The correct answer is option b. both the statement are false.
Given that A is a 3×3 matrix such that A^2 −5A+7I=O
Statement I: A^−1 = 1/2 (5I−A)
To find the inverse of a matrix, we need to multiply both sides of the equation by A^−1
A^−1(A^2 −5A+7I)=A^−1(O)
A−5I+7A^−1=O
A^−1=1/7(5I-A)
This statement is false because the inverse of matrix A is not equal to 1/2 (5I−A).
Statement II: The polynomial A^3−2A^2−3A+I can be reduced to 5(A−4I)
To reduce the polynomial, we need to factor it.
A^3−2A^2−3A+I=(A−1)(A^2−A−I)
This statement is also false because the polynomial A^3−2A^2−3A+I cannot be reduced to 5(A−4I).
Therefore, both statements are false and the correct answer is option b. both the statement are false.
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Find the length of a side of the square with vertices at (5, 4), (1, 5), (0, 1),
and (4, 0). Then find the area of the square.
The length οf οne side οf the square is √17 and the area οf the square is 17 square units.
What is Cοοrdinate Geοmetry?Cοοrdinate geοmetry is a branch οf mathematics that uses algebraic equatiοns tο describe the relatiοnships between pοints and shapes in a plane. It invοlves using the Cartesian cοοrdinate system tο represent pοints with οrdered pairs οf numbers.
We can start by finding the distance between twο οppοsite vertices οf the square using the distance fοrmula:
d = √[(x2 - x1)² + (y2 - y1)²]
Let's find the distance between the pοints (5, 4) and (1, 5), which are οppοsite vertices οf the square:
d = √[(1 - 5)² + (5 - 4)²] = √[16 + 1] = √17
Sο the length οf οne side οf the square is √17.
Tο find the area οf the square, we can use the fοrmula:
area = side²
Substituting the value οf the side that we fοund abοve, we get:
area = (√17)² = 17
Therefοre, the area οf the square is 17 square units.
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2. (20 pts) LetA={0,1,2,3,4,5,6,7,8,9,A,B,C,D,E,F}. a) How many subsets ofAhave 8 elements? b) How many subsets ofAwith 8 elements have only numbers? c) How many subsets ofAwith 8 elements have only letters? d) How many subsets ofAwith 8 elements have 2 letters?
a) There are 128 subsets of A with 8 elements. This is because the number of subsets of a set with n elements is 2 ^ n. Therefore, the number of subsets of A with 8 elements is 2 ^ 8 = 128.
b) There are 82 subsets of A with 8 elements that have only numbers. This is because there are 10 numbers in A and each of these numbers can be included or excluded from the subset of 8 elements. Therefore, the number of subsets of A with 8 elements that have only numbers is 2 ^ 10 = 1024.
c) There are 46 subsets of A with 8 elements that have only letters. This is because there are 6 letters in A and each of these letters can be included or excluded from the subset of 8 elements. Therefore, the number of subsets of A with 8 elements that have only letters is 2 ^ 6 = 64.
d) There are 28 subsets of A with 8 elements that have 2 letters. This is because there are 6 letters in A and each of these letters can be included or excluded from the subset of 8 elements twice. Therefore, the number of subsets of A with 8 elements that have 2 letters is 2 ^ 12 = 4096.
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In 1968 the remains of a young boy buried with over 100 tools of stone and antlers were found by accident by a construction worker on private property owned by the Anzick family in Montana. The bones were determined by radiocarbon-dating to be 12,600 years old. The half-life of Carbon-14 is 5730 years. What percent of the original amount of Carbon-14 was in the bone remains when found in 1968? Show how you obtained your equation and how you solved it. In 2014, a daughter of the Anzick family, Sarah Anzick, who was inspired by the finding and had become a genome researcher, was a member of the team that did DNA sequencing on the remains.
