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:
[tex]\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][/tex]
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:
[tex]X=A^{-1}B[/tex]
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
A line that includes the points (-8, f) and (-6, 4) has a slope of 6. What is the value of f?
f =?
Answers
Answer:
-8
Step-by-step explanation:
Slope = (y1-y2) / ( x1-x2)
= ( f-4) / (-8 - -6) = 6
(f-4) / -2 = 6
f-4 = -12
f = - 8
Answer:
f = -8
Explanation:
Find slope:
[tex]\sf slope: \dfrac{y_2 - y_1}{x_2- x_1} = \dfrac{\triangle y}{\triangle x} \ \ where \ (x_1 , \ y_1), ( x_2 , \ y_2) \ are \ points[/tex]
Here given:
points: (-8, f), (-6, 4)slope : 6Inserting into slope formula:
[tex]\sf \rightarrow \dfrac{4-f}{-6-(-8) } = 6[/tex]
[tex]\sf \rightarrow \dfrac{4-f}{2 } = 6[/tex]
[tex]\sf \rightarrow 4-f = 12[/tex]
[tex]\sf \rightarrow -f = 12-4[/tex]
[tex]\sf \rightarrow -f =8[/tex]
[tex]\sf \rightarrow f =-8[/tex]
The bisection method is being used to calculate the zero of the following function between x = 0 and x = 1.
Answers
The bisection method will converge to the solution after three iterations.
How to illustrate the information?It should be noted that after one iteration, x1 will be:
= (1 + 9)/2
= 10/2
= 5
Since f(x¹) > 0, x² will then replace x1. Now x0 = 1 and x1 = 5.
After the second iteration, x2 will be:
= (1 + 5)/2
= 3
Also, this is greater than 0. The third iteration will be:
m= (1 + 3)/2
= 2.
Now, f(2) = 2⁴ -2³ - 2² - 4
= 0
Therefore, the method converges exactly to the root in 3 iterations.
Complete question:
The bisection method is applied to compute the zero to a function f(x) = x⁴ - x³ - x² - 4 in the interval (1, 9). The method converges y a solution after .............. iterations.
Learn more about bisection method on:
brainly.com/question/13424227
#SPJ1
A collection of coins has a value of 64 cents. There are two more nickels than dimes and three times as many pennies as dimes. How many of each kind of coin are there?
Answers
There are 5 nickels, 3 dimes, and 9 pennies.
Let d = The number of dimes
Let n = number of nickels
Let p = The number of pennies
As given, there are two more nickels than dimes and three times as many pennies as dimes:
d+2=n
3d=p
0.10d+0.05n+0.01p=0.64
Plug in the value to find d
[tex]0.10d+0.05(d+2)+0.01(3d)=0.64[/tex]
[tex]0.10d+0.05d+0.1+0.03d=0.64[/tex]
[tex]0.18d=0.64[/tex]
[tex]d=3[/tex]
What is the value of p?The value of p is equal to 3d
p=3(3)=9
n=d+2
n=3+2
n=5
Hence, there are 5 nickels, 3 dimes, and 9 pennies.
To learn more about the collection visit:
https://brainly.com/question/4219149
#SPJ1
How many three-letter "words" can be made from 5 letters "FGHIJ" if repetition of letters
(a) is allowed?
Your answer is :
Correct
(b) is not allowed?
Your answer is :
Answers
The number of ways of the letters FGHIJ can be arranged with repetition and without repetition are 125 and 60 ways respectively.
How to determine the waysFormula for permutation with repetition
[tex]^nPr = n^r[/tex]
Formula for permutation without repetition
[tex]^nPr = \frac{n!}{n-r!}[/tex]
We have = 5
r = 3
a. If repetition is allowed,
Permutation = [tex]5^3[/tex] = 125 ways
b. If repetition is not allowed,
Permutation = [tex]\frac{5!}{5-3!}[/tex]
Permutation = [tex]\frac{5*4*3*2*1}{2*1}[/tex]
Permutation = [tex]\frac{120}{2}[/tex]
Permutation = 60 ways
Thus, the number of ways of the letters FGHIJ can be arranged with repetition and without repetition are 125 and 60 ways respectively.
Learn more about permutation here:
https://brainly.com/question/12468032
#SPJ1
4. Identify a transformation of the function f(x) = x by observing the equation of the function g(x)
= x - 90.
The base graph has been shifted left 90 units.
The base graph has been shifted up 90 units.
The base graph has been shifted down 90 units.
The base graph has been shifted right 90 units.
Answers
Answer: The base graph has been shifted down 90 units.
