on a certain day, the rate at which material is deposited at a recycling center is modeled by the function r, where r t( ) is measured in tons per hour and t is the number of hours since the center opened. using a trapezoidal sum with the three subintervals indicated by the data in the table, what is the approximate number of tons of material deposited in the first 9 hours since the center opened? (a) 68 (b) 70.5 (c) 85 (d) 136
Answers
The approximate number of tons of material deposited in the first 9 hours since the center opened is 68. Thus, option d is correct.
What is trapezoidal rule?The trapezοidal rule is a numerical integratiοn methοd used tο apprοximate the definite integral οf a functiοn. It divides the interval οf integratiοn intο sub-intervals and apprοximates the area under the curve by cοnstructing trapezοids.
The fοrmula fοr the trapezοidal rule is as fοllοws:
Apprοximatiοn = (h/2) * [f(a) + 2f(x₁) + 2f(x₂) + ... + 2f(xₙ₋₁) + f(b)]
where h is the width οf each sub-interval (given by (b - a) / n, where n is the number οf sub-intervals), f(xᵢ) represents the value οf the functiοn at each sub-interval endpοint, and a and b are the lοwer and upper limits οf integratiοn, respectively.
Using trapezoidal rule:
\($$\begin{aligned}& \rm T=\frac{2-0}{2}(R(0)+R(2))+\frac{7-2}{2}(R(2)+R(7))+\frac{9-7}{2}(R(7)+R(9)) \\& =1(15+9)+2.5(9+5)+1(5+4) \\& =24+2.5(14)+9=68\end{aligned}$$\)
Thus, The approximate number of tons of material deposited in the first 9 hours since the center opened is 68.
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Related Questions
Do these pairs of values (x and y) represent two quantities that are
proportional?
A. No, because not all of the pairs represent the same ratio.
B. Yes, because the ratios
2/5 and 6/15 are equal.
C. No, because the y-values are not increasing at a constant rate.
D. Yes, because the ratios are all positive.
Answers
Answer:
A. No, because not all of the pairs represent the same ratio
Tanya’s swim club increased their $29 membership fee by $6 a year. What is the approximate percent increase in the membership fee?
The approximate percent increase is 20%.
The approximate percent increase is 26%.
The approximate percent increase is 82%.
The approximate percent increase is 120%.
Answers
Answer: it's increased by around 20%, because when 35 and 29 are divided and you multiply the decimal by 100, when you ignore the "1" at the front, it shows an approximate 20% increase. The answer is A.
Step-by-step explanation: PLEASE MARK ME BRAINLIST
Answer:
A
Step-by-step explanation:
Pleaseeee helpppppp what’s the answer
Answers
Answer:
134 :)
Step-by-step explanation:
The quality control section of an industrial firm uses systematic sampling to estimate the average amount of fill in 12-ounce cans coming off an assembly line. The data in the accompanying table represent a 1-in-50 systematic sample of the production in one day. Estimate m and place a bound on the error of estimation. Assume N = 1800.
Answers
The estimated average amount of fill in 12-ounce cans coming off the assembly line is 127.14, with a margin of error of ±0.588, based on a 95% confidence level.
Based on the given information, the quality control section of the industrial firm is using systematic sampling to estimate the average amount of fill in 12-ounce cans coming off an assembly line.
The data in the table represents a 1-in-50 systematic sample of the production in one day. In order to estimate m, we need to use the formula:
m = (1/k) * Σx_i
where k is the sampling interval, x_i is the sample data, and Σx_i is the sum of the sample data.
From the table, we can see that the sampling interval (k) is 50, and the sum of the sample data (Σx_i) is 6,357. Therefore, we can estimate m as:
m = (1/50) * 6,357
m = 127.14
To place a bound on the error of estimation, we can use the formula:
E = z * (s / sqrt(n))
where E is the margin of error, z is the z-score based on the desired level of confidence (e.g. for a 95% confidence level, z = 1.96), s is the sample standard deviation, and n is the sample size.
