(a)Symmetric matrix -
Let matrix A be of order 3×3 =
[tex]\left[\begin{array}{ccc}1&3&8\\3&8&-4\\8&-4&6\end{array}\right][/tex]
So, the transpose of A will be -
A' =
[tex]\left[\begin{array}{ccc}1&3&8\\3&8&-4\\8&-4&6\end{array}\right][/tex]
So, we can say that A=A'. So, it is symmetric.
(b) Skew - symmetric matrix -
Let us consider a matrix B =
[tex]\left[\begin{array}{ccc}0&-6&4\\-6&0&7\\4&7&0\end{array}\right][/tex]
matrix B is said to be skew-symmetric if aij =−aji.
(B' =−B)
B' =
[tex]\left[\begin{array}{ccc}0&6&-4\\6&0&-7\\-4&-7&0\end{array}\right][/tex]
(c) A + A′ is a symmetric matrix for any square matrix A with real number entries, whereas A - A′ is a skew-symmetric matrix.
Proof: If B = A + A', then B ′ = (A + A ) ′
(A + B)′ = A′ + B′, thus = A′ + (A′)′
(as (A′)′ =A) = A′ + A
= B (because B + A = B + A′)
B = A+A′ is a symmetric matrix as a result.
Let C now equal A-A′.
Why does C' equal (A-A′)′=(A′)′?
= A′ - A (Why?)
=- (A - A′) = - C
A - A′ is a skew-symmetric matrix as a result.
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So i am have homework and it is asking me to show the ratios are equivalent by simplifying any 4 of them and i am stuck in that one i don't understant that can you help me pls can u explain me
The ratios are shown equivalent as by simplification done below.
Ratio is the representative of comparison of part of things in a complete thing. Equivalent ratios are collection of ratios that show same comparison. As per the given question, the equivalent ratios are calculated as follows -
First column -
Ratio = 6:2
Dividing both the parts of ratio by 2
Ratio = 3:1
Second column -
Ratio = 9:3
Dividing both the parts of ratio by 3
Ratio = 3:1
Third column -
Ratio = 12:4
Dividing both the parts of ratio by 4
Ratio = 3:1
Fourth column -
Ratio = 15:5
Dividing both the parts of ratio by 5
Ratio = 3:1
Similarly, for rest of the columns, division by 6, 7 and 8 of both parts of ratio will give the result 3:1. Hence, the given rations are shown as equivalent ratios, by simplifying into 3:1.
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Name the geometric term modeled by the given object.
a telephone pole
The geometric term modeled by the given object (a telephone pole) is a line
How to determine the geometric term?The given object is a telephone pole
The pole of a telephone pole is often straight.
This means that the telephone pole can be modelled by a line segment
Hence, the geometric term modeled by the given object (a telephone pole) is a line
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a rectangular plot of land measures 40.0 m by 120.0 m, with a parcel 10.0 m by 12.0 m out of one corner for an electrical transformer. what is the area, in meters squared, of the remaining plot?
The area of the remaining rectangular plot of land is 4680m²
Area of rectangle:
Area of rectangle means the area covered by the rectangle.
The formula for area of rectangle is
A = l x b
where,
l is the length of the rectangle
b is the breadth or width of the rectangle
Given,
A rectangular plot of land measures 40.0 m by 120.0 m, with a parcel 10.0 m by 12.0 m out of one corner for an electrical transformer.
Here we need to find the remaining area of the rectangular plot land.
For that first, we have to find the area of each separately,
Like,
The area of the rectangular plot is,
A₁ = 40.0 x 120.0 m²
A₁ = 4800m²
Similarly, the area of the electric transformer is,
A₂ = 10.0 x 12.0 m²
A₂ = 120m²
Now the remining area is,
A = A₁ - A₂
A = 4800 - 120 m²
A = 4680m²
Therefore, the area of the remaining rectangular plot is 4680m².
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Draw an irregular 14-sided polyhedron which has two congruent bases.
