The value of x is -4 and the value of y is -3.
What is linear equations?
An equation is said to be linear if the maximum power of the variable is consistently 1. Another name for it is a one-degree equation.
The linear equation's graph is a straight line.
The given system of linear equations is,
8x + 8y = -56 ...(1)
4x + 10y = -46 ...(2)
Divide equation (1) by 2, we get
4x + 4y = -28 ...(3)
Multiply equation (3) by -1
-4x - 4y = 28 ...(4)
Adding equations (2) and (4),
4x + 10y = -46
+ -4x - 4y = 28
____________________
6y = -18
y = -3
Substitute y = -3 in equation (1) and simplify, we get
x = -4.
Therefore, the value of x is -4 and the value of y is -3.
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a researcher uses an established behavioral observation measure to collect antisocial behavior scores for a group of elementary school children. the sample mean is 20 and the standard deviation is 3. on the z-score metric, what is the standard deviation of the behavior scores?
On the z-score metric, the standard deviation of the behaviour scores is 3.
It is given that a researcher uses an established behavioral observation measure to collect antisocial behavior scores for a group of elementary school children.The sample mean is given to be equal to 20.A dataset's mean (also known as the arithmetic mean, as opposed to the geometric mean) is the sum of all values divided by the total number of values. It is the most widely used measure of central tendency and is sometimes referred to as the "average."The standard deviation is given to be equal to 3.The standard deviation is a statistical metric that determines how much a bunch of values deviate from the mean.To learn more about standard deviation, visit :
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which two county libraries charge the same penalty per week
Answer:
where's the rest of the question⁉️
Which of the following is a graph of a function
Please help as soon as possible!!!!!!
In Emily's physics class, she had to solve the equation 9 = 12at2 + ut for u. Each step of her work is shown below.
Use the drop-down menus to explain each step.
The equation of u when it is the subject is u = 9/t - 12at
How to determine the solution for the equation for u?From the question, the original equation is given as
9 = 12at2 + ut
Next, we rewrite the equation to show the exponents
This is represented as
9 = 12at² + ut
To solve further, we simply isolate the variable term ut
This is done by subtracting 12at² from both sides of the equation
So, we have the following equation
9 - 12at² = 12at² - 12at² ut
Evaluate the like terms in the equation
So, we have
9 - 12at² = ut
Lastly, divide both sides of the equation by t
So, we have
(9 - 12at²)/t = ut/t
Evaluate the quotients
9/t - 12at = u
Make us the subject
u = 9/t - 12at
Hence, the solution for the equation for u is u = 9/t - 12at
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a box contains 2828 red balls, 2020 green balls, 1919 yellow balls, 1313 blue balls, 1111 white balls, and 99 black balls. what is the minimum number of balls that must be drawn from the box without replacement to guarantee that at least 1515 balls of a single color will be drawn?
7069 are the minimum number of balls that must be drawn without replacement to complete the requirement that all balls of a single color be drawn.
First of all, we’ll look at the worst possible scenario and determine the minimum number of balls needed. We know that the color we are looking for is not blue, nor white, nor black (as there are less than 1515 of the same color when talking about those). In our worst possible scenario, we’ll first pull out all the blue, white, and black balls. Add them up. That means that we’ll definitely pull out 2523 balls( 1111 white + 1313 blue + 99 black). We are not done yet. From all the given balls, we are left with red, green, and yellow colored balls. In our worst scenario, we’ll pull out 1514 balls of every single color, and then we’ll finish it with one color (it doesn’t matter which). Since, we have 3 different colors left, that’s 3*1515+1 = 4545+1 = 4546 that is 4546 more balls.
To finish, we simply add the first 2523 balls with 4546, yielding 2523+4546 = 7069 balls.