Since the standard deviation is not given, we can use the range of the sample data as an estimate of the standard deviation. From the table, we can see that the range is 2.4. Therefore, we can estimate s as:
s = range / 4
s = 0.6
Using a 95% confidence level, we can find the z-score as 1.96. The sample size (n) is 1800/50 = 36. Therefore, we can calculate the margin of error as:
E = 1.96 * (0.6 / sqrt(36))
E = 0.588
Therefore, we can place a bound on the error of estimation as:
127.14 ± 0.588
In this scenario, the quality control section of an industrial firm is using systematic sampling to estimate the average amount of fill in 12-ounce cans produced in one day.
To estimate the population mean (µ), you can calculate the sample mean (x) from the provided data. However, the data isn't given in the question, so I can't calculate the sample mean for you.
To place a bound on the error of estimation, you'll need the sample standard deviation (s) and sample size (n). Since the sampling rate is 1-in-50 and the total population (N) is 1800, the sample size (n) is 1800/50 = 36. With the provided data, you can calculate the sample standard deviation.
Once you have x and s, you can calculate the margin of error (E) using the t-distribution (assuming the population standard deviation is unknown). You'll need to find the t-score (t*) for a given confidence level (usually 95%) and degrees of freedom (df = n-1).
E = (t × s) / √n
The estimated population mean (µ) will be within the range of x ± E.
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get those points sis
Answers
Answer:
thanks
Step-by-step explanation:
what is the expected number of left-handed students in a typical class of 188 students, and with what standard deviation? what is the expected number of right-handed students (out of 188), and with what standard deviation?
Answers
The expected number of left-handed students in a typical class of 188 students can be estimated using the prevalence rate of left-handedness in the general population.
According to studies, approximately 10% of the population is left-handed. Therefore, we can expect around 18.8 left-handed students in a class of 188 students.
To calculate the standard deviation, we need additional information. The standard deviation depends on the variability of left-handedness in the population. Without this data, it is not possible to provide an accurate estimation of the standard deviation.
Similarly, the expected number of right-handed students can be estimated by subtracting the expected number of left-handed students (18.8) from the total number of students (188). This gives us an expected number of around 169.2 right-handed students.
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Before 8 A.M., there were 64 trucks and 24 cars in a parking lot. Between 8 A.M. and 9 A.M., more cars entered the parking lot and no trucks entered or exited the lot. At 9:00 A.M., the number of trucks represented 1/5 of the parking lot's vehicles. How many cars entered between 8 A.M. and 9 A.M? A. 56 B. 112 C. 148 D. 192 PLZ EXPLAIN
Answers
Answer:
232 cars
Step-by-step explanation:
Let's say the number of cars that entered is c.
At 9:00 am, there are a total of 24 + c cars and 64 trucks. We know that this value of 64 represents 1/5 of the total number of vehicles. The total number of vehicles is (24 + c) + 64 = 88 + c. So, we have:
64/(88 + c) = 1/5
Cross-multiply:
88 + c = 64 * 5 = 320
c = 320 - 88 = 232
Thus, the answer is 232 cars.
Note: as 232 doesn't show up in the answer choices, it's possible that the problem was copied correctly.
~ an aesthetics lover
Answer:
232 cars entered between 8 and 9
Step-by-step explanation:
at 9 am there are 64 x 5 vehicles total = 320
320 - 64 - 24 = 232
Between 2015 and 2021. Faimont Chateau Lake Louise has reduced water consurnption by 20,000 m3. To ensure our water quality, surface water quality samples are collected from Lake Louise and Louise Creek on an annual basis, as part of an ongoing water chemistry monitoring program. Based on the materials of the course, water quality concems involve analyzing the presence of trace minerals and__
a. vitamins b. oxygen c. nutrients d. nitrates
Answers
Water quality concerns, as part of the water chemistry monitoring program, involve analyzing the presence of trace minerals and nutrients in surface water samples collected from Lake Louise and Louise Creek. Correct option is C.
To ensure water quality, it is crucial to assess the presence of various substances in the water samples. While trace minerals are essential to understand the composition of the water and detect any potential contaminants or harmful elements, nutrients also play a significant role.
