Answer: y = -x+7
Step-by-step explanation:
Let's first set up it in slope-intercept form.
y = -x+b
We can find b using point (4,3).
Substitute 4 for x and 3 for y to get:
-3 + b = 4
b = 7
Therefore, the line is y = -x+7
Can someone answer this question
The equations and their graphs are:
Graph 4: I(x)=P(x)−4
Graph 2: I(x)=P(x+4)
Graph 1: I(x)=P(x)+4
Graph 3: I(x)=P(x−4)
Here we have,
to match the equations and their graphs:
The parent function is given as:
P(x) = x^2
As a general rule of function transformation, we have:
Vertical translation up: I(x) = P(x) + k
Vertical translation down: I(x) = P(x) - k
Horizontal translation left: I(x) = P(x + k)
Horizontal translation right : I(x) = P(x - k)
Using the above rules and the assumption that k is 4;
We have:
Vertical translation up: I(x) = P(x) + 4
Vertical translation down: I(x) = P(x) - 4
Horizontal translation left: I(x) = P(x + 4)
Horizontal translation right : I(x) = P(x - 4)
Hence, the graphs of the equations are:
Graph 4: I(x)=P(x)−4
Graph 2: I(x)=P(x+4)
Graph 1: I(x)=P(x)+4
Graph 3: I(x)=P(x−4)
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complete question;
Consider the function P(x)=x2, which is a parabola that opens upward, with a vertex at (0,0).
It undergoes four separate transformations as indicated by the graphs that follow.
P(x) represents the preimage and is placed correctly on all images. I(x) represents the image after the transformation.
Match each transformation indicated by I(x) to the correct graph.
Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.
I(x)=P(x)−4
I(x)=P(x+4)
I(x)=P(x)+4
I(x)=P(x−4)
Find the value of x. Round to the nearest tenth .
Answer:
23.8
Step-by-step explanation:
In a right-angled triangle, x ² + b ² = c ²
30.5 is c, we can choose b to be 19.1.
x ² + b ² = c ²
x ² = c ² - b ²
= 30.5² - 19.1²
= 565.44
x = √565.44
= 23.8 (to 3 significant figures)
i need serious help someone pleaseeeee
The value of c in the polynomial is - 7.
How to solve polynomials?The polynomial is given as follows:
p(x) = 2x³ - x² + cx + 2 . The value of c if x - 2 is a factor of p(x) can be computed as follows:
Therefore,
p(x) = 2x³ - x² + cx + 2
when x - 2 is a factor, p(x) = 0
Therefore,
0 = 2x³ - x² + cx + 2
Hence,
2(2)³ - (2)² + 2c + 2 = 0
16 - 4 + 2c + 2 = 0
12 + 2 + 2c = 0
2c = - 14
divide both sides by 2
c = - 14 / 2
c = - 7
Therefore,
c = -7
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Raina wants to buy a new house but needs money for the down payment. Her parents agree to lend her money at an annual rate of 6%, charged as simple
interest. They lend her $7000 for 5 years. She makes no payments except the one at the end of that time.
Answer the following questions. If necessary, refer to the list of financial formulas.
(a) How much total interest will Raina have to pay?
(b) What will the total repayment amount be (including interest)?
$
X
a. Raina will have to pay a total of $2100 in interest.
b. The total repayment amount, including interest, will be $9100.
How to Calculate Total Interest?To calculate the total interest and total repayment amount, we can use the formula for simple interest:
Simple Interest = Principal * Rate * Time
(a) Total interest:
Principal = $7000
Rate = 6% per year
Time = 5 years
Total Interest = Principal * Rate * Time
= $7000 * 0.06 * 5
= $2100
(b) Total Repayment Amount = Principal + Total Interest
= $7000 + $2100
= $9100
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Evaluate a - 13 when a = 33.
(a) 46
(b) 20
(c) -46
(d) -20
Answer:
(b) 20
Step-by-step explanation:
We are trying to solve a-13 = ____ for when a=33.
Substitute 33 for a.
33-13 = 20
the answer is b) 20
Triangle ABC is the preimage of a transformation that consists of a reflection across x -axis followed by a reflection across the y -axis. Which of the triangles is the image of △ABC under this transformation? Select the triangle that corresponds to the image △A′B′C′ .
The image triangle △A'B'C' is formed by reflecting triangle ABC across the origin, resulting in each point's coordinates being negated.
The preimage triangle ABC undergoes a reflection across the x-axis followed by a reflection across the y-axis.