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Please someone help me figure out this scientific notation question
Scientific notation: 10¹
Integer: 10
The average radius of the sun is 10 times greater than the average
Explanation:The average radius of Jupiter:
[tex]R_J=4.34\times10^4miles_{}_{}[/tex]The average radius of the sun:
[tex]R_s=4.32\times10^5miles[/tex]The ratio of the two Radii
[tex]\frac{R_s}{R_J}=\frac{4.32\times10^5}{4.34\times10^4}[/tex][tex]\begin{gathered} \frac{R_s}{R_J}=0.995\times10 \\ \frac{R_s}{R_J}=9.95 \\ \frac{R_s}{R_J}=10\text{ (to the nearest integer)} \end{gathered}[/tex]The average radius of the sun is 10 times greater than the average
The volume of a gas V held at a constant temperature in a closed container varies inversely with its pressure P. If the volume of a gas is 800 cubic centimeters when the pressure is 450 millimeters of mercury (mm Hg), find the volume when the pressure is 200 mm Hg.
SOLUTION:
Step 1:
In this question, we are given the following:
The volume of a gas V held at a constant temperature in a closed container varies inversely with its pressure P. If the volume of a gas is 800 cubic centimeters when the pressure is 450 millimeters of mercury (mm Hg), find the volume when the pressure is 200 mm Hg.
Step 2:
This is an application of Boyle's law which states that:
Boyle’s law is a gas law that states that the pressure exerted by a gas (of a given mass, kept at a constant temperature) is inversely proportional to the volume occupied by it. In other words, the pressure and volume of a gas are inversely proportional to each other as long as the temperature and the quantity of gas are kept constant.
[tex]\begin{gathered} Mathematically,\text{ we have that:} \\ V\text{ }\propto\text{ }\frac{1}{P} \\ Then,\text{ we have that:} \\ V\text{ =}\frac{k}{P}\text{ \lparen where k is a constant \rparen} \end{gathered}[/tex][tex]when\text{ V = 800 cubic centimetres , then P = 450 mm Hg}[/tex][tex]\begin{gathered} 800\text{ =}\frac{k}{450} \\ cross-multiply,\text{ we have that:} \\ \text{k = 800 x 450 = 360,000} \end{gathered}[/tex][tex]\begin{gathered} Then,\text{ the equation connecting V and P =} \\ \text{ V }=\frac{360,000}{P} \end{gathered}[/tex]Next:
[tex]when\text{ P = 200 mm Hg, we have that:}[/tex][tex]\begin{gathered} V\text{ = }\frac{360,000}{200} \\ \text{V = 1800 cubic centimetres } \end{gathered}[/tex]CONCLUSION:
The volume when the pressure is 200 mm Hg is:
[tex]V\text{ = 1800 cubic centimetres}[/tex]X=
////////////////////////
Answer: [tex]x=90[/tex]
Step-by-step explanation:
Using the alternate exterior angles theorem,
[tex]180-x=x\\\\180=2x\\\\x=90[/tex]
7+[-8-5^2]/(1-4)^3+17
2.6
Explanations:Given the expression;
[tex]\frac{7+\lbrack-8-5^2\rbrack}{(1-4)^3+17}[/tex]Simplify the expression in the bracket to have:
[tex]\begin{gathered} =\frac{7+\lbrack-8-25\rbrack}{(-3)^3+17} \\ =\frac{7+(-33)}{(-3\times-3\times-3)+17} \\ =\frac{7+(-33)}{-27+17} \end{gathered}[/tex]Simplify the result to have;
[tex]\begin{gathered} =\frac{7-33}{-10} \\ =\frac{-26}{-10} \\ =2.6 \end{gathered}[/tex]Hence the result of the given function on simplification is 2.6
most states run a lottery game in which players may select a three digit number, then later that day a televised drawing randomly selects a winning three digit number. suppose you select one three digit number and buy a ticket. what is the probability that your three digit number is an exact match with the winning three digit number?
The probability that the selected three digit number is an exact match with the winning three digit number = 1/1000
The 10 digits are 0, 1, 2, 3, 4, 5, 6,7, 8, 9. From these 10 digits 3 digits are selected.
Total number of ways of selecting a three-digit number = Number of ways of selecting a digit from 10 digits for each place(one's, ten's and hundred's place)
Thus a three-digit number can be selected in 10 x 10 x 10 = 1000 ways.
