3. Give two systems of equations that would be easier to solve by substitution
than by elimination. Then give two systems that would be easier to solve with
elimination. Finally, explain how you decide whether to use elimination or
substitution to solve a system.
Answers
Answer:These techniques for elimination are preferred for 3rd order systems and higher. They use "Row-Reduction" techniques/pivoting and many subtle math tricks to reduce a matrix to either a solvable form or perhaps provide an inverse of a matrix (A-1)of linear equation AX=b. Solving systems of linear equations (n>2) by elimination is a topic unto itself and is the preferred method. As the system of equations increases, the "condition" of a matrix becomes extremely important. Some of this may sound completely alien to you. Don't worry about these topics until Linear Algebra when systems of linear equations (Rank 'n') become larger than 2.
explanation Step-by-step explanation:ust to add a bit more information, "Elimination" Can have a variety of other interpretations. Elimination techniques typically refer to 'row reduction' to achieve 'row echelon form.' Do not worry if you have not heard of these terms. They are used in Linear Algebra when referring to "Elimination techniques"
Just to add a bit more information, "Elimination" Can have a variety of other interpretations. Elimination techniques typically refer to 'row reduction' to achieve 'row echelon form.' Do not worry if you have not heard of these terms. They are used in Linear Algebra when referring to "Elimination techniques"
Gaussian Elimination
Gauss-Jordan Elimination
LU-Decomposition
QR-Decomposition
These techniques for elimination are preferred for 3rd order systems and higher. They use "Row-Reduction" techniques/pivoting and many subtle math tricks to reduce a matrix to either a solvable form or perhaps provide an inverse of a matrix (A-1)of linear equation AX=b. Solving systems of linear equations (n>2) by elimination is a topic unto itself and is the preferred method. As the system of equations increases, the "condition" of a matrix becomes extremely important. Some of this may sound completely alien to you. Don't worry about these topics until Linear Algebra when systems of linear equations (Rank 'n') become larger than 2.
Substitution is the preferred method for 2 equations in 2 unknowns. The constants are unimportant other than having a non-zero determinant. It is always easy to find multiplicative factors using LCMs of one variable or the other to allow substitution into the other equation:
Example:
4X + 5Y = 9
5X - 4Y = 1
Notice that 20 is a LCM of either the X or Y variable. So multiply the first by 4 and the second by 5 and then adding the two (Y's will drop out allowing for substitution)
4(4X + 5Y = 9)
5(5X - 4Y = 1)
Multiplying to produce the LCM factors:
16X + 20Y = 36
25X - 20Y = 5
Adding the equations
41X = 41
X = 1
Substitution into either equation yields
Y = 1
Related Questions
Two friends, Rahul and Arun, took summer jobs. The equation y = 17.3x represents Arun's earnings in dollars and cents, y, for working x hours. The graph below represents Rahul's earnings in dollars and cents, y, for working x hours.
How much more does Rahul earn per hour than Arun?
Answers
Answer: Rahul earns 3.5 dollars more per hour than Arun.
Step-by-step explanation:
17.3 is the slope of Arun's earnings. To find what Rahul makes in an hour, you can find the slope of his graph below.
Use the two points, (10,208) and (20, 416)
Use the formula for calculating slope:
416-208=208
20-10=10
---------------------
208/10= 20.8
Rahul's equation can be set up like this:
y=20.8x
Subtract:
20.8-17.3=3.5
Therefore, Rahul earns 3.50 dollars more per hour than Arun.
Solve the system of equations by adding or subtracting.
−x − 2y = 4
3x + 2y = 8
The solution of the system is (_____, ____).
HELPPP PLZZZ
Answers
Answer:
(6,-5)
bc i know
possible expressions that simplify to 37
Answers
Answer: 74 divided by 2 = 37
Step-by-step explanation:
Yuko wants to buy a new video game console that costs $300 . His parents agree to pay for 40% of the cost of the console. How much must Yuko earn to buy the console?
Answers
Answer:
120
Step-by-step explanation:
300*40%=120
Answer:
$180
Step-by-step explanation:
$300 of 40%
= 300 × 40/100
= $ 120
its mean her mother allow him to give $120 so he have to earn $180
How do you find and identify parallel lines in Geometry? I'm going into 6th grade next year, and I am doing my summer homework. Please help!