To determine the image triangle △A'B'C', we need to understand the effects of these transformations.
Reflection across the x-axis flips the points of the preimage vertically, while reflection across the y-axis flips the points horizontally.
When both reflections are applied successively, the resulting image will be a reflection across the origin (0,0).
Given that, the image triangle △A'B'C' will be the reflection of triangle ABC across the origin.
In this case, the x-coordinate and y-coordinate of each point in triangle ABC will be negated to obtain the corresponding point in △A'B'C'.
Let's consider the points of triangle ABC:
A(x₁, y₁), B(x₂, y₂), C(x₃, y₃)
To obtain the corresponding points in △A'B'C', we negate the x and y coordinates:
A'(-x₁, -y₁), B'(-x₂, -y₂), C'(-x₃, -y₃)
Therefore, the image triangle △A'B'C' is formed by reflecting triangle ABC across the origin, resulting in each point's coordinates being negated.
Note: It's important to note that without the actual coordinates of triangle ABC, it's not possible to determine the specific shape or size of the image triangle △A'B'C'.
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find the area of each figure pls
Answer:
Step-by-step explanation:
1 = 20cm
2 = 0.56cm^2
3 = 77.5m2
The following table displays the number of sofas sold in a furniture store during certain months of the year.
Based on these data, the correct statement is B. The mean best describes the data.
What is the mean?The mean is one of the measures of central tendency.
The mean is also described as the average.
The average or mean is the quotient of the total data value divided by the number of data items.
Furniture Store Sofa Sales
January 255
February 234
March 263
April 229
May 248
Total sales = 1,229
The number of months of sales = 5
Mean = 245.8 (1,229 ÷ 5)
Thus, using the mean, we can conclude that the average sales from Januar to May were 245.8.
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Question Completion:The following table displays the number of sofas sold in a furniture store during certain months of the year.
Furniture Store Sofa Sales
January 255
February 234
March 263
April 229
May 248
Based on these data, which statement is correct?
A. There are outliers.
B. The mean best describes the data.
C. The median best describes the data.
D. The measure of variability that best describes the data is the IQR, 27.5.
what gives the response the sequare of the highwr common fact of 30 and 50
Answer:
GCF of 30 and 50 is 10 :}
What is the period of this function?
a.2
b.1
c.4
d.-1.15
The value of period of function is,
Period = 2
Since, A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
We have to given that;
The graph of function is shown in figure.
Since, The distance between the repetition of any function is called the period of the function.
And, For a trigonometric function, the length of one complete cycle is called a period.
Hence, By definition of period, we get;
The value of period of function is,
Period = 3 - 1
Period = 2
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Tanya flew 2,299 miles the first year on the job. She flew 3,831 miles the second year. Tanya flew 1,510 more miles the third year than the first and second years combined. How many miles did Tanya fly the third year?
Please help me!!
Answer: 7,640
Step-by-step explanation: Because we know that she flew 2,299 the first year and 3,831 the second, we can add them together to get: 6,130. It says that she flew 1,510 more miles the third year than the first and second combined. Therefore: 6,130 + 1,510 = 7,640
Vanessa makes 7 identical flower arrangements for the tables at a banquet. Each arrangement contains some roses and 9 tulips. Vanessa uses a total of 147 flowers to make the arrangements. How many roses are in each arrangement?
it is due today, please help me. If you just want points get out of my question page...
To completely solve the problem, Karim should convert the product back into standard decimal notation.
We cannot directly apply the product of powers property because the binomial is not raised to a power itself.
Miscellaneous problem(1) To convert a number from scientific notation to standard decimal notation, we multiply the coefficient (0.0258) by 10 raised to the power of the exponent (-8).
0.0258 × [tex]10^{-8[/tex] = 0.0258 × 0.00000001
= 0.000000000000258
(2) The product of powers property states that when you raise a term with an exponent to another exponent, you can simplify it by multiplying the exponents.
In the expression [tex](3z + y)^3[/tex], we have a binomial term (3z + y) raised to the power of 3. This is not a situation where we can directly apply the product of powers property because the binomial is not raised to a power itself.
To simplify the expression, we need to expand it using the binomial theorem or by applying the concept of binomial expansion.
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John borrowed $4,300.00 for 8 days at an annual simple interest rate of 13.75%. What is the amount of interest will John have to pay at the end of the loan?
John will have to pay $12.24 in interest at the end of the loan.
