9.8 Solving systems with cramer's rule  (Page 7/11)

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Men aged 20–29, 30–39, and 40–49 made up 78% of the population at a prison last year. This year, the same age groups made up 82.08% of the population. The 20–29 age group increased by 20%, the 30–39 age group increased by 2%, and the 40–49 age group decreased to $\text{\hspace{0.17em}}\frac{3}{4}\text{\hspace{0.17em}}$ of their previous population. Originally, the 30–39 age group had 2% more prisoners than the 20–29 age group. Determine the prison population percentage for each age group last year.

At a women’s prison down the road, the total number of inmates aged 20–49 totaled 5,525. This year, the 20–29 age group increased by 10%, the 30–39 age group decreased by 20%, and the 40–49 age group doubled. There are now 6,040 prisoners. Originally, there were 500 more in the 30–39 age group than the 20–29 age group. Determine the prison population for each age group last year.

20–29: 2,100, 30–39: 2,600, 40–49: 825

For the following exercises, use this scenario: A health-conscious company decides to make a trail mix out of almonds, dried cranberries, and chocolate-covered cashews. The nutritional information for these items is shown in [link] .

Fat (g) Protein (g) Carbohydrates (g)
Almonds (10) 6 2 3
Cranberries (10) 0.02 0 8
Cashews (10) 7 3.5 5.5

For the special “low-carb”trail mix, there are 1,000 pieces of mix. The total number of carbohydrates is 425 g, and the total amount of fat is 570.2 g. If there are 200 more pieces of cashews than cranberries, how many of each item is in the trail mix?

For the “hiking” mix, there are 1,000 pieces in the mix, containing 390.8 g of fat, and 165 g of protein. If there is the same amount of almonds as cashews, how many of each item is in the trail mix?

300 almonds, 400 cranberries, 300 cashews

For the “energy-booster” mix, there are 1,000 pieces in the mix, containing 145 g of protein and 625 g of carbohydrates. If the number of almonds and cashews summed together is equivalent to the amount of cranberries, how many of each item is in the trail mix?

Systems of Linear Equations: Two Variables

For the following exercises, determine whether the ordered pair is a solution to the system of equations.

$\begin{array}{l}3x-y=4\\ x+4y=-3\text{\hspace{0.17em}}\end{array}$ and $\text{\hspace{0.17em}}\left(-1,1\right)$

No

$\begin{array}{l}6x-2y=24\\ -3x+3y=18\text{\hspace{0.17em}}\end{array}$ and $\text{\hspace{0.17em}}\left(9,15\right)$

For the following exercises, use substitution to solve the system of equations.

$\begin{array}{l}10x+5y=-5\hfill \\ \text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}3x-2y=-12\hfill \end{array}$

$\left(-2,3\right)$

$\begin{array}{l}\frac{4}{7}x+\frac{1}{5}y=\frac{43}{70}\\ \frac{5}{6}x-\frac{1}{3}y=-\frac{2}{3}\end{array}$

$\begin{array}{l}5x+6y=14\\ 4x+8y=8\end{array}$

$\left(4,-1\right)$

For the following exercises, use addition to solve the system of equations.

$\begin{array}{l}3x+2y=-7\\ 2x+4y=6\end{array}$

$\begin{array}{r}3x+4y=2\\ 9x+12y=3\end{array}$

No solutions exist.

$\begin{array}{l}8x+4y=2\\ 6x-5y=0.7\end{array}$

For the following exercises, write a system of equations to solve each problem. Solve the system of equations.

A factory has a cost of production $\text{\hspace{0.17em}}C\left(x\right)=150x+15\text{,}000\text{\hspace{0.17em}}$ and a revenue function $\text{\hspace{0.17em}}R\left(x\right)=200x.\text{\hspace{0.17em}}$ What is the break-even point?

