Prove that if a and b are two matrices such that a+b and a*b are both defined, then a and b are square matrices

Answers

Answer 1

To multiply two matrices, i.e. of dimensions (mxn) and (nxp), the number of columns of the first matrix (n) must equal the number of rows of the second matrix (n), and to add two matrices together, their rows and columns must be equal. Then both must be square matrices.

Related Questions

Find the half-life of an element which decays by 3.411% each day. Hint: use y = ab^t.

Answers

a/2=a((100-3.411)/100)^t

a/2=a(0.96589)^t

0.5=0.96589^t

ln(0.5)=t(ln(0.96589))

t=ln(0.5)/ln(0.96589)

t≈19.97 days (to nearest hundredth of a day)

This is about half life of elements with exponential decay.

Half life = 20 years

We are given a decay rate of 3.411% per day.

We are given;

y = ab^(t)

Where;

t is the half life

y = a/2 is the amount of substance remaining after decay

a is amount of substance initially

b = 100% - 3.411% = 96.589% = 0.96589

Thus;

a/2 = a(0.96589)^(t)

a will cancel out to give;

0.5 = 0.96589^(t)

ln (0.5) = t(ln 0.96589)

t = ln(0.5)/ln(0.96589)

t = 19.968 days

This is approximately 20 days.

Read more at; brainly.com/question/13891943

Without using a trigonometric ratio, find the distance from the ship to the buoy, B. Round the distance to the nearest tenth of a mile.

Answers

Without using the trigonometry ratio, we can find the distance between the ship and the buoy by:

the distance between City and Lemont SUBTRACT the vertical distance between City and the point parallel to the Ship

The distance between the City and Lemont can be worked out using the Sin rule
[tex] \frac{57.8}{sin(36)}= \frac{City-Lemont}{sin(92)} [/tex]
[tex]City-Lemont= \frac{57.9sin(92)}{sin(36)} = 98.27.....[/tex]≈98.3

The vertical distance between the City and the point parallel to the ship can be worked out using the Pythagoras theorem
[tex] \sqrt{57.8^{2}- 44.6^{2} } =36.765... [/tex]≈36.8

The distance between the ship and the Buoy is given:
[tex]98.3-36.8=61.5 [/tex] miles

The sun produces 3.9 x 10^33 ergs of radiant energy per second. how many ergs of radiant energy does the sun produce in 3.25 x 10^3 seconds?

Answers

Answer:

1.2675 x 10^37

Step-by-step explanation:

you would have to first multiply 3.9 x 3.25 =12.675. It is not in scientific notation so you would have to change the decimal 1.2675 x 10^37

The ergs of radiant energy produced is: [tex]1.3* 10^{37}[/tex]

The rate of energy is given as:

[tex]Rate = 3.9 * 10^{33}\[/tex] radiant energy per second

The time is given as:

[tex]Time = 3.25 * 10^3[/tex] seconds

The amount of radiant energy produced in this time is:

[tex]Energy = Rate * Time[/tex]

So, we have:

[tex]Energy = 3.9 * 10^{33} * 3.25 * 10^3[/tex]

Multiply

[tex]Energy = 12.675* 10^{36}[/tex]

Rewrite as:

[tex]Energy = 1.2675* 10^{37}[/tex]

Approximate

[tex]Energy = 1.3* 10^{37}[/tex]

Hence, the ergs of radiant energy produced is: [tex]1.3* 10^{37}[/tex]

Answers

63/1000 as a fraction

What are the solutions to the quadratic equation (5y + 6)2 = 24? y = and y = y = and y = y = and y = y = and y =

Answers

For this case we have the following quadratic expression:

[tex] (5y + 6) ^ 2 = 24
[/tex]

From here, we must clear the value of y.