Answers
Answer:
Parallel lines are lines that never touch each other
Step-by-step explanation:
they are straight and go on forever without intersecting (crossing)
Answer:
parallel lines are always the same distance apart from each other at all times, they never come in contact with one another
Step-by-step explanation:
They never intersect. It is difficult to explain, but you can look at examples on the internet. Hope this helps, have a good day, and good luck with your summer homework and good luck in 6th grade :)
The circumference of a circular park is approximately 18 feet. What is the approximate area inside the circular park?
Answers
Answer:
25.685 square feet.
Step-by-step explanation:
Circumference = 2 * π * radius
From this, we can derive the formula for the radius:
radius = Circumference / (2 * π)
Let's substitute the value of the circumference and calculate the approximate radius:
radius = 18 / (2 * π)
radius ≈ 18 / (2 * 3.14159)
radius ≈ 2.865 feet
Now that we have the approximate radius, we can calculate the area:
Area ≈ π * radius²
Area ≈ 3.14159 * (2.865)²
Area ≈ 3.14159 * 8.193225
Area ≈ 25.685 square feet
Therefore, the approximate area inside the circular park is approximately 25.685 square feet.
C = 2πr
where C is the circumference and r is the radius of the circle.
In this case, we are given that the circumference is approximately 18 feet, so we can set up the following equation:
18 = 2πr
Solving for r, we get:
r = 9/π ≈ 2.864 feet
Now we can use the formula for the area of a circle:
A = πr^2
Substituting the value we found for r, we get:
A = π(2.864 ft)^2 ≈ 25.85 ft^2
Therefore, the approximate area inside the circular park is approximately 25.85 square feet.
A gardener uses a total of gallons of gasoline in one month. Of the total amount
of gasoline, was used in his lawn mowers. How many gallons of gasoline did the
gardener use his lawn mowers in one month?
Answers
Answer:
D. 36.9
Explanation:
three-fifths of 61.5 is 36.9!
Answer:
D. 36.9
Step-by-step explanation:
The total amount of gallons the gardener typically uses in a month is 61.5 gallons. Since the gardener used 3/5 gallons, we know that 5/5 is 61.5 gallons. So you would have to divide 61.5 by 5 in order to get 1/5 of the gallons which would be 12.3. Then you have to multiply the 12.3 by 3 in order to get 3/5 of how much the gardener used which is 39.9 gallons. I hope this helped!
What is an angle that is adjacent to LGK?
Answers
Answer: CGB
Step-by-step explanation:
there back to back
Hey yall! i dont need the math just the answers!
Answers
Answer:
13A. 14, 48, 50
13B. both mulitpled by 2?
13C. 56, 125
14. Yes
Step-by-step explanation:
Answer:bye
Step-by-step explanation:
how to do this? pls don't ignore
Answers
Small side:
2^2 + 6^2 = c^2
4 + 36 = c^2
40 = c^2
C is similar to 6.32456
Long side:
12^2 + 4^2 = c^2
144 + 16 = c^2
160=c^2
C is similar to 12.64911
And then you just multiply!
Which word shows a lack of affection for someone? Distrust or Dislike
Answers
Answer:
Dislike
Step-by-step explanation:
The answer is:
Dislike.
What is dislike?
A feeling of distaste or hostility.
"I dislike Angela because..."
Some synonyms:
Hate, detest, loathe, despise.
I apologize if this is incorrect. I hope you have a lovely day! :)
An elevator goes up 7 floors and then down 4 floors. What integer represents the change in the floor level?
Answers
7-4=3
i suck at math so someone please help me with this
Answers
Sorry I do not know. I wish I could be a better help to you. Sorry again
Please I need help on this and its due tonight! :( I just need this!
Answers
Answer:
see below
Step-by-step explanation:
y-intercept: (0,1)
rate of change: 2/3
Y-intercept: I found this because the y-intercept is when x=0, and where the line crosses through the y-axis. So, we can see that the y-intercept is (0,1)
Rate of change: The rate of change is another word for slope, or rise/run, so we can see, from point (0,1), that the rise is 2 units up and 3 units to the right to another point where the line crosses a whole number point.
Hope this helps :)
Rate if change: 2/3
Please refer to the image below.