So there are 1000 possibilities for a three digit number.
From this only one choice matches exactly with the winning number.
So the number of favorable outcome = 1
Hence, The probability that the selected three digit number is an exact match with the winning three digit number = 1/1000
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4. Find all values of x that make the statement true.
By solving ( 3 / x - 4) = (x - 5) / x equation we get ,
x = 10 and x = 2 .
Solution:
Given ( 3 / x - 4) = (x - 5) / x,
3x = (x - 5) (x - 4)
By solving this equation,
3x = x( x - 5 ) - 4( x- 5)
3x = x² - 5x - 4( x - 5)
3x = x² - 5x - 4x + 20
3x = x² - 9x + 20 = 0
3x - x² + 9x -20 = 0
12x - x² - 20 = 0
-x² + 12x -20 = 0
-1(x(x - 2 ) - 10( x - 2 )) = 0
-1( x - 10) ( x - 2) = 0
x - 10 = 0
x - 2 = 0
∴ x = 10
x = 2
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1+2 |x-1| less than or equal to 9
SOLUTION
The question is
[tex]1+2|x-1|\leq9[/tex]Now let's solve. This becomes
[tex]\begin{gathered} 1+2|x-1|\leq9 \\ 2|x-1|\leq9-1 \\ 2|x-1|\leq8 \\ \\ \text{dividing both sides by x we have} \\ \\ |x-1|\leq4 \end{gathered}[/tex]This becomes
[tex]\begin{gathered} x-1\leq4 \\ or \\ x-1\ge4 \end{gathered}[/tex]So we have our x as
[tex]undefined[/tex]4. The density of gold is 18 g/cm3. If the volume of a plece of gold is 13cm, how many grams will it be?
ANSWER:
Therefore there are about 234 grams
STEP-BY-STEP EXPLANATION:
We have that the density is given by this formula
[tex]\begin{gathered} d=\frac{m}{V} \\ \text{where m is the mass and V the volume} \end{gathered}[/tex]We have the value of the density and the volume, therefore we can calculate the number of grams as follows:
[tex]\begin{gathered} 18=\frac{m}{13} \\ m=18\cdot13 \\ m=234 \end{gathered}[/tex]Claudia can make 4 balloon animals in 12 minutes.How many balloon animals can she make in 21 minutes
Answer: Claudia can make 7 balloons in 21 minutes.
Step-by-step explanation:
21/12=1.75
1.75 x 4 = 7
6 divided by 396 long divison attatch work !
the population (in thousands) of raleigh, north carolina from 2000 through 2008 can be modeled by , where t is the year since 2000. in 2006, the population was 363,000. without rounding the value of k, use your model to predict the population in 2017, round to the nearest thousands. the population in 2017 is:
The value of k - 0.3753, used to predict the population in 2017, the population in 2017 is 508861.
population of given by P = 289.81e^Kt
in 2000 population P(0)=289.81 thousand
in 2006 population P(6) = 363000
363000 = 289810[tex]e^{k6}[/tex]
k = 1/6 ln | 363000 /289810 |
k = 0.3753
Population in 2017 --> t =17
P(15) = 289810[tex]e^{k6}[/tex]
P(15) = 508861.32
What is Population ?A population is the entire set of people in a group, whether that group is a country or a collection of people who share a certain trait. A population is the group of people from which a statistical sample is taken in statistics. It could be a collection of people, things, occasions, organizations, etc. To make inferences, use populations. A population can be all the students at a particular school. It would contain all the students who study in that school at the time of data collection
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PLEASE HELP ASAP! What is the rate of change (slope) and the initial value (y-axis) for this table?
Answer: m = 24
Step-by-step explanation:
The right side of the table is the x value, and the left side is the y value.
Pick two points, I will pick (1,35) and (3,83).
