The inverse of a matrix A is A^-1. And I, the identity matrix, is equal to A.A^-1.
The square matrix needs to be non-singular and have a non-zero determinant value in order to get the inverse matrix. Let's think about the 2 x 2 square matrix A.
Inverse of matrix:
A^(-1)=Adj A/|A|
A-1 stands for Inverse of Matrix for matrix A. There is a straightforward formula for calculating the inverse of a 2 × 2 matrix. In order to find the inverse of a matrix of order 3 or higher, we also need to be aware of the matrix's determinant and adjoint. When multiplied by the provided matrix, the other matrix that serves as the inverse of that matrix yields the multiplicative identity.
There are two ways to find a matrix's inverse. Through the use of an adjoint of a matrix and simple processes, it is possible to derive the inverse of a matrix. Row or column transformations can be used to carry out the basic operations on a matrix. Additionally, the adjoint and determinant of the matrix can be used to apply the inverse of matrix formula in order to get the inverse of a matrix.
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There are 27
basketball players on the Greenland Basketball Team.
Of the 27 players, 1/9 of them are left-handed. How
many players are left handed? Be sure to show your
Answer:
3 players
Step-by-step explanation:
So, all you have to do is multiply 27 by 1/9 to get 3. Or, you could try figure out what number needs to be multiplied by 9 to get 27, which is also 3.
what is the perimeter of the shape
Answer:that is an s
Step-by-step explanation:
si quema cuh
The function f(x)= 3/4(10)-x is reflected across the x-axis to create the function g(x). Which ordered pair is on g(x)?
Answer:
function 9 plus 10
Step-by-step explanation:
9-50 = 79
(x+3)(x+5) expand and simplify that pls
Answer:
x^2 + 8x + 15
Step-by-step explanation:
( x + 3 ) ( x + 5 )
1. distribute
( x + 3 ) ( x + 5 )
x^2 + 3x + 5x + 15
2. simplify
x^2 + 8x + 15
A local wine equipment manufacturer is planning to issue stocks. The company just paid a dividend of $3.60. They now expect to pay dividends to grow at 15% for the next 3 years and thereafter grow at an annual rate of 8%. What should be the price of the stock given these revised forecasts? Assume a rate of return of 16%
a.How does a cumulative voting system allow minority representation in corporations?
Based on these expected future dividends and the rate of return required by investors, the price of the stock should be $414 in year 1, $476 in year 2, $547 in year 3, $93.24 in year 4, $114.53 in year 5, and $138.49 in year 6.
To calculate the price of the stock, we need to first determine the expected future dividends. We know that the current dividend is $3.60, and we can use the dividend growth rate to calculate the expected future dividends.
For the first three years, we can use the 15% dividend growth rate to calculate the expected dividends as follows:
Year 1: $3.60 x 1.15 = $4.14
Year 2: $4.14 x 1.15 = $4.76
Year 3: $4.76 x 1.15 = $5.47
The Gordon growth model is as follows:
P = D / (r - g)
where:
P = price of the stock
D = expected dividend payment
r = rate of return required by investors
g = expected dividend growth rate
Using the formula, we can calculate the price of the stock as follows:
Year 1: P = $4.14 / (0.16 - 0.15) = $414
Year 2: P = $4.76 / (0.16 - 0.15) = $476
Year 3: P = $5.47 / (0.16 - 0.15) = $547
After year 3, the expected dividend growth rate is 8%, so we can use this rate to calculate the price of the stock beyond year 3.
Year 4: P = $5.47 x 1.08 / (0.16 - 0.08) = $93.24
Year 5: P = $5.96 x 1.08² / (0.16 - 0.08) = $114.53
Year 6: P = $6.47 x 1.08³ / (0.16 - 0.08) = $138.49
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Drew has two cats. One cat weighs 17 pounds, and the other one weighs 1212 pounds. Audrey’s dog weighs 33 pounds.
What is the difference in ounces between Audrey’s dog and the combined weights of Drew’s cats?
Enter your answer in the box.
Answer:
48 ounces.
Step-by-step explanation:
Steps:
Combine the weight of the cats.
12 (assuming it is a typo, 1212 pounds is a pretty big cat!) + 17 = 30 pounds
Convert to ounces.
33 pounds = 528 ounces
30 pounds = 480 ounces
Subtract the two/find the difference.
528 - 480 = 48.
The difference in ounces between Audrey's dog and the combined weights of Drew's cats is 48 ounces.
The altitude of a triangle is increasing at a rate of 1 centimeters/minute while the area of the triangle is increasing at a rate of 4 square centimeters/minute. At what rate is the base of the triangle changing when the altitude is 7 centimeters and the area is 91 square centimeters?
____ cm/min
Find the solution for x if |3 + 10x| = 23.
