Matrix A is invertible such that A⁻¹ = - A - 3I. This is solved using the Calely Hamilton Theorem.
What does the Calely Hamilton Theorem state?This theorem says that every square matrix satisfies its own characteristic equation. In other words, the scalar polynomial
p(λ) = det(λI − σ) also holds for the stress polynomial p(σ).
It also states that The roots λ₁, λ₂........λₙ of a typical equation (aₙλₙ + aₙ₋₁ λⁿ⁻¹ + ...... a₁ λ + a₀) will indicate the nature of the Matrix A. If either of the roots of the attributes equation is 0, the matrix's determinant becomes zero. As a result, the matrix is non-invertible.
Based on the above, we know that Matrix A fulfills the qualities below::
A²+3A + I = 0
Since every square matrix fulfills its own characteristic
λ₁ + λ₂ = -3
λ₁ x λ₂ = 1 ≠ 0
This is true for any order of a square matrix. That is:
λ₁ x λ₂ x λ₃ x........ x λₙ ≠ 0
Thus
|A| = λ₁ x λ₂ x λ₃ x........ x λₙ
|A| ≠ 0 → Invertibel Matrix
A² + 3A + I = 0
I = -A² - 3A
A⁻¹ x I = A⁻¹ (-A - 3A); hence
A⁻¹ = - A - 3I
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3. The expression 0.12 x+(x-35) models the final price of a scooter with an instant rebate in a state that charges sales tax.
- Which part of the expression represents the discounted price before tax?
- Which part of the expression represent the amount of sales tax, in dollars (not the tax rate, the amount of sales tax paid)?
The expression x - 35 represents the discounted price before tax. The expression 0.12x represent the amount of sales tax.
What is an expression?Expressions are defined as mathematical statements that have a minimum of two terms containing variables or numbers.
The expression given which models the final price of a scooter with an instant rebate in a state that charges sales tax is:
⇒ 0.12x + (x - 35)
As per the given expression,
The discounted price before tax = x - 35
The amount of sales tax = 0.12x
Thus, the expression x - 35 represents the discounted price before tax and the expression 0.12x represent the amount of sales tax.
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Help please and thank you
The continuous rate of growth is 50 %,the initial population is 940 and at time t = 5 11451 bacteria will be there.
a)
A exponential function is represented as:
n(t) = n(0) e^kt
where k is the continuous rate of growth.
Given problem:
The number of bacteria in a culture is given by:
n(t) = 940 e^0.5t
on comparing k = 0.5
= 0.5*100%
= 50 %
b)
On comparing with exponential function with given function.
n(0) = 940
which is the initial population.
c)
At t = 5
n(5) = 940*e^0.5*5
= 940*e^2.5
= 940*12.1824
≈ 11451
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Which event is most likely to occur?
A. Rolling a multiple of 4 on an eight-sided die, numbered from 1 to 8.
B. Spinning a spinner divided into five equal-sized sections colored red/green/yellow/blue/purple and landing on blue or green or purple.
C. Winning a raffle that sold a total of 100 tickets if you buy 24 tickets.
D. Reaching into a bag full of 38 strawberry chews and 2 cherry chews without looking and pulling out a strawberry chew.
Answer:
winning a raffle ticket is more like to occur because there is much more chance (24tickets) to win
Step-by-step explanation:
Answer:
D
Step-by-step explanation:
A would be 1/4 because there are 2 multiples of 4 so it would be 2/8 which would simplify to 1/4
B would be 3/5 since it’s 3/5 possibilities
C would be 12/50 because it would simplify from 24/100 to that
D would be 19/20 because there are 38 strawberry chews and + 2 cherry chews = 40 so 38/40 or 19/20
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Solve for y.
y² +4y+4=0
Answer:
y=-2
Step-by-step explanation:
[tex]y^2+4y+4=0\\y^2+2y+2y+4=0\\(y^2+2y)+(2y+4)=0\\y(y+2)+2(y+2)=0\\(y+2)=0\\and \\(y+2)=0\\y=-2[/tex]
[tex]Proof:\\(-2)^2+4(-2)+4=0\\4+(-8)+4=0\\8-8=0\\0=0[/tex]
Miguel drove for 8 hours at a constant rate. He drove a total of 424 miles.
Donna also drove at a constant rate. This table shows the number of miles she had driven in different numbers of hours.