Once you pick the points, input them in the rise over run formula:
y2-y1/x2-x1
83-35/3-1 = 48/2 = 24
Jane has a pre-paid cell phone with NextFell. She can't remember the exact costs, but her plan has a monthly fee and a charge for each minute of calling time. In June she used 200 minutes and the cost was $75.00. In July she used 680 minutes and the cost was $195.00.
We are given that Jane used 200 minutes and the cost was $75, and also she used 680 minutes and the cost was $195. To determine a function of the cost "C" as a function of the minutes "x" we will assume that the behavior of this function is that of a line. Therefore, the function must have the following form:
[tex]C(x)=mx+b[/tex]Where "m" is the slope and "b" the y-intercept. We will determine the slope using the following formula:
[tex]m=\frac{C_2-C_1}{x_2-x_1}[/tex]Where:
[tex](x_1,C_1),(x_2,C_2)[/tex]Are points in the line. The given points are:
[tex]\begin{gathered} (x_1_{},C_1)=(200,75) \\ (x_2,C_2)=(680,195) \end{gathered}[/tex]Substituting in the formula for the slope we get:
[tex]m=\frac{195-75}{680-200}[/tex]Solving the operations we get:
[tex]m=\frac{120}{480}=\frac{1}{4}[/tex]Now we substitute in the formula for the line:
[tex]C(x)=\frac{1}{4}x+b[/tex]Now we determine the value if "b" by substituting the first point. This means that when C = 200, x = 75.
[tex]200=\frac{1}{4}(75)+b[/tex]Solving the product:
[tex]200=18.75+b[/tex]Now we subtract 18.75 from both sides:
[tex]\begin{gathered} 200-18.75=b \\ 181.25=b \end{gathered}[/tex]Therefore, the formula of the cost is:
[tex]C(x)=\frac{1}{4}x+181.25[/tex]Part B. We are asked to determine the cost is there is a consumption of 323 minutes. To do that we will substitute in the formula for "C" the value of x = 323.
[tex]C(323)=\frac{1}{4}(323)+181.25[/tex]Solving the operations we get:
[tex]C(323)=262[/tex]Therefore, the cost is $262.
Answer:
Step-by-step explanation:
We will make use of algebra here.
First of all, we know that the monthly fee will be the same throughout all the months.
So, let's consider that cost to be the yet-to-find constant: [tex]a[/tex].
A charge is accumulated for every minute on the call, so let's consider that minutely charge to be the constant: [tex]b[/tex].
[tex]x[/tex] is the number of minutes spent on the call.
So, the total charge after talking for [tex]x[/tex] minutes would be:
[tex]b \times x\\=bx[/tex]
The monthly cost is the sum of the monthly fee and the total charge.
So, if this is represented mathematically, we get:
[tex]C(x)= a+bx[/tex]
A piece of information that we have is that, after calling for 200 minutes (which means [tex]x=200[/tex]), the monthly cost ( [tex]C(x)[/tex] ) would be $75.
Upon substituting these values in the equation we found above, we get:
[tex]C(x)=a+bx\\\\75=a+200b[/tex]
Similarly, we have another piece of information, which states that calling for 680 minutes ([tex]x=680[/tex]) produced a monthly cost of $195.
Upon substituting these values in the equation we found above, we get:
[tex]C(x)=a+bx\\\\195=a+680b[/tex]
And, thus we have found a system of equations:
[tex]a+200b=75\\a+680b=195[/tex]
For the first equation, let's make [tex]a[/tex] the subject:
[tex]a+200b=75\\\\a+200b-200b=75-200b\\\\a=75-200b[/tex]
Substitute this expression for [tex]a[/tex] into the second equation:
[tex]a+680b=195\\\\75-200b+680b=195\\\\75+480b=195[/tex]
Find the value of [tex]b[/tex] using this equation:
[tex]75+480b=195\\\\75+480b-75=195-75\\\\480b=120\\\\\frac{480b}{480}=\frac{120}{480}\\\\b=\frac{1}{4}[/tex]
Insert the value for [tex]b[/tex] into the expression for [tex]a[/tex]:
[tex]a=75-200b\\\\a=75-200(\frac{1}{4})\\\\a=75-50\\\\a=25[/tex]
Since we have the values for the constants [tex]a[/tex] and [tex]b[/tex], we can complete the function/equation [tex]C(x)[/tex]:
[tex]C(x)=a+bx\\\\C(x)=25+\frac{1}{4}x[/tex]
So, the answer for (A) is:
[tex]C(x)=25+\frac{1}{4}x[/tex]
For (B), we have to find the monthly bill/cost ( [tex]C(x)[/tex] ) when 323 minutes have been spent on calling.