Nutrients in water refer to substances such as nitrogen and phosphorus, which are essential for the growth and survival of aquatic organisms. However, excessive nutrient levels can lead to water quality issues such as eutrophication, harmful algal blooms, and oxygen depletion. Monitoring and analyzing nutrient levels in surface water samples help identify any imbalances and potential ecological impacts.
The ongoing water chemistry monitoring program at Faimont Chateau Lake Louise collects annual surface water samples from Lake Louise and Louise Creek to ensure the continued evaluation of trace minerals and nutrients. This proactive approach allows for the early detection of any deviations from desired water quality standards, enabling appropriate actions to maintain the ecological health of the water resources.
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Systolic blood pressure for a group of women is normally distributed, with a mean of 121 and a standard deviation of 9. Find the probability that a woman selected at random has the following blood pressures. (Round your answers to four decimal places.) (a) greater than 136 (b) less than 114 (c) between 114 and 128
Answers
the probability that a woman selected at random has a blood pressure between 114 and 128 is 0.5588.
What is a Z-table?A z-table also known as the standard normal distribution table, helps us to know the percentage of values that are below (or to the left of the Distribution) a z-score in the standard normal distribution.
Given the mean is 121 while the standard deviation of the women is 9. Therefore, Using the z-table, the probability can be found.
(a) The probability that a woman selected at random has blood pressures greater than 136.
\(P(x > 136) = 1 - P(x < 136)\\\\P(x > 136) = 1 - P(z < \dfrac{x-\mu}{\sigma})\)
\(=1 - P(z < \dfrac{136-121}{9})\\\\=1 - P(z < 1.667)\\\\=1-0.9515\\\\=0.0485\)
(b) The probability that a woman selected at random has a blood pressure less than 114.
\(P(x < 114)= P(z < \dfrac{114-121}{9})\\\\\)
\(= P(z < -0.77)\\\\= 0.2206\)
(c) The probability that a woman selected at random has a blood pressure between 114 and 128.
\(P(114 < x < 128)= P(\dfrac{114-121}{9} < z < \dfrac{128-121}{9})\\\\\)
\(= P(-0.77 < z < 0.77)\\\\= P(z < 0.77)-P(z < -0.77)\\\\= 0.7794 - 0.2206\\\\=0.5588\)
Hence, the probability that a woman selected at random has a blood pressure between 114 and 128 is 0.5588.
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What is the value of fraction 1 over 3 x2 + 5.2y when x = 3 and y = 2?
Answers
Answer:
1over 38
Step-by-step explanation:
U substitute the values of x and y on the given equation
Robin drew a circle with center D and diameter AB of 13 inches. What is the radius RD of the circle?
Answers
Answer:
The radius is...
Step-by-step explanation:
Diameter = radius x 2
13 / 2
Radius is 6.5 of the circle.
On his first day of school, Kareem found the high temperature in degrees Fahrenheit to be 76.1°. He plans to use the function C of F = five-ninths (F minus 32) to convert this temperature from degrees Fahrenheit to degrees Celsius. What does C(76.1) represent? the temperature of 76.1 degrees Fahrenheit converted to degrees Celsius the temperature of 76.1 degrees Celsius converted to degrees Fahrenheit the amount of time it takes a temperature of 76.1 degrees Fahrenheit to be converted to 32 degrees Celsius the amount of time it takes a temperature of 76.1 degrees Celsiu
Answers
Answer:
(A)the temperature of 76.1 degrees Fahrenheit converted to degrees Celsius
Step-by-step explanation:
Kareem plans to use the function \(C(F) = \dfrac59(F-32)\) to convert temperature from degrees Fahrenheit to degrees Celsius.
The function gives a result in degrees Celsius. Therefore, 76.1 is in degree Fahrenheit and the result C(76.1) will be in degree Celsius.
Therefore, C(76.1) represents the temperature of 76.1 degrees Fahrenheit converted to degrees Celsius.
The correct option is A.