How do the unit rates compare?
Select from the drop-down menus to correctly complete the statement.
Miguel has a
Choose...
unit rate of change than Donna because
Choose...
is greater than
53 mph
.
Number of hours Total miles driven
3 144
6 288
9 432
Miguel has a higher unit rate of change than Donna because 53mph is greater than 48mph.
What is unit rate?The unit rate is used to show the relationship between the variables illustrated. Since Miguel drove for 8 hours at a constant rate and drove a total of 424 miles. The rate will be:
= 424 / 8
= 53 miles per hour.
The unit rate for Donna will be:
Miles / Time
= 144 / 3
= 48 miles per hour.
Therefore, Miguel has a higher rate.
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3/5 + 7/8 + 3/10 = plssss ghelp
Answer:
[tex]\frac{71}{40}[/tex]
or
71/40
Explanation:
[tex]\frac{3}{5} + \frac{7}{8} + \frac{3}{10}[/tex]
LCM (Least Common Multiple) of 5, 8, and 10 = 40
5 × 8 = 40
8 × 5 = 40
10 × 4 = 40
(8 × [tex](\frac{3}{5} )[/tex] ) + (5 × [tex](\frac{7}{8} )[/tex] ) + (4 × [tex](\frac{3}{10} )[/tex] )
[tex]\frac{24}{40} + \frac{35}{40} + \frac{12}{40}[/tex]
[tex]\frac{71}{40}[/tex]
How many people were surveyed for the bar graph below?
A. 17
B. 34
C. 21
D. 6
The number of people surveyed in the bar graph is 34
What is bar graph?The visual display of data (often grouped) in the shape of vertical or horizontal rectangular bars, with the length of the bars corresponding to the measure of the data, is called a bar graph.
How to find the number of people surveyedThe number of people surveyed is calculated by adding up the frequencies of each bar
The frequency shows the number of people using cell phones starting from zero cell phone user which is 1 to 6 cell phone users which is 5
The calculation
1 + 5 + 6 + 8 + 9 + 5 = 34
Hence the number people surveyed is gotten to be 34
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need help with both of these please. give 20 points
The following gives the variations:
m= -4p -----------> direct variation
r=9/t----------->indirect variation
n=(1/2)f----------->direct variation
u=2/z----------->indirect variation
The value of y when x=2 is -14
What are direct and indirect variations ?
One quantity directly changes in response to a change in another quantity, which is referred to as direct variation. This suggests that if one quantity increases, the other will follow suit and rise in proportion. In a similar manner, if one quantity declines, the other amount also declines.
When one parameter declines while the other rises or vice versa, this is known as inverse variation. This means that the magnitude or absolute value of one item decreases as the other quantity rises, resulting in a constant value for their product. This item is also referred to as the proportionality constant.
m= -4p -----------> direct variation
r=9/t----------->indirect variation
n=(1/2)f----------->direct variation
u=2/z----------->indirect variation
General equation for an indirect variation:
y = k/x
substitute y=7 and x= -4
7=k/-4
k=7*-4 = -28
To find y when x=2:
Substitute x=2 and k=-28 into the equation
y=-28/2 = -14
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For scores that are normally distributed with a mean score of 120 and a standard
deviation of 20.
1) What % of the data is between 80 and 160?
2) What % of the data is below 100?
3) 68% of the scores are between what scores?
4) Find the z-score for a score of 155.
5) Find the z-score for a score of 90.
6) Find a score that is 3 standard deviations above the mean.
7) Find a score that is 2.5 standard deviations below the mean
Answer:
Step-by-step explanation:
The standard normal distribution is a normal distribution of standardized values called z-scores. A z-score is measured in units of the standard deviation. For example, if the mean of a normal distribution is five and the standard deviation is two, the value 11 is three standard deviations above (or to the right of) the mean. The calculation is as follows:
x = μ + (z)(σ) = 5 + (3)(2) = 11
The z-score is three.
The mean for the standard normal distribution is zero, and the standard deviation is one. The transformation
z=x-u/o produces the distribution Z ~ N(0, 1). The value x comes from a normal distribution with mean μ and standard deviation σ.
