Given the matrices A and B below, find A + B and 3A

Given The Matrices A And B Below, Find A + B And 3A

Answers

Answer 1

The value of A+B is [tex]\left(\begin{array}{ccc}3&-3\\10&4.5\\10&-1\end{array}\right)[/tex] and the value of 3A is  [tex]\left(\begin{array}{ccc}6&-9\\0&15\\21&-6\end{array}\right)[/tex] .

How to add two matrices?

To add two matrices, we have to add the element present in the same position in the respective matrices.

(A+B)ij= Aij + Bij

where i is the no. of row and j is the no. of column.

How to multiply a scalar by the matrix?

In order to multiply a scalar by the matrix, we have to multiply that scalar with every element of the matrix.

nA= nAij

Here given matrix is

A= [tex]\left(\begin{array}{ccc}2&-3\\0&5\\7&-2\end{array}\right)[/tex]

and the other matrix is

B= [tex]\left(\begin{array}{ccc}1&0\\10&-1/2\\3&1\end{array}\right)[/tex]

The sum of the matrix is A+B=  [tex]\left(\begin{array}{ccc}2&-3\\0&5\\7&-2\end{array}\right)[/tex]+  [tex]\left(\begin{array}{ccc}1&0\\10&-1/2\\3&1\end{array}\right)[/tex]

⇒ A+B =[tex]\left(\begin{array}{ccc}2+1&-3+0\\0+10&5+(-1/2)\\7+3&-2+1\end{array}\right)[/tex]

⇒ A+B= [tex]\left(\begin{array}{ccc}3&-3\\10&4.5\\10&-1\end{array}\right)[/tex]

the value of 3A= 3 [tex]\left(\begin{array}{ccc}2&-3\\0&5\\7&-2\end{array}\right)[/tex]=  [tex]\left(\begin{array}{ccc}6&-9\\0&15\\21&-6\end{array}\right)[/tex]

Therefore the value of A+B is [tex]\left(\begin{array}{ccc}3&-3\\10&4.5\\10&-1\end{array}\right)[/tex] and the value of 3A is  [tex]\left(\begin{array}{ccc}6&-9\\0&15\\21&-6\end{array}\right)[/tex] .

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Related Questions

The ordered pair below is a solution to which equation? (2, 12) A.y=1/5x B.y=1/2x C. y = 2x D. y = 6x

Answers

D. y = 6x...subbing in (2,12)...x = 2 and y = 12
    12 = 6(2)
    12 = 12 (correct)

so (2,12) is a solution to : y = 6x

Answer:

D. y = 6x

Step-by-step explanation:

In order to conclude which pair is a real solution to one of these equations, we need to evaluate the point in each equation.

Let:

[tex](x,y)=(2,12)[/tex]

So, this pair will be a solution if when evaluating the value of x=2 in the function the result is y=12.

For A.

[tex]y(x)=\frac{1}{5}x \\\\y(2)=\frac{2}{5} =0.4\neq12[/tex]

This pair is not a solution to this equation.

For B.

[tex]y(x)=\frac{1}{2}x\\\\y(2)=\frac{2}{2} =1 \neq 12[/tex]

This pair is not a solution to this equation.

For C.

[tex]y(x)=2x\\\\y(2)=2*2=4 \neq 12[/tex]

This pair is not a solution to this equation.

For D.

[tex]y(x)=6x\\\\y(2)=6*2=12[/tex]

This pair is a solution to this equation.

original amount 90$ new amount 84.50 what's the percent of change?

Answers

percent change=100 times change/original

change=original-new
change=90-84.50=5.5

percent change=100 times 5.5/90
percent change=550/90
percent change=6.11111
percent change=6.1%

The percent of change from the original amount of $90 to the new amount of $84.50 is approximately a 6.11% decrease.

To calculate the percent of change, we need to determine the difference between the original and new amounts, then divide that difference by the original amount and multiply by 100 to get the percentage. In this case, the original amount is $90, and the new amount is $84.50. The difference between these two amounts is $90 - $84.50 = $5.50. We then take this change and divide it by the original amount: $5.50 / $90. Finally, to get the percent change, we multiply by 100:

($5.50 / $90)  times 100 = 6.11%

The percent of change from the original amount of $90 to the new amount of $84.50 is approximately 6.11% decrease.

write a polynomial function in standard form with zeros at -3,-1, and 1

Answers

F(x)=(x+3)(x+1)(x-1)

Answer:

Should be f(x) = x^3 + 3x^2 − x − 3  because this is written in standard form.