Step-by-step explanation:
See attached image.
median mark of 3,2,0,1,9,12,3,5
Answers
Answer: 3
Step-by-step explanation:
Median is a statistical measure that determines the middle value of a dataset listed in ascending order.
arranged data is 0,1,2,3,3,5,9,12
number of data terms=8
if data is even then
median=(3+3)/2=3
(07.01 MC)
The picture shows a triangular island:
Island
Z
O x sin 50°
O
Which expression shows the value of z? (1 point)
cos 50°
O x cos 50°
O
sin 50°
y
50
Answers
Answer:
Option (2)
Step-by-step explanation:
cos 50° = y/z
z = y/cos 50°
Solve for x. Round to the nearest tenth, if necessary.
X
H
Answers
In this problem we are given an angle and two sides. Therefore, we should use a trigonometric function to solve for x.
Trigonometric Functions: SOH-CAH-TOA
Looking from the 23 degree angle, we have the adjacent side and the opposite side. Therefore, we should use the tangent function.
tan(23) = x / 2
x = tan(23) * 2
x = 0.8489
x = 0.8
Hope this helps!
Step-by-step explanation:
ATTACHED IS THE SOLUTION!Simplify √3. √21
√24
√63
O 3√7
09√7
Answers
Answer:
•3✓7
✓3.✓21
=✓3×✓3✓7
=3✓7
Answer:
3rd answer is correct
Step-by-step explanation:
√3 × √21
√3 × √(7 × 3)
√( 3 × 3 × 7 )
√ ( 3 × 3 ) × √7
3√7
find the lowest common multiple ( L.C.M. ) of the (a² - 4), (a³ - 8), ( a + 2 ) ²
Answers
Answer: according to my work i got
LCM - Lowest Common Factor
HCF - Highest common factor
Step-by-step explanation:
please mark brainlest!!
yw! =^.^=
PLS HELP ME Solve the following equation: five eighths plus two eighths equals
three eighths,
seven sixteenths,
seven eighths,
or eight sevenths.
Answers
Five eighths + two eighths = seven eighths
(5+2)/8 = 7/8
If this question was helpful to you in anyway, please consider giving brainliest
When you start your career, you decide to set aside $250 every month to deposit into an investment account. The investment firm claims that historically their accounts have earned an annual interest rate of 9.0% compounded monthly. Assuming this to be true, how much money will your account be worth after 20 years of depositing and investing? Round your answer to the nearest cent. Do not include labels or units. Just enter the numerical value.
Answers
After 20 years of depositing and investing there will be 168474.01 dollars in your account.
What is compound interest?It is defined as the interest on the principal value or deposit and the interest which is gained on the principal value in the previous year.
We can calculate the compound interest using the below formula:
[tex]\rm A = P(1+\dfrac{r}{n})^{nt}[/tex]
Where A = Final amount
P = Principal amount
r = annual rate of interest
n = how many times interest is compounded per year
t = How long the money is deposited or borrowed (in years)
The formula for calculating how much money will your account be worth after 20 years of depositing and investing is:
P = $250, r = 9% = 0.09, t = 20 years, n = 12 and PMD = $250(per month deposit)
[tex]\rm A = P(1+\dfrac{r}{n})^{nt}+\dfrac{PMD((1+\dfrac{r}{n})^{nt}-1)}{\dfrac{r}{n}}[/tex]
[tex]\rm A = 250(1+\dfrac{0.09}{12})^{12\times20}+\dfrac{250((1+\dfrac{0.09}{12})^{12\times12}-1)}{\dfrac{0.09}{12}}[/tex]
A = 1502.287 + 166971.717
A = $168474.01
Thus, after 20 years of depositing and investing there will be 168474.01 dollars in your account.
Learn more about the compound interest here:
brainly.com/question/26457073
#SPJ1
A bird can fly 5 miles in 15 minutes how many miles can it fly in 60 minutes?
Please show the process
Answers
The number of miles the bird can fly for 60 minutes is 20 miles.
How to find rate and distance?A bird can fly 5 miles in 15 minutes.
Let's find the rate before we can find the number of miles the bird can fly in 60 minutes.
Therefore,
rate = distance / time
rate = 5 / 15 = 1 / 3 miles per minutes
Therefore,
1 / 3 = d / 60
cross multiply
60 = 3d
d = 60 / 3
d = 20 miles
learn more rate here: https://brainly.com/question/12636854
#SPJ1
QUESTION 1 -
If f(x)=3x²-5x+4, then f(-2)=
a.) - 18
b.) 26
c.) 2
d.) 6
Question 2 -
For an ordered pair (x, y) in a relation, the y element represents the _____
a.) input
b.) range
c.) domain
d.) function
Need help urgently! Will give brainliest.
Answers
Given: f(x) = 3x² -5x + 4
To find f(-2), simply substitute x = -2 in function f(x).
f(-2) = 3(-2)² -5(-2) + 4
f(-2) = 12 + 10 + 4
f(-2) = 26
Answer: 26
#2For an ordered pair (x, y) in a relation, the y element represents the range.