A one-way data table summarizes
A. a single input's impact on the output of interest
B. values of the input cells that will cause the single output value to equal zero
C. multiple input's impact on a single output of interest
D. values of cells when not all of the model is observable on the screen
Answer:
A
Step-by-step explanation:
hope this helps! :) Hope you have. a great day
Examine the following typical corporate bond listing:
In the name column, NYTel is the abbreviated name of the company (New York Telephone) issuing the bond. What was the closing price of the bond? What was the dollar amount? (See attachments)
a. 101 3/4; $101,750
b. 7 1/4; $7250
c. 101 3/4; $1017.50
d. 107 1/4; $1072.50
Answer:
C. 101 3/4; $1017.50
Step-by-step explanation:
Correct on E2020!
please help due tomorrow
Given are the number of pens and + in students bag.
We can see from the dataset graph that -
for number of pens, 3 pens are found in maximum number of bags of students. So the modal number will be 3.for number of pencils, 9 pencils are found in maximum number of bags of students. So the modal number will be 9.Therefore -
the modal number number of pens will be 3.the modal number number of pencils will be 9.To solve more questions on mean, median and mode, visit the link below-
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HElP ME PLEASE AnYONE
Answer:
[tex]y=2x+3[/tex]
Step-by-step explanation:
We know that [tex]m=\frac{5-3}{1-0}=2[/tex] and that the [tex]y[/tex] intercept is 3.
helpppppppppppppppppppppppppppp
Answer:
[tex]\huge\boxed{\sf x = 5}[/tex]
Step-by-step explanation:
Given function:g(x) = -3x + 8
Given that, g(x) = -7
-7 = -3x + 8
Subtract 8 to both sides
-7 - 8 = -3x
-15 = -3x
Divide -3 to both sides
5 = x
OR
x = 5
[tex]\rule[225]{225}{2}[/tex]
Three-fourths of a number is one-eighth. Find the number.
Answer:
1/6
Step-by-step explanation:
Let x = number.
3/4 x = 1/8
Multiply both sides by 8.
8 × 3/4 x = 8 × 1/8
6x = 1
x = 1/6
Answer: 1/6
Find the values of x and y in the diagram below.
A graduate student wanted to estimate the average time spent studying among graduate students at her school. She randomly sampled graduate students from her school and obtained a hours/week. In the context of the problem, which of the following interpretation is correct?
A. There is a 99% chance that the average amount of time spent studying for all graduate students at this student's school is between 173 and 22.5 hours per week OH
b. Graduate Mudents at this student's school study between 173 and 22 5 hours per week 99% of all weeks during the year
C. At this student's school 99% of all graduate students study between 17 3 and 22.5 hours per week, on average
D. Approximately 99% of all random samples of graduate students from this school will give a mean number of hours studied per week between 172 and 225
E. We are 99% sure that the average amount of time spent studying among graduate students at this student's school is between 17.3 and 22 5 hours per week
The average amount of time spent studying among graduate students at this student's school is between 17.3 and 22.5 hours per week. which is the correct interpretation would be option (A).
What is the arithmetic mean?The arithmetic mean is defined as the ratio of the sum of observations to the total number of observations.
A graduate student wanted to determine the average time spent studying between many graduate students at her school. She took a random sample of graduate students from her school and obtained an hour per week.
In the context of the problem,
We are 99% sure that the average amount of time spent studying among graduate students at this student's school is between 17.3 and 22.5 hours per week.
Therefore, the correct interpretation would be option (A).
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The fraction is between 1/2 and 3/4.
Write down all the possible values of n. Optional working
n =
The possible fraction n is n = 5/8
How to determine the possible fraction?From the question, we have the following statement that can be used in our computation:
The fraction is between 1/2 and 3/4.
This fraction is represented by n
So, we have
n is between 1/2 and 3/4.
The fractions 1/2 and 3/4 can be rewritten as
1/2 = 4/8
3/4 = 6/8
This means that
n is between 4/8 and 6/8
The number 5 is between 4 and 6
So, we have
5/8 is between 4/8 and 6/8
This means that
n = 5/8
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Which is the correct way to model the equation Negative x + 8 = 7 x + (negative 8) using algebra tiles? 1 positive x-tile and 8 positive unit tiles on the left side; 7 positive x-tiles and 8 positive unit tiles on the right side 8 positive unit tiles on the left side; 7 positive x-tiles and 8 negative unit tiles on the right side 1 negative x-tile and 8 positive unit tiles on the left side; 7 positive x-tiles and 8 negative unit tiles on the right side 8 positive x-tiles and 1 negative unit tile on the left side; 8 negative x-tiles and 7 positive unit tiles on the right side
The correct way to model the equation -x + 8 = 7x + (-8) is given by the option shown as follows:
1 negative x-tile and 8 positive unit tiles on the left side; 7 positive x-tiles and 8 negative unit tiles on the right side.