An irregular 14-sided polyhedron which has two congruent bases is as shown in the attached file.
What is a Polyhedron?
A polyhedron is a three dimensional solid shape made by joining together polygons.
For example we can consider a prism having 12-sided regular polygons as bases because then there would be 2 bases and 12 lateral sides for a total of 14 sides for the polyhedron.
Since the lateral faces are rectangles and not 12-sided polygons like the bases, the polyhedron is an irregular polyhedron.
Applying the above, we can draw an irregular 14-sided polyhedron which has two congruent bases as shown in the attached file.
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5 1-3a
Note: Please make sure to properly format your answers. All dollar figures in the answers need to include the dollar sign and any amount over 1,000 should include the comma
($2,354.67). All percentage values in the answers need to include a percentage sign (%). For all items without specific rounding instructions, round your answers to two decimal
places, show both decimal places (5.06).
The variance of a distribution is 195. What is the standard deviation, rounded to the nearest thousandth?
Applying the square root of the variance, the standard deviation of the distribution is of 13.964.
What is the standard deviation of a distribution?The standard deviation of a distribution is given by the square root of the variance of the distribution.
For this problem, the variance of the distribution is of 195, hence the standard deviation is:
s = sqrt(195) = 13.964.
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Evaluate the expression when a = 7 and c= -3.
-a+4c
Hello,
[tex] - a + 4c = - 7 + 4 \times ( - 3) = - 7 - 12 =- 19[/tex]
Answer:
-19
Step-by-step explanation:
-7 + 4(-3)
-7 - 12= -19
NEED HELP FAST, GIVING AWAY 99 POINTS.
Evaluate the numerical expression.
3/2 − (−1/4)
A -1/2
B -3/2
C 7/4
D 4/5
Answer:
The answer is C. 7/4 :)
Where on the number line would you plot the square roots of the numbers 70, 85, 99, and 112?
a. 4
b. 5
c. between 4 and 5
d. between 64 and 125
We have to plot the square roots of the numbers 70, 85, 99, and 112 between 64 and 125 ( d )
First, we must evaluate the square root of given numbers.
√70 = √ ( 2 × 5 ×7 ) = 8.36
√85 = √ ( 5 × 17 ) = 9.22
√99 = √( 9 × 11 ) = 3√11 = 9.95
√112 = √( 4 × 4 × 7 ) = 4 √7 = 10.58
All these numbers ( 8.36, 9.22, 9.95 , 10.58 ) belong between, square roots of √64 and √125 which are 8 and 15. So we have to put these numbers in between the square roots of 64 and 125 on the number table.
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Yo help please I need this done it's about rational or irrational numbers u have to figure out if it's either rat or irr. If it's rational then figure out if it is a integers. If it's a integers then figure out if it's a whole number if it is then figure out if it's a natural number. Here's the order of it. R I W N and if it's irr then it's just I
All the numbers have been analyzed for being rational and irrational .
For -1 :
It is a rational number = R
It is an integer = I
For 2 / 3:
It is a rational number = R
For - 4.8 :
It is a rational number = R
For 7:
It is a rational number = R
It is an integer = I
It is an whole number = W
It is a natural number = N
For - 32 / 95
It is a rational number = R
For - 20 / 4 = -5:
It is a rational number = R
It is an integer = I
For 0:
It is a rational number = R
It is an integer = I
It is an whole number = W
For - 7.34:
It is a rational number = R
For 7 / 1239:
It is a irrational number = I
For √5:
It is a irrational number = I
Therefore, all the numbers have been analyzed for being rational and irrational .
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Randy's swimming coach kept track of his average 50-meter lap times during the first 3 weeks of training. How much greater was the percent of change from Week 1 to Week 2 than from Week 2 to Week 3? Round to the nearest tenth of a percent.
The percent of the first change is greater by 2.36%.