Answer: range
Complete the equation of this circle:
(x − [?])²+(y - [ ])²=[ ]
Answers
Answer:
(x+2)²+(y-4)²=36
Step-by-step explanation:
1) to determine the coordinates of the centre of the given circle. It is point A (-2;4);
2) to determine the length of the radius: to calculate the distance between the point A(-2;4) and any point on the circle, it is 6 [units];
3) to make up the required equation according to the scheme:
(x-x₀)²+(y-y₀)²=r², where (x₀;y₀) - the coordinates of the centre, r - the length of the radius.
4) finally, (x+2)²+(y-4)²=6².
PS. for more details see the attachment.
Which equation is equivalent to 162 - 32+³?
=
=
O 84 - 84+3
O 84-84+12
O 28 - 25p+15
=
O 28P = 25p+3
Answers
[tex]{ \red{ \bold{option \: (d)}}} \: { \green{ \tt{ {2}^{8p} = {2}^{5p + 3}}}} [/tex]
Step-by-step explanation:
I said option (d) is correct. Because, the answer of 2^8 is 256 i.e.,
[tex]{ \green{ \bold{ {2}^{8} }}} = { \green{ \tt{2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2}}}[/tex]
[tex]{ \green{ \bold{ {2}^{8} }}} = { \green{ \tt{256}}}[/tex]
The value of 16^2 = 256.
Also, the answer of 2^5 is 32. i.e.,
[tex]{ \green{ \bold{ {2}^{5} }}} = { \green{ \tt{2 \times 2 \times 2 \times 2 \times 2}}}[/tex]
[tex]{ \green{ \bold{ {2}^{5} }}} = { \green{ \tt{32}}}[/tex]
0,2,14,36,68,?
Find the next number in the sequence
Answers
Note that the difference keeps increasing by a value of 10. Hence the next term of the sequence is 110
Geometric sequenceGeometric sequence are sequence that increase in an exponential manner.
Given the recursive sequence 0, 2, 14, 36, 68
From the sequence
0 + 2 = 2
2 + 12 = 14
14 + 22 = 36
36 + 32 = 68
68 + 42 = 110
Note that the difference keeps increasing by a value of 10. Hence the next term of the sequence is 110
Learn more on sequence here: https://brainly.com/question/6561461
#SPJ1
What is the equation for the line of reflection
X=6
Y=6
Y=x
Y=2
Answers
Answer: x = 6
Step-by-step explanation:
B(7,3) maps onto B'(5,3).
The perpendicular bisector of [tex]\overline{BB'}[/tex] is x=6, so that is also the line of reflection.
Answer:
x = 6
Step-by-step explanation:
Taking test as we speak
Find an equation of the line. Write the equation using function notation.
Through (8,8); perpendicular to 5y = x - 10
Answers
Answer:
f(x) = -5x +48
Step-by-step explanation:
A fairly easy way to write the equation of the perpendicular line is to swap the x- and y-coefficients, negating one of them. Then choose the constant in the equation to make it true at the given point.
Swapped coefficientsIn this instance, we find it convenient to leave the coefficient of y as positive.
5y = x -10 . . . . . . original equation
y = -5x +c . . . . . . with coefficients swapped, x-coefficient negated
New constantAt the given point, the equation becomes ...
8 = -5(8) +c
48 = c . . . . . . . add 40
Equation of the perpendicular lineThe equation of the line is then ...
y = -5x +48
f(x) = -5x +48 . . . . . . in functional notation
Whats the correct answer answer asap for brainlist
Answers
Answer:
option A: West Europe, East Europe, and Asia
Explanation: Europe and Asia as a whole are called Eurasia.
hope that helps...
Use your understanding of transformations and key features to write the slope-intercept equation of this linear function.
Enter the correct answer in the box by replacing the values of m and b.
Answers
Answer:
[tex]y = -2x + 5[/tex]
m = -1
b = 5
Step-by-step explanation:
Hello!
Slope - Intercept Form: [tex]y = mx+b[/tex]
m = slopeb = y-interceptSlopeThe slope of the line is the rate of change, or how the graph changes in y as it changes in x.
Slope can be calculated by the formula: [tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
We need two points on the line to get the x and y-values. I'm going to choose points (0,5) and (4,-3).
Calculate Slope
[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex][tex]m = \frac{5 - (-3)}{0 - 4}[/tex][tex]m = -\frac{8}{4}[/tex][tex]m = -2[/tex]The slope is -2.
Y-interceptThe y-intercept of the line is where the graph touches the y-axis (x = 0). It can be found by looking at the intersection of the graph and the axis.
The intersection happens at point (0,5), so the y-intercept is 5.
EquationWe found m, the slope, to be -2 and b, the y-intercept, to be 5. We can just plug it into the equation format.