Answer:
A
Step-by-step explanation:
I took the review on EDGE
Ross is wrapping a gift. the package is shaped like the cylinder shown. what is the least amount of paper he need to cover the entire cylinder? use 3.14 for pi
A. 402.92 in2
B. 602. 88 in3
C. 1004.8 in2
D. 2411.52 in3
12 points :)
Answers
Your answer to this question would be A.
(Aka) 401.92 in sq 2
Answer:
a ;)
this answer was to short so i had to add stuff.
The probability of a New York teenager owning a skateboard is 0.37, of owning a bicycle is 0.81 and of owning both is 0.36. If a New York teenager is chosen at random, what is the probability that the teenager owns a skateboard or a bicycle
Answers
According to the question The probability that a New York teenager owns a skateboard or a bicycle is 0.82.
Let's denote the event of owning a skateboard as \(\(A\)\) and the event of owning a bicycle as \(\(B\).\)
We are given:
\(\(P(A) = 0.37\)\) (probability of owning a skateboard)
\(\(P(B) = 0.81\)\) (probability of owning a bicycle)
\(\(P(A \cap B) = 0.36\)\) (probability of owning both skateboard and bicycle)
To find the probability that the teenager owns a skateboard or a bicycle \((\(A \cup B\))\) , we can use the formula:
\(\[P(A \cup B) = P(A) + P(B) - P(A \cap B)\]\)
Substituting the given values:
\(\[P(A \cup B) = 0.37 + 0.81 - 0.36\]\)
Calculating:
\(\[P(A \cup B) = 0.82\]\)
Therefore, the probability that a New York teenager owns a skateboard or a bicycle is 0.82.
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I’ll give 100 points please help look at the picture for question
Answers
Answer:
17-7
Step-by-step explanation:i think its 17-7 Hope this helps !
A - B = 2 and A + 2 = b
find the value of A and B
Answers
A and B's values are not specified.
Given A-B = 2 and A+2 = B.
Take the A+2=B first.
A =B-2
Replace the value of A in A-B=2 with the value of A=(B-2)
A-B=2
B-2-B=2
-2=2
As a result, the equations lack a true solution.
These two lines are actually parallel, thus they never cross. So there is no answer.
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For each of the following scenarios, determine whether the mean or median better represents the data (place a check mark in the appropriate box). For each case, explain why you chose that particular average. The following three scenarios below do not have a specific data set. Be sure to consider all possibilities/outcomes! "Create" a data set if you need to.
Answers
In each scenario, the choice between mean and median as a representative measure of central tendency depends on the nature of the data and the specific context..
1. Scenario: Income distribution of a population
- If the income distribution is skewed or contains extreme values (outliers), the median would be a better representation of the central tendency. This is because the median is not influenced by outliers and provides a more robust estimate of the "typical" income level. However, if the income distribution is approximately symmetric without outliers, the mean can also be an appropriate measure.
2. Scenario: Exam scores in a class
- If the exam scores are normally distributed without significant outliers, the mean would be a suitable measure as it takes into account the value of each score. However, if there are extreme scores that deviate from the majority of the data, the median may be a better representation. This is especially true if the outliers are indicative of errors or exceptional circumstances.
3. Scenario: Housing prices in a city
- In this case, the median would be a more appropriate measure to represent the central tendency of housing prices. This is because the housing market often exhibits a skewed distribution with a few high-priced properties (outliers). The median, being the middle value when the data is sorted, is not influenced by these extreme values and provides a better understanding of the typical housing price in the city.
Ultimately, the choice between mean and median depends on the specific characteristics of the data and the objective of the analysis. It is important to consider the distribution, presence of outliers, and the context in which the data is being interpreted.
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Toko sepatu memberi diskon 30% untuk semua barang.Jika tasya membeli sepasang sepatu dan ia membayar Rp 336.000,00 setelah mendapat diskon,harga sepasang sepatu tersebut sebelum diskon adalah
Answers
Answer:
IDR 480,000
Step-by-step explanation:
Persentase diskon = Harga lama - Harga baru / Harga lama
Harga lama = Harga sebelum diskon = x
Harga Baru = IDR 336000
Persentase diskon = 30%
Karenanya:
30% = x - 336000 / x
30/100 = x - 336000 / x
0.3 = x - 336000 / x
Cross Multiply
0.3 × x = x - 336000
0.3x = x - 336000
x - 0.3x = 336000
0.7x = 336000
x = 336000 / 0.7
x = IDR 480,000
In a survey, more college students indicated that they would enroll in a particular course when they were told that 70 percent of students passed it last year than when they were told that 30 percent of students failed it last year. The results of the survey best illustrate
Answers
The results of the survey best illustrate the framing effect.