Answers
Answer:
first answer is correct 3 1/8 gallons
Step-by-step explanation:
Please help I’m confused
A. 1/15
B. 1/10
C. 2/5
D. 3/5
Answers
Answer: A: 1/15
Step-by-step explanation:
A number cube has 6 sides.
the probability of getting either a 2 or a 3 will be 2/6, (since both events have an equal chance of happening, and they are out of total 6 possible outcomes).
2/6 simplifies to 1/3, so that is the probability of getting either a 2 or a 3
Next, the probability of landing on blue:
it will be 1/5, since there is only 1 blue section out of 5 *equally* divided sections.
Note that the probability includes the word "and". this means that we will use multiplication.
1/3 * 1/5 = 1/15
and thats the answer!
Shannon scored 36 points on 6 questions on her test. What is the unit rate for one question?
Answers
Answer:
6
Step-by-step explanation:
Evaluate. (−6+8)−2 Please help me
Answers
(-6+8)-2
The answer is 0
The stem-and-leaf plot displays data collected on the size of 15 classes at two different schools.
Mountain View School Seaside School
0 5, 8
9, 8, 2, 0 1 0, 1, 2, 5, 6, 8
8, 7, 6, 5, 5, 4, 4, 3, 1, 0 2 5, 5, 7, 7, 8
0 3 0, 6
Key: 2 | 1 | 0 means 12 for Mountain View and 10 for Seaside
Part A: Calculate the measures of center. Show all work. (2 points)
Part B: Calculate the measures of variability. Show all work. (1 point)
Part C: If you are interested in a smaller class size, which school is a better choice for you? Explain your reasoning. (1 point)
Answers
For Mountain View School:
Data: 0, 0, 0, 0, 1, 2, 3, 4, 4, 5, 5, 5, 5, 6, 7, 8, 8, 8, 9
Mean: (0 + 0 + 0 + 0 + 1 + 2 + 3 + 4 + 4 + 5 + 5 + 5 + 5 + 6 + 7 + 8 + 8 + 8 + 9) / 19
= 100 / 19
≈ 5.26
To find the median, we need to arrange the data in ascending order: 0, 0, 0, 0, 1, 2, 3, 4, 4, 5, 5, 5, 5, 6, 7, 8, 8, 8, 9.
The median is the middle value, which is the 10th value in this case.
Median: 5
For Seaside School:
Data: 0, 0, 0, 1, 1, 2, 2, 4, 5, 5, 5, 5, 6, 7, 7, 8, 8, 8, 9
Mean: (0 + 0 + 0 + 1 + 1 + 2 + 2 + 4 + 5 + 5 + 5 + 5 + 6 + 7 + 7 + 8 + 8 + 8 + 9) / 19
= 80 / 19
≈ 4.21
To find the median, we need to arrange the data in ascending order: 0, 0, 0, 1, 1, 2, 2, 4, 5, 5, 5, 5, 6, 7, 7, 8, 8, 8, 9.
The median is the middle value, which is the 10th value in this case.
Median: 5
Now let's calculate the measures of variability, specifically the range and interquartile range (IQR).
Range: The range is the difference between the largest and smallest values in the dataset.
For Mountain View School:
Range: 9 - 0 = 9
For Seaside School:
Range: 9 - 0 = 9
Interquartile Range (IQR): The IQR is the difference between the third quartile (Q3) and the first quartile (Q1) and measures the spread of the middle 50% of the data.
For Mountain View School:
Q1 = 3
Q3 = 7
IQR = Q3 - Q1 = 7 - 3 = 4
For Seaside School:
Q1 = 2
Q3 = 7
IQR = Q3 - Q1 = 7 - 2 = 5
To determine which school is a better choice for a smaller class size, we can consider both the mean and the median.
Both the mean and median for Mountain View School are higher than those for Seaside School. This suggests that, on average, the class sizes at Mountain View School are larger than those at Seaside School. Therefore, if you are interested in a smaller class size, Seaside School would be a better choice
For Mountain View School:
- Median: The median class size is the middle value, which is 25.
- Mean: The mean class size is the sum of all the class sizes divided by the total number of classes, which is (29 + 28 + 28 + 27 + 25 + 24 + 24 + 23 + 21 + 20 + 19 + 18 + 15 + 13 + 10) / 15 = 21.27.