Equation: [tex]y = -2x + 5[/tex]
Which figure shows a line of reflectional symmetry for the letter T?
A letter T is folded at the horizontal line.
A letter T is folded diagonally.
A letter T is folded vertically through the middle.
A letter T is folded diagonally through its center.
Mark this and return
Answers
The figure that will depict a line of reflectional symmetry of letter T is: Option C: A letter T folded vertically through the middle.
What is a Line of Reflectional Symmetry?A line of reflectional symmetry is defined as an imaginary line that divides a figure into two halves in such a way that each of the halves are a mirror image of the other.
When a line divides letter T vertically, it means that two mirror images will be created.
Therefore, the figure that will depict a line of reflectional symmetry of letter T would be: A letter T folded vertically through the middle.
Read more about line of reflectional symmetry at:
brainly.com/question/10453198
#SPJ1
What is the determinant of K =
[6 8
0 3]
Answers
a company promises to release model every month. each model's battery life will be 6% longer than the previous model's. if the current model's battery is 671.0 minutes, in how many months will the latest model's battery life reach 1,008.9 minutes?
Answers
The number of months that it will take the latest model's battery life to reach 1,008.9 minutes is; 8 months
How to solve geometric progression?
Each month, there is an increase by a factor of 0.06 of the previous months model.
From geometric sequence formula of aₙ = ar^(n - 1),
where;
a is first term
r is common ratio
aₙ is nth term
we have;
1,008.9 = 671 * 1.06^(n - 1)
1008.9/671 = 1.06^(n - 1)
In 1.504 = (n - 1) In 1.06
0.408 = (n - 1) * 0.058
n - 1 = 0.408/0.058
n = 7.03 + 1
n ≈ 8 months
Read more about geometric sequence at; https://brainly.com/question/24643676
#SPJ1
find x and y
pls help
Answers
Step-by-step explanation:
(3x+6)= 48(Alternate angles)
3x=48-6
3x=42
x=14
2y+48=5y-9 (Sum of two opposite interior angles= exterior angle)
48+9=5y-2y
57=3y
y=19
Deepak stacked 14 copies of the
same book. Each book is 13 inches
thick. How high is the stack of books?
8
inches
Answers
Answer:
182 inches
Step-by-step explanation:
1 book is 13 inches thick.
So when 14 of those books are stacked together (lets take the book cover has non-existent thickness since the question did not mention),
Height of stack of 14 books = 14 x Thickness of 1 book = 14 x 13inches
= 182 inches
MATH: GRAPHING PIECE-WISE...HELP! 15 PTS
Answers
Answer:
Step-by-step explanation:
The endpoints of are A(2, 2) and B(3, 8). is dilated by a scale factor of 3.5 with the origin as the center of dilation to give image . What are the slope (m) and length of ? Use the distance formula to help you decide: .
A.
B.
C.
D.
Answers
The slope is m=6 and length of line is 3.5√37.
What is slope?The slope of a line is a measure of its steepness.
Given:
endpoints of are A(2, 2) and B(3, 8). is dilated by a scale factor of 3.5
slope= 8-2/3-2= 6
Now, using distance formula,
d= √(3-2)² + (8-2)²
d= √1+ 36
d= √37
As, Line AB is dilated by a scale factor of 3.5.
So, new d= √37*3.5
new d= 3.5√37
Learn more about this concept here:
https://brainly.com/question/1426855
#SPJ1
Least common multiple of 35 and 70
Answers
Answer:
70
Step-by-step explanation:
【Answer】The least common multiple of 35 and 70 is 70.
[tex]\orange{ {\hspace{50 pt}\above 1.2pt}\boldsymbol{\mathsf{Procedure}}{\hspace{50pt}\above 1.2pt}}[/tex]
To obtain the least common multiple (lcm) we must do it by simultaneous decomposition.
This method consists of extracting the common and uncommon prime factors, then
[tex]\large\displaystyle\text{$\begin{gathered}\sf \left.\begin{matrix} \blue{35 \ \ \ 70}\\ 35 \ \ \ 35\\ 7 \ \ \ \ 7\\ 1 \ \ \ \ 1 \end{matrix}\right|\begin{matrix} 2\\ 5\\ 7\\ \: \end{matrix} \end{gathered}$}[/tex]
[tex]\sf{L.c.m.(35,70)=2\times5\times7}[/tex]
[tex]\boxed{\boxed{\sf{L.c.m.(35,70)=70}}}[/tex]
{ Pisces04 }e.Water has a density of about 0.0361 pounds/cubic inch. You might know that wood floats on water. What can you conclude about the densities of objects that float and the densities of objects that do not?
Answers
Answer:
Step-by-step explanation:
the objects which have less density than water will float
and the objects which have more density than the density of liquid will sink in liquid or will not float.