For this, we follow the following steps:

1) We clear the square term:

[tex] (5y + 6) =+/-\sqrt{24} [/tex]

[tex] (5y + 6) =+/-2\sqrt{6} [/tex]

2) Pass the value of 6 by subtracting:

[tex] 5y =-6+/-2\sqrt{6} [/tex]

3) Pass the value of 5 to divide:

[tex] y =\frac{-6+/-2\sqrt{6} }{5} [/tex]

Answer:

The solutions to the quadratic equation are:

[tex] y =\frac{-6+2\sqrt{6} }{5} [/tex]

[tex] y =\frac{-6-2\sqrt{6} }{5} [/tex]

Balcony and orchestra tickets were sold for a Friday night concert last week. The balcony and orchestra tickets sold for $35 and $45, respectively. If 90 tickets were sold, and the total revenue was $3550 for the night, find the number of balcony and orchestra tickets sold.

Answers

x = balcony and y = orchestra

x + y = 90....x = 90 - y
35x + 45y = 3550

35(90 - y) + 45y = 3550
3150 - 35y + 45y = 3550
-35y + 45y = 3550 - 3150
10y = 400
y = 400/10
y = 40 <== 40 orchestra tickets

x = 90 - y
x = 90 - 40
x = 50 <== 50 balcony tickets

A radio telescope has a parabolic surface, as shown below.
If the telescope is 1 m deep and 12 m wide, how far is the focus from the vertex? (5 points)

Answers

check the picture below.

so.. "p" is the distance from the vertex to either, the focus point or the directrix.

thus the focus is "p" units from the vertex.

now, if we set the parabola at the origin, like in the picture, and then use another point on the parabola, let's say we'll use (6,1), then

[tex]\bf \textit{parabola vertex form with focus point distance}\\\\ \begin{array}{llll} (y-{{ k}})^2=4{{ p}}(x-{{ h}}) \\\\ \boxed{(x-{{ h}})^2=4{{ p}}(y-{{ k}})} \\ \end{array} \qquad \begin{array}{llll} vertex\ ({{ h}},{{ k}})\\\\ {{ p}}=\textit{distance from vertex to }\\ \qquad \textit{ focus or directrix} \end{array}\\\\ -------------------------------\\\\[/tex]

[tex]\bf \begin{cases} h=0\\ k=0 \end{cases}\implies (x-0)^2=4p(y-0)\implies x^2=4py \\\\\\ \begin{cases} x=6\\ y=1 \end{cases}\implies (6)^2=4p(1)\implies \cfrac{6^2}{4}=p\implies \cfrac{36}{4}=p\implies 9=p[/tex]

Final answer:

For a parabolic dish, the focus is at a depth equal to one-fourth of the square of the width of the dish's aperture. Given the width as 12m, the focus of the radio telescope is 36m from the vertex.

Explanation:

For a parabolic dish like a radio telescope, the focus (or focal point) is located at the depth equal to one-fourth of the square of the width (i.e., one-fourth of the square of the diameter) of the dish's aperture.

Given the width (diameter) of the dish is 12 meters, we square it to get 144. Quarter of this value is 36 m. So, the focus is 36 m from the vertex of the parabola represented by the dish's surface.

Learn more about Parabolic Dish Focus here:

https://brainly.com/question/32342363

#SPJ3

The variable Z is directly proportional to X. When X is 5, Z has the value 55.

What is the value of Z when X = 12

Answers

z is directly proportional to x, that means :
z = k.x, with k is the coefficient of proportionality:
Let calculate k:
When x = 5, z = 55. Plug in:
55 = k.5 → k=55/5 ; k =11
The value of z when = 12 is : z= kx; z = 11(12) and z = 132

Direct variation is of the form y=kx, in this case:

z=kx, we are given the point (5,55) so we can solve for the constant of variation

55=5k divide both sides by 5

11=k so our equation is:

z=11x, so when x=12

z=11(12)

z=132

What is next number after 2 7 8 3 12 9

Answers

2+5=77+1=88-5=33+9=1212-3=9Can someone help me and tell me why i can not figure this out?

Consider a game in which player 1 moves first. the set of actions available to player 1 is a1={a,b,c}. after observing the choice of player 1, player 2 moves. the set of actions available to player 2 is a2={a,b,c,d}. at how many information sets does player 2 move?

