's this point on the graph to figure out what B. Is. And the way that we can do that is just by plugging in 64 for Y and three for X. So we're going at 64 is equal to be Raised to the 3rd power. And so now we can just Raise both sides of this equation to the 1/3 power to get rid of this three and the exponents. So you'd have 64 to the one third and beat the third to the one third. And so 64 to the one third power comes out to be four, so then four is equal to be. So our equation then would be wise equal to four, raise the X power

Okay. So we're told that we're trying to find a function Y. Is equal to be raised the X power. So we're really just looking for our base here be and we're also told that our function passes through the point negative two common 64. So what we can do is we can just plug in negative two and 64 for X and Y into our equation to then solve for B. So If we do that, we're going to have 64 is equal to be raised to the negative to power. And so what we can do now is we can say be erased the negative to power. That's actually just equal to one over B squared. And then we can multiply both sides by B squared. So this is still equal to 64. So we have 64 times B squared is equal to one. And so now we can divide both sides by 64. So we have B squared is equal to one, divided by 64. and now we can square root both sides, so we square both sides. The square of B squared is just be in the square of one is one, So we have one still in the numerator, in the squared of 64 is eight, so this comes out to be B is equal to 1/8. So now our equation why is equal to one divided by eight or 18 to the X. Power.

If we're taking a look at the scores and we throw out the lowest and the highest or gonna throw out, we're gonna throw out a six were throughout out on nine and we multiply. That's some by the degree. Vertical difficulty, which is three. So what we're looking at here is three times eight plus seven plus eight plus eight plus seven. Okay, this is the scores with the highest nine taken out and the lowest six taken out. And so well, you do all of our addition first. Eight plus seven plus eight plus eight plus seven is 38 in three times. 38 is 114. That's