Answer:
x=2 and 2.6
Step-by-step explanation:
The required solutions for the given function |3 + 10x| = 23 are x = 2 and x = -2.6.
What is absolute value?Absolute value is defined as the magnitude or size of a number, no negatives are allowed. The distance a number is from 0 on the number line is known as the absolute value of the number.
The function is given in the question as:
|3 + 10x| = 23
To solve for x, we can begin by expressing the absolute value as a piecewise function:
|3 + 10x| = 23
(3 + 10x) = 23, if 3 + 10x ≥ 0
-(3 + 10x) = 23, if 3 + 10x < 0
If 3 + 10x ≥ 0, then 3 + 10x = 23, so x = (23 - 3) / 10 = 2.
If 3 + 10x < 0, then -(3 + 10x) = 23, so 3 + 10x = -23. This means that x = (-23 - 3) / 10 = -2.6.
Thus, the solutions for x are x = 2 and x = -2.6.
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95 +(-68) = 36 explain
Answer:
That is false.
Step-by-step explanation:
The left side would be 95-68, which equals 27, which isn't 36.
Please help asap.......
Answer:
Hello!!! Princess Sakura here ^^
Step-by-step explanation:
The answer is choice B. It has a reflectional symmetry because if you cut it in half (vertical line) it will look exactly the same on the other side.
The two shapes below are scaled copies
of one another. The base lengths are
shown. What is the scale factor going
from the first figure to the second?
15
6
Answer:
2/5 or 0.4.
Step-by-step explanation:
6/15 = 2/5
S A black bear was tracked across Central Florida logging approximately 120 miles in 30 days.
For 24 miles of M34’s journey, he was tracked walking along the Kissimmee River.
How many days was he traveling along the Kissimmee River?
Answer: 6 days
120 miles divided into 30 days is 4 miles per day.
24 miles divided by 4 miles is 6 , which means the bear spent 6 days walking along Kissimmee River.
I hope this helped & Good Luck <3 !!
Please help fast please
Answer:
See image
Step-by-step explanation:
It cant be wrong
Arrange the quantities in order from smallest to largest.
2.6 km, 109,000 mm, 41.7 hm
The order of the values using the basic unit of meters from smallest to largest. is: 109000 mm < 2.6 km < 41.7 hm
What are the units of measurement of distance or length?
Distance is the gap between any two points under consideration.
The basic unit for measuring distance is the meter.
There are larger as well as smaller units for measuring length or distance which are based on the unit of meter.
The units are as follows:
millimeter, mm = 0.001 m
centimeter, cm = 0.01 m
decimeters, dm = 0.1 m
meter, m = 1 m
kilometer, km = 1000 m
hectometer, hm = 100 m
Now to compare the given quantities making the units same as two quantities can only be compared only when there units are same :
Considering the given values;
2.6 km = 2600 m
109,000 mm = 109 m
41.7 hm = 4170 m
Therefore, after comparison arranging the quantities in order from smallest to largest is 109000 mm < 2.6 km < 41.7 hm
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Help me please
Thank you !!
Answer:
Isosceles
Step-by-step explanation:
Think of Isosceles as eye-sosceles, you likely have 2 eyes as an Isosceles triangle has 2 equal sides
Hope this helped :)
Understanding of Multiplying by a Fraction Name: Draw a number line model to represent each multiplication problem. Then solve the problem.2/3×1/2=how do you do this
We have following:
1.
\(\frac{2}{3}\cdot\frac{1}{2}=\frac{2\cdot1}{3\cdot2}=\frac{2}{6}=\frac{1}{3}\)2.
\(\frac{5}{6}\cdot\frac{3}{4}=\frac{5\cdot3}{6\cdot4}=\frac{15}{24}=\frac{5}{8}\)The angle bisectors of triangle XYZ meet at point P. What is the measure of angle PYK
Answer:
Step-by-step explanation:
m∠PYK = 27°
7.
(02.01 MC)
Six-year-old students at an elementary school were given a 20-yard head start in a race. The graph shows how far the average student ran in 30 seconds.
A line graph with Distance, in yards, on the x axis and Age of Runner on the y axis. The x axis has a scale from 0 to 80 in increments of 10. The y axis has a scale of 0 to 8 in increments of 2. A straight line connecting 20, 6 and 60, 6 is drawn.
Which statement best describes the domain of the function represented in the graph? (1 point)
6 ≤ x ≤ 60, or x is from 6 to 60
6 ≤ x ≤ 20, or x is from 6 to 20
0 ≤ x ≤ 20, or x is from 0 to 20
20 ≤ x ≤ 60, or x is from 20 to 60
HELP
The domain of the function represented in the graph will be 20 ≤ x ≤ 60, or x is from 20 to 60. Then the correct option is D.
What is a line segment?A line segment in mathematics has two different points on it that define its boundaries.
