Answers
The only matrix that is certainly symmetric is a)\((a^2 - b^2).\)
We know that a matrix A is symmetric if it is equal to its transpose, that is \(A = A^T.\)
a) \((a^2 - b^2)\)
We can write the transpose of this matrix as
\((a^2 - b^2)^T = (a^2)^T - (b^2)^T = a^2 - b^2\), which is equal to the original matrix. Therefore, this matrix is symmetric.
b) (A+B)(A-B)
Expanding this expression, we get \((A+B)(A-B) = A^2 - AB + BA - B^2.\)
Taking the transpose of this, we get \((A^2)^T - (AB)^T + (BA)^T - (B^2)^T = A^2 - BA + AB - B^2.\)
Since AB and BA may not be equal, we cannot say for certain that this matrix is symmetric.
c) ABA
Taking the transpose of this matrix, we get\((ABA)^T = A^T B^T A^T\). Since \(A^T and B^T\) may not commute, we cannot say for certain that this matrix is symmetric.
d) ABAB
Taking the transpose of this matrix, we get \((ABAB)^T = B^T A^T B^T A^T\). Again, since \(A^T and B^T\) may not commute, we cannot say for certain that this matrix is symmetric.
Therefore, the only matrix that is certainly symmetric is a) \((a^2 - b^2).\)
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Related Questions
Mr. Poplin asked his students to write the following expression: "Two to the fifth power plus seven squared" Which answer choice shows this expression? A 52 - 27 B (2-5) + (7.2) © 25-74 D 2572
Answers
Answer:
B
Step-by-step explanation:
they rest The two by five and separate the square
Here's a graph of a linear function. Write the
equation that describes that function.
xpress it in slope-intercept form.
Answers
Answer:
the slope intercept form is y = (1/2)x - 1
Step-by-step explanation:
The slope-intercept form is, y = mx + b
We see from looking at the graph that,
at x = 0, y = -1
So, from this we find that b = -1
at x = 2, y = 0,
now, we find the slope m,
using,
\(m = \frac{y_{2} -y_1}{x_2-x_1}\)
Using x_2 = 2, y_2 = 0,
x_1 = 0, y_1 = -1, we get,
m = (0-(-1))/(2-0)
m = 1/2
So, the slope intercept form is,
y = (1/2)x - 1
Which of the following is the best translation for the expression below?
2x - 5
Twice a number x minus five.
The difference of five and twice a number x.
Five more than twice a number x.
Twice the difference of five and x.
Answers
The best description of the numerical expression 2x - 5 is,
The difference of five and twice a number x.
What are some alternative names for arithmetic operations?Addition is also known as the sum, subtraction is also known as the difference, multiplication is also known as the product, and division is also known as the factor.
A mathematical statement expressed as a string of numbers and unknowable variables is known as a numerical expression. Statements can be used to create numerical expressions.
The statement to the numerical expression 2x - 5 would be
The difference of five and twice a number x.
As we can not use the statement twice a number x minus five because the term 'minus' can not be used.
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Do the side lengths 4, 8, and 10 form a triangle? Select the correct answer and reasoning. Question 11 options: A) Yes, because the sum of any two side lengths is greater than the third side length. B) No, because 4 + 8 is greater than 10. C) Yes, because the sum of all three side lengths is greater than 20. D) No, because the third side length is greater than the sum of the other two side lengths.
Answers
Answer:
A) Yes, because the sum of any two side lengths is greater than the third side length.
The triangle inequality theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. In this case, 4 + 8 = 12, which is greater than 10, and the other two combinations (4 + 10 and 8 + 10) also satisfy this rule. Therefore, the given side lengths do form a triangle.
Step-by-step explanation:
Find the polar coordinates of rectangular coordinates (-√2,1). Limit θ to the interval [0,2pi) and round 2 dceimal places if needed
Answers
The point (-√2,1) can also be represented as (√3, 5.18) in polar coordinates.
