Are the following two matrices inverses of one
another? (Urgent please help)
A=[ 4 2] B= [ -4 -2]
[-11 -6] [ 11 7]
a)Yes, because they are opposites.
b)Yes, because their product is equal to the
identity matrix
c)No, because they are not opposites.
d)No because their product is not equal to the matrix
Answers
Answer: D
Step-by-step explanation:
![Are The Following Two Matrices Inverses Of Oneanother? (Urgent Please Help)A=[ 4 2] B= [ -4 -2] [-11](https://i5t5.c14.e2-1.dev/c-qa-images/answers/attachments/N7tqNVeKzyqpBGrsHIXpQLEsjYTMhTZu.png)
The correct answer is d) No because their product is not equal to the identity matrix.
The matrices are given in the question as follows:
[tex]A= \left[\begin{array}{ccc}4&2\\-11&-6\end{array}\right] \\B= \left[\begin{array}{ccc}-4&-2\\11&6\end{array}\right][/tex]
To determine if two matrices are inverses of each other, we need to check if their product is equal to the identity matrix.
Let's calculate the product of matrices A and B:
[tex]A{\times}B = \left[\begin{array}{ccc}4\times-42+2\times11&4\times-2+2\times6\\-11\times-4+(-6\times11)&-11\times-2-6\times6\end{array}\right][/tex]
Simplifying the calculations to get:
[tex]A{\times}B = \left[\begin{array}{ccc}6&4\\-22&-14\end{array}\right][/tex]
The resulting matrix is not equal to the identity matrix:
[tex]A{\times}B = \left[\begin{array}{ccc}1&0\\0&1\end{array}\right][/tex]
Therefore, matrices A and B are not inverses of each other.
The correct answer is d) No because their product is not equal to the identity matrix.
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Related Questions
You invest $2,800 in an account that pays an interest rate of 6.5% compounded continuously calculate the balance of your account after 19 years. Round your answer to the nearest hundredth
Answers
Answer:
$9627.46
Step-by-step explanation:
-The amount after 19 years for a 6.5% compounded continuously is given by the formula:
[tex]A=Pe^{rt}[/tex]
Where:
A is the final amount after investment
P is the initial amount invested
r is the stated annual interest rate.
t is period of investment
#We then substitute our values in the equation to solve for A:
[tex]A=Pe^{rt}\\\\=2800e^{19\times 0.065}\\\\=9627.46[/tex]
Hence, the amount after 19 years is $9,627.46
The lifespans of lizards in a particular zoo are normally distributed. The average lizard lives 3.1 years; the standard deviation is 0.6 years. Use the empirical rule (68-95-99.7%) to estimate the probability of a lizard living longer than 2.5 years.
(Please help!!)
Answers
Answer:
84%
Step-by-step explanation:
Using the formula of z=(x-mean)/standard deviation. You get a z score of -1. Given the Empirival rule, 68% of all the values fall within 1 standard deviation. So the remaining 32% of values fall outside of this range. Since we have a negative 1, we only care about the lower half or 16%. In context of the problem this means that 16% of the all lizards live less than 2.5 years, so since the questions asks the opposite, we just subtract that value from 100%. 100-16=84
I need help. Look at picture
Choose 1 answer:
A. -4.63 x 10^13
B. -28.7
C. -1.65
D. -0.14
Answers
y = 6x - 14
y = - 8x
Answers
Answer:
x = 1 and y = -8x
Step-by-step explanation:
Answer:
{y,x} = {-8,1}
Step-by-step explanation:
Solve by Substitution :
// Solve equation [2] for the variable y
[2] y = -8x
// Plug this in for variable y in equation [1]
[1] (-8x) - 6x = -14
[1] - 14x = -14
// Solve equation [1] for the variable x
[1] 14x = 14
[1] x = 1
// By now we know this much :
y = -8x
x = 1
// Use the x value to solve for y
y = -8(1) = -8
Solution :
{y,x} = {-8,1}
find the slope of the line (-3,-3) (1,1)
Answers
Answer: The slope is m = 1
Step-by-step explanation:
-To find the slope, you need the slope formula:
[tex]m=\frac{y2-y1}{x2-x1}[/tex] where you have [tex](x1,y1)[/tex] and [tex](x2,y2)[/tex] on the equation.