A line segment is sometimes referred to as a section of a path that joins two places.
Six-year-old students at an elementary school were given a 20-yard head start in a race. The graph shows how far the average student ran in 30 seconds.
A line graph with Distance, in yards, on the x-axis and Age of the Runner on the y-axis. The x-axis has a scale from 0 to 80 in increments of 10. The y-axis has a scale of 0 to 8 in increments of 2. A straight line connecting 20, 6, and 60, 6 is drawn.
The domain of the function represented in the graph will be 20 ≤ x ≤ 60, or x is from 20 to 60. Then the correct option is D.
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Answer:
the correct option is D
Step-by-step explanation:
please help i’ll mark you
Answer:
Quadrant 1: (6, 6)
Quadrant 2: (-1,6) and (-1,2)
Quadrant 3: (-6,-2)
Quadrant 4: (6,-2) and (1,-6)
Step-by-step explanation:
what is the slope of the line -3y=12x+6
Answer:
Step-by-step explanation:
uhh
HELP ASAP!!!! simplify 3^2-4/5
Answer:
9-4/5
5/5 = 1
Step-by-step explanation:
Answer:
1
9-4/5 is equal to 5/5 which is equal to 1
Ceasar opens a bank account and makes an initial deposit of $800. The banker tells Ceasar that he is going to receive an annual rate of 10% compounded continuously on his investment. Find the bank balance assuming Ceasar leaves the account untouched for 8 years. asnwer this question using the fomula A(t) = Pe^(rt). please show work plese
Answer:
Initial Deposit= $800
Annual rate= .1%
Leaves= 8 years
8 x .1= .8
$800 x .8= $640
$800+$640= $1,440
So your answer is $1,440 is the bank balance in 8 years
Step-by-step explanation:
hope i help have a great day
Find the equation to the line
The equation of the line is y = 2/3x + 1
How to determine the equation of the line?The graph represents the given parameter
From the graph, we have the following points that can be used in our computation:
(x, y) = (0, 1) and (3, 3)
The equation of the line is then calculated using the following equation
y = (y₂ - y₁)/(x₂ - x₁) * (x - x₁) + y₁
Where
(x, y) = (0, 1) and (3, 3)
Substitute the known values in the above equation, so, we have the following representation
y = (3 - 1)/(3 - 0) * (x - 0) + 1
Evaluate
y = 2/3 (x - 0) + 1
So, we have
y = 2/3x + 1
Hence, the line equation is y = 2/3x + 1
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Which of the following statements could be a correct step in solving this equation:
12x−7=13(x−12)
A. 12x−7=13x−12
B. 3x−42=2(x−12)
C. 3x−7=2(x−12)
D. 3x−7=2x−12
Answer:
A
Step-by-step explanation:
I think the answer is A because you have to use 13 to multiply what's in the bracket in order to collect like terms but 13 *12 won't give you 12. That's the reason why am confused
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Answer:
\(\textsf{1.(a)} \quad x^2-14x+\boxed{49}=\left(x-\boxed{7}\right)^2\)
\(\textsf{1.(b)} \quad 9x^2 + 30x +\boxed{25}= \left(3x +\boxed{5}\right)^2\)
\(\begin{aligned}\textsf{2.(a)}\quad3x^2-24x+48&=3\left(x^2-\boxed{8}\:x+\boxed{16}\right)\\&=3\left(x-\boxed{4}\right)^2\end{aligned}\)
\(\begin{aligned}\textsf{2.(b)}\quad \dfrac{1}{2}x^2+8x+32&=\dfrac{1}{2}\left(x^2+\boxed{16}\:x+\boxed{64}\right)\\&=\dfrac{1}{2}\left(x+\boxed{8}\right)^2\end{aligned}\)
Step-by-step explanation:
Question 1(a) When completing the square for a quadratic equation in the form ax² + bx + c where the leading coefficient is one, we need to add the square of half the coefficient of the x-term:
\(x^2-14x+\left(\dfrac{-14}{2}\right)^2\)
\(x^2-14x+\left(-7\right)^2\)
\(x^2-14x+49\)
We have now created a perfect square trinomial in the form a² - 2ab + b². To factor a perfect square trinomial, use the following formula:
\(\boxed{a^2 -2ab + b^2 = (a -b)^2}\)
Therefore:
\(a^2=x^2 \implies a=1\)
\(b^2=49=7^2\implies b = 7\)
Therefore, the perfect square trinomial rewritten as a binomial squared is:
\(x^2-14x+\boxed{49}=\left(x-\boxed{7}\right)^2\)
(b) When completing the square for a quadratic equation where the leading coefficient is not one, we need to add the square of the coefficient of the x-term once it is halved and divided by the leading coefficient, and then multiply it by the leading coefficient:
\(9x^2 + 30x +9\left(\dfrac{30}{2 \cdot 9}\right)^2\)
\(9x^2 + 30x +9\left(\dfrac{5}{3}\right)^2\)
\(9x^2 + 30x +9 \cdot \dfrac{25}{9}\)
\(9x^2 + 30x +25\)
