What method of matrixes would be used for this question? ( Inverse Matrices, Cramer's Rule, Gaussian Elimination, and Gauss-Jordan Elimination)
May’s restaurant ordered 200 flowers for Mother’s Day. They ordered carnations at $1.50/each, roses at $5.75 each, and daisies at $2.60 each. They ordered mostly carnations, and 20 less roses than daisies. The total order came to $589.50. How many of each type of flower was ordered?
Answers
Answer:
(d) Gauss-Jordan Elimination
80 carnations; 50 roses; 70 daisies
Step-by-step explanation:
The given relations can be written as equations, which can be expressed as one matrix equation. Any of the methods listed can be used to solve the matrix equation.
EquationsIf we let c, r, d represent numbers of carnations, roses, and daisies ordered, respectively, then the given relations can be written as ...
c + r + d = 200 . . . . . . 200 flowers were ordered
0c -r +d = 20 . . . . . . . . . . . . . 20 more daisies than roses were ordered
1.50c +5.75r +2.60d = 589.50 . . . . . the total value of the order
Matrix EquationWritten as a matrix equation, it will be of the form ...
AX = B
where A is the square matrix of variable coefficients, X is the column vector of variables, and B is the column vector of equation right-side constants. This is the matrix equation:
\(\left[\begin{array}{ccc}1&1&1\\0&-1&1\\1.50&5.75&2.60\end{array}\right] \left[\begin{array}{c}c\\r\\d\end{array}\right] =\left[\begin{array}{c}200\\20\\589.50\end{array}\right]\)
Solution MethodsThe mathematical operations required to find the equation solution can be briefly described as ...
Inverse Matrices
The coefficient matrix is inverted and multiplied by the constant column vector:
\(X=A^{-1}B\)
The inversion operation requires computation of 10 determinants, of which 9 are of 2×2 matrices. That's a total of about 39 multiplications, 9 divisions, and 20 additions.
Cramer's Rule
Using Cramer's rule requires computation of 4 determinants of 3×3 matrices. The total number of operations comes to about 48 multiplications, 3 divisions, and 20 additions.
Gaussian Elimination
To obtain the upper triangular matrix that results from Gaussian Elimination requires about 11 multiplications, 11 additions, and 2 divisions. This finds the value of one variable, but the others must be found by substitution into the remaining two equations, requiring an additional 3 multiplications and 3 additions.
Gauss-Jordan Elimination
This method starts with an augmented matrix that appends column vector B to the square matrix A. The result of this is shown in the attachment. It is a diagonal matrix with the variable values a direct result of the matrix operations. The calculator's RREF( ) function performs matrix row operations to transform the augmented matrix to this Reduced Row-Echelon Form. About 6 multiplications, 6 additions, and 4 divisions are required.
Clearly, Gauss-Jordan Elimination is the method that requires the least computational work, so it would probably be used for this question.
FlowersThe attachment shows the order to be ...
80 carnations50 roses70 daisies__
Additional comment
The estimates of computational load presented by each of the solution methods are not intended to be exact counts. For this specific problem, some of the operations can be avoided due to the fact that some coefficients are already 1. Also, some computations are not needed simply because they are intended to produce an outcome that is already known. The intention is to give an idea of the relative difficulty of using these different methods.
In some cases, computationally less-efficient methods may be preferred because they are simpler to describe.
Related Questions
Use an integer to represent the following.A voltage drop of 21 volts.
Answers
A reduction or drop is usually represented by a negative sign alongside the quantity of the drop.
In this case, the quantity of the drop is 21.
Hence, the integer used to represent the situation is:
\(-21\)How do I solve 5(24,500)+4b+3(10,100)=$210,400
Answers
Answer:
use a calculator
Step-by-step explanation:
what is x? how would i find the value of x?
Answers
Use the next trigonometric ratio to find the value of x:
\(sin\theta=\frac{opposite}{hypotenuse}\)For angle x:
\(\begin{gathered} sinx=\frac{9}{29} \\ \\ x=\sin^{-1}(\frac{9}{29}) \\ \\ x\approx18º \end{gathered}\)Then, the value of x is 18ºName:
1. Dane deposited $5,000 in a savings account. The amount in the account after 1, 2, and 3 years is shown
below.