-Next, you put the two points to the equation:
[tex]m=\frac{1+3}{1+3}[/tex]
-And then you solve the equation:
[tex]m=\frac{1+3}{1+3}[/tex]
[tex]m=\frac{1+3}{1+3} = \frac{4}{4}=1[/tex]
[tex]m=1[/tex]
The slope of line having (-3,-3) (1,1) as points is 1 .
Given,
Points: (-3,-3) (1,1)
To find the slope, you need the slope formula:
m = y2 -y1 /x2 - x1
Here,
(x1 , y1 ) = (-3,-3)
(x2 , y2) = (1,1)
So,
Substitute the values in slope formula ,
m = y2 -y1 /x2 - x1
m = 1 - (-3)/1 - (-3)
m = 4/4
m = 1
Thus the slope of line is 1 .
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Un local de Santa Bárbara fue pintado por 4 personas emprendedoras que se unieron para montar un negocio de lácteos; Juan, Pedro, Carlos y Mario; Juan pintó 2/7 del local, Pedro pintó 5/14 y Carlos pintó 2/14; ¿qué fracción pintó Mario?
Answers
Answer:
The proportion of premises painted by Mario is [tex]\frac{3}{14}[/tex].
Step-by-step explanation:
The question is:
A local in Santa Bárbara was painted by 4 enterprising people who got together to start a dairy business; Juan, Pedro, Carlos and Mario; Juan painted 2/7 of the premises, Pedro painted 5/14 and Carlos painted 2/14; What fraction did Mario paint?
Solution:
Consider the proportion of the total premises painted is 1.
The four enterprising people who got together to start a dairy business are:
Juan (J), Pedro (P), Carlos (C) and Mario (M).
The proportion of premises painted by Juan is:
[tex]P(J)=\frac{2}{7}[/tex]
The proportion of premises painted by Pedro is:
[tex]P(P)=\frac{5}{14}[/tex]
The proportion of premises painted by Carlos is:
[tex]P(C)=\frac{2}{14}[/tex]
Compute the proportion of premises painted by Mario as follows:
P (M) = 1 - P (J) - P (P) - P (C)
[tex]=1-\frac{2}{7}-\frac{5}{14}-\frac{2}{14}\\=\frac{14-4-5-2}{14}\\=\frac{3}{14}[/tex]
Thus, the proportion of premises painted by Mario is [tex]\frac{3}{14}[/tex].
The circumference of a circle is 31.4 miles. What is the circle's radius?
Answers
Answer:
About 5 miles or 4.9974 miles
Step-by-step explanation:
Formula: C = 2*π*r
31.4 miles = 2*π*r
Solve for r, the radius
r = 31.4 / 2*π = 4.9974 miles or about 5 miles
NEED HELP ASAPPP !! find the y-intercept of the line of the graph.
Answers
Answer:
the Y intercept is (0,-2)
Step-by-step explanation:
It is the point on the graph which the line goes through the Y axis
Kinleigh makes gift baskets to sell. The first day she made 3 baskets. Each day she plans on making 2 more baskets than the previous day. If there are 12 total work days until the day she begins to sell the baskets, how many total baskets will she have to sell?
Answers
Answer:
168 baskets
Step-by-step explanation:
i did it the dumb way and just did 3+5+7+9+11+13+15+17+19+21+23+25 = 168
Consider this study: A New York Times article published on April 24, 2007, reported the research of Dr. Giorgio Vallortigara, a neuroscientist at the University of Trieste, Italy, and his two colleagues. The researchers asked whether a dog wags its tail in a preferred direction in response to positive stimuli and in another direction in response to negative stimuli. To answer their question, they recruited 30 dogs that were family pets. Filming each dog from above, they allowed it to view (through a slat in its cage) three positive stimuli separately, in order of descending positivity: its owner, an unfamiliar human, and a cat. All the dogs responded by wagging their tails to the right. But when the dogs were presented with an unfamiliar, aggressive dog, a negative stimulus, all dogs wagged their tails to the left. Which of the following statements is the research hypothesis for this study?
a. A dog's tail will wag differently in response to positive stimuli and to negative stimuli.b. A dog's tail will wag more to the left in response to positive stimuli and more to the right in response to negative stimuli.c. A dog's tail will wag more to the right in response to positive stimuli and more to the left in response to negative stimuli.d. There will be no difference in a dog's tail wagging while viewing positive and negative stimuli.