Answers

since player 1 moves first, At the Time player-2 Only has 3 information sets to move at which means from player 1 's A ( player-2 can play a,b,c,d) , player-1's B ( player-2 can play a,b,c,d)and player-1's C ( player-2 can play a,b,c,d).

The three vertices drawn on a complex plane at represented by 0+0i, 4+0i, and 0+3i. What is the length of the hypotenuse

Answers

check the picture below

you can pretty much get the values for "a" and "b" from the grid.

There are 36 girls and 40 boys at a summer camp. The campers will be divided into equal-sized groups. Each group will have the same number of girls and the same number of boys. What is the greatest number of groups that can be formed?

Answers

The maximum number groups would be 4, which contain 9 girls and 10 boys in each group.
Hope it helps.

The question asks you to split these numbers into smaller ones.
This is called the prime factorization of a number:
Lets do this for 36 first, can it be diveded by the smallest prime? (2) Yes, 36/2=18 can 18 still be dived by 2? Yes, 18/2=9 . Can 9 be divided by 2? No, so we move up in primes. Can it be divieded by 3, yes 9/3=3 and 3 is a prime so we can stop.
What we concluded is that 36=2*2*3*3
Lets do this with 40 too, 40/2=20, 20/2=10, 10/2=5 and that is a prime so we can stop.
40=2*2*2*5

Now will you figure out how does this help you?

The slope of a vertical line is zero. true or false

Answers

it is true because the y and x will always be the same number and a vertical line has no slope thus equaling 0,0

The solution is False

The slope of a vertical line is given by the equation Slope m = undefined

What is an Equation of a line?

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given data ,

Let the line be represented as A

Now , the line A is a vertical line

So , the equation of line will be represented as y = mx + c

where m is the slope of the line

And , Slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

The slope of a vertical line is infinite or undefined as it has no y-intercept

Because , the change is x is 0

So , the denominator of the fraction is 0 and division by 0 is undefined

Slope m = ( y₂ - y₁ ) / 0

Hence , the slope m is undefined

To learn more about equation of line click :

https://brainly.com/question/14200719

#SPJ5

The excluded values of a rational expression are 2 and 5. Which of the following could be this expression?

Answers

A value will be excluded from a rational expression if it causes the denominator to be zero as dividing by zero is undefined.

An example that would work for your specific question is:

[tex] y = \frac{(x - 3)(x-1)}{(x-2)(x-5)} [/tex]

If you plug in either 2 or 5 into this equation the denominator will be zero causing the expression to undefined there, so the values 2 and 5 are excluded from the domain of the expression.

Answer: d on eng

Step-by-step explanation:

last year, Carmen opened an investment account with $7400. At the end of the year, the amount in the account had decrease buy 26.5%. How much is this decrease in dollars? How much money was in her account at the end of the year?

Answers

The account decreased by
7,400×0.265=1,961

The account at the end of the year
7,400−1,961=5,439

Final answer:

The decrease in Carmen's account was $1961, which is 26.5% of her original investment of $7400. Hence, by subtracting this decrease from the original investment, we find that Carmen had $5439 left at the end of the year.

Explanation:

The decrease in Carmen's account over the year is 26.5% of the original investment of $7400. In mathematical terms, we can calculate this value by multiplying the original investment by the percentage decrease, using the formula: Decrease = Original Amount * Percentage Decrease.

In Carmen's case, this would be $7400 * 0.265 (converted from 26.5%). Upon calculating, we find that the decrease is $1961.

Now, to find how much money Carmen had at the end of the year, we subtract this decrease from the original amount invested. Again, using the formula: Final Amount = Original Amount - Decrease, we plug in the numbers to get $7400 - $1961, which equals $5439. This is how much Carmen had left in her account at the end of the year after the decrease.

Learn more about Percent decrease

https://brainly.com/question/14808025

#SPJ3

How do you rename 5400

Answers

Answer: "Fifty-four hundred" .
__________________________________________________

Timothy explains to his brother that the model y=4mt has a constant of variation of 4 and is an example of _____ variation.

Answers

directly proportional ? (but what's mt?)

Answer:

Joint variation.