$5,240, $5,480, $5,720, ...
Which function represents the total amount in her account at the end of t years?
A. M(t) = 5000 + 2400
B. M(t) = 5240 +2400
C. M(t) = 5000t + 240
D. M(t) = 5240t + 240
Answers
Answer:
I dont kn0w try g00gle searches
Answer:
B. M(t)= 5240+240t
Step-by-step explanation:
cause
A cardboard tube used for storing posters has the shape of a cylinder. It is 100 centimeters long and has a diameter of 8 canimeters. What is the volume of the tube
Answers
Answer:
\(Volume = 5028.6cm^3\)
Step-by-step explanation:
Given
\(Height = 10cm\)
\(Diameter = 8cm\)
Required
Determine the volume
The volume of a cylinder is calculated as thus:
\(Volume = \pi r^2h\)
Where \(r = radius\)
\(r = \frac{1}{2} * Diameter\)
\(r = \frac{1}{2} * 8cm\)
\(r = 4cm\)
\(h = 100cm\)
Take
\(\pi = \frac{22}{7}\), so we have
\(Volume = \pi r^2h\)
\(Volume = \frac{22}{7} * 4^2 * 100\)
\(Volume = \frac{22}{7} * 16 * 100\)
\(Volume = \frac{22 * 16 * 100}{7}\)
\(Volume = \frac{35200}{7}\)
\(Volume = 5028.6cm^3\)
Distinguish what a ray, line segment and line are in your own words. Then, compare
and contrast the three geometric figures.
Answers
Answer: A ray starts from a point and goes to infinity. A line has no end points. A line segment has two endpoints. A line segment connects both endpoints.
Step-by-step explanation:
did this explain it
WILL GIVE BRAINLIEST IFFFF CORRECT!!!!
Answers
Explanation:
M represent the number of minutes. The equation shows the .15m . Meaning that they charge .15 cents every minute PLUS a flat fee of $35. The second part of the equation is the same; they charged .25 cents every m ( .25m) PLUS a flat fee of $20. All of this was shown in the last question if you look closely.
Draw lines to match equivalent time intervals.
day
5 days
6 days
120 hours
13 weeks
144 hours
-12
10 days
720 minutes
91 days
240 hours
Answers
Answer:
120h = 5 days
240h = 10 days
144h = 6 days
720m = 1/2 (half a day)
13w = 91 days
please make this brainliest
Using the given diagram, solve for x.
x=
Answers
Step-by-step explanation:
since the whole biggest triangle is a right triangle so ,
\( {x}^{2} = {20}^{2} + {18}^{2} \\ {x}^{2} = 400 + 324 \\ {x}^{2} = 724 \\ x = \sqrt{724} = 26.907 = 26.91\)
Which of the following could be an equation of the form y=-x^3+ax^2+bx+c for some real numbers a,b,?
Answers
Answer:
Bottom left graphStep-by-step explanation:
Given function:
y = -x^3 + ax^2 + bx + cThis is a third degree function with negative leading coefficient.
This is therefore decreasing function and can have one local maximum and one local minimum.
From the given graphs we can see only bottom left one can be a matching one.
Which of the following numbers is a factor of 55?
Choose 1 answer:
Choose 1 answer:
(Choice A)
A
6
(Choice B)
B
3
(Choice C)
C
5
(Choice D)
D
7
Answers
Answer:
Choice C: 5
Step-by-step explanation:
55 is a composite number. 55 = 1 x 55 or 5 x 11. Factors of 55: 1, 5, 11, 55. Prime factorization: 55 = 5 x 11 it should be 5 if 11 isn't an option to
Jake left the gym at 6:22 he exercised for 45 mins. What time did he arrive
Answers
I did this by working backwards, subtracting 22 from 45 to get 23. Then we subtract 23 from 60, which is an hour in terms of minutes, and get 37. So that is the minutes, and then we just bring it down one in the hour column considering that 45 minutes isn’t above an hour.
All of the license plates in a particular state feature three letters followed by three digits (e.g. ABC 123). How many different license plate numbers are available to the state's Department of Motor Vehicles?