Step-by-step explanation:

what is 0.6(r 0.2)=1.8

Answers

Isolate the variable by dividing each side by factors that don"t contain the variable.
r=15

the solution to the equation [tex]\(0.6(r - 0.2) = 1.8\) is \(r \approx 3.2\).[/tex]

To solve the equation 0.6(r - 0.2) = 1.8, we first distribute the 0.6 to the terms inside the parentheses:

0.6r - 0.6(0.2) = 1.8

0.6r - 0.12 = 1.8

Next, we add 0.12 to both sides of the equation to isolate 0.6r:

0.6r - 0.12 + 0.12 = 1.8 + 0.12

0.6r = 1.92

Now, to solve for r, we divide both sides of the equation by 0.6:

[tex]\[ \frac{0.6r}{0.6} = \frac{1.92}{0.6} \][/tex]

[tex]\[ r = \frac{1.92}{0.6} \][/tex]

[tex]\[ r \approx 3.2 \][/tex]

So, the solution to the equation [tex]\(0.6(r - 0.2) = 1.8\) is \(r \approx 3.2\).[/tex]

The probable question maybe:

solve the equation 0.6(r - 0.2) = 1.8

change 50/16 into a mixed number .Reduce your answer to lowest terms a.48 3/16
b.3 1/25
c.3 1/8
d.4 7/8 ? ...?

Answers

C IS THE ANSWER 3 1/8
First you need to see how many times 16 can go in 50. It goes 3 times (3•16=48) so you have 3 wholes. If you have 48, but had 50, there's 2 left over. So the answer is 3 2/50, which equals 3 1/25

Sal's Sandwich Shop sells wraps and sandwiches as part of its lunch specials. The profit on every sandwich is $2 and the profit on every wrap is $3. Sal made a profit of $1,470 from lunch specials last month. The equation 2x + 3y = 1,470 represents Sal's profits last month, where x is the number of sandwich lunch specials sold and y is the number of wrap lunch specials sold. Change the equation to slope-intercept form. Identify the slope and y-intercept of the equation. Be sure to show all your work. Describe how you would graph this line using the slope-intercept method. Be sure to write using complete sentences. Write the equation in function notation. Explain what the graph of the function represents. Be sure to use complete sentences. Graph the function. On the graph, make sure to label the intercepts. You may graph your equation by hand on a piece of paper and scan your work or you may use graphing technology. Suppose Sal's total profit on lunch specials for the next month is $1,593. The profit amounts are the same: $2 for each sandwich and $3 for each wrap. In a paragraph of at least three complete sentences, explain how the graphs of the functions for the two months are similar and how they are different. Below is a graph that represents the total profits for a third month. Write the equation of the line that represents this graph. Show your work or explain how you determined the equations. graph of line going through ordered pairs (0, 300) and (450, 0)

Answers

Since both functions follow the form of 2X + 3Y = c in general, where c is some constant, both functions will have the same slope as of -2/3. However, both graph will not have the same Y-intercept as the profits are different. Similarly, the X-intercept will also be different due to the profits.

I hope my answer has come to your help. Have a nice day ahead and may God bless you always!

Peter has five times as much money as david both.if peter gves $28 to david, both of them will have equal amount of money. how much money did peter had in the beginning?

Answers

Just set up two simple simultaneous equations:
 
First, let P = Peter's starting money
and D = David's starting money
 
P = 5*D  (Peter has 5 times as much as David)
P - 28 = D + 28 (Peter gives $28 to David, and both have the same now)
 
P = D + 56
 
substitution reveals that
 
D + 56 = 5D
56 = 4D
 
Therefore,
David = 14, and Peter = 70

Jasmin read 1 3/4 pages in one minute. Armando read 1 1/2 times the number of pages that Jasmin read. How many pages did Armando read? Express your answer in simplest form. PLZZZZZ HELPP!!!!!!!!!!!!!!

Answers

Armando reads 7/8 pages, since u said ''times'' that calls for multiplication so jasmine reads 1 3/4 and Armando reads 1/2 times that so that means 1/2 * 1 3/4 = 7/8. So in conclusion, Armando reads 7/8 pages total.

Hope this helps and if it does, happy studying and don't forget to mark as brainliest.

"Which ranges describe the cluster in the scatter plot?



Choose exactly two answers that are correct.


