Show a cofactor expansion and find the determinant of each matrix. List 3 properties of each matrix using the invertible matrix theorem. A=
⎣
⎡
3
0
−3
3
−1
−1
4
5
2
0
3
−1
−2
1
8
4
⎦
⎤
B=
⎣
⎡
−1
1
2
0
3
−2
3
3
4
⎦
⎤
The determinant of A is -74 and the determinant of B is -3. The determinant of A can be found using cofactor expansion.
The cofactor of entry (i,j) in a matrix A is the determinant of the matrix that results from deleting row i and column j from A. The determinant of A is then the sum of the products of the entries in row i and their corresponding cofactors.
In this case, the determinant of A is
det(A) = (3)(5) - (-1)(-1) = 16
The determinant of B can be found using the same method. The determinant of B is
det(B) = (-1)(4) - (1)(-2) = -2
The invertible matrix theorem states that a matrix A is invertible if and only if its determinant is non-zero. Therefore, both A and B are invertible matrices.
Here are 3 properties of each matrix:
A is a 4x4 matrix.
B is a 3x3 matrix.
The determinant of A is -74.
The determinant of B is -3.
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In the diagram below, triangle ABC is similar to triangle DEC what is the value of X
Answer:
|
V
Step-by-step explanation:
Since triangles ABC and DEC are similar to each other, to find x, a missing side of a triangle, you will have to put it in an equation.
You didn't really put a diagram so it's kind of impossible to help answer this question. Try reposting with a picture so I can answer for you :)
How do you work the problem 6y < 18 out
Answer:
y<3
Step-by-step explanation:
6y<18
y<18/6
y<3
I hope this helps
Answer: you can see what number times 6 gets you 18 so it would be y<3
Step-by-step explanation:
The local humane society is restocking on cat food to prepare for kitten season. Very young kittens need kitten formula which costs $3.99 per bottle. Older kittens need wet cat food which costs $1.50 per can.
Answer:
ow much money (before tax) will the humane society spend if they buy 30 bottles of kitten formula and 120 cans of wet food ?
PART C) if you add 7% sales tax to the purchase of the bottles of kitten formula and cans of wet cat food , how would the algebraic expression used in parts A and B change
Step-by-step explanation:
Answer:
ow much money (before tax) will the humane society spend if they buy 30 bottles of kitten formula and 120 cans of wet food ?
Step-by-step explanation:
please help me with question 21
Using the central angle theorem, we can find the arm length of BD to be 118units.
Option C is correct.
Define central angle theorem?The angle that an arc occupies at the centre of a circle is twice as large as the angle it occupies anywhere else around the circle's circumference, according to the central angle measure theorem.
Here in the question,
Length of the arc AC = 59.
As we can see that there is a quadrilateral inscribed inside the circle.
Arc AC = 1/2 arc BD
⇒ arc BD = 2 × arc length AC
⇒ arc BD = 2 × 59
⇒ arc BD = 118.
Therefore, the length of the arc BD = 118 units.
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Using the central angle theorem, we can find the arm length of BD to be 118units.
Option C is correct.
Define central angle theorem?The angle that an arc occupies at the centre of a circle is twice as large as the angle it occupies anywhere else around the circle's circumference, according to the central angle measure theorem.
Here in the question,
Length of the arc AC = 59.
As we can see that there is a quadrilateral inscribed inside the circle.
Arc AC = 1/2 arc BD
⇒ arc BD = 2 × arc length AC
⇒ arc BD = 2 × 59
⇒ arc BD = 118.
Therefore, the length of the arc BD = 118 units.
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Help me find the answer
Tan 0 and Cot O
Answer:
Step-by-step explanation:
we can say the angle is also +45° going in the clock wise direction. so take Tan(45)= 1
Cot(45) = 1
b/c Tan(45) = Sin(45) /Cos(45) = (\(\sqrt{2}\)/2) / (\(\sqrt{2}\)/2) ofc that's just 1
b/c Cot(45) = Cos(45) / Sin(45) , which is the same as above 1
BRAINLIEST BRAINLIEST
PLEASE ANSWER AND TELL ME IF YOU KNOW WHAT THE BOOK IS CALLED
Answer:
This book is known as HOME WORK book Hope this helps you Have a nice day ahead Do mark as brainliest ✌️Answer:
its a personal math trainer book
Multiple Choice:
Suppose a triangle has sides 3, 4, and 5. Which of the following MUST be true?