What is the framing effect?People make choices based on whether possibilities are given with positive or negative connotations, such as as a gain or a loss, according to a cognitive bias known as the framing effect.
When provided with a positive frame, people tend to avoid danger, but when offered with a negative frame, they tend to seek out hazards.
The scenario of framing effect defines gain and loss as descriptions of results.
The idea aids in the development of framing effect understanding in social movements as well as in the creation of political opinion, where spin plays a significant role in political opinion polls that are framed to encourage a response advantageous to the group that commissioned the poll. It has been asserted that the framing effect is invalidating political polls.
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A recipe uses 2 cups of sugar to make 32 brownies. how many X cups of sugar are needed for 72 brownies?
Answers
Answer:
4.5
Step-by-step explanation:
The circumference of a circle is increasing at a rate of pi over 2 m/h at a certain instant the circumference is 12 pi meters what is the rate of change of the area of the circle at that instant in square meters per hour
Answers
Answer: 3pi
Step-by-step explanation:
Guessed and it was right, sorry don’t have an explanation.
The rate of change of the area of the circle at that instant in square meters per hour will be 3π.
What is the rate of change?The pace at which one quantity changes in relation to another is known as the rate of change function.
Given that the circumference of a circle is increasing at a rate of π / 2 m/h at a certain instant the circumference is 12 π meters.
The rate of change of circumference will be calculated as,
dc/dt = π/2
d (2πr)/ dt = π / 2
dr / dt = 1 / 4
The rate of change in the area,
A = πr²
dA / dt = ( 2πr ) dr / dt
dA/dt = 12π x ( 1 / 4)
dA/dt = 3π
Therefore, the rate of change of the area of the circle at that instant in square meters per hour will be 3π.
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How is this wrong? Reflect shape A in the x-axis.
Answers
Answer:
Your answer is wrong because you reflected it over the y-axis, not the x-axis. To find the correct answer, plot a triangle with vertices at (1, -1), (4, -1) and (4, -3). Note that we switch the sign of the y-coordinate when reflecting over the x-axis.
The line with equation 5y - 4x = k , where k is a constant , does not intersect the circle with equation (x - 3) ^ 2 + (y + 2) ^ 2 = 41. Find the range of possible values of k .
Answers
SOLUTION
Write out the equation of the line and the circle, we have
\(\begin{gathered} 5y-4x=k\rightarrow5y-4x-k=0 \\ \text{and } \\ (x-3)^2+(y+2)^2=41 \end{gathered}\)We want to find the possible values of for which the line does not intersect the circle this implies that the distance of the from the center of the circle to the line is greater than the radius of the circles.
From the equation of the circle, we have the radius to be
\(\begin{gathered} (x-3)^2+(y+2)^2=41 \\ \text{Hence } \\ \text{center}=(3,-2),\text{raduis}=\sqrt[]{41} \end{gathered}\)The distance is given by
\(\begin{gathered} d=\frac{|Ax_1+By_1+c|}{\sqrt[]{A^2+B^2}} \\ \text{Where } \\ c=k,(x_1,y_1)=(3,-2),A=-4,B=5 \end{gathered}\)Then
\(\begin{gathered} d=\frac{|-4(3)+5(-2)+(-k)|}{\sqrt[]{(-4)^2+5^2}} \\ \text{Then } \\ d=\frac{|-12-10-k|}{\sqrt[]{41}} \end{gathered}\)if d >r, we have
\(\begin{gathered} |-22-k|>\sqrt[]{41} \\ \text{When } \\ -22-k>0\Rightarrow k\le22 \end{gathered}\)when
\(\begin{gathered} |-22-k|=-22-k>41\Rightarrow-k>41+22\Rightarrow-k>63 \\ \text{Then } \\ k<-63 \end{gathered}\)So,
\(K<-63\text{ or K>-22}\)because
\(\begin{gathered} -22-k<0\Rightarrow k>-22 \\ |-22-k|=22+k>41\Rightarrow k>19 \end{gathered}\)Hence
We have
\(k<-63\text{ or k>19 are the possible values of k}\)Hence
The possible vales of k are
K<-63 or K>19
lin and kara are planning a party. lin spent $20 on invitations and decorations. kara spent 4x that amount on food and entertainment. how much did they spent all together on the party?