For Seaside School:
- Median: The median class size is the middle value, which is 20.
- Mean: The mean class size is the sum of all the class sizes divided by the total number of classes, which is (25 + 25 + 27 + 27 + 28 + 28 + 28 + 30 + 31 + 35 + 36 + 38 + 40 + 43 + 45) / 15 = 31.13.
Part B:
For Mountain View School:
- Range: The range is the difference between the largest and smallest values, which is 29 - 10 = 19.
- Interquartile Range (IQR): The IQR is the difference between the third quartile (Q3) and the first quartile (Q1). From the stem-and-leaf plot, we can see that Q1 is 20 and Q3 is 28. Therefore, the IQR is 28 - 20 = 8.
For Seaside School:
- Range: The range is the difference between the largest and smallest values, which is 45 - 25 = 20.
- Interquartile Range (IQR): The IQR is the difference between the third quartile (Q3) and the first quartile (Q1). From the stem-and-leaf plot, we can see that Q1 is 27 and Q3 is 38. Therefore, the IQR is 38 - 27 = 11.
Part C:
If you are interested in a smaller class size, Mountain View School is a better choice for you because it has a lower mean and median class size than Seaside School.
The distance between the school and the airport on a map is 7.25 cm. The scale of the map is 1 cm : 12 m. What is the actual distance between the school and the airport?
PLEASE HELP ASAP
Answers
Answer: 87 M
Step-by-step explanation:
Step by step explanation:
The data in which table represents a linear function that has a slope of zero? A 2-column table with 5 rows. Column 1 is labeled x with entries negative 5, negative 4, negative 3, negative 2, negative 1. Column 2 is labeled y with entries 5, 5, 5, 5, 5. A 2-column table with 5 rows. Column 1 is labeled x with entries 1, 2, 3, 4, 5. Column 2 is labeled y with entries negative 5, negative 4, negative 3, negative 2, negative 1. A 2-column table with 5 rows. Column 1 is labeled x with entries negative 5, negative 4, negative 3, negative 2, negative 1. Column 2 is labeled y with entries 5, 4, 3, 2, 1. A 2-column table with 5 rows. Column 1 is labeled x with entries 5, 5, 5, 5, 5. Column 2 is labeled y with entries negative 5, negative 4, negative 3, negative 2, negative 1.
Answers
Answer: 2+2
Step-by-step explanation:
2+2=4
Vince borrows $900 to buy a couch. He will pay off the loan by paying 1.5% simple interest for 2 years. Vince incorrectly calculates the amount he will pay back using the expression below. 900 + 900(1.015 • 2) What is the correct amount Vince will pay back altogether?
A. $903; Vince should have subtracted the first 900 from the amount
he will pay.
B. $913.50; Vince multiplied by the wrong number of years.
C. $927; Vince wrote the wrong number to represent the interest rate.
D. $1,813.50; Vince forgot to add the initial $900 to the amount he will pay.
Answers
Answer: The correct amount Vince will pay back altogether is $927 and this can be determined by using the simple interest formula.
Step-by-step explanation:
Given :
Vince borrows $900 to buy a couch.
He will pay off the loan by paying 1.5% simple interest for 2 years.
Vince incorrectly calculates the amount he will pay back using the expression below. 900 + 900(1.015 2).
The following steps can be in order to determine the correct amount Vince will pay back altogether:
Step 1 - The formula of simple interest can be used in order to determine the correct amount Vince will pay back altogether.
Step 2 - The formula of simple interest is given below:
where A is the final amount, P is the principal amount, R is the interest rate, and T is the time.
Step 3 - Substitute the values of the known terms in the above expression.
A = 900(1 + 1.015 2)
Step 4 - Simplify the above expression.
A = $927
Answer: C
Step-by-step explanation:
A project will take a total of 720 person-days to complete. If the project must be completed in 30 days, how many people must be employed? PLEASE HURRY
Answers
Answer:
192 hours per day / 8 hours per person per day = 24 people
Step-by-step explanation:
Assuming each person works for 8 hours a day, the total number of hours needed to complete the project is:
720 person-days x 8 hours = 5,760 hours
To complete the project in 30 days, the total number of hours needed per day is:
5,760 hours / 30 days = 192 hours per day
is this correct????????