A.between 8 and 10 years of age


B.between 32 and 72 pages read


C.between 10 and 12 years of age


D.between 32 and 38 pages read"

Answers

The correct answers are: A and C <---------
    
          Hope i helped!:)

Answer:

A and C

Step-by-step explanation:

A.between 8 and 10 years of age

C.between 10 and 12 years of age

China issued the largest stamp ever, 210mm Long and 65mm wide. Find the ratio of length to width

Answers

210 : 65 
----------------------
42 : 13 is the ratio of 210mm long and 65mm wide
----------
divide both numbers by 5
Final answer:

The ratio of the length to the width of the largest stamp ever issued by China, having dimensions of 210mm long and 65mm wide, is approximately 3.23:1 after dividing the length by the width.

Explanation:

To answer the question about the ratio of the length to the width of the largest stamp ever issued by China, we need to follow a few simple steps. First, we have the dimensions of the stamp: 210mm long and 65mm wide.

Step 1: Identify the numbers given. In this case, the length of the stamp is 210mm, and the width is 65mm.

Step 2: To find the ratio of length to width, we need to divide the length by the width. So, 210 divided by 65 gives us approximately 3.23 (rounded to two decimal places).

Therefore, the ratio of the length to the width of the largest stamp ever issued by China, in simplest form, is approximately 3.23:1.

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HEELLLPPP ME?!?!?!? ANYONE?




Solve the system of equations and choose the correct ordered pair.

3x + 2y = 12
6x + 3y = 21

A. (4, 3)
B. (4, 0)
C. (2, 3)
D. (3, 2)

Answers

I hope this helps you

Gary bought a car for $40,000. If V = 40,000(.85)t represents the value of the car after t years, how long will it take the car to be worth less than one-fourth of its purchase price? ...?

Answers

9 years 
Years Value 
1 34000 
2 28900 
3 24565 
4 20880.25 
5 17748.2125 
6 15085.980625 
7 12823.08353125 
8 10899.6210015625 
9 9264.6778513281 
10 7874.9761736289 

I hope my answer has come to your help. Thank you for posting your question here in Brainly. We hope to answer more of your questions and inquiries soon. Have a nice day ahead!

Answer:

D) 9 years

Step-by-step explanation:

The universal set is the set of rational numbers. S is the set of integers. Which represents Sc?The universal set is the set of rational numbers. S is the set of integers.

Which represents Sc?

Answers

The universal set is the set of rational numbers. S is the set of integers. represents by the below:

{x|x is a rational non-integer}

Thank you for posting your question here at brainly. I hope the answer will help you. Feel free to ask more questions.

Final answer:

To find Sc, which represents the complement of set S, we need to determine the elements that are in the universal set but not in S. Sc represents the set of all rational numbers that are not integers.

Explanation:

To find Sc, which represents the complement of set S, we need to determine the elements that are in the universal set but not in S. The universal set, in this case, is the set of rational numbers, which includes all numbers that can be expressed as a quotient or fraction. Set S is the set of integers, which includes the whole numbers and their negatives.

So, to find the complement of S, we need to consider all rational numbers that are not integers. This includes numbers with decimals or fractions that are not whole numbers. For example, 4.5, -3.2, and 1/2 would be in the complement of S.

Therefore, Sc represents the set of all rational numbers that are not integers.

Write log6 5 as a logarithm of base 4.

1) (log4)5/(log4)6
2) (log4)6/(log4)5
3) (log5)4/(log6)4
4) (log6)4/(log5)4 ...?

Answers

The answer is 1) (log4)5/(log4)6

We will use the change-of-base formula: [tex]log_a(x)= \frac{log_b(x)}{log_b(a)} [/tex]

So, if we want to write log6 5 as a logarithm of base 4. in these example a = 6, x = 5, b = 4:
[tex]log_6(5)= \frac{log_4(5)}{log_4(6)}[/tex]

The value of log₆ 5 as a logarithm of base 4 is,

⇒ log₄ 5 / log₄ 6

We have to given that;

Logarithmic function is,

⇒ log₆ 5

Now, WE can write in as a logarithm of base 4 as;

Since, WE know that;

⇒ logₐ b = logₓ b / logₓ a

Hence, By above rule we get;

⇒ log₆ 5

⇒ log₄ 5 / log₄ 6

Thus, The value of log₆ 5 as a logarithm of base 4 is,

⇒ log₄ 5 / log₄ 6

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A fence post is 1.9 meters long. It is placed in a hole that is 0.65 meter deep. How far above the ground is the top of the fence post? Enter your answer as a decimal in the box.