A. The triangle in question may or may not be a right triangle.
B. The triangle in question is a right triangle.
C. The triangle in question is not a right triangle.
Answer:
b. the triangle is not a right triangle
Step-by-step explanation:
Answer:
The triangle in this particular question may or may not be a right angled triangle
Step-by-step explanation:
~basically triangle are known to have 3 sides otherwise we would not call it a triangle...however in this particular question they may be no definite answer and triangle with 3 sides can be any sort of triangle:
-isosceles triangle with 3 uneven sides
-right angled triangle like stated with an hypotenuse
or
-scalene triangle with simply to equal sides...
glad I could help thumbs
disclaimer this answer may not be accurate and I do not take any responsibility if this answer is wrong thank you
Determine the interval in which this function is DECREASING
Answer:
4
Step-by-step explanation:
4
In the rectangle shown below, EC =
3. What is the area of the shaded region?
A. 20
B. 16
C.12
D. 10
E. 8
Calculate the following dosage. Do not write the units in the answer. Round the number to the nearest tenth.
Order: Famotidine 40 mg IV daily
Available: Famotidine 20 mg/2 mL
____mL
The required volume of Famotidine is 4 mL.
To calculate the required volume in milliliters (mL) for the provided dosage of Famotidine, we can use the following formula:
Volume (mL) = (Dosage ordered / Available dosage) * Volume per dose
We have:
Dosage ordered = 40 mg
Available dosage = 20 mg/2 mL (This means there are 20 mg of Famotidine in 2 mL)
Volume per dose = 2 mL
Let's substitute these values into the formula:
Volume (mL) = (40 mg / 20 mg) * 2 mL
Simplifying the expression:
Volume (mL) = 2 * 2 mL
Volume (mL) = 4 mL
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a hiker (h) walks on the flat ground towards a distinct rock (r) in the forest. between two points (without changing her direction) separated by 500 ft she observes the peak (top) of the rock at 300 and at 350 elevation angles
The height of peak is around 2346.9 feet according to stated angles and distance.
The flat base, vertical height of the peak and angle of elevation form a right angled triangle. Hence, the trigonometric relation that will form is -
tan theta = perpendicular/base.
Let the distance between peak and hiker be x from the point of 500 feet
The height based on the first elevation angles of 30° -
tan 30° = perpendicular/(500 + x)
Perpendicular = 0.577 × (500 + x)
Performing multiplication
Perpendicular = 288.67 + 0.577x
The height based on the second elevation angles of 35° -
tan 35° = perpendicular/x
Perpendicular = 0.7 × x
Performing multiplication
Perpendicular = 0.7x
Now equating the height of peak -
288.67 + 0.577x = 0.7x
0.7x - 0.577x = 288.67
0.123x = 288.67
x = 288.67/0.123
x = 2346.9 feet
Hence, the height of peak is 2346.9 feet.
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The complete Ques is -
A hiker (H) walks on the flat ground towards a distinct rock (R) in the forest. Between two points (without ch anging her direction) separated by 500-ft she observes the peak (top) of the rock at 30° and 35° el evation angles. Determine the height to the peak of the rock from the level of the flat ground. A. 315 ft B. 553 ft C. 1123 ft OD. 1645
answer question 4 and 5
Answer:
4. A 5. B
Step-by-step explanation:
A hypothesis is an educated guess. When you write a report you should use an if, then statement.
An observation is a fact, not an opinion.
What is the slope of a line that passes through the two points (12, -18) and (11,12)
After 10% tax, the phone cost $220. What was the original price?
Answer:
$198
Step-by-step explanation:
To find how much the tax was, we multiply 10% by 220. We do this in decimal form, so we write it as 0.1*220. 0.1*220 is 22. Although, we don't stop there. Now that we know how much tax is, we must subtract the tax from the price with tax to find the OG price. 220-22 is 198. That means our answer is $198. Hope this helps!
13.
What is the circumference of a circle whose area is 16 pi?
A. 64 pi
B. 32 pi
C. 8 pi
D. 4 pi
Answer:
What is the circumference of a circle whose area is 16 π ?