Answers
Step-by-step explanation:
for each letter position there are 26 choices.
and each of these 26 choices can be combined with the next 26 choices.
so, they alone are 26×26×26 = 26³ = 17,576
then we have the three number positions.
each has 10 options.
so, they are 10×10×10 = 10³ = 1000
and both combined are
26³×10³ = 17,576,000 different number plates
The number of different license plate numbers are available to the state's Department of Motor Vehicles is 17,575,000.
What is fundamental counting principle?The fundamental counting principle or basic principle of counting is a method or a rule used to calculate the total number of outcomes when two or more events are occurring together.
This principle states that the total number of outcomes of two or more independent events is the product of the number of outcomes of each individual event.
For each letter position there are 26 choices, and each of these 26 choices can be combined with the next 26 choices.
so, they alone are 26×26×26 = 26³ = 17,576
then we have the three number positions, each has 10 options.
so, they are 10×10×10 = 10³ = 1000
and both combined are;
26³×10³ = 17,576,000 different number plates.
Hence the number of different license plate numbers are available to the state's Department of Motor Vehicles is 17,575,000.
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Find the rank of the matrix [
2 − 1 − 3 − 1
1 2 3 − 1
1 0 1 1
0 1 1 − 1
]
Answers
The rank of the matrix is 3, since there are three linearly independent rows.
The rank of a matrix is the maximum number of linearly independent rows or columns in the matrix. It is denoted by the symbol "rank(A)" for a matrix A.
To find the rank of the matrix:
[-2, -1, -3, -1] [ 1, 2, -3, -1] [ 1, 0, 1, 1] [ 0, 1, 1, -1]
We can perform row operations to reduce the matrix to row echelon form, which will help us determine the rank.
\(R_2 = R_2 + 2R_1 R_3 = R_3 + 2R_1 R_4 = R_4 + R_2\)
This gives us the following matrix:
[-2, -1, -3, -1] [ 0, 0, -9, -3] [ 0, -1, -1, 1] [ 0, 0, -4, -4]
We can see that the third row is not a linear combination of the first two rows, and the fourth row is not a linear combination of the first three rows. Therefore, the rank of the matrix is 3, since there are three linearly independent rows.
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I need help with this and if so can you pls give an explanation?
Answers
Answer:
ty
Step-by-step explanation:
construct a right-angled isosceles triangle whose equal side measure 2 cm
Answers
A construction of a right-angled isosceles triangle whose equal side measure 2 cm is shown in the image attached below.
What is an isosceles right triangle?In Mathematics, an isosceles right triangle can be defined as a type of right-angled triangle in which two (2) of its side lengths are equal and one of its angle is a right angle.
What are the steps for the construction of a right-angled isosceles triangle?Generally speaking, the steps that are required for the construction of a right-angled isosceles triangle include the following:
You should draw a line segment, with line AB equal to 2 cm (AB = 2cm).At point A, draw an angle with a measure of 90 degrees (90°).You should draw an arc of radius from point A in order to intersect the perpendicular drawn at point A at the point C.You should join point A and point B.In conclusion, triangle ABC (ΔABC) is the required right-angled isosceles triangle as shown in the image attached below.
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IXL math problem
……………..
Answers
Answer:
FI = 48
Step-by-step explanation:
We know that FI and IH are equal. so we can build an equation to solve this tricky and messy question which tries to scare you by giving additional information.
z + 22 = 4z -56
z - 4z = -56 - 22
-3z = -78
z = -78 / -3
z = 26
so we know FI = z + 22
= 26 + 22
= 48
Ben rented a car. It cost $30.00 plus $0.25 per mile. If Ben paid $85.00 for the car rental, how many miles did he drive the car? Write an equation and then use your equation to find your answer.