Answers
Answer:
a. A dog's tail will wag differently in response to positive stimuli and to negative stimuli.
Step-by-step explanation:
A research hypothesis is a proposition that can be tested about the possible outcome of a study based on different stimuli.
A research hypothesis is a specific, clear, and testable proposition or predictive statement about the possible outcome of a scientific research study based on a particular property of a population, such as presumed differences between groups on a particular variable or relationships between variables.
Before a quantitative study takes place, it is important to state the research hypothesis because it is very important to the study.
There is usually an expectation or predicted outcome of the study because the research is determined by the hypothesis.
So it was already hypothesised that a dog would wag its tail in a preferred direction when it is faced with negative or positive stimuli. So the hypothesis was tested as different sets of dogs were placed in a cage and introduced to different stimuli.
From the observation of the researchers, all the dogs wagged their tails to the right when they saw a familiar face (positive stimuli) and wagged their tails to the left when they faced an aggressive dog (negative stimuli)
4x - 9y = -21
- 4x – 3y = 9
Answers
Answer:
(-3,1)
y= 1
x= -3
Step-by-step explanation:
4x-9y=-21
-4x-3y=9
solve the equation
4x=-21+9y
-4x-3y=9
substitute the value of 4x onto an equation
-1(-21+9y)-3y=9
multiply -1 to the numbers in parenthesis
-21+-9-3y=9
add -9 to 9 and put the negative on nine as a positive.
-21-3y=18
add -21 to 18 but since 21 is a negative the equation is subtraction.
-3y=-3
divide Both sides by -3
y=1
substitute the value of y into an equation
-4x-3•1=9
multiply 3 to 1
-4x-3=9
put -3 as a positive and add 3 to 9
-4x=12
divide both sides by -4
x= -3
(-3,1)
The solution for x and y in the given equations is x = 27 and y = 11.
Let's consider the second equation, -x + 3y = 6, and rewrite it in the form ax + by = c.
To get the equation in the required form, we'll rearrange the terms:
-x + 3y = 6
Add x to both sides:
3y = x + 6
Now, subtract 6 from both sides:
3y - 6 = x
This equation can be rewritten in the form ax + by = c by swapping sides:
x = 3y - 6
Now, let's substitute this expression for x into the first equation: 4x - 9y = 9.
4x - 9y = 9 becomes 4(3y - 6) - 9y = 9.
Simplify the equation: 12y - 24 - 9y = 9.
Combine like terms: 3y - 24 = 9.
Add 24 to both sides: 3y = 33.
Divide both sides by 3: y = 11.
Substitute y = 11 into x = 3y - 6: x = 3 × 11 - 6.
Calculate: x = 33 - 6 = 27.
Therefore, the solution for x and y in the given equations is x = 27 and y = 11.
Complete Question:
4x-9y=9; -x+3y=6 Rewrite one of the two equations above in the form ax + by = c, where a, b, and c are constants, so that the sum of the new equation and the unchanged equation from the original system results in an equation in one variable.
If the smaller pyramid has a surface area of 25.49 ft2, what is the surface area of the larger pyramid? Round to the nearest hundredth.
height 6 small pyramid
height 15 large pyramid
Answers
Answer:
[tex]A = 159.31\,ft^{2}[/tex]
Step-by-step explanation:
Let consider that both pyramid are simmilar. The surface area of the pyramid is directly proportional to the square of the height is:
[tex]A = (25.49\,ft^{2})\cdot \left(\frac{15\,ft}{6\,ft} \right)^{2}[/tex]
[tex]A = 159.31\,ft^{2}[/tex]
what is the volume in cubic ft of a rectangular prism with a height of 17ft a width of 13 ft and a length of 12ft
Answers
Answer:
The answer is 2652 ft^3 (cubed)
Step-by-step explanation:
To find the volume of a rectangular prism, you need to multiply base X height or Bh.