A. 64 π
B. 32 π
C. 8 π
D. 4 π
Step-by-step explanation:
its 8 π cause it said it was correct
Jaon went hopping
He bought a watch and a pair of trainer for a total price of £53. 55
Thi price include a 15% loyalty dicount
Before the dicount, the trainer were priced at £38
Work out the price of the watch before the dicount
The price of the watch before the discount is calculated to be £24.44.
As the total price of the watch and a pair of trainers is £53. 55 and the price of the trainer before the discount was £38, we first calculate the price of the trainers after the discount as follows;
discount on a pair of trainers = 15/100 × 38 = £5.7
cost of trainers after discount = £38 - 5.7 = £32.3
Now the price of the watch after the discount can be calculated by subtraction as follows;
price of watch after discount = total price - price of trainers after discount
price of watch after discount = £53. 55 - £32.3
price of watch after discount = £21.25
Now the price of the watch before the discount can be calculated as follows;
price of watch before discount = £21.25 × 15/100
price of watch before discount = £21.25 + £3.1875
price of watch before discount = £24.44
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Please help with problem 10
Answer:
A. 0
Step-by-step explanation:
Slope tells you steepness or flatness of your line.
If you know two points on a line find slope by subtracting the y's and put that on top of a fraction. And subtract the x's and put that on the bottom of the fraction.
Subtract y's: 3 - 3
Put it on top: 0/...
Subtract x's: 5 - -4
same as 5+4
Put that on the bottom: 0/9
slope, usually called m, is 0/9, which is 0.
Notice if you graph these two points its a hOrizOntal line. HOrizOntal lines have zerO slope.
What is the volume of this cone?
Answer:
\(V=209\ cm^3\)
Step-by-step explanation:
The height of this cone, h = 8 cm
The radius of this cone, r = 5 cm
We need to find the volume of this cone. The formula for the volume of a cone is given by :
\(V=\dfrac{1}{3}\pi r^2 h\)
Put all the values,
\(V=\dfrac{1}{3}\times 3.14\times 5^2 \times 8\\\\=209.33\approx 209\ cm^3\)
So, the volume of this cone is equal to \(209\ cm^3\).
A message digest is defined as him) - (m*7;2 MOD 7793. If the message m = 23, calculate the hash
The hash of the given message is 135.
In computing, a message digest is a fixed-sized string of bytes that represents the original data's cryptographic hash. This hash is used to authenticate a message, guaranteeing the integrity of the data in the message.
Here, it is given the message m = 23
The formula to calculate hash is him) - (m*7;2 MOD 7793.
So, let's calculate the hash : him) - (m*7;2 MOD 7793(him) - (23*7;2 MOD 7793
⇒ (8*23) - (49 MOD 7793)
⇒ 184 - 49= 135.
So, the hash of the given message is 135.
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simplify the following expression: 2^-3÷2^5
Answer:
Exact Form:
1/256
Decimal Form:
0.00390625
Step-by-step explanation:
i need helllllllllllllllllllllllllllllllllllllllllllp
In a survey of 439 teenagers in the US, 14% said that they worked during their summer vacation. a) What is the Margin of Error for this sample proportion
Answer:
\(0.0166\)
Step-by-step explanation:
Let the sample proportion be \(\hat{p}=0.14\) and the sample size be \(n=439\):
\(\displaystyle \text{Margin of Error}=\sqrt{\frac{\hat{p}(1-\hat{p})}{n}}\\\\\text{Margin of Error}=\sqrt{\frac{0.14(1-0.14)}{439}}\\\\\text{Margin of Error}=\pm0.0166\)
explain to them the process for combining integers. Helps pls 15 point
Angela used 25 cups of flour to make 5 batches of lemon cookies. She used 12 cups of flour to make 3 batches of vanilla cookies. Which type of cookie uses more flour?
Answer:
the lemon cookies they use more
Step-by-step explanation:
Matt is organising an event. He buys some party bags and some toys for the party bags from a shop. The party bags are sold in packs. There are 105 party bags in each pack. Each pack costs £1.32 The toys are sold in packs. There are 84 toys in each pack. Each pack costs £4.15 Matt buys exactly the same number of party bags as toys. What is the least amount of money he could pay?
The least amount of money he could pay for the conditions that he will for the given information is = £ 3053.4
What about least amount?
In mathematics, the term "least amount" is not commonly used. However, a similar term that is often used is "minimum".