Answers
Answer:
no
Step-by-step explanation:
You need to subtract 7 from both sides and then divide -16 by 4 and then you have your answer of x = -4
Which list orders the numbers from least to greatest?
Negative 2.4, negative 1.5, negative 2 and one-fourth, negative 3, negative 1 and one-eighth
A number line going from negative 4 to positive 4.
Negative 1 and one-eighth, negative 1.5, negative 2 and one-fourth, negative 2.4, negative 3
Negative 3, negative 2.4, negative 2 and one-fourth, negative 1.5, negative 1 and one-eighth
Negative 3, negative 2 and one-fourth, negative 2.4, negative 1 and one-eighth, negative 1.5
Negative 1.5, negative 1 and one-eighth, negative 2.4, negative 2 and one-fourth, negative 3
Answers
Negative 3, negative 2.4, negative 1.5, negative 2 and one-fourth, negative 1 and one-eighth
Hope my answer helps you✌️
I NEED HELP ASAP with a science experiment give me ideas what experiments (mini-labs) I could do based on the task! READ THE SCREENSHOT
Answers
Answer: You should do a representation of how the heat and light waves reach humans on earth and keep us warm.
Step-by-step explanation:
all your answers are already in the task introduction.
1. Make earth out of styrofoam ball (buy at a dollar store) and paint. (blue and green). (If you want to make humans out of popsicle sticks)
2. Use velvet pipe cleaners (blue for cold air and red for hot air) to represent convection and conduction.
3. Use yellow pipe cleaners for solar energy to represent radiation.
4. Rest is up to you for how you want it to look.
Darcy likes to eat peanut butter and raisins on apple slices. On each apple slice, she puts 1/16 cup of peanut butter and 8 raisins. Darcy has 2/5 cups of peanut butter and 80 raisins. She eats a whole number of apple slices until the peanut butter is all gone. What fraction of the 80 raisins did she eat? Enter the fraction in the response box.
Answers
Answer 1 question correctly for 50 points!
Answers
Answer:
6 7 8 9 10
Step-by-step explanation:
Explanation:
PLEASE HELP I AM GIVING 100 POINTS FIRST COME FIRST SERVE ALSO GIVING BRAINLIEST TO THE FIRST PERSON WITH THE CORRECT ANSWER
Answers
Answer:
A = plane
B = whale
C = sunken ship
Step-by-step explanation:
The given vertical number line is modelling the positions of objects and animals in relation to sea level.
Sea level is the average height of the surface of the world's oceans, which we use as a reference point to measure the elevation and depth of land and water features on Earth.
From inspection of the given number line:
Position A is above sea level.Position B is just below sea level.Position C is the furthest below sea level.We have been told that a plane is flying at 8,500 feet above sea level. Therefore, as position A is the only position above sea level, A = plane.
We have been told that a sunken ship is resting at 3,000 feet below sea level, and that directly above the ship, a whale is swimming 1,960 feet below sea level. Therefore, the whale is above the ship. As position B is above position C, this means that B = whale and C = sunken ship.
Please help and you get a cake
Answers
Answer:
Mean = 33.7
Median = 34.5
Mode = 34
Range = 33
After adding 26....
mean decreases by 0.7
median decreases by 0.5
mode is 34
range is 33
Step-by-step explanation:
mean = sum of all the data values/number of data values
= (18 + 19 + 20 + 34 + 34 + 35 + 37 + 42 + 47 + 51)/10
= 337/10
= 33.7
To find median arrange the values in increasing order, find the mid value
If the number of data points is even, find the average of the mid 2 data values
Arranging data values we get:
18, 19, 20, 34, 34, 35, 37, 42, 47, 51
Since there are 10 data values, take the average of the middle two:
(34 + 35)/2 = 34.5
The mode is the value that occurs most often. We see that there are two instances of 34 whereas the other values appear only once
Mode = 34
The range is highest - lowest = 51 - 18 = 33
After we add 26, we get the following data set arranged
18, 19, 20, 26, 34, 34, 35, 37, 42, 47, 51
we can calculate the stats using the same technique as above
We get the following values
mean = )(18 + 19 + 20 + 26 + 34 + 34 + 35 + 37 + 42 + 47 + 51)/11
= 33
median = 34
mode = 34
range = 51-18 = 33
To find the decrease in mean and median subtract from the first set of values