To solve for D in the equation CB(A^T)DB(C^T)A = CB^T, we use matrix inverse properties and step-by-step multiplication from both sides to isolate D, resulting in D = (A^T)^-1 B^-1 B^T (A^-1)(C^T)^-1.
Assuming that all matrices are n x n and invertible, the problem is to solve for matrix D. Starting with the given equation CB(A^T)DB(C^T)A = CB^T, we can manipulate both sides using the properties of matrices and their inverses to isolate D.
First, we multiply both sides from the left by (C^T)^-1, which is the inverse of C^T. This gives us B(A^T)DB(C^T)A = B^T because (C^T)^-1C^T = I, where I is the identity matrix.
Next, we multiply both sides from the left by B^-1 to get (A^T)DB(C^T)A = B^-1B^T. Then, we proceed to multiply both sides from the right by A^-1 to cancel A on the left-hand side, which gives (A^T)DB(C^T) = B^-1B^T(A^-1).
Continuing, we multiply both sides from the left by the inverse transpose of A, written as (A^T)^-1, resulting in DB(C^T) = (A^T)^-1B^-1B^T(A^-1).
Finally, we multiply both sides from the right by (C^T)^-1 to isolate D, which leads us to the solution D = (A^T)^-1B^-1B^T(A^-1)(C^T)^-1.
The solution utilizes properties such as the uniqueness of matrix inverses, the associative nature of matrix multiplication, and the property that the inverse of a matrix transpose is the transpose of the inverse matrix.
a magazine costs 3.50 how much can you buy with 100$
What is the time 23 hours after 8:00 pm
Use the substitution method to solve the system of equations. 2x - y = 10 3x - 2y = 8
Answer:
x=12, y=14
Step-by-step explanation:
[tex]2x - y = 10[/tex]
Solve the equation for y. Subtract 2x from both sides
[tex]- y = -2x+10[/tex]
Divide both sides by -1
[tex]y=2x-10[/tex]
Substitute 2x-10 for y in the second equation
[tex]3x - 2(2x-10)= 8[/tex]
[tex]3x - 4x+20= 8[/tex]
[tex]-1x+20= 8[/tex]
Subtract 20 from both sides
[tex]-1x= -12[/tex]
Divide both sides by -1
x= 12
[tex]y=2x-10[/tex]
Substitute 12 for x
[tex]y=2(12)-10=14[/tex]
y=14
Carla's plant was 10 2/3 inches tall. Yolanda's was 8 3/4 inches tall.
How much taller was Carla's plant than Yolanda's?
A.
1 11/12 in.
B.
2 1/12 in.
C.
2 5/12 in.
D.
2 11/12
Answer: 128/12 > 105/12
Step-by-step explanation:
10 2/3 inches=32/3 inches
8 3/4 inches= 35/4 inches
Find the common denominator, in this case, 12.
128/12 inches is Carla's plant
105/12 inches is Yolanda's plant.
128/12 > 105/12. Therefore, Carla's plant is taller than Yonlanda's
Carolyn is building a pen for her dog. The perimeter of the pen is 52 ft
a) Explain how you can use a proportion to convert the perimeter into yards and feet.
b) The fencing material is sold by the yard. It costs 10.99 per yard. What is the cost of material before taxes
Carolyn's dog pen with a 52 ft perimeter is approximately 17.33 yards in length. Fencing material costs $10.99 per yard, making the total cost before taxes around $190.44.
Carolyn is constructing a dog pen with a perimeter of 52 feet. To convert the perimeter from feet to yards, we can use the fact that 1 yard equals 3 feet. Since she is purchasing fencing material by the yard, Carolyn needs to know the total length of fencing in yards. This requires setting up a proportion:
1 yard / 3 feet = x yards / 52 feet
Multiplying both sides by 52 gives us x = 52 / 3 yards. Upon calculating, we find that the pen's perimeter is approximately 17.33 yards.
Since the fencing material costs $10.99 per yard, to find the total cost before taxes, we multiply the number of yards needed by the price per yard:
17.33 yards × $10.99/yard = $190.4367
The cost for the fencing materials before taxes is approximately $190.44.
Amelia receives a treat bag. the treat bag contains 10 gumballs, 5 pixie sticks, 2 bracelets, and 3 chocolates. If Amelia selects 3 items from her treat bag without looking and gives them to her sister, which could not represent a possible outcome for the items Amelia selects?
F. gumball, gumball, gumball
G. pixie stick, gumball, chocolate
H. bracelet, bracelet, bracelet
J. gumball, gumball, pixie stick
36% of what number is 180?
The area of a rectangle painiting is given by the trinomial x^2-9x-36. what are the possible dimensions of the painting ? use factoring
The first term is, x2 its coefficient is 1 .
The middle term is, -9x its coefficient is -9 .