A. $20
B. $80
C. $100
D. $120
Answers
Answer:
C. 100$
Step-by-step explanation:
Its really easy you just do 4 x 20 then you get 80 then you add 20 because your finding the total which 20 + 80 = 100
the area of a circle is 616 m square find the radius 5 equals to 22/7
Answers
Step-by-step explanation:
\(here \: is \: your \: solution : - \\ \\ GIVEN \: \: -:- \\ \\ = > \: area \: of \: circle \: = 616 \: m {}^{2} \\ \\ \ = > pi = 22 \div 7 \\ \\ = > we \: need \: to \: find \: radius \: \\ \\ = > area \: of \: circle \: = \pi \: r {}^{2} \\ \\ = > \: \pi \: r {}^{2} = 616 \: m {}^{2} \\ \\ = > \: r {}^{2} \times (22 \div 7) = 616 \\ \\ = > \: r {}^{2} =( 616 \times 7) \div 22 \\ \\ = > \: r { }^{2} = 4312 \div 22 \\ \\ = > r {}^{2} = 196 \\ \\ = > \: r = \sqrt{196} \\ \\ = > \: r = 14 \: \: \: (ANSWER✓✓✓) \\ \\ HOPE \: IT \: HELPS \: YOU \: (◕ᴗ◕✿)\)
how many cuboids are there in an 8-dimensional data cube if there were no hierarchies associated to any dimension?
Answers
An 8-dimensional data cube with no hierarchies associated with any dimension will contain (2^8) cuboids. Therefore, the answer is 256 cuboids.A data cube is a three-dimensional structure that stores data as dimensions, hierarchies, and measures.
The data cube's structure is dependent on the dimensions, hierarchies, and measures. A data cube can be created using the following formula: Data Cube = (Dimension 1 Size) * (Dimension 2 Size) *...* (Dimension n Size) For example, if a data cube has 3 dimensions, A, B, and C, with sizes 3, 4, and 5, respectively, then the total number of cells will be (3*4*5), or 60 cells.In an 8-dimensional data cube, the number of cuboids can be calculated by taking the power of 2 of the number of dimensions, since each dimension can either be included or excluded from a cuboid. Therefore, 2^8 = 256 cuboids.
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find the value of c if a line with slope 3/4 passes through the points (1,8) and (5,c) PLEASE HELP
Answers
The value of c, if a line with a slope of 3/4 that passes through the points (1,8) and (5,c), is 11.
What is the equation of a line?A line is a one-dimensional shape that is straight, has no thickness, and extends in both directions indefinitely. The equation of a line is given by,
y =mx + c
where,
x is the coordinate of the x-axis,
y is the coordinate of the y-axis,
m is the slope of the line, and
c is the y-intercept.
Given that the line has a slope of 3/4 and passes through the point (1,8). Therefore, we need to substitute the slope and the coordinates in the equation of the line, to get the value of the y-intercept.
y = mx + c
8 = (3/4)(1) + c
8 = (3/4) + c
c = 8 - (3/4)
c = 29/4
Now, the line also passes through (5,c), therefore, if we substitute the value of slope and y-intercept in the equation,
y = mx + c
c = (3/4)(5) + (29/4)
c = (15/4) + (29/4)
c = 44/4
c = 11
Hence, the value of c, if a line with a slope of 3/4 that passes through the points (1,8) and (5,c), is 11.