1. Multiply length by width12 X 13 = 156 ft^2 (squared)2. Multiply base by height156 ft (squared) X 17 ft = 2652 ft^3 (cubed)Answer:2654
Step-by-step explanation:
30 points and brainliest
Answers
Answer:A
Step-by-step explanation:
Because 4 is negative and would go left and 5 is positive so it would go up
David is a car salesman. He earns a salary of $750 a month, plus a commission of $300 per car that he sells. David needs to earn a minimum of $3,500 per month. write an inequality, for the number of sales he needs to make.
Answers
Answer:
3500-750=2750
2750/300=9.1677
he gets 750 per month .. this means he is sure to get $750 every month.. so he already have $750 out of the 3500 so I subtract it... and 300 per car ,so I divide it , so that I can get the amount of car he needs to sell to get 3500
The inequality representing the minimum number of cars David needs to sell to earn at least $3,500 per month is x>=10, with x being the number of cars sold.
To determine the inequality for the number of sales David needs to make to earn a minimum of $3,500 per month, we consider his monthly income which includes a base salary and commission for cars sold. David earns a base salary of $750 plus a commission of $300 for each car he sells. Let's denote the number of cars David sells in a month as x.
The total monthly income David gets from commission by selling x cars is $300x. So, the total monthly income David earns is $750 (base salary) plus $300x (commission from sales), or $750 + $300x in total.
Since David needs to earn at least $3,500 monthly, his total monthly income must be greater than or equal to $3,500. We can represent this as the following inequality:
$750 + $300x >=$3,500
To find the minimum number of cars David needs to sell, we now solve for x:
Subtract $750 from both sides: $300x >=$2,750.Divide both sides by $300: x >=9.17.Since David cannot sell a fraction of a car, he needs to sell at least 10 cars to meet his financial goal.
Therefore, the inequality for the number of sales David needs to make at least $3,500 per month is x >=10.
Avery has a new job making smoothies at jumble juices.She got her first paycheck for 2 weeks of work.Her gross income was $450.Jumble juices withheld $58.50 in federal income tax and $26.70 in other taxes.What is avery's net income for the two weeks?
Answers
Answer:
$364.8
Step-by-step explanation:
To find the net income, we subtract deductions from the gross income. Deductions mainly include federal taxes/PAYE, NHIF, NSSF, Morgage loans. Therefore expressed as
Net income= Gross income- Deductions
Given information
Gross income=$450
Deductions
$58.5+$26.7=$85.2
Net salary will be $450-$85.2=$364.8
Therefore, rhe net salary will be equivalent to $364.8
A student draws the net below to show the dimensions of the container that is shaped like a right rectangular prism. What is the surface area , in square inches of the container?
Answers
Answer:
The correct option is;
D) 62 in²
Step-by-step explanation:
Here we have from the drawing, the dimensions of the right rectangular prism are;
Height = 2 in.
Width = 5 in
Length = 3 in
Therefore the surface area is found as follows;
Surface area of right rectangular prism = 2 × Height × Width + 2 × Height × Length + 2 × Width × Length
Surface area of right rectangular prism = 2 × 2 × 5 + 2 × 2× 3+ 2 × 5× 3 = 20 + 12 + 30 = 62 in².
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Mimi opened a savings account 6 years ago. The account earns 1% interest, compounded monthly. If the current balance is $1,000.00, how much did she deposit initially?
Round your answer to the nearest cent.
Answers
Answer: the initial amount is $941.6
Step-by-step explanation:
We would apply the formula for determining compound interest which is expressed as
A = P(1 + r/n)^nt
Where
A = total amount in the account at the end of t years
r represents the interest rate.
n represents the periodic interval at which it was compounded.
P represents the principal or initial amount deposited
From the information given,
A = $1000
r = 1% = 1/100 = 0.01
n = 12 because it was compounded 12 times in a year.
t = 6 years
Therefore,.