Answers

1.9-0.65=1.25. The fence post is 1.25 meters above the ground
1.90-0.65=1.25 meters

21 is 60 percent of what number

Answers

the answer to the equation is 11

Write your own word problem, then create the slope intercept form equation.

Answers

Jamie has 100 dollars and wishes to purchase DVDs for 12 dollars each. She wants to know how much money she will have after buying the DVDs. Let w be the amount of money Jamie has left, and d is the amount of DVDs she buys.
the slope equation would be w=100-12d

The slope-intercept form equation for the word problem is [tex]\( y = \frac{3}{4}x + 1 \).[/tex]

Let's consider a word problem where a local gym charges a $1 sign-up fee and $3 for every hour of use. If we let [tex]\( x \)[/tex] represent the number of hours a member uses the gym and [tex]\( y \)[/tex] represent the total cost, we can write an equation in slope-intercept form.

The slope-intercept form of a linear equation is given by [tex]\( y = mx + b \)[/tex], where [tex]\( m \)[/tex] is the slope of the line and [tex]\( b \)[/tex] is the y-intercept.

In this scenario, the slope [tex]\( m \)[/tex] is the cost per hour, which is $3. The y-intercept [tex]\( b \)[/tex] is the initial sign-up fee, which is $1.

Therefore, the equation representing the total cost [tex]\( y \)[/tex] as a function of the number of hours [tex]\( x \)[/tex] used at the gym is:

[tex]\[ y = 3x + 1 \][/tex]

However, to make the equation more precise and to express the cost per hour as a fraction, we can write $3 as [tex]\( \frac{3}{1} \)[/tex] and then multiply both the numerator and the denominator by 4 to get [tex]\( \frac{3 \times 4}{1 \times 4} = \frac{12}{4} \)[/tex]. Simplifying the fraction [tex]\( \frac{12}{4} \)[/tex] gives us [tex]\( \frac{3}{4} \)[/tex]per hour.

Thus, the final slope-intercept form equation for the word problem is:

[tex]\[ y = \frac{3}{4}x + 1 \][/tex]

a country's population in 1995 was 56 million in 2002 it was 59 million. estimate the population in 2016

Answers

I hope this helps you

Answer:

69 420 911

Step-by-step explanation:


The ratio of an objects wait on Earth to its weight on Neptune is 5:7. How much would a person who weighs 150 pounds weigh on Neptune

Answers

NOTE: I think you mean weight not wait lol

The ratio  "5:7:

Means for every 5 pounds on earth is an extra 2 pounds (or 7 pounds) on Neptune.

So to get from 5 to 150 is a factor of 30. So our ratio is now

"150:210"

So the object weighs "210"

Solve the system of equations below by graphing them with a pencil and paper. Choose the correct ordered pair (b, u).

u = -b + 21
u = -2b + 30 ...?

Answers

u = -b + 21 . . . (1)
u = -2b + 30 . . . (2)
Equating (1) and (2),
-b + 21 = -2b + 30
-b + 2b = 30 - 21
b = 9
u = -9 + 21 = 12

Therefore, (b, u) = (9, 12).

Match the inequality to the graph of its solution.
a. n/4 ≤ -1
b. -10 ≥ -100
c. 5x ≥ 20

Answers

Part (a):
The given inequality is: 
n/4 ≤ -1
we need to isolate the n on one side of the inequality. To do this, we will multiply both sides by 4 as follows:
n/4 x 4 ≤ -1 x 4
The inequality now is:
n ≤ -4
The correct graph representing this is graph (b)

Part (b):
The given inequality is: 
-10 ≥ -100
So, we will just search for the graph the shows that -10 is greater than the -100
The correct graph representing this is graph (a)

Part (c):
The given inequality is:
5x ≥ 20
we need to isolate the x on one side of the inequality. To do this, we will divide both sides by 5 as follows:
5x/5 ≥ 20/5
The inequality now is:
x ≥ 4
The correct graph representing this is graph (c)

Answer:

idiot

Step-by-step explanation:

its b a c i think

what is the circumference this unit circle

Answers

Unit circle is the circle with radius of 1. Therefore, the circumference of the unit circle is 2pi*r. R equals to 1, so the circumference is just 2pi

The circumference of a unit circle is calculated using the formula C = 2πr. For a unit circle, where the radius (r) is 1, the circumference (C) is 2π, approximately 6.2832.

The Circumference of a Unit Circle

In mathematics, the circumference of a circle is the distance around its perimeter. For a unit circle, which is a circle with a radius of 1, the formula to calculate circumference is given by C = 2πr, where r is the radius.