How to model the equation?The equation is modeled according to the signals of each coefficient, with:
Negative terms are modeled by negative tiles.Positive terms are modeled by positive tiles.The equation in this problem is given as follows:
-x + 8 = 7x + (-8).
Then the tiles of each term are:
-x -> 1 negative x - tile. -> left side.8: 8 positive tiles on the left side.7x: 7 x-tiles on the right side.+ (-8) = - 8 -> 8 negative x-tiles on the right side.More can be learned about equations at https://brainly.com/question/24808124
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A t-shirt increased in price by 1/4
After the increase it was priced at £65.
What was the original price of the t-shirt?
Answer:
£52 was the original price
Step-by-step explanation:
I need help with this
The option that can be used to verify the trigonometric identity, [tex]tan\left(\dfrac{x}{2}\right)+cot\left(x \right) = csc\left(x \right)[/tex] is option C;
C. [tex]tan\left(\dfrac{x}{2} \right) + cot\left(x \right) = \dfrac{1-cos\left(x \right)}{sin\left( x \right)} +\dfrac{cos \left(x \right)}{sin\left(x \right)} =csc\left(x \right)[/tex]
What is a trigonometric identity?A trigonometric identity is an equations that consists of trigonometric functions that remain true for all values of the argument of the functions
The specified identity is presented as follows;
[tex]tan\left(\dfrac{x}{2} \right)+cot(x)=csc(x)[/tex]
The half angle formula for tangent indicates that we get;
[tex]tan\left(\dfrac{1}{2} \cdot \left(\eta \pm \theta \right) \right) = \dfrac{tan\left(\dfrac{1}{2} \cdot \eta \right)\pm tan\left(\dfrac{1}{2} \cdot \theta \right)}{1 \mp tan\left(\dfrac{1}{2} \cdot \eta \right)\times tan\left(\dfrac{1}{2} \cdot \theta \right)}[/tex]
[tex]\dfrac{tan\left(\dfrac{1}{2} \cdot \eta \right)\pm tan\left(\dfrac{1}{2} \cdot \theta \right)}{1 \mp tan\left(\dfrac{1}{2} \cdot \eta \right)\times tan\left(\dfrac{1}{2} \cdot \theta \right)}=\dfrac{sin \left(\eta\right) \pm sin\left(\theta \right)}{cos \left(\eta \right) + cos \left(\theta \right)} = -\dfrac{cos \left(\eta\right) - cos\left(\theta \right)}{sin \left(\eta \right) \mp sin \left(\theta \right)}[/tex]
When η = 0, we get;
[tex]-\dfrac{cos \left(0\right) - cos\left(\theta \right)}{sin \left(0 \right) \mp sin \left(\theta \right)}=-\dfrac{1 - cos\left(\theta \right)}{0 \mp sin \left(\theta \right)}=\dfrac{1 - cos\left(\theta \right)}{sin \left(\theta \right)}[/tex]
Therefore;
[tex]tan\left(\dfrac{x}{2} \right)=\dfrac{1 - cos\left(x \right)}{sin \left(x \right)}[/tex]
[tex]cot\left(x \right) = \dfrac{cos(x)}{sin(x)}[/tex]
[tex]tan\left(\dfrac{x}{2} \right)+cot(x)= \dfrac{1 - cos\left(x \right)}{sin \left(x \right)} +\dfrac{cos(x)}{sin(x)}[/tex]
[tex]\dfrac{1 - cos\left(x \right)}{sin \left(x \right)} +\dfrac{cos(x)}{sin(x)}=\dfrac{1-cos(x)+cos(x)}{sin(x)} = \dfrac{1}{sin(x)}[/tex]
[tex]\dfrac{1 - cos\left(x \right)}{sin \left(x \right)} +\dfrac{cos(x)}{sin(x)}=\dfrac{1}{sin(x)}=csc(x)[/tex]
Therefore;
[tex]tan\left(\dfrac{x}{2} \right)+cot(x)= \dfrac{1 - cos\left(x \right)}{sin \left(x \right)} +\dfrac{cos(x)}{sin(x)} = csc(x)[/tex]
The correct option that can be used to verify the identity is option C
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Ethan did a maths test marked out of 80 and got 92.5% correct. He also
did an English test marked out of 64 and got 18.75% correct.