1000 = P(1 + 0.01/12)^12 × 6
1000 = P(1 + 0.00083)^72
1000 = P(1.00083)^72
1000 = 1.062P
P = 1000/1.062
P = $941.6
Dracula's mortgage payment was $1,250 is automatically deducted from his paycheck each month. His company has decided to pay his mortgage as a bonus for the next 17 months. Dracula removes his mortgage deduction from his monthly paychecks. How much money does Dracula gain from this bonus?
Answers
Answer:
He will $21250
Step-by-step explanation:
If $1250 will be paid from Dracula bonus for the next 17 month, then on this paycheck, he will gain
17*1250 = $21250
how to find the volume of a right rectangular prism
Answers
Answer: i believe it's v=whl... is this correct?
Step-by-step explanation:
what is the answer to log100
Answers
Answer:
the answer is 2
Step-by-step explanation:
Answer:
2
Step-by-step explanation:
Helllllllllppppp plllllsssss
Ryder found the volume of the figure below by using the steps shown.
A rectangular prism with a length of 40 millimeters, width of 30 millimeters, and height of 5 millimeters. A rectangular pyramid with a base of 30 millimeters by 40 millimeters and a height of 95 millimeters.
Total Volume = B h + one-half B h
Equals 5 (40) (3) + one-half (40) (30) (95)
Equals 6,000 + 57,000
Equals 63,000 cubic millimeters
What mistake, if any, did Ryder make?
Ryder determined the volume correctly.
Ryder used the wrong formula for the total volume.
Ryder used the wrong height for the pyramid.
Ryder did not apply the order of operations correctly.
Answers
The total volume of the figure is 44000 mm³. Ryder used the wrong formula for the total volume.
The composite figure is formed by combinning pyramid and a rectangular prism.
Volume of a rectangular prismvolume of rectangular prism = Bh
where
B = base areah = height of the rectangular prismVolume of a rectangular pyramidvolume of rectangular pyramid = 1 / 3 Bh
where
B = base areah = height of the pyramidTherefore, the total volume is as follows:
total volume = Bh + 1 / 3 Bh
total volume = 40 × 30 × 5 + 1 / 3 (30 × 40) × 95
total volume = 6000 + 1 / 3 (114000)
total volume = 6000 + 38000
total volume = 44000 mm³
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help someone ???
its due today
Answers
Answer:
y = 3/5
Step-by-step explanation:
Step 1: Flip the equation.
−5y=−3
Step 2: Divide both sides by -5.
After dividing both sides by 5, they should cancel out, leaving you with 3/5.
Nasim is making hot sauce. She puts in chile peppers and tomatoes in a ratio of 1 to 3. If she puts in 9 tomatoes, how many chile peppers should she put in?
Answers
Answer: 3
Step-by-step explanation:
Nasim is making hot sauce. Nasim puts in chile peppers and tomatoes in a ratio of 1 to 3.
Assuming Nasim puts in 9 tomatoes, the number of chile peppers should she put will be:
Ratio of chile peepers to tomato= 1;3
Since she put 9 tomatoes, chile peppers= (1×9)/3 = 9/3 = 3.
For 1 chile peeper, there'll be 3 tomatoes.
For 3 chile pepper, thee will be 9 tomatoes.
Answer: She needs to add 3 chile peppers.
Step-by-step explanation:
The ratio of chile peppers to tomatoes is 1:3
this means that for each 3 tomatoes, she puts one chile pepper.
Then if she puts 9 tomatoes, this means that she puts 3 tomatoes 3 times.
And we know that for each 3 tomatoes she needs to add 1 chile pepper, then she needs to add 1 chile pepper 3 times:
3*1 = 3 chile peppers.
She needs to add 3 chile peppers.
if m∠XAB = 32, what is m∠BAC?
A.) 16
B.) 58
C.) 64
D.) 32
Answers
Answer:
the answer is c
Step-by-step explanation:
the picture in the attached figure
we know that
The construction shown is an angle bisector
m<XAB=m<CAX
so
m<BAC=2*[m<XAB]-----> 2*32°----->m<BAC= 64°
PLZ HELP ASAP GEOMETRY
Answers
Answer:
D.
Step-by-step explanation:
Edgardo has a drink cooler that holds 4 gallons of water. He is filling the cooler with a 1−quart container. How many times will he have to fill the quart container to fill the cooler?