To find the percent of the original amount of Carbon-14 in the bone remains when found in 1968, we can use the following formula:
A = A0 * (1/2)^(t/h)
Where A is the final amount of Carbon-14, A0 is the original amount of Carbon-14, t is the time elapsed, and h is the half-life of Carbon-14.
Plugging in the given values, we get:
A = A0 * (1/2)^(12600/5730)
Simplifying the exponent, we get:
A = A0 * (1/2)^2.199
Using a calculator, we find that (1/2)^2.199 is approximately 0.153, so:
A = A0 * 0.153
This means that the final amount of Carbon-14 is 15.3% of the original amount of Carbon-14. Therefore, the percent of the original amount of Carbon-14 in the bone remains when found in 1968 is 15.3%.
As for the second part of the question, Sarah Anzick was a member of the team that did DNA sequencing on the remains in 2014. This allowed for further analysis and understanding of the remains and their significance in terms of human history and evolution.
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EQUATIONS AND INEQUALITIES Solving a word problem with two unknowns using a linear... A washer and a dryer cost $615 combined. The washer costs $85 less than the dryer. W
The cost of the washer is $265 and the cost of the dryer is $350.
To solve this word problem with two unknowns using a linear equation, we can use the following steps:
Define the variables: Let W represent the cost of the washer, and D represent the cost of the dryer.Write the equation based on the given information: W + D = $615, and W = D - $85Substitute one equation into the other to solve for one variable: (D - $85) + D = $615Simplify the equation: 2D = $700Solve for the variable: D = $350Substitute the value of D back into one of the original equations to find the value of W: W = $350 - $85 = $265So, the cost of the washer is $265 and the cost of the dryer is $350.
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If G (with 2 or more nodes) is connected, then all nodes must have degree bigger equal to 1.
true or false
The statement "If G is connected with 2 or more nodes, then all nodes must have a degree bigger or equal to 1." is true.
This is because a connected graph is defined as a graph in which there is a path between any two nodes. If a node has a degree of 0, that means it is not connected to any other nodes, and therefore the graph cannot be connected. So, in order for G to be connected, all nodes must have a degree of at least 1.
In conclusion, the answer is true.
What is a node?A node is a point where several elements are connected.
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Three squares with areas of 112 cm2,28 cm2, and 63 cm2 are displayed on a computer monitor. What is the sum (in radical form) of the perimeters of these squares? The sum of the perimeters is cm.
The sum of the perimeters of the three squares displayed on the computer monitor is 36√7 cm.
The sum of the perimeters of the three squares displayed on the computer monitor can be found by first finding the side length of each square, and then multiplying that side length by 4 to find the perimeter of each square. Finally, we add the perimeters of the three squares together to find the sum of the perimeters.
For the first square with an area of 112 cm^2, the side length is √112 cm, or 4√7 cm. The perimeter of this square is 4(4√7 cm) = 16√7 cm.
For the second square with an area of 28 cm^2, the side length is √28 cm, or 2√7 cm. The perimeter of this square is 4(2√7 cm) = 8√7 cm.
For the third square with an area of 63 cm^2, the side length is √63 cm, or 3√7 cm. The perimeter of this square is 4(3√7 cm) = 12√7 cm.
The sum of the perimeters of these three squares is 16√7 cm + 8√7 cm + 12√7 cm = 36√7 cm.
Therefore, the sum of the perimeters of the three squares displayed on the computer monitor is 36√7 cm.
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I neeeeddd help pls help me
what is the value of (3-5)^4 (2)-16+2?
Chiang is retiling the kitchen floor with his parents. How many square feet of tile do they need?
Height: cm Volume: cm^(3) Length: Width: Height: Volume: a multiplication sentence that you could use to calculate the volume for m 1. Include the units in your sentences.
The multiplication sentence will be: Volume = Length × Width × Height.
Each of these measurements should be in centimeters (cm) in order to calculate the volume in cubic centimeters (cm^3).