To find the polar coordinates of the rectangular coordinates (-√2,1), we can use the following formulas:
r = √(x² + y²)
θ = tan^⁻1(y/x)
Plugging in the given values of (-√2,1), we get:
r = √((-√2)² + 1²) = √(2 + 1) = √3
θ = tan^⁻1(1/(-√2)) ≈ 2.0344 radians
Note that since the point (-√2,1) is in the second quadrant, we need to add π to the value of θ obtained from the inverse tangent in order to obtain an angle in the interval [0,2π). Thus, we have:
θ ≈ 2.0344 + π ≈ 5.1779 radians
Rounding to 2 decimal places as needed, we get the polar coordinates of (-√2,1) as (r,θ) ≈ (√3, 5.18).
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A balloon filled with helium gas has a volume of 326 mL at a pressure of 1 atm. The balloon is released and reaches an altitude of 6.5 km, where the pressure is at 0.5 atm. Assuming that the temperature has remained the same, what volume does the gas occupy at the height? Answer in units of mL.
Answers
The volume of the gas at the height (i.e 6.5 Km) is 652 mL
Data obtained from the question\(\text{Initial volume} \ (\text{V}_1) = \text{326 mL}\)\(\text{Initial pressure} \ (\text{P}_1) = \text{1 atm}\)\(\text{Temperature = Constant}\)\(\text{Final pressure} \ (\text{P}_2) = \text{0.5 atm}\)\(\bold{Final \ volume \ (V_2) = \ ?}\)The final volume of the gas can be obtained by using the Boyle's law equation as shown below:
\(P_1V_1 = P_2V_2\)
\(1 \times 326 = 0.5 \times V_2\)
\(326 = 0.5 \times V_2\)
Divide both side by 0.5
\(V_2 = \dfrac{326}{0.5}\)
\(\boxed{\bold{V_2 = 652 \ mL}}\)
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Find unit rate $602 for 20 hours of work
Answers
Find the area of the figure pictured below.
15 yd
10 yd
17 yd
5 yd
A
Answers
First find the area of the square, then the triangle.
15 times 17 = 255 sq. yd
Triangle:
(5 times 5)/2 = 12.5 sq. yd
Your answer is 267.5 sq. yd
Hope this helps.
write 1/4 + 1/4+1/4+1/4+1/4+1/4+1/4 as a multiplication problem then find the product
Answers
9514 1404 393
Answer:
7(1/4) = 7/4 = 1 3/4
Step-by-step explanation:
Multiplication is used to simplify repeated addition. The multiplier represents the number of times the sum includes the repeated value.
Here, the term 1/4 appears in the sum 7 times. That means we can write the equivalent expression ...
7 × 1/4 . . . . written as a multiplication expression
The product is found by multiplying the numerator of the fraction by the integer factor.
7 × 1/4 = 7/4
This improper fraction can be written as a mixed number.
7/4 = 1 3/4 . . . . the value of the sum
Answer:
1/4 + 1/4+1/4+1/4+1/4+1/4+1/4
(1/4) x 7
Step-by-step explanation:
My name is Pauley the Parrot and I have a dilemma. Blackbeard found a
chest full of gold and he wanted to divide it evenly among the crew. The
chest weighed 12 pounds because it was filled to the top with gold. There
are 24 crew members (including myself and Blackbeard) on the boat. I told
him that if he gave each crew member 2 lbs. of gold there would be enough
to go around. Blackbeard said that he could give each crew member { lb of
gold and there would be enough to go around.
Can you help us figure out who is correct? Make sure to explain who was
correct, and why the other person was incorrect. Maybe, I can split my
earnings with you!
Thank you!
Pauley the Parrot
Answers
Answer:
bh
Step-by-step explanation:
You’re splitting the gold between the people, but there is less gold, so you would divide the number of people by the amount of gold. You get 0.5, so each person would get 0.5 lb.
what is the area of this shape? the answer isn't 92 cm squared
Answers
Answer:
80cm^2
Explanation:
Okay to do this, it's often better to find the area of each shape separately.
Let's start with the top rectangle:
4cm*7cm = 28cm^2
Bottom rectangle:
to find the length of it, we just add 3cm and 7cm which = 10cm
so:
10cm*4cm = 40cm^2
And finally the triangle:
to find the bottom side: 13cm - 7cm - 3cm = 3cm
to find the height: 4cm + 4cm = 8cm
so:
8cm*3cm*/2 = 24cm/2
= 12cm^2
Now we add them all up:
28 + 40 + 12 = 80cm^2
Answer:
Corrected Question:[ Refer to the above attachment ]
Solution:In the given figure there are two shapes:
A RectangleA TriangleFirst, we have to find the area of Rectangle ABGF & DCGE. After that, area of triangle CHB.