So, we just have to substitute [tex]x[/tex] for 323, since [tex]x[/tex] represents the number of minutes spent on calling:
[tex]C(x)=25+\frac{1}{4}x\\\\C(x)=25+\frac{1}{4}(323)\\\\C(x)=25+80.75\\\\C(x)=100.75[/tex]
The answer for (B) is [tex]\$100.75[/tex]
Find the value of $x$ so that the ratios are equivalent.
$3$ to $2$ and $x$ to $18$
x=27
I think it's because if 3 is to 2 then 18+9=27. which means 27 is to 18.
A man is lying on the beach, flying a kite. he holds the end of the kite string at ground level and estimates the angle of elevation of the kite to be 50
The kite's height above the earth is 287 feet.
A right-angled triangle is formed by the length of the string, the height of the kite (h) above ground, and the perpendicular distance from the end of the kite string to the man.
The link between the lengths and angles of a right-angled triangle is demonstrated through trigonometry.
Using trigonometric ratios,
the height of the kite above the ground is
sin(55) = h ÷ 350
h = 287 ft
As a result, the kite's height above ground is 287 feet.
A trigonometric function is a real function in mathematics that relates the angle of a right triangle to the ratio of the lengths of the sides. They are frequently used in earth sciences such as navigation, structural mechanics, astrophysics, geography, and many other fields.
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if 5% of all vehicles travel less than 39.13 m/h and 10% travel more than 73.25 m/h, what are the mean and standard deviation of vehicle speed? (round your answers to three decimal places.) mean standard deviation
The mean is 58.319 m/h and the standard deviation is 11.665 m/h of the vehicle speed if 5% of all vehicles travel less than 39.13 m/h and 10% travel more than 73.25 m/h.
The mean and standard deviation of the vehicle speed can be calculated by using the formula for z-score.
The z-score of measure X can be given as;
Z = X - μ / σ
In this case, 39.13 m/h is the 5th percentile; therefore when X = 39.13, Z has a p-value of 0.05, hence Z = -1.645
Z = X - μ / σ
-1.645 = (39.13 - μ) / σ
39.13 - μ = -1.645σ
μ = 39.13 + 1.645σ
Additionally, 73.25 m/h is the 90th percentile (100 - 10 = 90), therefore when X = 73.25, Z has a p-value of 0.9, hence Z = 1.28
1.28 = (73.25 - μ) / σ
73.25 - μ = 1.28σ
μ = 73.25 - 1.28σ
We can find the standard deviation by equalling both equations as follows;
39.13 + 1.645σ = 73.25 - 1.28σ
1.645σ + 1.28σ = 73.25 - 39.13
2.925σ = 34.12
σ = 34.12/2.925 = 11.665 m/h
Now the mean can be calculated as follows;
μ = 73.25 - 1.28σ
μ = 73.25 - 1.28(11.665)
μ = 58.319 m/h
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how to find the inverse of f(x) = 3x - 7
To get the inverse of this function you need two steps. First, we leave the variable [tex]x[/tex] alone in the function. Finally, write [tex]f^{-1}(x)[/tex] where you see the letter [tex]x[/tex] and [tex]x[/tex] where you see the letter [tex]y[/tex].
First step:Leave the variable [tex]x[/tex] alone.
[tex]y=3x-7[/tex][tex]y+7=3x[/tex][tex]\frac{y+7}{3}=x[/tex]Last step:Make lettering according to the rule above.