Step-by-step explanation:

There are four types of variation,

Direct variation : When a variable varies directly as another variable,

Example : y varies directly with x ⇒ y = kx,

Where, k is the constant of variation,

Inverse variation : When a variable varies inversely as another variable,

Example : y varies inversely with x ⇒ [tex]y=k\frac{1}{x}[/tex]

Joint variation : When a variable varies directly with two or more than two variables,

Example : y varies directly with both x and z ⇒ y = kxz

Combined variation : When a variable varies both directly and indirectly as another variables,

Example : y varies directly with x and inversely with z ⇒ [tex]y=k\frac{x}{z}[/tex]

Now, here the given expression,

y = 4mt,

Where, y, m and t are variables and 4 is the constant of variation,

⇒ y varies directly as both m and t,

⇒ y = 4mt is an example of joint variation.

Evaluate the integral. (use c for the constant of integration.) sin^2(πx) cos^5(πx) dx

Answers

Using the identity cos^2(A)=1-sin^2(A)
transform
integral of sin^2(πx)cos^5(πx)dx
=integral of sin^2(πx)[1-sin^2(πx)]^2 cos(πx)dx
=integral of [sin^2(πx)-2sin^4(πx)+sin^6(πx)]cos(πx)dx
using the substitution u=sin(πx), du=πcos(πx)dx
=integral of [u^2-2u^4+u^6] (du/π)
=1/π[u^3/3-(2/5)u^5+u^7/7] + C
back substitute u=sin(πx)
=1/π[sin(πx)^3/3-(2/5)sin(πx)^5+sin(πx)^7/7]
or
=sin(πx)^3/3π-2sin(πx)^5/5π+sin(πx)^7/7π

Henry recorded the number of miles he biked each day for a week. His miles were 25, 40, 35, 25, 40, 60, and 75. Enter the data into the statistics calculator. What is the standard deviation of the miles Henry biked to the nearest tenth?

Answers

The standard deviation of the miles Henry biked to the nearest tenth is 17.1. The standard deviation is calculated following the steps below.

Calculation of standard deviation

First calculate the mean of the numbers that where given which is = 25 + 40 + 35 + 25 + 40 + 60+ 75/7

= 300/7

= 42.9

Then for each number, subtract the Mean and square the result.

(25 - 42.9)² = −17.9² = 320.41

(40-42.9)² = -2.9²= 8.42

(35-42.9)² = -7.9² = 62.41

(25-42.9)² = −17.9² = 320.41

(40-42.9)² = -2.9²= 8.42

(60-42.9)² = 17.1²= 292.41

(75-42.9)² = 32.1²= 1030.41

Then work out the mean of those squared differences. That is,

320.41+ 8.42+62.41+320.41+8.42+292.41+1030.41/7

= 2042.89/7

= 291.8

Take the square root of 291.8 which is,

√291.8 = 17.08215443

= 17.1 to the nearest tenth.

Therefore, the standard deviation of the miles Henry biked to the nearest tenth is = 17.1

Learn more about standard deviation here:

https://brainly.com/question/12402189

Answer:

17.1

Step-by-step explanation:

got it right

On Saturday, a local hamburger shop sold a combined total of 273 hamburgers and cheeseburgers. The number of cheeseburgers sold was two times the number of hamburgers sold. How many hamburgers were sold on Saturday?

Answers

Final answer:

To determine the number of hamburgers sold on Saturday, we used the given total of 273 burgers and the relationship that cheeseburgers were twice as numerous as hamburgers. By setting up an equation and solving for the number of hamburgers, we found that 91 hamburgers were sold.

Explanation:

The question asks us to determine how many hamburgers were sold on Saturday given that the total number of hamburgers and cheeseburgers sold was 273, and the number of cheeseburgers was two times the number of hamburgers. Let's denote the number of hamburgers as H and the number of cheeseburgers as C. The problem states that C = 2H. The total number of burgers sold was H + C = 273. Substituting C with 2H, we get H + 2H = 273.