The minimum value of a set of numbers or a function is the smallest value within that set or function. For example, if we have the set of numbers {2, 5, 7, 8, 10}, the minimum value is 2.
Similarly, in the context of optimization problems, we often seek to find the minimum value of a function to achieve the best possible outcome. This can involve finding the minimum value of a cost function in order to minimize the cost of a process, or finding the minimum value of a profit function to maximize the profit of a business.
According to the given information:
Set the number of party bags pack as x , toy pack as y
Since, 105 party bags in a pack , £1.32
84 toys in a pack £4.15.
Hence, 105x = 84y , cost = 105x × 1.32x + 84y × 4.15 = 763.35x
Find the least common multiple
Hence, 84 × 5 = 420 , 105 × 4 = 420
x =4
y =5
least cost = 105 × 1.32 × 4 + 84×4.15 ×5
= £3053.4
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3 Four bakers shared 5 kilograms of sugar equally. How much sugar did they each receive?
Answer:
5kg divided by 4 bakers.
5/4= 1.25kg or 1 1/4kg
Answer:
35
Step-by-step explanation:
5*3+4*5
Help out with this question please!
Answer:
my answer is A
Step-by-step explanation:
if you work out the equation where you know that at the x intercept y=0 you will find A to be true
for all numbers a and b such that a < b, find the vari- ance of the uniform distribution on the interval [a, b].
The slope field for the differential equation dy/dx = x² y² can be generated by plotting short line segments at each point (x, y) in the x-y plane. The direction of each line segment is determined by the value of x and y at that point, with steeper slopes indicating a larger rate of change.
To generate a slope field for the differential equation dy/dx = x² y², we need to plot short line segments at each point (x, y) in the x-y plane. The direction of each line segment is determined by the value of x and y at that point, with steeper slopes indicating a larger rate of change.
First, we can identify the stationary points of the differential equation by setting dy/dx = 0. This gives us the two lines y=0 and x=0, which intersect at the origin. We can see from the equation that any solution passing through the origin will have a slope of zero at that point, so the slope field will have horizontal lines for y=0 and vertical lines for x=0.
Next, we can look for other interesting features of the slope field. One such feature is the line y=1/x, which is a solution to the differential equation. To see this, we can substitute y=1/x into the equation and verify that both sides are equal. Along this line, the slope of the solution will be zero, since both x and y are changing at the same rate. Therefore, the slope field will have horizontal line segments along the curve y=1/x.
Overall, the slope field for dy/dx = x² y² will have horizontal lines for y=0, vertical lines for x=0, and horizontal line segments for y=1/x. In between these features, the slope of the line segments will increase as we move away from the origin, indicating that the rate of change of the solution is increasing.
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In a hand of 13 cards chosen at random from an ordinary deck of 52 cards, let X be
the number of spades. Find E(X) and V ar(X). (Note: In the 52 cards, 13 of them are
spades.)
The values of E(X) = 3.25 and Var(X) ≈ 2.238 for the number of spades in a hand of 13 cards chosen at random from a 52-card deck.
To find E(X) and Var(X) for the number of spades in a hand of 13 cards chosen at random from a 52-card deck, we will use the concepts of probability and statistics.
E(X), or the expected value, is the average number of spades you would expect to get in a hand of 13 cards. To find E(X), we can use the formula:
E(X) = (Number of spades in the deck / Total number of cards in the deck) * Number of cards drawn
E(X) = (13 spades / 52 cards) * 13 cards drawn
E(X) = (1/4) * 13
E(X) = 3.25
So, the expected number of spades in a 13-card hand is 3.25.
Next, let's find Var(X), or the variance, which is a measure of how much the number of spades can vary from the expected value. We can use the formula for variance of a hypergeometric distribution:
Var(X) = (Number of cards drawn * Number of spades * Number of non-spades) / ((Total number of cards in the deck)^2 * (Total number of cards in the deck - 1))
Var(X) = (13 cards drawn * 13 spades * 39 non-spades) / ((52 cards)^2 * (52 cards - 1))
Var(X) = (13 * 13 * 39) / (52 * 52 * 51)
Var(X) ≈ 2.238
So, the variance for the number of spades in a 13-card hand is approximately 2.238.
In summary, E(X) = 3.25 and Var(X) ≈ 2.238 for the number of spades in a hand of 13 cards chosen at random from a 52-card deck.
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