[tex]\frac{x+7}{3} =f^{-1}(x)[/tex]there is an ongoing debate about how many spaces should be placed after a period in typed documents. alana read about a study where 100100100 participants all read the same document typed in courier new font. half of the participants were randomly assigned the document with one space after each period, and the other half were given the document with two spaces after each period. participants who read the document with two spaces after each period were able to finish reading significantly faster than those with one space after each period. alana concluded that using two spaces after each period will help people read all documents faster. why is alana's conclusion not appropriate?
Alana's conclusion from the study is not appropriate.
Why is Alana's conclusion from the study is not appropriate?
In this study, there was no attempt made to research the alternative fonts. Alana reads about the study that includes only courier new font and arrives at a conclusion.The study in inconsistent with the standard scientific methods as it is not inclusive of all factors and possibilities and is thus inappropriate.What is an appropriate study?
The achievement of the research objectives is ensured by an appropriate study design. The important element of appropriate studies known as formulated research are missing from observational studies.Observational studies are in which the outcome is not tried to be altered through analysis unlike appropriate studies.This describes an investigation of a specific phenomenon that meets all requirements and adheres to the scientific method.To learn more about appropriate studies, refer:
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TEST SCORES The average test score in a class is 74%. Half of the class scored within 7 points of the average.
One student received a score of x%. Which shows an expression that could be used to determine how far the student's score is from the average?
A. |74-7|
B. |x|-74
C. |x-74|
D. 74-|7|
It is to be noted that the absolute expression that shows how far the student's score is from the average is given as: "| x - 74| (Option C)
What is the justification for the above result?The student obtained a score of x% based on the question. As a result, x% might be larger or lower than the average score of 74%.
To establish how distant the student's score is from the average, we must subtract the student's score from the average score; i.e. (x - 74)
This difference, however, might be negative: as a result, the absolute value of (x - 78) must be calculated, yielding |x - 74|.
As a result, the phrase that may be used to assess how distant the student's score is from the average is as follows: |x - 74| which is the same as option c - An Absolute expression.
Absolute expressions are or modulus of a real number x, abbreviated |x| in mathematics, is the non-negative value of x regardless of its sign.
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10. The data set below shows the mileage and selling prices of eight used cars of the same model. Mileage Price 21,000 $16,000 34,000 $11,000 41,000 $13,000 43,000 $14,000 65,000 $10,000 72,000 $12,000 76,000 $7,000 84,000 $7,000 (a) Calculate r , the correlation coefficient between these two variables. r = (b) Interpret the value of r : the association is positive or negative and (strong or moderate or weak or negligible) (c) Compute the regression line for predicting price from mileage. ˆ y = x + (d) Predict the price of a car with 30,000 miles. $ (e) Does the student with 43,000 miles on it have a higher or lower price than the one predicted by the regression line? Higher Lower
Step 1
Plot a graph with the given table.
Step 2
Calculate r, the correlation coefficient between the two variables.
[tex]\begin{gathered} \text{From the graph,} \\ r\text{ = }-0.839 \end{gathered}[/tex]Step 3
Interprete the value of r
[tex]\text{The association is a strong and negative relationship}[/tex]Step 3
Compute the regression line for predicting price from mileage
[tex]\hat{y}=-0.118136x+17688.4[/tex]Step 4
Predict the price of a car with 30,000 miles
[tex]\begin{gathered} \hat{y}=-0.118136(30000)+17688.4 \\ \hat{y}=-3,544.08+17688.4 \\ \hat{y}=\text{\$}14,144.32 \end{gathered}[/tex]Step 5
[tex]\begin{gathered} \hat{y}=-0.118136(43000)\text{ + 17688.4} \\ \hat{y}=-5079.848+17688.4 \\ \hat{y}=\text{\$}12608.552\text{ } \\ \hat{y}\approx\text{\$12608.55} \\ \text{The given price for the mileage of 43000 is \$}14000 \\ \text{Therefore, the student with 43000 mileage on it will have a higher price than the one predicted by the regression line.} \end{gathered}[/tex]after 5 seconds the height of the ballon is 20 feet
Please help
graph x<2.