To calculate the volume of a rectangular prism, you can use the multiplication sentence: Volume = Length × Width × Height. Each of these measurements should be in centimeters (cm) in order to calculate the volume in cubic centimeters (cm^3).
For example, if the length of the rectangular prism is 5 cm, the width is 3 cm, and the height is 2 cm, the multiplication sentence would be:
Volume = 5 cm × 3 cm × 2 cm
The volume of this rectangular prism would be 30 cm^3.
In general, the multiplication sentence to calculate the volume of a rectangular prism is:
Volume = Length × Width × Height
Make sure to include the units (cm) in your multiplication sentence in order to get the correct answer in cubic centimeters (cm^3).
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the permulation [[1,2,3,4,5,6],[6,5,4,3,2,1]]can be written as a product of disjoint cycles as
The permutation [[1,2,3,4,5,6],[6,5,4,3,2,1]] can be written as a product of disjoint cycles as (1,6)(2,5)(3,4).
A permutation can be represented as a product of disjoint cycles. A cycle is a sequence of numbers that are permuted in a circular fashion. For example, the cycle (1,2,3) means that 1 is permuted to 2, 2 is permuted to 3, and 3 is permuted to 1.
To write the given permutation as a product of disjoint cycles, we can start with the first number in the first row, 1, and see where it is permuted to in the second row. In this case, 1 is permuted to 6. Then we look at where 6 is permuted to, which is 1, completing the cycle (1,6).
Next, we move on to the next number in the first row that has not been included in a cycle, which is 2. We see that 2 is permuted to 5, and 5 is permuted to 2, completing the cycle (2,5).
Finally, we move on to the next number in the first row that has not been included in a cycle, which is 3. We see that 3 is permuted to 4, and 4 is permuted to 3, completing the cycle (3,4).
Therefore, the given permutation can be written as a product of disjoint cycles as (1,6)(2,5)(3,4).
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The length of the base of an isosceles triangle is x. The length of a leg is 3x-4. The perimeter of the triangle is 90 . Find x.
Answer:
X = 31 1/3
Step-by-step explanation:
3x - 4= 90
Step 1:
* opposite operation *
90 + 4 = 94
94/3 = 31 1/3
CHECK
*Replace x with your solution(s)*
3(3 1/3) - 4
3 x 31/3 = 94
94-4= 90
Visual domain and range
Determine the range of the following graph
Answer:
[-4, 2]
Step-by-step explanation:
You want the range of the graph shown.
RangeThe range is the vertical extent of the graph. This graph has a minimum at y=-4 and a maximum of y=2. All values between these are represented, so the range is ...
[-4, 2] . . . . or -4 ≤ y ≤ 2
PLEASE HELP
Find the value of each trigonometric value.
The trigonometric value of angle Cos Z would be = 77°
What is a trigonometric value?A trigonometric value is defined as those values that are based on three major trigonometric ratios such as the Sine, Cosine, and Tangent.
According to the rules of trigonometry the following is carried out:
Sine or sin θ = Side opposite to θ / Hypotenuse = XY / XZ
Cosines or cos θ = Adjacent side to θ / Hypotenuse = YZ / XY
Tangent or tan θ =Side opposite to θ / Adjacent side to θ = XY / YZ.
Therefore, the trigonometric value of cos Z = adj/hypo = 9/40 = 0.225
Z = Cos^-1 0.225.
Z = 76.9 = 77°
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Let R be a ring such that x = x2 for all x ∈ R. Prove that R is a ring commutative.
Yes, the given ring is commutative.We have that, a commutative ring in abstract algebra is a ring that satisfies a +b = b+a (for a defined operator).
Given: R is a ring such that [tex]$x = x^2$[/tex] for all [tex]$x\in R$[/tex].
To prove: R is a ring commutative.
Proof:
Let [tex]$a$[/tex] and [tex]$b$[/tex] be arbitrary elements in [tex]$R$[/tex].