To calculate the amount of interest John will have to pay at the end of the loan, we can use the formula for simple interest:
Interest = Principal * Rate * Time
Given:
Principal (P) = $4,300.00
Rate (R) = 13.75% per annum
Time (T) = 8 days
First, we need to convert the rate from an annual percentage to a daily rate. Since there are 365 days in a year:
Daily Rate = (Rate / 100) / 365 = (13.75 / 100) / 365 = 0.0003767
Now we can calculate the interest:
Interest = Principal * Rate * Time
= $4,300.00 * 0.0003767 * 8
= $12.24
Therefore, John will have to pay $12.24 in interest at the end of the loan.
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Part 1 An aquarium in Watertown, USA needs to confirm their measurements to be sure there is enough room for incoming injured whales coming from another aquarium on the coast.
Main Show Tank Calculation:The main tank has a radius of 95 feet. What is the volume of the quarter-sphere sized tank? Round your answer to the nearest whole number. You must explain your answer using words, and you must show all work and calculations to receive credit.
Holding Tank Calculations: The holding tanks are congruent in size, and both are in the shape of a cylinder that has been cut in half vertically. The bottom of the tank is a curved surface. What is the volume of both tanks if the radius of tank #1 is 15 feet and the height of tank #2 is 120 feet? You must explain your answer using words, and you must show all work and calculations to receive credit.
Density Calculation: Using the calculations for the main and holding tanks above, what is the maximum number of killer whales allowed in the main show tank at any given time? The maximum density of killer whales per cubic foot is 0.000021142, You must explain your answer using words, and you must show all work and calculations to receive credit.
The volume of the quarter-sphere tank is approximately 1,387,244 cubic feet.
The volume of tank 1 is 353h cubic feet, and the volume of tank 2 is 31,416 cubic feet.
The main tank is in the shape of a quarter-sphere, which means it is a quarter of a full sphere.
The volume of a sphere is given by the formula V = (4/3)πr³, where r is the radius of the sphere.
Given that the radius of the main tank is 95 feet
we can substitute this value into the formula to calculate the volume:
V = (4/3)π(95³) = 1,387,244 cubic feet.
The holding tanks are in the shape of cylinders that have been cut in half vertically.
The volume of a cylinder is given by the formula V = πr²h, where r is the radius of the base and h is the height.
For tank 1, the radius is given as 15 feet. Since it is a half-cylinder, we divide the volume by 2:
V1 = (1/2)π(15²)h = 353h cubic feet.
For tank 2, the height is given as 120 feet.
V2 = (1/2)π(15²)(120) = 31,416 cubic feet.
The maximum density is 0.000021142 killer whales per cubic foot
we can calculate the maximum number of killer whales as follows:
Number of killer whales = (Volume of main show tank) / (Density of killer whales)
Number of killer whales = 1,387,244 / 0.000021142 ≈ 65,606,197.
Therefore, the maximum number of killer whales allowed in the main show tank at any given time is 65,606,197
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ANSWER ASAP!! (GIVING BRAINLIEST IF CORRECT!!)
A scale has a percent error of 5%. The actual mass of a rock is 30 g.
The scale is likely to show the mass as either;
A: 25 g. or 30 g.
B: 25.5 g. or 30.5 g.
C: 28 g or 31.5 g.
D: 28.5 g. or 31.5 g.
Answer:
ans d
Step-by-step explanation:
5 percent of 30 is 1.5 so d
Prepare accounting equation:
a. Started business with Cash Rs. 250,000.
b. Purchased goods amounting to Rs. 45,000 on credit from Harish .
c. Goods costing to Rs.80,000 was sold for Rs.1,25,000 on credit.
d. Salaries outstanding Rs. 5000
e. Rent paid Rs. 50,000
f. Withdrawn by owner for personal use Rs.25,000.
assets = liabilities + capital
The accounting equation is:
Assets (Rs. 1,75,000 - Rs. 35,000) = Liabilities (Rs. 45,000 + Rs. 5,000) + Capital (Rs. 20,000)
We have,
Based on the given transactions, we can prepare the accounting equation as follows:
a. Started business with Cash Rs. 250,000.
Assets: Cash = Rs. 250,000
b. Purchased goods amounting to Rs. 45,000 on credit from Harish.
Assets: Cash = Rs. 250,000, Inventory = Rs. 45,000
Liabilities: Accounts Payable = Rs. 45,000
c. Goods costing to Rs. 80,000 was sold for Rs. 1,25,000 on credit.