Answers
Answer:
16 times
Step-by-step explanation:
Given:
Edgardo has a drink cooler that holds 4 gallons of water.
He is filling the cooler with a 1−quart container.
Question asked:
How many times will he have to fill the quart container to fill the cooler?
Solution:
Capacity of container = 1 quart
As we know:
1 quart = 0.25 gallon
Edgardo has to fill drink cooler having capacity of 4 gallons.
0.25 gallon is filled by filling the container = 1 time
1 gallon is filled by filling the container = [tex]\frac{1}{0.25}[/tex] times
4 gallons is filled by filling the container = [tex]\frac{1}{0.25}\times4=16\ times[/tex]
Thus, he will have to fill the quart container 16 times to fill the cooler.
Stephanie wants to check if the top of a side table she saw for sale is perfectly rectangular. She measured the dimensions of the table and found the following:
Length of table: 15 inches
Width of table: 7.5 inches
Diagonal length of table: 17 inches Is the table perfectly rectangular?
Answers
Using the Pythagorean theorem to check for a right angle, Stephanie's table measurements of 15 inches by 7.5 inches with a diagonal of 17 inches do not satisfy the theorem. Hence, the table is not perfectly rectangular.
To determine if Stephanie’s table is perfectly rectangular, we can apply the Pythagorean theorem, which states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. If the table is perfectly rectangular, the diagonal should be the hypotenuse of a right triangle formed by the length and width of the table.
The formula for the Pythagorean theorem is “a2 + b2 = c2”, where c is the hypotenuse, and a and b are the other two sides of the triangle. For Stephanie’s table: Length (“a”) = 15 inches, Width (“b”) = 7.5 inches, and Diagonal length (“c”) = 17 inches.
Let’s calculate it:
a^2 = 15^2 = 225
b^2 = 7.5^2 = 56.25
c^2 = 17^2 = 289
Add a2 and b2 together:
225 + 56.25 = 281.25
Since 281.25 is not equal to 289, the table is not perfectly rectangular because the measurements do not satisfy the Pythagorean theorem.
The table is not perfectly rectangular because the measured diagonal does not satisfy the Pythagorean Theorem with the given length and width.
To determine if Stephanie's table is perfectly rectangular, we can use the Pythagorean Theorem, which states that for a right-angled triangle, the square of the length of the hypotenuse (diagonal) is equal to the sum of the squares of the other two sides.
Let's denote:
Length (L) = 15 inches
Width (W) = 7.5 inches
Diagonal (D) = 17 inches
According to the Pythagorean Theorem:
D2 = L2 + W2
Now, substitute the given values:
172 = 152 + 7.52
289 = 225 + 56.25
289 = 281.25
Since 289 is not equal to 281.25, the table is not perfectly rectangular. Therefore, the measurements indicate that the table does not form a perfect rectangle.
What< and > this stand for??
Answers
Answer:
< lesser to
>greater to
Answer: < less than
> greater than
Step-by-step explanation: hope this helps!!!
Edith will be handing out school spirit ribbons in class on Monday. She needs 50 ribbons that are each 20 cm long — a total of 1,000 cm of ribbon — but the fabric store only sells ribbons by the meter.
How many meters of ribbon does Edith need?
A.
100,000 m
B.
1 m
C.
0.1 m
D.
10 m
Answers
Answer:
It would be 10 because 1000 cm equals 10 m
Enjoy :]
Step-by-step explanation:
Edith needs 10 meters of ribbon to make all 50 school spirit ribbons. To convert from centimeters to meters, we divide by 100. Therefore, 1,000 centimeters is equal to 10 meters.
Explanation:To answer how many meters of ribbon Edith needs, we first need to understand the relationship between centimeters and meters. In one meter, there are 100 centimeters. Thus, to convert centimeters to meters, we can divide by 100.
Edith needs a total of 1,000 cm of ribbon. In order to convert this to meters, we would do the following calculation: 1000 cm ÷ 100 = 10 meters.
So, the correct answer is D. 10 m. Edith needs to buy 10 meters of ribbon from the fabric store. This is necessary to have enough ribbon to make all 50 school spirit ribbons that are each 20 cm long.
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