Solving for H, we combine like terms to get 3H = 273, and then we divide both sides by 3 to find H = 273 / 3. Therefore, H = 91. So, 91 hamburgers were sold on Saturday.

805 tens in standard form

Answers

805 tens = 805 x 10 = 8,050

To write 8,050 in standard form, we have
[tex]805\ tens=8,050=8.05\times10^3[/tex]

Nate rides his bike to school every day. From his home he rides 2.5 miles north, and then six miles west. If a straight line is drawn from Nate's house to the school, find the distance between these two locations.

Answers

use Pythagorean Theorem

2.5^2 + 6^2 = x^2

6.25 +36 = 42.25

x= sqrt(42.25) = 6.5 miles

By the Pythagorean Theorem, the length of the hypotenuse of a right triangle is equal to the sum of the side lengths squared, mathematically:

h^2=x^2+y^2

h^2=6^2+2.5^2

h^2=36+6.25

h^2=42.25

h=√(42.25) miles

h=6.5 miles

Which expression is equivalent to 3(8 + 7)? 24 + 7 24 + 21 11 + 10 11 + 7

Answers

Multiply 3&8 and 3&7, this expands it to 24 + 21.

3(8 + 7) = 3(8) + 3(7)...distributive property
= 24 + 21

answer is
24 + 21

in the final event of a track meet, 6 runners run a 100 meter dash. A) How many possible arrangements are there for the medal winners (gold, silver and bronze)? B) state whether it is a combination or permutation

Answers

6 runners, 3 medals, how many ways to give them? well, runner say 2 could get gold or not, bronze or not and silver or not, and so can any other runnner, and the order "does matter", it makes a distinction, thus, is a Permutation

[tex]\bf _nP_r=\cfrac{n!}{(n-r)!}\qquad \qquad _6P_3=\cfrac{6!}{(6-3)!}[/tex]

Answer:

120 possible arrangements.

It is a permutation

Step-by-step explanation:

Imagine that you are going to give the gold medal to any of the 6 runners. There would be 6 possibilities; now, imagine that you are going to give the gold and the silver medals random in the same way: you could give the gold medal to a person and you would have 5 possibilities to give the silver medal (you can't give both medals to the same person). So, note that for each possibility to give the gold medal there would be 5 possibilities to give the silver one.

Analogously, if you give the three medals random and supposing that you have already given the gold one, for each possibility to give the silver medal you would have 4 possibilities to give the bronze one. That is the reason for the calculation to be a multiplication:

N= Total number possibilities:

[tex]N=6*5*4=120[/tex]

This also can be seen as a permutation. A permutation is a reorganization of elements where the order matters. In this case, it is not just relevant who are the winners (who receive the medal), but their order. A combination just helps us to make groups without taking in mind the order, but the permutation does consider that.

The permutation can be learnt by the formula:

[tex]N=\frac{p!}{(p-n)!}[/tex]

where p is the total ef elements and n is the amount of elements of each subgroup that I want to built. In this case, our population 'p'=6, and we want to organize them in groups of 3 (n=3) where it is important for us the order:

[tex]N=\frac{6!}{(6-3)!}=6*5*4=120[/tex]

subtract one- fifth from seven times w

Answers

We can write one fifth as [tex] \frac{1}{5} [/tex]

7 times of w , we can write as = 7w

Now we have to subtract one fifth from seven times of w.

So we can write it in algebraic expression as

[tex]7w - \frac{1}{5} [/tex]

Which set of numbers does 8 2/3 belong to

Answers

real and rational numbers

find the coefficient of x^6 in the binomial expression of (2x+3)^9

Answers

Its 2 bc its in front of the variable

By the Binomial Theorem:
(a + b)^n = sum(k=0 to n) [C(n, k) * a^(n - k) * b^k].

By letting a = 2x, b = 3, and n = 9
(2x + 3)^9 = sum(k=0 to 9) [C(9, k) * (2x)^(9 - k) * 3^k].
As you can see, the power of x is 9 - k. Since we want the x^6 term:
9 - k = 6 ==> k = 3
Thus, letting k = 3 yields the term containing x^6 to be:
C(9, 6) * (2x)^(9 - 3) * 3^4 = 435456x^6.
.