Answer:
Bottom right
Step-by-step explanation
Answer:
first answer is correct
3:5:7=....:30:...
help me keeds please
Answer:
3=6 5=10 7=14
Step-by-step explanation:
here's how to do it u wwould have to sum (+) up all the ratios then it would give u 15 after then u divide the sum by 15 hen u multiply by ratios .
(a) Find an angle between 0° and 360° that is coterminal with 600°.(b) Find an angle between 0 and 2n that is coterminal withЗп2
Coterminal Angles are angles that share the same initial side and terminal sides.
Finding coterminal angles is as simple as adding or subtracting 360° or 2π to each angle, depending on whether the given angle is in degrees or radians.
QUESTION A
The angle is given as 600°.
To find the coterminal angle between 0° and 360°, we subtract 360° from the angle.
Therefore,
[tex]\text{Coterminal angle = 600 - 360 = 240}\degree[/tex]The coterminal angle is 240°.
QUESTION B
The angle is given as
[tex]-\frac{3\pi}{2}[/tex]To get an angle between 0 and 2π, we will add 2π to it.
Hence, we have
[tex]\begin{gathered} \text{Coterminal angle = 2}\pi-\frac{3\pi}{2} \\ =\frac{\pi}{2} \end{gathered}[/tex]The coterminal angle is π/2.
Make up a word problem to solve for system of equations. Be creative
Consider the following problem.
A student library has 24 tables, X tables with 4 seats each, Y tables with 6 seats each, and Z tables with 10 seats each. The total seating capacity of the cafeteria is 148. For a special student academic meeting, half of the X tables, 1/4 of the Y tables, and 1/3 of the Z tables will be used, for a total of 9 tables. Determine X, Y, and Z.
The conditions of this problem give rise to the following system of equations
[tex]x\text{ +y + z = 24}[/tex][tex]4x\text{ + 6y + 10z = 148}[/tex][tex]\frac{1}{2}x\text{ + }\frac{1}{4}y+\frac{1}{3}z\text{ = 9}[/tex]Multiplying the second equation by 1/2 and the third equation by 12, we get:
[tex]x\text{ +y + z = 24}[/tex][tex]2x\text{ + 3y + 5z = 74}[/tex][tex]6x\text{ + 3}y+4z\text{ = 108}[/tex]Now, multiply the first equation by -2 and add it to the second equation. In this way we obtain:
[tex]x\text{ +y + z = 24}[/tex][tex]y+3z\text{ =26}[/tex][tex]6x\text{ + 3}y+4z\text{ = 108}[/tex]Multiply the first equation by -6 and add it to the last equation. In this way we obtain:
[tex]x\text{ +y + z = 24}[/tex][tex]y+3z\text{ =26}[/tex][tex]\text{ -3y -2z = -36}[/tex]Finally, the process is completed by adding the second multiplied by 3 to the third equation.
[tex]x\text{ +y + z = 24}[/tex][tex]y+3z\text{ =26}[/tex][tex]7z\text{ = 42}[/tex]then, if we perform back substitution we get the desired solutions:
[tex]x=10[/tex][tex]z=6[/tex]and
[tex]y=8[/tex]We can conclude that the correct answer is:
Answer:Problem:
A student cafeteria has 24 tables, X tables with 4 seats each, Y tables with 6 seats each, and Z tables with 10 seats each. The total seating capacity of the cafeteria is 148. For a special student meeting, half of the X tables, 1/4 of the Y tables, and 1/3 of the Z tables will be used, for a total of 9 tables. Determine X, Y, and Z.
System of equations:
[tex]x\text{ +y + z = 24}[/tex][tex]4x\text{ + 6y + 10z = 148}[/tex][tex]\frac{1}{2}x\text{ + }\frac{1}{4}y+\frac{1}{3}z\text{ = 9}[/tex]Solution for this system of equations:
[tex]x=10[/tex][tex]y=8[/tex][tex]z=6[/tex]