Time in 1st week = 28.8 sec
Time in 2nd week = 27.6 sec
Time in 3rd week = 27.1 sec
∴ Change of time from week 1 to week 2 = (28.8 - 27.6) sec
= 1.2 sec
∴ Percent of change from week 1 to week 2 = [tex]\frac{time change}{1st week time} \times 100[/tex] %
= [tex]\frac{1.2}{28.8} \times 100[/tex] %
= 4.17%
∴ Change of time from week 2 to week 3 = (27.6 - 27.1) sec
= 0.5 sec
∴ Percent of change from week 2 to week 3 = [tex]\frac{Time change}{2nd week time} \times 100[/tex] %
= [tex]\frac{0.5}{27.6} \times 100[/tex] %
= 1.81%
∴ The greater change was in the first week. The amount by which it was greater is = (4.17 - 1.81) %
= 2.36%
Answer) The percent of the first change is greater by 2.36%.
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Evaluate the expression when x=3 , y=−4 , and z=−6.
z−2xy=
x = 3 , y = −4 , and z = −6
z-2xy =
Substitute the value of x,y and z in the expression.
-6-2(3)(-4)
-6-2(-12)
-6+24
18
The graph shows the cost, c, in dollars of using a carpooling
service for d days. Which equation represents the cost of the carpooling service?
A c = = d
B c = 6d
C d = 6c
D c = 6
Answer: where is the graph?
The recommended mass of a Soccer ball is 0.43 kilogram. The actual mass is allowed
to vary by up to 20 grams.
a. Write and solve an absolute value equation to find
the minimum and maximum acceptable soccer ball
masses.
b. A soccer ball has a mass of 423 grams. The soccer
ball loses 0.016 kilogram of mass over time. Is the
mass now acceptable? Explain.
The absolute value equation is:
|M - 430g| = 20g
And the solutions are M = 410g and M = 450g
b) No, the mass is not acceptable.
How to write the absolute value equation?We know that the recomended mass is 0.43kg, with an accepted error of 20 grams.
Where:
0.43kg = 0.43*1000g = 430g
Then the minimum mass accepted is: 430g - 20g = 410g
The maximum mass accepted is: 430g + 20g = 450g
These are the solutions, and the absolute value equation is, if M is the mass:
|M - 430g| = 20g
b) If the ball has a mass of 423g it is in the accepted range, if now it loses 0.016kg:
0.016kg = 0.016*1000g = 16g
The new mass is:
423g - 16g = 407g
This is smaller than the minimum accepted mass, then this mass is not acceptable.
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Rosa ran the hurdles in 58.32 seconds. maya ran the hurdles in 54.078 seconds. what is the difference between the two times? 3.954 seconds 4.242 seconds 4.258 seconds 5.758 seconds
Answer:
Step-by-step explanation: 4.242
The difference of time taken by Rosa and Maya to ran the hurdles is 4.242 seconds .
The correct option is B .
Given, time taken by Rosa and Maya to ran the hurdles.
Time taken by Rosa to ran the hurdle = 58.32 seconds .
Time taken by Maya to ran the hurdle = 54.078 seconds .
Difference between the time taken:
Rosa is taking more time to cover the distance than Maya . Thus the speed of Rosa is less than the speed of Maya .
Relationship between speed, time and distance.
Distance = Speed × Time
Subtract time taken by Rosa to ran the hurdle from time taken by Maya to ran the hurdle.
= 58.32 - 54.078
= 4.242 seconds
Therefore the correct option is B .
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Cuánto es 15–4(n–2)=27
Answer:
tu respuesta es -1
Step-by-step explanation:
15-4(n-2) =27
15-4n+8=27
15-4n+8=27
23-4n=27
-4n+23=27
-4n+23-23=27-23
-4n=27-23
-4n=4
[tex]\frac{-4}{4} \frac{4}{4}[/tex] =-1
Is (2,-1) a solution of 2x-y=5? Explai
how your work.
Answer:
Yes, (2, -1) is a solution.