Answers
Answer:
220 miles
Step-by-step explanation:
85-30=55
55/.25=220
220 = miles
Answer:
Equation:
30 + 0.25x = 85
Work:
30 + 0.25x = 85
85 - 30 = 55
55 / 0.25 = 220
Final answer:
200 miles
Step-by-step explanation:
Hope this helped and have a nice day!!!
free think fast 20X10
Answers
Answer:
200 yessir
Step-by-step explanation:
Determine the key features of a function whose value is defined as six less than triple some quantity. (2 points)
The slope is _____
the x-coordinate of the x-
Intercept is_____
and the y-coordinate of the y-intercept is_____
:: 6
:: 2
:: 3
:: 1/3
:: -6
Can y’all help me put three of these options in the right places :)
Answers
Answer:
The slope is 3
Hence the x-coordinate of the x- intercept is 2
Hence the y-coordinate of the y- intercept is -6
Step-by-step explanation:
We are to first write the statement six less than triple some quantity as an expression:
let the quantity be x
Triple the quantity to have 3x
six less than triple some quantity will be expressed 3x - 6
The required function is f(x) = 3x - 6
This is in standard form of equation of a line y = mx+c
m is the slope
c is the y-intercept
Comparing 3x - 6 with mx+c
3x = mx
3 = m
m = 3
The slope is 3
x intercept occurs at when f(x) = 0
Substitute into f(x) = 3x-6
0 = 3x-6
-3x = -6
x = 2
Hence the x-coordinate of the x- intercept is 2
y intercept occurs at when x = 0
Substitute into f(x) = 3x-6
f(x) = 3(0)-6
f(x) = -6
Hence the y-coordinate of the y- intercept is -6
Translate the following verbal statement into an algebraic equation and then solve:
Julio bought a refrigerator on sale for $200, which was one-half of the original price. What was the original price of the refrigerator?
Answers
The original price of the refrigerator was $400.
The statement "Julio bought a refrigerator on sale for $200 was one-half of the original price" can be translated into an algebraic equation as follows:
1/2x = 200
x represents the original price of the refrigerator.
This equation states that half of the original price is equal to $200 is the sale price that Julio paid.
To solve for x, we can multiply both sides of the equation by 2 gives us:
x = 2 × 200
x = 400
We can check this answer by verifying that half of $400 is indeed equal to $200 was the sale price that Julio paid.
We translated the verbal statement into an algebraic equation and solved for the unknown variable to find that the original price of the refrigerator was $400.
The phrase "Julio bought a refrigerator on sale for $200 was one-half of the original price" may be transformed into the following algebraic equation:
The initial cost of the refrigerator is 1/2x = 200x.
According to this calculation, Julio paid $200 for the item, which is equal to half of the original price.
By multiplying both sides of the equation by 2, we may find the value of x as follows:
x = 2 × 200 x
= 400
By confirming that half of $400 is actually equal to $200, which was the sale price paid by Julio, we can confirm this response.
The spoken statement was converted into an algebraic equation and the unknown variable was solved for in order to determine that the refrigerator's initial cost was $400.
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PLEASE HELP Find the value of x.
X
15
12
Answers
Answer: x = 9
Step-by-Step Solution:
Hypotenuse = 15 units
Base = 12 units
Altitude = x units
Using Pythagoras Theorem,
=> Hypotenuse^2 = Base^2 + Altitude^2
(15)^2 = (12)^2 + x^2
225 = 144 + x^2
225 - 144 = x^2
81 = x^2
x^2 = 81
x = √81
=> x = 9
Therefore, Altitude = 9 units
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Madison Middle School spends $750 per year on club activities. They spend at least twice that amount on after-school activities. Write an inequality that represents how much they spend on after-school activities.
Answers
Answer:
x ≥ 1500
Step-by-step explanation:
Which expressions are factors of the expression
-24xyz - 12xy + 20xyz
Answers
Answer:
xy
2xy
4
Step-by-step explanation:
A factor is a number of term you can factor out of each part of the expression/ or divide it by.
In -24xyz - 12xy + 20xyz
All three parts have xy, so it is a factor
All three don't have 12xz, because -12xy doesn't have z variable for instance.
All three have 2xy.
All three can't factor out 3y, because you can't divide 20 by 3 nicely.
All three can't factor out 4yz, because middle term -12xy doesn't have z.
All three can't factor out 12, because you can't nicely divide 20/12.
All three can factor out 4, because -24, -12, and 20 are all divisible by 4.
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Two cars travel at the same speed to different destinations. Car A reaches its destination in 25 minutes. Car B reaches its destination in 35 minutes. Car B travels 4 miles farther than Car A. How fast do the cars travel?