The last term, "the constant", is -36
Step-1 : Multiply the coefficient of the first term by the constant 1 • -36 = -36
Step-2 : Find two factors of -36 whose sum equals the coefficient of the middle term, which is -9 .
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -12 and 3
x2 - 12x + 3x - 36
Step-4 : Add up the first 2 terms, pulling out like factors :
x • (x-12)
Add up the last 2 terms, pulling out common factors :
3 • (x-12)
Step-5 : Add up the four terms of step 4 :
(x+3) • (x-12)
Which is the desired factorization
a dragongfly traveled at a rate of 35 miles per hour for 2.5 hours .what distance did the dragonfly travel?
$800,000 if your rate of return is 5.3% compounded monthly
If you deposit the amount you need to achieve your goal in 20 years, how much will your savings be worth after 10 years?
PLEASE HELP BEGGGING YOU
the point Q(9,-1) is reflected across the y axis. Use arrow notation to describe the original point and its reflection
Q(9,-1)----Q(9,1)
Q(9,-1)----Q (-9,1)
Q(9,-1) ------Q(-9,-1)
Q(9,-1) ----Q(9,-1)
Answer:
C is the answer.
Step-by-step explanation:
When you reflect over the y-axis, the y-axis will remain the same and the x-axis will change from either positive to negative, or negative to positive in this case it is positive to negative.
each month for 7 months, samuel mows 3 lawns. how many more lawns does he need to mow before he has mowed 29 lawns?
The seats at a local baseball stadium are arranged so that each row has five more seats than the row in front of it. If there are four seats in the first row, how many total seats are in the first 24 rows?
These are the choices
1,476
2,856
2,952
1,428 ...?
the ordered pair for an x-intercept has an x-value of 0 A.True or False
The ordered pair for an x-intercept has an x-value of 0 has some value of x and it has zero value for y, So it is a False statement.
What is the equation of line?The equation of a straight line is a relationship between x and y coordinates, The general equation of a straight line is y = mx + c, where m is the slope of the line and c is the y-intercept.
Given statement,
the ordered pair for an x-intercept has an x-value of 0
we can see in graph that when line intersect the x axis, the x coordinate of that point is known as x-intercept,
suppose, we have one line , y = 3x+3
so when we draw graph for it,
and if we see x-intercept
it will come out as, 0 = 3x+3 ⇒ x = -1
It is clear that value of x is not zero
hence, the given statement is false
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Which of the following represent x=1/2y written in general form
1/2x-y=0
2x-y=0
x-1/2y=0
Answer:
Option 2 - [tex]2x-y=0[/tex]
Step-by-step explanation:
Given : Expression [tex]x=\frac{1}{2}y[/tex]
To find : Write the given expression in general form?
Solution :
Step 1 - Write the given expression
[tex]x=\frac{1}{2}y[/tex]
Step 2 - Multiply 2 both side,
[tex]2x=\frac{2}{2}y[/tex]
Step 3 - Solve the expression
[tex]2x=y[/tex]
[tex]2x-y=0[/tex]
Therefore, The general form of given expression is [tex]2x-y=0[/tex]
Hence, Option 2 is correct.
Gina works at a diner. She earns $6 each hour plus tips.In one week,she worked 37 hours a week and earned $43 in tips.How much did she make altogether? Write an equation. Use a variable for the unknown.Solve.
Rewrite with only sin x and cos x.
cos 3x
cos x - 4 cos x sin2x
-sin3x + 2 sin x cos x
-sin2x + 2 sin x cos x
2 sin2x cos x - 2 sin x cos x
Final answer:
To rewrite expressions using only sin x and cos x, we can use trigonometric identities like [tex]cos 2x = 1 - 2sin^2 x[/tex] and sin 2x = 2sin x cos x. By applying these identities, we can simplify the given expressions.
Explanation:
To rewrite the given expressions using only sin x and cos x, we can use the following trigonometric identities:
[tex]cos 2x = 1 - 2sin^2 x[/tex]sin 2x = 2sin x cos x[tex]sin 3x = 3sin x - 4sin^3 x[/tex]Using these identities, we can rewrite the expressions as follows:
cos 3x = [tex]4cos^3 x - 3cos x[/tex]cos x - 4cos x sin^2 x = cos x - 4sin x cos x sin x = [tex]cos x - 4sin^3 x cos x[/tex]-sin 3x + 2sin x cos x = [tex]-(4sin^3 x) + 2sin x cos x[/tex] = [tex]-4sin^3 x + 2sin x cos x[/tex]-sin 2x + 2sin x cos x = -2sin x cos x + 2sin x cos x = 0[tex]2sin^2 x cos x - 2sin x cos x[/tex] = 2sin x cos x (sin x - 1)Eric sells shirts. It costs him $100 to buy all the shirts and $10 to print designs on the shirts. Eric sells each shirt for $4. So far Eric has sold 20 shirts. Eric uses an equation to calculate his total profit.