Step-by-step explanation:
Plug in 2 for x and -1 in for y and see if it is a true statement.
2x - y = 5
2(2) - (-1) = 5
4 - (-1) = 5 Subtracting a negative number is the same as adding a positive number
4 + 1 = 5
5 = 5 Since this statement is true, (2,-1) is a solution.
State the property that justifies the statement.
If x/3=-15, then x=-45.
The value of x will be -45 by the multiplicative property for the given expression x/3=-15.
What is an expression?The mathematical expression is the combination of numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also be used to denote the logical syntax's operation order and other properties.
The given expression is x/3=-15. The value of x will be calculated as below:-
x/3=-15.
x = -15 x 3
x = -45
Therefore, the value of x will be -45 by the multiplicative property.
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The width of a rectangle is five less than three times the length of the rectangle. If the perimeter of the rectangle is 70 inches what are the dimensions of the rectangle?
Step-by-step explanation:
Do you mean width equal 5
Determine which sequences of transformations could be applied to the parent function, f(x) = x, to obtain the graph above. Reflect over the y-axis, vertically stretch by a factor of 2, and then shift up 6 units Shift left 3 units, reflect over the y-axis, and then vertically stretch by a factor of 2 Shift up 6 units, reflect over the x-axis, and then vertically stretch by a factor of 2 Shift left 2 units, reflect over the y-axis, and then vertically stretch by a factor of 6 Reflect over the x-axis, vertically stretch by a factor of 2, and then shift up 6 units Shift right 3 units, reflect over the y-axis, and then vertically stretch by a factor of 2
The sequence of transformations could be applied to the parent function, f(x) = x, to obtain the graph is E. Shift up 6 units, reflect over the x-axis, and then vertically stretch by a factor of 2.
What is transformation?It should be noted that transformation simply means the movement of an object from a position to another position.
In this case, the sequence of transformations could be applied to the parent function, f(x) = x, to obtain the graph is to shift up 6 units, reflect over the x-axis, and then vertically stretch by a factor of 2.
Therefore sequence of transformations could be applied to the parent function, f(x) = x, to obtain the graph is E. Shift up 6 units, reflect over the x-axis, and then vertically stretch by a factor of 2.
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there are 11 books on a shelf. 9 of these books are new. the rest of them are used
1. Turn this standard notation 25,000,000 into scientific notation.
Answer:
25,000,000 = 2.5 × 10^7
The ^ is raised to the power.
Hope this helps :)
Step-by-step explanation:
2.5 × 10^7 = 25,000,000
suppose that a function f has domain (-2,2) and range (-3,5). what is the domain of the function f(2x)?
The domain of the function f(2x) is (-1, 1).
Given that a function f has domain (-2,2) and range (-3,5).
We need to determine the domain of the function f(2x).
To determine the domain of the function f(2x), we need to consider how the original domain (-2,2) is affected by the transformation of multiplying the input by 2.
When we multiply x by 2, it stretches or compresses the function horizontally.
In this case, multiplying by 2 will stretch the original domain by a factor of 1/2.
To find the new domain, we divide the original domain endpoints by 2:
New domain = (-2/2, 2/2) = (-1, 1)
Therefore, the domain of the function f(2x) is (-1, 1).
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Any genius willing to help :) , I'll give you a brainliest if you do.
Answer:
00
Step-by-step explanation:
a certain composer wrote 10 symphonies, 4 piano concertos (music for piano and orchestra), and 35 piano sonatas (music for solo piano). a. how many ways are there to play first a symphony and and then a piano concerto? b. the manager of a radio station decides that on each successive evening (7 days a week), a symphony will be played followed by a piano concerto followed by a piano sonata. for how many nights could this be carried out before exactly the same program would have to be repeated? about how many years would this be? (round to the nearest year).
(a) According to the question, a composer wrote [tex]10[/tex] symphonies, [tex]4[/tex] piano concerts (piano and orchestra) and [tex]35[/tex] piano sonatas (solo piano):
Here, determine how many ways are there to play first a symphony and then piano concerto.