[tex]$a+b = (a+b)^2 = a^2 + 2ab + b^2$[/tex]
[tex]$b+a = (b+a)^2 = b^2 + 2ab + a^2$[/tex]
Therefore, [tex]$a+b = b+a$[/tex]. Thus, R is a ring commutative.
Q.E.D.
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If 6 screws weigh more than 7 nails, which is heavier, 7 screws or 8 nails?
Answer:
The 7 screws offer superior tensile strength over the 8 nails. The 7 screws are heavier.
1. Which three-dimensional tigure will this net make! (1 point)
The three-dimensional figure this net will make is a triangular prism and is denoted as option B.
What is a Three-dimensional figure?
This is defined as a solid figure or an object or shape that has three dimensions such as length, width, and height.
An example is the triangular prism is a polyhedron made up of two triangular bases and three rectangular sides and from the net given above we can deduce that the triangular prism can be formed from it due to the shape and vertices.
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katie runs a stable that boards a range of horses 3 of them being bay 19 of them being white 1 of them being gray 4 of them being black and 3 of them being palomino out of the next 15 horses should you expect to be black horses
We can expect 2 black horses out of a sample of 15 horses from the stable.
What is probability?To determine how likely something is gonna occur, use probability. The event is typically stated as a number between 0 and 1, with 0 denoting impossibility and 1 denoting certainty.
To solve it, we need to use the information provided about the proportion of different horse colors in the stable to estimate the number of black horses we would expect to find in a sample of 15 horses.
According to the information provided, there are 3+19+1+4+3= 30 horses in the stable, and 4 of them are black. Therefore, the proportion of black horses in the stable is:
4/30 = 0.1333...
So, if we were to randomly select 15 horses from the stable, we would expect approximately 13.33% of them to be black. To find the expected number of black horses in a sample of 15 horses, we can multiply the proportion by the sample size:
0.1333... x 15 = 1.999...
Rounding to the nearest whole number, we can expect 2 black horses out of a sample of 15 horses from the stable.
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PLEASE HELP ME
The first two steps in the derivation of the quadratic formula by completing the square are shown below.
Which answer choice shows the correct next step?
Answer:
The correct next step is the answer choice
x^2+b/a x=-c/a
Step-by-step explanation:
$30 for 100 flyers or $65 for 250 flyers?
Answer:
To compare the cost of each option, we need to calculate the cost per flyer.
For the first option, the cost per flyer is:
30 dollars / 100 flyers = 0.3 dollars/flyer
For the second option, the cost per flyer is:
65 dollars / 250 flyers = 0.26 dollars/flyer
Therefore, the second option is cheaper per flyer. However, if you only need 100 flyers, the first option would be more cost-effective.
Step-by-step explanation:
Answer: $65 for 250 flyers is cheaper
Step-by-step explanation:
30 dollars per 100 flyers - 30/100 = 0.30 or 30 cents per flyer
65 dollars per 250 flyers - 65/250 = 0.26 or 26 cents per flyer
HELPPPOP i dont know WHAT THE ANSWER ISS
Alina flipped a nickel 10 times. It landed on heads 7 times and tails 3 times. If she flips the coin again, what is the probability of getting tails?
Answer:
Probability=number of chances/total possible outcome
P=3/10
An account with an initial balance of $1250 earns interest that is compounded quarterly. If no other deposits or withdrawals are made, the account will have a balance of $1406.08 after 9 months. Find the annual interest rate.
Answer:
Let's first calculate the number of compounding periods in a year, given that the interest is compounded quarterly:
Number of compounding periods in a year = 4 (since there are 4 quarters in a year)
Next, let's use the formula for compound interest to find the annual interest rate:
A = P (1 + r/n)^(nt)
Where:
A is the balance after t years
P is the principal (initial balance)
r is the annual interest rate (what we are looking for)
n is the number of compounding periods in a year
t is the time in years
We know that P = $1250, A = $1406.08, n = 4, and t = 9/12 years (since the interest is earned for 9 months).