What is the slope of the equation modeling this situation?
To find the slope of the equation modeling Eric's situation, subtract the total cost from the selling price per shirt, resulting in a loss of $106 per shirt sold.
The slope of the equation modeling Eric's situation can be calculated as follows:
Profit per shirt = Selling price per shirt - Total cost per shirtProfit per shirt = $4 - ($100 + $10)Profit per shirt = $4 - $110 = -$106The slope, which represents the profit per shirt, is -$106, indicating a loss of $106 for each shirt sold.
What is the domain of the quadratic function graphed below?
What is the equation in point slope form of the line that passes through the point (2, 6) and has a slope of 5?
y−2=5(x−6)
y+2=5(x+6)
y−6=5(x−2)
y+6=5(x+2)
Answer:
The answer is Y-6=5(x-2)
Sketch each parabola using the given information.
vertex (3, 6), y-intercept 2
How many grams are in 40 hectograms
There are 4000 grams in 40 hectograms.
To convert from hectograms to grams, you need to know that there are 100 grams in 1 hectogram.
Therefore, to find out how many grams are in 40 hectograms, you can use the conversion factor:
40 hectograms * 100 grams/hectogram = 4000 grams
So, there are 4000 grams in 40 hectograms.
To learn more about `hectograms; -
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The ratio of m∠PQR to m∠PQS is 5:9. What is m∠RQS?
10°
40°
50°
80°
One number is 3 less than twice another. If their sum is 39, find the numbers.
Which of the following systems of equations represents the word problem?
A.y = 2x - 3 and y = x + 39
B.y = 2x - 3 and x + y = 39
C.y = 2(x - 3) and x + y = 39 ...?
Let
y------> one number
x-----> another number
we know that
[tex]y=2x-3[/tex] ------> equation A
[tex]x+y=39[/tex] ------> equation B
substitute equation A in equation B
[tex]x+[2x-3]=39[/tex]
[tex]3x=39+3[/tex]
[tex]x=42/3=14[/tex]
Find the value of y
[tex]y=2*14-3=25[/tex]
the numbers are [tex]25[/tex] and [tex]14[/tex]
therefore
the answer is the option B
[tex]y=2x-3[/tex] and [tex]x+y=39[/tex]
The length of a rectangle is 3 meters more than twice its width. the length of this rectangle is 10 meters. write an equation to solve the perimeter of this rectangle
Greatest common factor of 12, 60, and 68
A donut shop is experimenting with two new types of cream-filled treats, one with raspberry filling, and the other with peach. A batch of raspberry donuts cooks in 11 minutes while a batch of peach donuts cooks in only 8 minutes.
Let x represent the number of raspberry-filled donuts and let y represent the number of peach-filled donuts. Write an inequality to represent how many batches of the new type of donuts can be produced in a 10 hour day.
Answer:
The required inequality is [tex]11x + 8y \leq 600[/tex]
Step-by-step explanation:
Given : A donut shop is experimenting with two new types of cream-filled treats, one with raspberry filling, and the other with peach.
A batch of raspberry donuts cooks in 11 minutes while a batch of peach donuts cooks in only 8 minutes.
Let x represent the number of raspberry-filled donuts and let y represent the number of peach-filled donuts.
To write : An inequality to represent how many batches of the new type of donuts can be produced in a 10 hour day.
Solution :
Time taken to cook the raspberry donuts = [tex]11x[/tex] minutes
Time taken to cook the peach donuts = [tex]8y[/tex] minutes
Donuts produced in 10 hours
1 hours = 60 minutes
10 hours = 60 × 10 = 600 minutes
Total time ≤ 600 minutes
Therefore, the required equation is
→ [tex]11x + 8y \leq 600[/tex]
A pack with 6 cans of juice costs 3.48. What it the unit price?
A.0.49 per can B.0.50 per can C.0.58 per can D.0.60 per can**my answer??**
The unit price of one can of juice, when a 6-pack costs $3.48, is $0.58 per can.
The question asks us to calculate the unit price of a juice can when a pack of 6 cans costs $3.48.
To find the unit price, we divide the total cost of the pack by the number of cans in a pack.
In this case, we divide $3.48 by 6, which gives us $0.58.
$3.48 / 6 = $0.58
Therefore, the unit price per can is $0.58.
4x + 5x + 12 = -6 (given)
9x + 12 = -6 (simplify)
9x = -18 (subtraction)
x = -2 (addition)
Which reason is incorrect?
A) addition
B) given
C) simplify
D) subtraction
Answer:
Addition
Step-by-step explanation:
USA Testprep
what is 3/20 as a decimal equivalent