Assets: Cash = Rs. 250,000, Accounts Receivable = Rs. 1,25,000
Inventory: Rs. 45,000 - Rs. 80,000 = Rs. -35,000 (Assuming no additional purchases or returns)
Liabilities: Accounts Payable = Rs. 45,000
Capital: Retained Earnings = Rs. 1,25,000 - Rs. 80,000 = Rs. 45,000
d. Salaries outstanding Rs. 5,000.
Liabilities: Salaries Payable = Rs. 5,000
e. Rent paid Rs. 50,000.
Assets: Cash = Rs. 250,000 - Rs. 50,000 = Rs. 2,00,000
f. Withdrawn by owner for personal use Rs. 25,000.
Assets: Cash = Rs. 2,00,000 - Rs. 25,000 = Rs. 1,75,000
Capital: Retained Earnings = Rs. 45,000 - Rs. 25,000 = Rs. 20,000
Now, let's summarize the accounting equation:
Assets:
Cash = Rs. 1,75,000
Inventory = Rs. -35,000 (negative value indicates loss or returns)
Liabilities:
Accounts Payable = Rs. 45,000
Salaries Payable = Rs. 5,000
Capital:
Retained Earnings = Rs. 20,000
Therefore,
The accounting equation is:
Assets (Rs. 1,75,000 - Rs. 35,000) = Liabilities (Rs. 45,000 + Rs. 5,000) + Capital (Rs. 20,000)
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The graph shows an exponential function relating the balance in
an investment account to the time in years.
What does the y-intercept represent?
O
the time it takes the account to reach its maximum
value
O the maximum value of the account
O the initial balance of the account
O the amount the account increases by each year
Account balance (5)
1600
1400
1200
1000
800
600
The value of the y-intercept represent,
⇒ the amount of the account increases by each year.
We have to given that;
The graph shows an exponential function relating the balance in an investment account to the time in years.
Now, From graph we have;
The value of the y-intercept represent,
⇒ the amount of the account increases by each year.
Thus, value of the y-intercept represent,
⇒ the amount of the account increases by each year.
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A manager drew this box-and-whisker plot to represent the number of minutes each of his 27 employees took on their break. Each employee took a different amount of time.
How many employees took a break longer than 49 minutes?
Help please!
Note: Put the correct answer! I don't want to get this wrong!
Thank you <3
Approximately 7 employees took a break longer than 49 minutes.
We have,
In a box-and-whisker plot, the box represents the interquartile range (IQR), which includes the middle 50% of the data.
The line within the box represents the median.
The "whiskers" extend to the minimum and maximum values, excluding any outliers.
Given the information provided:
Median = 41
Q1 = 37
Q3 = 49
Largest = 55
Smallest = 35
Since Q3 represents the upper quartile and corresponds to the boundary for the upper 25% of the data, we can conclude that 25% of the employees took a break longer than 49 minutes.
Now,
The number of employees who took a break longer than 49 minutes can be estimated by calculating 25% of the total number of employees:
25% of 27 employees
= (25/100) x 27
= 6.75
Since we cannot have a fractional number of employees, we round up to the nearest whole number.
Therefore,
Approximately 7 employees took a break longer than 49 minutes.
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What is the period of this function?
Drag each number to a box to complete the table. Each number may be used once or not at all.
8,000533,00021,000
Kilometers Meters
1
2,000
5,000
8
Each number should be dragged to a box to complete the table as follows;
Kilometers Meters
1 1,000
2 2,000
3 3,000
5 5,000
8 8,000
What is a conversion factor?In Science and Mathematics, a conversion factor is a number that is used to convert a number in one set of units to another, either by dividing or multiplying.
Generally speaking, there are one (1) kilometer in one thousand (1,000) meters. This ultimately implies that, a proportion or ratio for the conversion of kilometer to meters would be written as follows;
Conversion:
1 kilometer = 1,000 meters
2 kilometer = 2,000 meters
3 kilometer = 3,000 meters
4 kilometer = 4,000 meters
5 kilometer = 5,000 meters
6 kilometer = 6,000 meters
7 kilometer = 7,000 meters
8 kilometer = 8,000 meters
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Missing information:
The question is incomplete and the complete question is shown in the attached picture.
Find the surface area of the composite solid to the nearest hundredth.
A composite solid of a square prism with a square pyramid extending from the top and bottom face of the prism. The width, length, and height of the prism are all 5 inches. The slant height of the pyramid on the bottom of the prism is 7.5 inches. The height of the pyramid on top of the prisim is 3 inches.