So, the probability is [tex](10P1) (4P1) = (10)(4)= 40[/tex]
Therefore, there are [tex]40[/tex] ways to play first a symphony and then piano concerto.
(b)The manager of a radio station decides that on each successive evening, a symphony will be played followed by a piano concerto followed by a sonata.
Here determine how many nights could be carried out before the same program would get repeated.
So, the probability would be [tex](35)(10)(4)=1440[/tex]
Therefore, [tex]1440[/tex] nights are carried out before the same program gets repeated.
Now, to calculate the years: [tex]\frac{1440 nights}{365days} = 3.95 years[/tex]
Therefore, it would be [tex]3.95[/tex] years.
What is probability?
Probability is the method to measure the occurred events or the occurrence of the events. It is also used to analyze the outcomes of random events. For example, to calculate the probability of a playing card which is 52 in numbers. And it is divided into four cards and each are in the count of 13.These four cards are heart, spades, diamond and club.
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Solve for X
4(5x+6)=12
-3(2x-4)=18
26=2(3x-2)
The value of x in the equations are:
1. x = -3/5
2. x = -1
3. x = 5
How to Solve an Equation?Given the equations above, to solve for x, isolate x as the variable in the equation to one side of the equation.
a. 4(5x+6) = 12
Apply the distributive property
20x + 24 = 12
20x = 12 - 24
20x = -12
x = -12/20
x = -3/5
b. -3(2x - 4) = 18
Apply the distributive property
-6x + 12 = 18
-6x + 12 - 12 = 18 - 12
-6x = 6
x = 6/-6
x = -1
c. 26 = 2(3x - 2)
Apply the distributive property
26 = 6x - 4
26 + 4 = 6x
30 = 6x
5 = x
x = 5
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How many 5-letter words can be made from the letters WASTEFUL if
repetition of letters is allowed? And if repetition is not allowed
Answer w a s t e f u l
Step-by-step explanation:
theres 7 words on it
Gogglejaws can eat 36 fish in one minute.
How many fish could Gogglejaws eat in 2.2
hours?
Answer:
3752
Step-by-step explanation:
there are 60 minutes in an hour so multiply 2.2 times 60
2.2 • 60 = 132 minutes
132 min • 36 fish = 3752
Find the square root of 0.81
A. 0.009
B. 0.09
C. 0.9
D. 9
Answer: C. 0.9
I used a caculator.
The edge of a circular flower bed, 320 ft in diameter, needs mulch. How many cubic
yards (yd³) of mulch do you need if you want the mulch to cover 2 ft in from the edge to a
depth of 3.5 inches, all the way around
868.34 cubic yards (yd³) of mulch is needed to cover 2 ft in from the edge to a depth of 3.5 inches,
To calculate square feet for a circular area, measure the distance from the center of the bed to the outer edge (this is the radius R) .Then area is given by square meters of circular area = [tex]R\times R\times\ 3.14[/tex] ....(1)To determine the amount of mulch you need 1. Multiply the square feet of your bed by the number of inches of mulch you want to deep . 2. Divide this number by 324 . You will get the amount of mulch you need in a cubic yard.It is given that a circular flower bed, 320 ft in diameter which means radius[tex]=\frac{320}{2}= 160 \ ft[/tex]
Putting r = 160 in equation (1) , we get
[tex]A=160\times160\times3.14\\A=80384 \ ft \ sqaure \ units[/tex]
We need the mulch 3.5 inches deep
[tex]80384\times3.5=281344[/tex]
On dividing the above number by 324 , we will get the required cubic yards [tex]\frac{281344}{324} =868.34[/tex]
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Simplify the expression.
a + b + 2a + 2b + 5 - b
3a + 2b + 5
3a + 4b + 5
2a + 4b + 5
2a + 2b + 5
Answer:
the answer is 3a+2b+5.
I hope this will help