1) Area of Rectangle ABGF:
As, we know:
Formula for Area :-
★ Length × Breadth ★
where,
Length = FA = 4cm Breadth = GF = 10cm ( 7+3 )➝ 4 cm × 10 cm
➝ 40 cm²
Hence, the area of Rectangle ABGF is 40cm².
2) Area of Rectangle DCGE:
As, we know:
Formula for Area :-
★ Length × Breadth ★
where,
Length = ED = 4cm Breadth = DC = 7cm➝ 4 cm × 7 cm
➝ 28 cm²
Hence, the area of Rectangle DCGE is 28cm².
3) Area of Triangle CHB:
As, we know:
Formula for Area :-
★ ½ ( base × height ) ★
where,
Base = 3cm Height = 8cm➝ ½ ( 3cm × 8cm )
➝ ½ ( 24cm )
➝ ½ × 24cm
➝ 12 cm²
Hence the Area of Triangle CHB is 12cm².
Now, Area of Given Shape is:
➝ 40cm² + 28cm² + 12cm²
➝ 52cm² + 28cm²
➝ 80cm²
Thus, the area of the given shape is 80cm².
____________________Additional Information:[ Formula's for Area ]
★ Square = (Side)²
★ Rectangle = Length × Breadth
★ Triangle = ½bh
★ Circle = πr²
There are 63 students marching in a band, and they’re marching in 7 rows. How many students are in each row?
Answers
If red is = -1 and yellow is = +1
what problem and solution are modeled below?
A. - 5 + 8 = 3
B. -10 - 3 = -13
C. 10 + - 3 = 8
D. -8 + 5 = - 3
Answers
Answer:
D.
MARK ME BRAINLIEST CORRECT AMSWER IS GIVEN3. Write the following using exponential notation:
(5.
5.5.5.5.5.5.5.5.5) (7.7.7.7.7.7.7.7.7.7.7.7.7.7)
Answers
Answer:
5.5.5.5.5.5.5.5.5 in exponential notation is 5^9
7.7.7.7.7.7.7.7.7.7.7.7.7.7 in exponential notation is 7^13
Therefore, (5.5.5.5.5.5.5.5.5) (7.7.7.7.7.7.7.7.7.7.7.7.7.7) in exponential notation is:
5^9 * 7^13
Help please i mark brainliest !!!
Answers
Point slope form: y - y1 = m(x - x1)
y1 = y-point
m = slope
x1 = x-point
Using what we wrote above, we can solve the question.
y1 = -2
m = -2/3
x1 = 4
Therefore, the point is (4, -2) and the slope is -2/3
Best of Luck!
Bonnie has a container in the shape of a rectangular pyramid. The formula for the surface area of the enclosed space is S = lw + 0.5Ph. Solve for P.
P = S − lw − 0.5h
P = S + lw + 0.5h
P = The quantity S minus l times w all divided by 0.5 times h
P = S divided by the quantity l times w plus 0.5 times h
Answers
Answer:
Answer: P = The quantity S minus l times w all divided by 0.5 times h
Step-by-step explanation:
Hope this helps.
(ECONOMICS- sorry there’s no button for it )
What motivates producers and consumers in the black market
Answers
The motivations for producers and consumers in the black market are largely driven by financial incentives and a desire to avoid legal consequences.
The black market refers to the illegal trade of goods and services that are not permitted by law, such as drugs, counterfeit items, and stolen goods. Producers and consumers in the black market are motivated by a variety of factors, including:
High profits, Producers in the black market can earn higher profits than they would in legal markets due to the lack of regulation and taxes.
Escaping legal consequences: Producers and consumers may participate in the black market to avoid legal consequences, such as fines or imprisonment, for engaging in illegal activities.
Limited availability, Some goods and services are only available on the black market due to legal restrictions or limited supply.
Low prices, Consumers in the black market can often purchase goods and services at lower prices than in legal markets due to the lack of taxes and regulations.