The surface area of the composite solid is 255 square inches.
How to find the surface area of the composite solid?We will compute the surface area of each component and then add them together to find the surface area of the composite solid.
First, the surface area of the square prism:
Given: The square prism has a width, length, and height of 5 inches each.
Formula for the surface area of a rectangular prism: 2lw + 2lh + 2wh
Surface area of the prism = 2(5 * 5) + 2(5 * 5) + 2(5 * 5)
= 2(25) + 2(25) + 2(25)
= 50 + 50 + 50
= 150 square inches
Next, the surface area of the square pyramid at the bottom:
Given: The slant height of the pyramid on the bottom of the prism = 7.5 inches.
The base of the pyramid is a square with a side length of 5 inches.
Formula to find the lateral surface area of a square pyramid: (perimeter of base) * slant height / 2.
The base is a square, the perimeter is 4 times the side length.
Lateral surface area of the bottom pyramid = (4 * 5) * 7.5 / 2
= 20 * 7.5 / 2
= 150 / 2
= 75 square inches
Then, the Surface area of the square pyramid at the top:
Given: The height of the pyramid on top of the prism = 3 inches.
The base of the pyramid is a square with a side length of 5 inches.
Lateral surface area of the top pyramid = (4 * 5) * 3 / 2
= 20 * 3 / 2
= 60 / 2
= 30 square inches
Finally, we shall find the total surface area by summing up the surface areas of each component in this way:
Total surface area = Surface area of the prism + Surface area of the bottom pyramid + Surface area of the top pyramid
= 150 + 75 + 30
= 255 square inches
Therefore, the surface area of the composite solid = 255 square inches.
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The sales tax rate for the state of Washington was 9.2%.
a) What is the state sales tax on a $2,800 used car in Washington?
b) What is the final cost of the car, including tax?
a) The state sales tax on a $2,800 used car in Washington is given as follows: $257.6.
b) The total cost of the car, including tax, is given as follows: $3,057.6.
How to obtain the sales tax and the total cost of the car?The sales tax and the total cost of the car are obtained applying the proportions in the context of the problem.
The sales tax rate is given as follows:
9.2%.
Hence, for a car of $2,800, the sales tax is given as follows:
0.092 x 2800 = $257.6.
The total cost is then obtained adding the base cost to the sales tax, as follows:
2800 + 257.6 = $3,057.6.
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You have $400,000 saved for retirement. Your account earns 10% interest. How much will you be able to pull out each month, if you want to be able to take withdrawals for 20 years?
You will be able to withdraw $3,548.50 per month for 20 years if you have $400,000 saved for retirement and earn 10% interest.
To calculate the monthly withdrawals for a given time period, we can use the present value annuity formula. This formula allows us to calculate the fixed monthly withdrawal amount needed to deplete a given initial amount (in this case, $400,000) over a specified time period (20 years) at a given interest rate (10%).
The formula for present value annuity is:
PMT = PV * r / (1 - (1 + r)⁻ⁿ)
Where:
PMT = the fixed monthly withdrawal amount
PV = the present value of the initial investment ($400,000)
r = the interest rate per month (10%/12 = 0.00833)
n = the total number of monthly withdrawals (20 years * 12 months per year = 240)
Plugging in the values, we get:
PMT = 400,000 * 0.00833 / (1 - (1 + 0.00833)⁻²⁴⁰) = $3,548.50 (rounded to the nearest cent)
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A cube has a depth of 9 dm. What is the volume of the cube?
The volume of the cube is 729 dm³
How to find the volume of the cube?Remember that all the dimensions on a cube are the same ones, then we have:
Length = Width = Depth.
And for any prism, the volume is the product between the 3 dimensions, then for any cube the volume is:
V = Length*Width*Depth.
In this case we know that the depth is 9dm, then also is the length and the width, and thus, the volume of this cube is:
V = 9dm*9dm*9dm = 729 dm³
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A survey of 800 nurses yielded the following information. 555 were health club members, 430 were smokers, and 320 of the health club members were smokers. How many of the 800 surveyed nurses were health club members or were smokers
Step-by-step explanation:
800 in total.
555 health club members.
430 smokers.