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The present ratio of ages of P & Q is 4 : 6. If
the sum of present ages of P & Q is 50 years,
then the sum of ages of P & Q before 4 years is
Answers
The sum of ages of P & Q before 4 years is 42 years.
Let present age of P is 4x years and the present age of Q is 6x years.
According to the problem, the sum of the present ages of P and Q is 50 years, so we have:
4x + 6x = 50
10x = 50
then, x = 5
So the present age of P is 4 * 5 = 20 years and the present age of Q is 6 * 5 = 30 years.
To find the sum of their ages before 4 years, we subtract 4 from each of their present ages:
20 - 4 = 16 years (for P)
30 - 4 = 26 years (for Q)
hence, sum of their ages before 4 years is 16 + 26 = 42 years.
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Therefore, the age of P 4 years ago was 7 years - 4 years = 3 years and the age of Q 4 years ago was 6 * 7 years - 4 years = 38 years.
The sum of their ages before 4 years is 3 years + 38 years = 41 years
What is the solution to this system of equa
4x + 5y = 7
3x - 2y = -12
Answers
Answer:
\(\fbox{\begin{minipage}{8em}(x, y) = (-2, 3)\end{minipage}}\)
Step-by-step explanation:
Given:
4x + 5y = 7
3x - 2y = -12
Solve for:
x and y
Solution:
Step 1: Find the good approach
There are plenty of ways to solve system of linear equations. For a problem requiring solving only 2 variables, one of the good methods is trying to eliminate all components containing 1 variable, then solve for remaining variable only. Afterwards, substitute the variable found, back into one of original equations to work out the eliminated variable.
Step 2: Perform the calculation
Transform the original system into new one which is easier for eliminating:
4x + 5y = 7
3x - 2y = -12
<=>
3*(4x + 5y) = 3*7 (multiply both sides of 1st equation by 3)
4*(3x - 2y) = 4*(-12) (multiply both sides of 2nd equation by 4)
As you might see, we intentionally try to create the components containing x, that share the same coefficient ( 3 x 4 = 4 x 3 = 12), this would help the next eliminating step.
<=>
12x + 15y = 21
12x - 8y = -48
Now, we see that if we subtract 2nd equation from 1st equation, we will completely eliminate components containing x.
<=>
(12x - 12x) + (15y - (-8y) = 21 - (-48)
Then, we do the simplification:
<=>
23y = 69
We finally divide both sides of equation by 23, to work out y.
<=> (23/23)y = 69/23
<=> y = 3
Now we substitute y back into 1st original equation, we have:
4x + 5y = 7 or 4x + 5*3 = 7
<=> 4x + 15 = 7
We move all numbers to the right side, except the components containing x (notice the change of sign of number from + to -)
<=> 4x = 7 - 15
<=> 4x = -8
We finally divide both sides of equation by 4, to work out x.
<=> (4/4)x = -8/4
<=> x = -2
Now, we conclude the solution of this system of linear equation is:
(x, y) = (-2, 3)
Hope this helps!
:)
The solution to the given system of equations is (-2, 3).
What is a linear system of equations?A system of linear equations consists of two or more equations made up of two or more variables such that all equations in the system are considered simultaneously. The solution to a system of linear equations in two variables is any ordered pair that satisfies each equation independently.
The given system of equations are 4x+5y=7 ---------(I) and
3x-2y= -12 ---------(II)
Multiply equation (I) by 3, we get
12x+15y=21 ---------(III)
Multiply equation (II) by 4, we get
12x-8y=-48 ---------(IV)
Subtract equation (IV) from equation (III), we get
12x+15y-(12x-8y)=21-(-48)
12x+15y-12x+8y=21+48
23y=69
y=3
Substitute y=3 in equation (I), we get
4x+5(3)=7
4x+15=7
4x=-8
x=-2
So, solution is (-2, 3)
Therefore, the solution to the given system of equations is (-2, 3).
To learn more about the linear system of an equations visit:
https://brainly.com/question/27664510.
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(3a - 1/2) (3a - 1/2)
Answers
Answer: The answer is 9a^2 - 3a + 1/4
Step-by-step explanation:
Hope this helpfull.
But Im so sorry if this not helpfully