We have now created a perfect square trinomial in the form a² + 2ab + b². To factor a perfect square trinomial, use the following formula:
\(\boxed{a^2 +2ab + b^2 = (a +b)^2}\)
Therefore:
\(a^2=9x^2 = (3x)^2 \implies a = 3x\)
\(b^2=25 = 5^2 \implies b = 5\)
Therefore, the perfect square trinomial rewritten as a binomial squared is:
\(9x^2 + 30x +\boxed{25}= \left(3x +\boxed{5}\right)^2\)
\(\hrulefill\)
Question 2(a) Factor out the leading coefficient 3 from the given expression:
\(3x^2-24x+48=3\left(x^2-\boxed{8}\:x+\boxed{16}\right)\)
We have now created a perfect square trinomial in the form a² - 2ab + b² inside the parentheses. To factor a perfect square trinomial, use the following formula:
\(\boxed{a^2 -2ab + b^2 = (a -b)^2}\)
Factor the perfect square trinomial inside the parentheses:
\(=3\left(x-\boxed{4}\right)^2\)
(a) Factor out the leading coefficient 1/2 from the given expression:
\(\dfrac{1}{2}x^2+8x+32=\dfrac{1}{2}\left(x^2+\boxed{16}\:x+\boxed{64}\right)\)
We have now created a perfect square trinomial in the form a² + 2ab + b² inside the parentheses. To factor a perfect square trinomial, use the following formula:
\(\boxed{a^2+2ab + b^2 = (a +b)^2}\)
Factor the perfect square trinomial inside the parentheses:
\(=\dfrac{1}{2}\left(x+\boxed{8}\right)^2\)
Step-by-step explanation:
Since ABCD is a rectangle
⇒ AB = CD and BC = AD
x + y = 30 …………….. (i)
x – y = 14 ……………. (ii)
(i) + (ii) ⇒ 2x = 44
⇒ x = 22
Plug in x = 22 in (i)
⇒ 22 + y = 30
⇒ y = 8
=) A student is taking a standardized test
consisting of multiple choice questions for
which there are five options for each question.
Four points are awarded for each correct
answer, but the student loses 2 points for an
incorrect answer. Questions left blank neither
receive nor lose points. Is it in the student's
best interest to guess?
Answer:
in this problem. Not that the total number of ways of taking one or more alternative out of ...
Step-by-step explanation:
Answer:
No.
Step-by-step explanation:
Well, honestly not sure how to solve this but I'll try.
Each correct answer is giving 4 points but the probability to choose the correct one is 1/5
Each incorrect one gives -2 points and the chance to pick a wrong answer is 4/5.
Obviously, the chance to lose points is more. But is taking the risk and guessing worth it? Well, it depends on how many points the correct answer gives. If it makes up for the possible loss of points, then it is in his interest to guess, otherwise he will end up losing more than they win.
If we sum the two chances to find averagely how many points the student will get, then I guess that would be the correct answer:
4(1/5) + (-2)(4/5) = 4/5 - 8/5 = -4/5
He will get averagely -4/5 points, so I believe it isn't in his interest. It means that the points he gets don't make up for the possible loss of points if you choose answers randomly. (Wow, I'm glad teachers don't do this on tests 0_0)
This is my theory though, not sure how to go for solving this, just thinked logically. I hope this helps, but don't trust me and copy paste my answer on your test or whatever. Think if this is correct first because I'm not sure
help plsssssssssssssssss I BEGGGGGG
What is exactly the relation between a Rhombus, rectangle, parallelogram, and square explain please i will mark brainliest only IF you explain
Any rhombus is a parallelogram, but not the other way around. If you were to make a Venn Diagram, the "rhombus" portion is entirely inside the set of "parallelograms".
The same can be said about rectangles as well. Any rectangle is a parallelogram, but not the other way around.
If we overlapped the region of rectangles and rhombuses, then we form the region for squares. A square is a combination of a rhombus and a rectangle.
Any square has all four sides the same length (property of a rhombus) and all angles equal to 90 (property of a rectangle). Since a square inherits properties of a rectangle and rhombus, it automatically makes any square a parallelogram.
Check out the venn diagram below.
A fraction is shown. 8/16 Which expression is equivalent to this fraction?
Answer:
1/2
Step-by-step explanation:
Which of the following is true of a radius of a circle?
(1) Radius is the distance from the center to any point on the circle.
(2) A circle may have radii with different values.
(3) Radius is half the diameter in any circle
Select one:
Only (1) and (2)
Only (2) and (3)
Only (1) and (3)
All (1), (2) and (3)