320 health club members (that means out of the total of 555) were smokers.
that means that
555 - 320 = 235 health club members were not smokers.
and out of the 430 smokers 320 were also health club members.
that means that
430 - 320 = 110 smokers were not health club members.
the question how many were health club members or smokers means how many people were either health club members or smokers.
so, we need to combine the sets of health club members and smokers.
the number of elements in the resulting set is not just the sum of elements of both sets, because some elements are in both sets and would be counted twice.
therefore, we have a few alternatives :
1. add both sets and then subtract the common part (people being in both sets), as this removes the double counting :
555 + 430 - 320 = 665
2. start with the common part (people that are in both sets) and add the extra people in both sets (health club members that do not smoke, and smokers that are not health club members) :
320 + 235 + 110 = 665
3. start with one of the full sets (e.g. all health club members) and add the extra people of the other set (all smokers that are not also health club members) :
555 + 110 = 665
or all smokers plus all health club members that were not smokers :
430 + 235 = 665
as you can see, as expected, the answer is always the same :
out of the 800 nurses 665 were health club members or smokers.
lan is 1.83m tall
Donna is 6cm shorter
What is Donna's height in metres?
Answer:
Step-by-step explanation:
lan is 1.83m tall. Donna is 6cm shorter. What is Donna's height in metres? 1.77m. Bath. √34°. 20m. 11m. 11x14. Work out the range. 3 8 4 8 3 5 9. 9-3=6.
Calculus Integral Questions Unit 2 Lesson 5 Fundamental Theorem of Calculus
Answer: b and c
Step-by-step explanation:
Answer:
The first question is 3 and the third question is the one with = 20
I have no answer for the second
The other answer left by farrelljacob646 is incorrect
9.7/0.0268
need help please
This is a basic arithmetic problem and the solution to 9.7/0.0268 is equal to 361.94
Understanding Basic Arithmetic OperationBasic Arithmetic Operations are fundamental to solving mathematical problems and they are addition (+), subtraction (-), multiplication (×) and division (÷).
1. Addition:
Addition is the process of combining two or more numbers to find their total or sum. The symbol used for addition is "+". For example, to add the numbers 3 and 5, you write it as:
3 + 5 = 8
Here, 3 and 5 are added together to get the sum, which is 8.
2. Subtraction:
Subtraction is the process of finding the difference between two numbers. The symbol used for subtraction is "-". For example, to subtract 5 from 8, you write it as:
8 - 5 = 3
Here, 5 is subtracted from 8 to get the difference, which is 3.
3. Multiplication:
Multiplication is the process of repeated addition or combining equal groups. The symbol used for multiplication is "×" or "*". For example, to multiply 4 and 6, you write it as:
4 × 6 = 24
Here, 4 is multiplied by 6 to get the product, which is 24.
4. Division:
Division is the process of dividing a number into equal parts or finding how many times one number is contained within another. The symbol used for division is "÷" or "/". For example, to divide 20 by 5, you write it as:
20 ÷ 5 = 4
Here, 20 is divided by 5 to get the quotient, which is 4.
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Can someone help me please
(a) The given system of equation as an augmented matrix is [tex]\left[\begin{array}{cccc}1&3&0&150\\0&1&0&250\\-1&-1&1&400\end{array}\right][/tex];
(b) For the given augmented matrix, the system of equations is
-5x-6y-4z=400;
y+z=100;
-3x-3y-2z=150;
A "system-of-equations" is a set of two or more equations which contain multiple variables. The solution to the system of equations is the set of values for the variables that satisfy all the equations in the system.
An "Augmented-Matrix" is a way to represent a system of linear equations in a concise and organized manner. It is obtained by writing the coefficients of the variables and the constants in each equation in a rectangular array, with each row representing an equation.
Part(a) : The system-of-equations is given as :
x + 3r +0m = 150
0x + r + 0m = 250
-x - r + m = 400,
We see that the first column of the matrix will have 1, 0, -1,
the second-column will have 3, 1, -1 ;
the third-column will have 0, 0, 1.
So, the Augmented Matrix is represented as : [tex]\left[\begin{array}{cccc}1&3&0&150\\0&1&0&250\\-1&-1&1&400\end{array}\right][/tex].
Part(b) :
The augmented-matrix is given as : [tex]\left[\begin{array}{cccc}-5&-6&-4&400\\0&1&1&100\\-3&-3&-2&150\end{array}\right][/tex],
In this matrix, the terms in the "first-column" will be multiplied by variable"x";
the terms in the "second-column" will be multiplied by variable"y"; and
the terms in the "third-column" will be multiplied by variable"z";
The term sin the "fourth-column" represents the output value.
So, "system-of-equation" will be represented as : -5x - 6y - 4z = 400;
0x + y + z = 100;
-3x - 3y - 2z = 150.
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