Hours worked: 40 Rate: $3.85 Wages: ?

Answers

Answer: $154.00

Step-by-step explanation:

I am assuming you are looking for how much the person made.

Multiply 40 hours times $3.85

$154.00

Felicia invested money at an interest rate of 4%. After six months, she had earned $90.00 interest. How much money did Felicia invest?

Answers

The formula is
I=prt
I interest earned 90
P amount invested?
R interest rate 0.04
T time 6/12
Solve the formula for p
P=I÷rt
P=90÷(0.04×(6÷12))
P=4,500 ....answer

Answer:

the answer is 4500 i got it right

Step-by-step explanation:

A math teacher gave her class two tests. 27% of the class passed both tests and 51% of the class passed the first test. What percent of those who passed the first test also passed the second test?

Answers

Assume that there are 100 students in the class.

(Working with numbers is easier than working with percentages).

There are 27 students who passed both tests, and 51 who passed only the first test.
The 27 students who passed both tests are included in the 51 who passed the first test.

We are asked "What percent of those who passed the first test also passed the second test?"

so we are asked "what percent of 51 is 27?"

let 51 be 100%
then 27 is [tex] \frac{27*100}{51} [/tex]%=52.941%

Answer: 52.941%

Other Questions

a line perpendicular to a plane, would intersect the plane at one what What is the maximum and minimum amount of ordinary shares to be invested in Hollard? A(n) _______ website provides accommodations to individuals with visual, auditory, physical, and neurological disabilities. What is the overall fusion reaction that converts mass into other forms of energy in the suns core? what is the overall fusion reaction that converts mass into other forms of energy in the suns core? 3 helium nuclei become 1 carbon nucleus e = mc2 4 hydrogen nuclei become 1 helium nucleus 2 hydrogen nuclei become 1 helium nucleus? Given the expression 5a2b 13ab + 7a3 4b, do the following as instructed below: 1. Write the polynomial in descending order.2. Classify the polynomial by the number of terms.3. State the degree of the polynomial.Thank you !! objects that exhibit projectile motion follow what kind of path What is the simplified form of 20 times x to the fifth power over 15 times y to the sixth power times the fraction 5 times y to the fourth power over 6 times x squared? The person probably most responsible for the direct labor efficiency variance is A person walks first at a constant speed of 5.10 m/s along a straight line from point circled a to point circled b and then back along the line from circled b to circled a at a constant speed of 2.75 m/s. (a) what is her average speed over the entire trip? 3.57 correct: your answer is correct. m/s If the measures of the angles of a triangle are in the ratio of 19:13:4, then the expressions 19x, 13x, and 4xrepresent the measures of these angles.Find these angle measures. Use the diagram of the right triangle above and round your answer to the nearest hundredth. If measure B= 60 degrees and a = 10 meters, find b. Write $4,915 for 72 shares of stock as a unit rate. Round to the nearest hundredth if necessary. what is the most prominent figurative language element in the excerpt from the poem the first snowfall beginning of mill and the end of chain, creates two other words? Unless otherwise posted, what is the speed limit in a school zone? florida f(x) = 5x 4 and g(x) = 3x 2, find (f g)(x). When converting from kilometers to meters, the decimal is moved _______. a. three places to the left b. two places to the left c. three places to the right d. two places to the right. Which orbital would the electron of a ground state hydrogen atom occupy? 1s 1p 2p none of the above 0s? Find the value of angle M Read the passage. During the whole of a dull, dark, and soundless day in the autumn of the year, when the clouds hung oppressively low in the heavens, I had been passing alone, on horseback, through a singularly dreary tract of country, and at length found myself, as the shades of evening drew on, within view of the melancholy House of Usher. I know not how it wasbut, with the first glimpse of the building, a sense of insufferable gloom pervaded my spirit . . . In this excerpt from Edgar Allan Poe's "The Fall of the House of Usher," what mood do these lines evoke in the reader? one of hostility one of bleakness one of serenity one of terror Steam Workshop Downloader