Answers
Step-by-step explanation:
speed = distance / time
distance = speed × time
they both have the same speed.
distanceB = distanceA + 4
so,
distanceA = speed × 25 min
distanceB = distanceA + 4 = speed × 35 min
distanceA = speed × 35 - 4
both distanceA expressions must be equal :
speed × 25 = speed × 35 - 4
subtract 25speed from both sides
0 = speed × 10 - 4
add 4 to both sides
4 = speed×10 min
divide both sides by 10 min
4 miles / 10 min = speed
to get the usual miles per hour, we need to multiply numerator and denominator by the same number, so that the denominator is 1 hour = 60 minutes.
as we cab see, we need to multiply by 6/6 :
4/10 × 6/6 = 24/60 = 24 miles per hour.
You have a square that has a side length of $1$ centimeter. Each minute, $2$ centimeters are added to the side length. After $10$ minutes, what will be the difference between the area of the last square and the area of the initial square in square centimeters (do not include the units in your answer)?
Answers
Answer:
Difference in area of the last square and the initial square = 440 cm²
Step-by-step explanation:
Length of the side of a square = 1 cm
Area of the square = (side)² = 1 cm²
Addition of side length every minute = 2 cm
After x minutes length of each side of the square = (1 + 2x) cm
If x = 10 minutes
Length of each side of the square = [1 + 2(10)]
= 21 cm
Area of the square after 10 minutes = (21)²
= 441 cm²
Therefore, difference in area of the last square and area of the initial square
= 441 - 1
= 440 cm²
A bag had 100 mangoes. 2/5 are rotten and 1/3 are green. How many mangoes are ripe?
Answers
Answer:
about 27 are ripe
Step-by-step explanation:
100 mangos
5*20=100
2*20=40
40 are rotten
3*33=99 which is about 100
1*33=33
33 are green
40+33=73
100-73=27
For f(x) = 3x+1 and g(x) =x to the power of 2 -6, find (f+g)(x)
Answers
(f + g)(x) = \(x^{2}\) + 3x - 5 , when f(x) = 3x + 1 and g(x) = \(x^{2}\) - 6
Given, that f(x) = 3x + 1 and g(x) = \(x^{2}\) - 6
Now, we have to find (f + g)(x).
So, (f + g)(x) is defined as f(x) + g(x)
(f + g)(x) = f(x) + g(x)
On substituting the values of f(x) and g(x), we get
(f + g)(x) = (3x + 1) + ( \(x^{2}\) - 6)
(f + g)(x) = (3x + \(x^{2}\) - 5)
(f + g)(x) = ( \(x^{2}\) + 3x - 5 )
Hence, (f + g)(x) = \(x^{2}\) + 3x - 5
(f + g)(x) = \(x^{2}\) + 3x - 5
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Determine whether each of the following are functions :
Answers
Answer:
a and b are and C is not. b is called an exponential function and a is another function that I forgot the name of.
Answer:
Functions - a and cNon- function - bStep-by-step explanation:
This is verified with a vertical line test.
If a graph of a function is intersected by a vertical line at more than one point, it is not a function. This comes from the definition of a function.
We can see that the graphs a and c pass the vertical line test but the graph b fails, since at any positive x, the vertical line has two - y coordinates per each x- coordinate.
you're valuing horn of plenty mining, inc.'s, stock in order to compare its value to its market price. you believe that the company will pay total dividends of $1.45 in 2015 and $1.56 in 2016. you also believe the company's stock price will be $35.80 at the end of 2016. if the appropriate discount rate is 12 percent, what's the value of horn of plenty mining's stock? a. $39.22 b. $38.31 c. $36.87 d. $37.43
Answers
Step 1: Calculate the present value of each dividend payment.
PV(2015) = $1.45 / (1 + 0.12)^1 = $1.29
PV(2016) = $1.56 / (1 + 0.12)^2 = $1.22
Step 2: Calculate the present value of the expected stock price at the end of 2016.
PV(2016 stock price) = $35.80 / (1 + 0.12)^2 = $28.33
Step 3: Add up the present values of the dividend payments and stock price to get the total stock value.
Stock value = PV(2015) + PV(2016) + PV(2016 stock price) = $1.29 + $1.22 + $28.33 = $30.84
Therefore, the value of Horn of Plenty Mining's stock is $30.84, which means that the correct option is e) None of the above.