$\left(300,60,000\right)$

A performer charges $\text{\hspace{0.17em}}C\left(x\right)=50x+10\text{,}000,\text{\hspace{0.17em}}$ where $\text{\hspace{0.17em}}x\text{\hspace{0.17em}}$ is the total number of attendees at a show. The venue charges $75 per ticket. After how many people buy tickets does the venue break even, and what is the value of the total tickets sold at that point? $\left(400,30,000\right)$ Systems of Linear Equations: Three Variables For the following exercises, solve the system of three equations using substitution or addition. Questions & Answers I've run into this: x = r*cos(angle1 + angle2) Which expands to: x = r(cos(angle1)*cos(angle2) - sin(angle1)*sin(angle2)) The r value confuses me here, because distributing it makes: (r*cos(angle2))(cos(angle1) - (r*sin(angle2))(sin(angle1)) How does this make sense? Why does the r distribute once Carlos Reply How can you tell what type of parent function a graph is ? Mary Reply generally by how the graph looks and understanding what the base parent functions look like and perform on a graph William if you have a graphed line, you can have an idea by how the directions of the line turns, i.e. negative, positive, zero William y=x will obviously be a straight line with a zero slope William y=x^2 will have a parabolic line opening to positive infinity on both sides of the y axis vice versa with y=-x^2 you'll have both ends of the parabolic line pointing downward heading to negative infinity on both sides of the y axis William y=x will be a straight line, but it will have a slope of one. Remember, if y=1 then x=1, so for every unit you rise you move over positively one unit. To get a straight line with a slope of 0, set y=1 or any integer. Aaron yes, correction on my end, I meant slope of 1 instead of slope of 0 William what is f(x)= Karim Reply I don't understand Joe Typically a function 'f' will take 'x' as input, and produce 'y' as output. As 'f(x)=y'. According to Google, "The range of a function is the complete set of all possible resulting values of the dependent variable (y, usually), after we have substituted the domain." Thomas Sorry, I don't know where the "Â"s came from. They shouldn't be there. Just ignore them. :-) Thomas GREAT ANSWER THOUGH!!! Darius Thanks. Thomas Â Thomas It is the Â that should not be there. It doesn't seem to show if encloses in quotation marks. "Â" or 'Â' ... Â Thomas Now it shows, go figure? Thomas what is this? unknown Reply i do not understand anything unknown lol...it gets better Darius I've been struggling so much through all of this. my final is in four weeks 😭 Tiffany this book is an excellent resource! have you guys ever looked at the online tutoring? there's one that is called "That Tutor Guy" and he goes over a lot of the concepts Darius thank you I have heard of him. I should check him out. Tiffany is there any question in particular? Joe I have always struggled with math. I get lost really easy, if you have any advice for that, it would help tremendously. Tiffany Sure, are you in high school or college? Darius Hi, apologies for the delayed response. I'm in college. Tiffany how to solve polynomial using a calculator Ef Reply So a horizontal compression by factor of 1/2 is the same as a horizontal stretch by a factor of 2, right? KARMEL Reply The center is at (3,4) a focus is at (3,-1), and the lenght of the major axis is 26 Rima Reply The center is at (3,4) a focus is at (3,-1) and the lenght of the major axis is 26 what will be the answer? Rima I done know Joe What kind of answer is that😑? Rima I had just woken up when i got this message Joe Can you please help me. Tomorrow is the deadline of my assignment then I don't know how to solve that Rima i have a question. Abdul how do you find the real and complex roots of a polynomial? Abdul @abdul with delta maybe which is b(square)-4ac=result then the 1st root -b-radical delta over 2a and the 2nd root -b+radical delta over 2a. I am not sure if this was your question but check it up Nare This is the actual question: Find all roots(real and complex) of the polynomial f(x)=6x^3 + x^2 - 4x + 1 Abdul @Nare please let me know if you can solve it. Abdul I have a question juweeriya hello guys I'm new here? will you happy with me mustapha The average annual population increase of a pack of wolves is 25. Brittany Reply how do you find the period of a sine graph Imani Reply Period =2π if there is a coefficient (b), just divide the coefficient by 2π to get the new period Am if not then how would I find it from a graph Imani by looking at the graph, find the distance between two consecutive maximum points (the highest points of the wave). so if the top of one wave is at point A (1,2) and the next top of the wave is at point B (6,2), then the period is 5, the difference of the x-coordinates. Am you could also do it with two consecutive minimum points or x-intercepts Am I will try that thank u Imani Case of Equilateral Hyperbola Jhon Reply ok Zander ok Shella f(x)=4x+2, find f(3) Benetta f(3)=4(3)+2 f(3)=14 lamoussa 14 Vedant pre calc teacher: "Plug in Plug in...smell's good" f(x)=14 Devante 8x=40 Chris Explain why log a x is not defined for a < 0 Baptiste Reply the sum of any two linear polynomial is what Esther Reply divide simplify each answer 3/2÷5/4 Momo Reply divide simplify each answer 25/3÷5/12 Momo how can are find the domain and range of a relations austin Reply the range is twice of the natural number which is the domain Morolake A cell phone company offers two plans for minutes. Plan A:$15 per month and $2 for every 300 texts. Plan B:$25 per month and $0.50 for every 100 texts. How many texts would you need to send per month for plan B to save you money? Diddy Reply 6000 Robert more than 6000 Robert For Plan A to reach$27/month to surpass Plan B's $26.50 monthly payment, you'll need 3,000 texts which will cost an additional$10.00. So, for the amount of texts you need to send would need to range between 1-100 texts for the 100th increment, times that by 3 for the additional amount of texts...
Gilbert
...for one text payment for 300 for Plan A. So, that means Plan A; in my opinion is for people with text messaging abilities that their fingers burn the monitor for the cell phone. While Plan B would be for loners that doesn't need their fingers to due the talking; but those texts mean more then...
Gilbert