Plugging these values into the formula, we get:
$1406.08 = $1250 (1 + r/4)^(4/3)
Dividing both sides by $1250 and taking the cube root of both sides, we get:
1 + r/4 = (1406.08/1250)^(3/4)
1 + r/4 = 1.038
Subtracting 1 from both sides, we get:
r/4 = 0.038
Multiplying both sides by 4, we get:
r = 0.152
Therefore, the annual interest rate is 15.2%.
i need help on my dividend
Answer:
ok divide is easy
Step-by-step explanation:
dividing is not adding or subtracting
Three painters are working on painting a fence: Abel, Baker and Chuck. Abel could paint the whole fence himself in 18 hours. Baker paints twice as fast as Abel. Chuck paints three times as fast as Abel. How long does it take them working all together?
The combined rate of all three workers is 6 fences per 3 hours.
To find out how long it would take for all three painters to paint the fence together, we need to find the combined rate of work for Abel, Baker, and Chuck.
Let's first find the rate of work for each painter individually.
Abel's rate of work is 1/18 of the fence per hour (since he can paint the whole fence in 18 hours).
Baker's rate of work is twice as fast as Abel's, so his rate of work is 2/18 (or 1/9) of the fence per hour.
Chuck's rate of work is three times as fast as Abel's, so his rate of work is 3/18 (or 1/6) of the fence per hour.
Now, to find the combined rate of work for all three painters, we simply add their individual rates of work together:
1/18 + 1/9 + 1/6 = 1/18 + 2/18 + 3/18 = 6/18 = 1/3
This means that together, the three painters can paint 1/3 of the fence per hour.
To find out how long it would take them to paint the whole fence, we simply divide the total amount of work (1 whole fence) by their combined rate of work (1/3 of the fence per hour):
1 ÷ 1/3 = 3
So it would take the three painters 3 hours to paint the whole fence together.
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can someone please answer these questions for me
The answers for each line are:
a) the slope is -2
b) The slope is 2/5 and the y-intercept is -2.
c) x = 10/4
d) y = -7x - 2
How to get the slope of the line?A linear equation can be written as:
y = a*x + b
Where a is the slope and b is the y-intercept.
We know that if the line passes through (x₁, y₁) and (x₂, y₂), then the slope is:
a = (y₂ - y₁)/(x₂ - x₁)
a) Then the slope of the line that passes through (2, -5) and (-2, 3) is:
a = (3 + 5)/(-2 - 2) = 8/-4 = -2
b) The line is 2x - 5y = 10
Isolating y we will get:
5y = 2x - 10
y = (2/5)*x - 2
The slope is 2/5 and the y-intercept is -2.
c) Here we need to solve:
-4 = (1 + 9)/(0 - x)
-4*-x = 10
x = 10/4
d) if the slope is -7, then we have:
y = -7x + b
And the line also passes through (-1, 5), then:
5 = -7*-1 + b
5 = 7 + b
5 - 7 =b
-2 = b
The line is:
y = -7x - 2
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If I was asked to think of a number and multiply it by 2 I would get 2x
Answer:
5x - 3
Step-by-step explanation:
Given:
A Number and multiply it by 2.
To Find:
to write it algebraically
Solution:
Let the number that was asked to think to be x.
Then it is multiplied by 2 which becomes 2x.
Now the number is multiplied by 5.
So, x multiplied by 5 will become 5x.
Then, 5x is subtracted from 3.
So, we can write it as 5x - 3
Therefore, it can be written as 5x - 3 algebraically.
Use Euclid's first book to prove what specific quadrilaterals are produced by perpendicular, unequal, bisecting diagonals.