Desire for anonymity, The black market can provide anonymity for both producers and consumers, allowing them to engage in illegal activities without fear of detection or retribution.
However, participating in the black market also comes with significant risks, including the possibility of arrest, fines, and even violence.
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please help ASAP if u can!! :))))
Answers
Answer:
the answer is 32cm squared
Step-by-step explanation:
The angle of elevation to the top of a Building in New York is found to be 5 degrees from the ground at a distance of 2 miles from the base of the building. Using this information, find the height of the building.
Answers
We are given:
Horizontal distance of the point of observation from the building = 2 miles
Angle of elevation of the building = 5 degrees
Finding the height of the Building:
Let the height of the building be x miles
In the given case, the following right-angled triangle will be formed
We know that: Tan(θ) = Opposite / Adjacent
So, Tan(5°) = x / 2
0.0875 = x/2 [since Tan(5°) = 0.0875 ]
x = 0.175 [Multiplying both sides by 2]
Height in Meters:
We know that 1 mile = 1609.344 meters
So, we can say that:
1609.344 meters / 1 mile = 1
Multiplying the height of the building by 1
0.175 miles * 1
since 1 = 1609.344 meters / 1 mile:
0.175*1609.344 meters
\(0.175 miles * \frac{1609.344 meters}{1 mile}\)
Here, the 'miles' in the numerator and the denominator will cancel out
281.6 meters
Hence, the height of the Building is 281.6 m OR 0.175 miles
When the coordinates (1, 1), (4,4), (7, 1), and (4, -2) are joined, which shape is formed?
Answers
Check the picture below.
someone pls help solve this
Answers
Answer:
`y = 2
y = -1
Step-by-step explanation:
Im not very good at explaining things im new at so all i can get s the answer
helo please show work
Answers
Answer:
Step-by-step explanation:
Solution:
We can simplify the ratio 305 : 60 by dividing both terms by the greatest common factor (GCF).
The GCF of 305 and 60 is 5.
Divide both terms by 5.
305 ÷ 5 = 61
60 ÷ 5 = 12
Therefore:
305 : 60 = 61 : 12
A family has two cars. The first car has a fuel efficiency of 25 miles per gallon of gas and the second has a fuel efficiency of 15 miles per gallon of gas. During one particular week, the two cars went a combined total of 1525 miles, for a total gas consumption of 75 gallons. How many gallons were consumed by each of the two cars that week?
Answers
first car is x
second car is y
25x+30y=1550
x+y=55
Multiply the second equation by -25 for elimination method to cancel out x
-25x-25y=-1375
Add the two equations
5y=175
y=35
Plug this value into the second equation
x+35=55
x=20
Final answers:
First car=20 gallons
Second car=35 gallons
Find the area of a regular heptagon with a side length of 14 units. Use 2 decimal places
in your calculations.
Answers
Answer:
Area of heptagon = 712.26 square units
Step-by-step explanation:
Given the following data;
Side length = 14 units
A heptagon is a polygon with seven sides.
Mathematically, the area of a heptagon is given by the formula;
Area of heptagon = 3.634a²
Where;
a represents the side length.
Area of heptagon = 3.634 * 14²
Area of heptagon = 3.634 * 196
Area of heptagon = 712.26 square units
Help me find the volume of the composite figure
Answers
Answer:
\(V = 97.911in^3\)
Step-by-step explanation:
Given
Shapes: Cube and Cone
Required
Determine the volume
First we calculate the volume of the cube
\(V_1 = l^3\)
Where
l = side length = 5.1
\(V_1 = 5.1^3\)
\(V_1 = 132.651\)
Next, calculate the volume of the cone using:
\(V_2 = \frac{\pi r^2h}{3}\)
Where
h = 5.1
\(r = \frac{1}{2} * Diameter\)
\(r = \frac{1}{2} * 5.1\)
\(r = 2.55\)
So, we have:
\(V_2 = \frac{\pi r^2h}{3}\)
\(V_2 = \frac{\pi * 2.55^2 * 5.1}{3}\)
\(V_2 = \frac{22 * 2.55^2 * 5.1}{7*3}\)
\(V_2 = \frac{729.5805}{21}\)
\(V_2 = 34.74\)
The volume of the figure is:
\(V=V_1 - V_2\)
\(V_1 = 132.651\)
\(V = 132.651 - 34.74\)
\(V = 97.911in^3\)
If an exterior angle of a regular polygon is 21.2º, how many sides does the polygon have?