Since the radius of a unit circle is 1, substituting in the formula gives us:

C = 2π(1) = 2π

Thus, the circumference of a unit circle is 2π, which is approximately 6.2832 when using the value of π ≈ 3.1416.

Select all that justify the following statement.

10 + x 12 = 12x + 10
a) commutative - addition
b) distributive
c) associative - multiplication
d) symmetric
e) commutative - multiplication
f) associative - addition
g) identity - addition

Answers

This one 10 + x12 = 12x + 10 is a) commutative - addition
And this 10 + x12 =10 + 12x is e) commutative - multiplication

So you use them both. And they're both correct. 

Answer:

The statement satisfied the  expression 10 + x 12 = 12x + 10 is

Option (e) i.e commutative - multiplication and Option (a) i.e commutative - addition .

Step-by-step explanation:

Commutative Property

Let a, b be two numbers thus they satisfied the commutative property

i.e a + b = b + a

As given the expression.

10 + x ×12 = 12x + 10

First apply the Option (e) i.e Commutative - multiplication.

Thus expression becomes

10 + 12x = 12x + 10

Now apply the Option (a) i.e Commutative - addition.

Therefore the statement satisfied the  expression 10 + x 12 = 12x + 10 is

Option (e) i.e commutative - multiplication and Option (a) i.e commutative - addition .





A stone is dropped into a lake, creating a circular ripple that travels outward at a speed of 40 cm/s. Find the rate at which the area within the circle is increasing after each of the following.
after 1 s = after 3 s = after 7 s =

Answers

given : dr/dt = 40 cm/s A = πr^2 dA/dt = 2π r dr/dt case 1: when s = 1, r = 40 dA/dt = 2π(40)(40) = 3200π cm^2/sec case 2: when s = 3, r = 3(4) = 120 cm dA/dt = 2π(120)(40) = 9600π cm^2/sec case 3: ... your turn .....

Please help me with an addition formula problem!


Solve the system by the elimination method. Check your work.

2a + 3b = 6

5a + 2b - 4 = 0

Answers

2a + 3b = 6
5a + 2b = 4

We multiply the first equation by 5 and the second by 2 and and subtract the second from the first:

10a + 15b = 30
-10a -4b = -8

11b = 22
b = 2

2a + 3(2) = 6
2a = 0
a = 0

Checking,
5(0) + 2(2) = 4
4 = 4, true

What is the value of X plez?

Answers

Not sure however I keep getting 1

How did 25/10 gets simplified tho??

Answers

25 / 5 = 5 
10 / 5 = 2 

so the fraction can be simplified to 5/2
You have to find the highest common factor for both

so for 25/10 the highest common factor is 5. So you have to divide both numbers by 5 to simplify it.

25/10 = 5/2

:)

8) g(n) = 3n + 2

Perform the indicated operation
f (n) = 2n
2
+ 5
Find g( f (2))

Answers

The answer is: 41

Step 1: Calculate f(2).
Step 2: Calculate g(f(2)).

Step 1.
f(n) = 2n² + 5

If n = 2, then f(n) = f(2) = ?

f(2) = 2 * 2² + 5 = 2 * 4 + 5 = 8 + 5 = 13


Step 2.
g(n) = 3n + 2

If n = f(n), then g(n) = g(f(n)).
If f(2) = 13, then g(f(2)) = g(13) = ?

g(13) = 3 * 13 + 2 = 39 + 2 = 41

Write the following equation in general form 4x-6y=14

a. 4x-6y-14=0
b. 2x-3y=7
c. 2x-3y-7=0

Answers

Final answer:

The equation 4x - 6y = 14 can be written in general form as 4x - 6y - 14 = 0, which is option (a). This is the standard general form for a linear equation.

Explanation:

The equation given, 4x - 6y = 14, needs to be written in the general form. The general form of a linear equation is Ax + By + C = 0, where A, B, and C are constants. To rewrite the given equation in general form, we simply need to move all terms to one side of the equation. So the general form of the given equation is:

4x - 6y - 14 = 0.

This matches option (a) from the choices provided. It is important to note that a linear equation represents a straight line when graphed on the coordinate plane. The general form is helpful for various applications, including determining the x and y-intercepts.

Doug dives from a platform that is 7.5 meters above water. His dive takes him 2.1 meters below the surface of the water. How far does Doug​'s dive take him​?

Answers

Not so sure.. but I got 9.6 meters below water level.
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