By using Euclid's first book, we can prove that the quadrilateral produced by perpendicular, unequal, bisecting diagonals is a kite. A kite is a quadrilateral with two pairs of adjacent sides that are equal in length. In this case, the two pairs of adjacent sides are formed by the diagonals bisecting the quadrilateral into four smaller triangles with equal areas.
According to Euclid's first book, when two lines intersect at a right angle (perpendicular), they form four right angles. In the case of a quadrilateral with perpendicular, unequal, bisecting diagonals, the diagonals intersect at a right angle and divide the quadrilateral into four smaller triangles with equal areas.
1. Draw a quadrilateral with perpendicular, unequal, bisecting diagonals.
2. Label the points where the diagonals intersect as A, B, C, and D.
3. Label the point where the diagonals intersect as E.
4. Use Euclid's first book to prove that the angles at E are all right angles.
5. Use Euclid's first book to prove that the four triangles formed by the diagonals are congruent (equal in area).
6. Use the definition of a kite to prove that the quadrilateral is a kite (two pairs of adjacent sides are equal in length).
7. Therefore, the quadrilateral produced by perpendicular, unequal, bisecting diagonals is a kite.
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First give the technology formula for the given function and then use technology to evaluate the function for the given values of x (when defined there). (Round all answers to four decimal places.)
h(x) =
x2 − 8 / x2 + 8
; x = 0.5, 1.5, 2.5, ..., 10.5
A. (x^2 + 8)/(x^2 − 8)
B. (x^2 − 8)/(x^2 + 8)
C. (x − 8)^2/(x + 8)^2
D. (x − 8)^2/(x^2 + 8)
h(0.5) = h(1.5) = h(2.5) = h(3.5) = h(4.5) = h(5.5) = h(6.5) = h(7.5) = h(8.5) = h(9.5) = h(10.5) =
The technology formula for the given function is B. (x^2 − 8)/(x^2 + 8).
We can use technology, such as a graphing calculator or an online math solver, to evaluate the function for the given values of x. Here are the steps to do so:
1. Enter the technology formula (x^2 − 8)/(x^2 + 8) into the calculator or solver.
2. Enter the values of x one at a time and evaluate the function for each value.
3. Round all answers to four decimal places.
Here are the results:
h(0.5) = 0.9310
h(1.5) = 0.6765
h(2.5) = 0.5161
h(3.5) = 0.4196
h(4.5) = 0.3548
h(5.5) = 0.3103
h(6.5) = 0.2778
h(7.5) = 0.2533
h(8.5) = 0.2346
h(9.5) = 0.2199
h(10.5) = 0.2081
Therefore, the function evaluated at the given values of x is as follows:
h(0.5) = 0.9310
h(1.5) = 0.6765
h(2.5) = 0.5161
h(3.5) = 0.4196
h(4.5) = 0.3548
h(5.5) = 0.3103
h(6.5) = 0.2778
h(7.5) = 0.2533
h(8.5) = 0.2346
h(9.5) = 0.2199
h(10.5) = 0.2081
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Use the given information to find the exact function value. Simplify your answer as much as possible. Rationalize the denominator if necessary. sin a = 5/13, 0 < a < ????/2
The given information tells us that the sin a is equal to 5/13, and that 0 is less than a, which is less than π/2. Therefore, the exact function value for sin a is 5/13 and the value for a is approximately 5/12.
We are given that sin(a) = 5/13 and 0 < a < π/2. We can use the Pythagorean identity cos²(a) + sin²(a) = 1 to find cos(a):
cos²(a) + sin²(a) = 1
cos²(a) + (5/13)² = 1
cos²(a) = 1 - (5/13)²
cos²(a) = 144/169
cos(a) = ± 12/13
Since 0 < a < π/2, we know that cos(a) > 0. Therefore, cos(a) = 12/13. We can use the definition of tangent to find tan(a):
tan(a) = sin(a)/cos(a) = (5/13)/(12/13) = 5/12
Therefore, the exact function value we were asked to find is tan(a) = 5/12.
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