Answers
Answer:
option 4. 17
Step-by-step explanation:
sum of angles = exterior angle x n
360° = 21.2° n
n = 360 / 21.2
n = 17
Number of sides of the regular polygon with exterior angle 21.2° is equals to 17 sides.
What is polygon?" Polygon is defined as the two dimensional geometric shape which has n number of finite sides."
Formula used
360° = (Exterior angle of polygon ) × ( number of sides of polygon)
According to the question,
Given,
Exterior angle of a regular polygon = 21.2º
'n' represents the number of sides
Substitute the value in the formula to get number of sides,
\(360\°= (21.2\°) (n)\)
⇒ \(n = \frac{360\°}{21.2\°}\)
⇒ \(n= 16.98\)
⇒ n≈ 17 sides
Hence, number of sides of the regular polygon with exterior angle 21.2° is equals to 17 sides.
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A shipping box is 36 inches by 24 inches by 18 inches
how many cubic feet can it hold
Answers
Answer:
To find the volume of the shipping box in cubic feet, we need to convert the dimensions from inches to feet and then calculate the volume.
Given:
Length = 36 inches
Width = 24 inches
Height = 18 inches
Converting the dimensions to feet:
Length = 36 inches / 12 inches/foot = 3 feet
Width = 24 inches / 12 inches/foot = 2 feet
Height = 18 inches / 12 inches/foot = 1.5 feet
Now, we can calculate the volume of the box by multiplying the length, width, and height:
Volume = Length * Width * Height
Volume = 3 feet * 2 feet * 1.5 feet
Volume = 9 cubic feet
Therefore, the shipping box can hold 9 cubic feet.
Step-by-step explanation:
First convert the units because it's asking for the cubic feet but they give us the measurements in inches.
To convert inches to feet we divide the number by 12.
36 ÷ 12 = 3
24 ÷ 12 = 2
18 ÷ 12 = 1.5
Now to find the volume, we multiply it all together.
3 × 2 × 1.5 = 9
It can hold 9 cubic feet.
Hope this helped!
Help what’s the answer
Answers
Answer:
Difference=£2.4
Step-by-step explanation:
Here in shop A
130 cm=£1.82
1 cm=£1.82/130
1 cm=0.014
Now
400 cm=0.014*400
=£5.6
Again, In shop B
235cm=£1.88
1 cm=£1.88/235
1 cm=£0.008
Now
400cm=0.008*400
=£3.2
Now,
Difference=£5.6-£3.2
=£2.4
Write 69200000 in scientific notation
Answers
69200000 in scientific notation is 6.92 × 10⁷.
How to represent number in scientific notation?Scientific notation is a form of presenting very large numbers or very small numbers in a simpler form.
Scientific Notation is a special way of writing numbers:
For example 800 is written as 8 × 10² in Scientific Notation.
Therefore, let's write the scientific notation of the number 69200000.
Hence,
69, 200, 000 = 6.92 × 10⁷
The logic is that we will count backwards until we meet the last number. Since we counted towards the left side, the exponent will be positive.
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Determine the point estimator you would use and calculate the value of the point estimate. Tonya wants to estimate what proportion of the seniors in her school plan to attend the prom. She interviews an SRS of 50 of the 750 seniors in her school and finds that 36 plan to go to the prom
Answers
According to the information provided, it should be noted that the 750 seniors in her school make up the population of interest, and the parameter of interest is the percentage of seniors who intend to attend the prom.
Given,
Additionally, a strictly random sample is required in order to create a confidence interval. Additionally, the sample size should be examined to see if it adequately represents the population.
Using the z critical of 1.645, a 90% confidence interval will be built. The sample proportion in this case will be:
= 36/50 = 0.72
Q = 1 - 0.72 = 0.28
n = 50
As a result, the standard error will be equal to 50 squared times the multiplication of 0.72 and 0.28. This amounts to 0.0635.
For a big sample randomly selected among 750 seniors, the interval on the context suggests that we are 90% confident that the fraction of those who desire to attend the prom falls within the interval.
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