How many more marks did Ethan get in the maths test than the English
test?
Answer:
[tex]62[/tex]
Step-by-step explanation:
based on the given:
(Note: of ⟹ multiplication, percentage ⟹ ÷100, the number of marks he got in math more than English ⟹ the value he got in math minus the value he got in English)
Moving on, for math test:
80 × 92.5/100 = 74
For English test:
64 × 18.75/100 = 12
Now, the number of marks he got in math more than English ⟹ 74 - 12 = 62
Therefore, final answer is 62
I hope this helpsThe sum of three consecutive even numbers is 120. What is the smallest of the three numbers?
Answer:
Step-by-step explanation:
the consecutive are 39,40,41 and the smallest here is 39
Hope this helped
Four and two thirds plus seven ninths
Answer:
5 and two ninths
Step-by-step explanation:
Answer:
4/3=4*3+3*3=12/9+7/9=19/9
Step-by-step explanation:
En fait il faut le mettre au même dénonminateur puis additionner les numérateur.
The ratio of men to women at a college is 7 to 5. how many women students are there if there are 350 men?
Mark on the number line with a cross the fraction of the
shape from
(a) that is shaded.
b) Mark on the number line with a cross the fraction of the shape from (a) that is shaded.
a)
5/8
Step-by-step explanation:
ok hope it will help you thanks for watching hope it will happen
find the sum of the AP 1 + 3 ½/2 +6.... 101
Answer:
2091
Step-by-step explanation:
[tex]1+3.5+6+\cdots+101 \\ \\ n=\frac{101-1}{2.5}+1=41 \\ \\ a=1 \\ \\ d=2.5 \\ \\ S=\frac{41}{2}[2(1)+(41-1)(2.5)] \\ \\ =2091[/tex]
The —-
of a quadratic equation is ax² +bx+c = 0, where a 0 and a, b, and care integers
The degree of the quadratic equation, ax² +bx+c = 0 will be 2.
What is a quadratic equation?Any equation of the form ax² +bx+c = 0 where x is variable and a, b, and c are any real numbers where a ≠ 0 is called a quadratic equation. Any function of the form of the given form where x is variable and a, b, and c are any real numbers where a ≠ 0 is called a quadratic function.
It is given that the equation is,
ax² +bx+c = 0
The highest power of the quadratic equation is the degree to that quadratic equation. The highest power of the given quadratic equation is 2.
Thus, the degree of the quadratic equation, ax² +bx+c = 0 will be 2.
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need help pls thank you
a) The value of b if the total number of students is 55 is; b = 8
b)i) Probability that the student passed both french and german is 19/55
ii) Probability that the student passed exactly one of the two subjects is; 36/55
How to interpret Venn Diagrams?A venn diagram is used to compare and contrast two different ideas.
We are given that;
Number of students that passed French only = 17
Number of students that passed German only = 11
Number of students that passed both French and German = 19
Number of students that did not pass any of the 2 subjects = b
Total number of students = 55
Thus;
a) To get the value of b that will represent the number of students who didn't pass any of the 2 subjects will be calculated as;
b = 55 - (17 + 11 + 19)
b = 8
b)i) To get the probability that the student passed both french and german is given by the formula;
P(Paased french and german) = Number that passed french and german/Total number of students = 19/55
ii) To get the Probability that tells us the student passed exactly one of the two subjects is;
(17/55) + (19/55) = 36/55
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the dimensions of a square are altered so that one dimension is increased by 5ft while the other is decreased by 3ft. the area of the resulting rectangle is 84ft squared. what is the perimeter of the original square
The perimeter of the original square is 36 ft.
What is rectangle?A rectangle is a part of a quadrilateral, whose sides are parallel to each other and equal.
Let the side of square is x,
When one side is increased by 5 ft, the side = 5+x,
And other side is decreased by 3 ft, the side = x-3.
Also given that, the area of rectangle = 84 square ft
The area of rectangle = length×width
84 = (5+x)×(x-3)
By solving the equation, the value of x is 9,
Therefore, the side of the square is 9 ft
Perimeter of the square = 4x = 4×9 = 36 ft
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