Answer: Aₙ = 3*Aₙ₋₁ - 12
Step-by-step explanation:
Here our terms will be denoted as:
Aₙ
Where this is the n-th term of the sequence.
Now we have that the recurrence relation is defined by:
"by multiplying the prior term by 3 and subtracting 12."
Then we will have that:
Aₙ = 3*Aₙ₋₁ - 12
That is the equation to find all the terms in our sequence (remember that we need to know the initial term, A₀ in order to find all the other ones)
Let A and B be symmetric nxn matrices. For each of the following, determine whether the given matrix must be symmetric or could be nonsymmetric.a) C = A + Bb) D = A^2c) E = ABd) F = ABAe) G = AB + BAf) H = AB-BA
The matrices C, D, F, and G are symmetric while matrix H is skew-symmetric and matrix E is non-symmetric.
A matrix is an array of elements(numbers) in a peculiar order. A matrix with m rows and n columns is said to be of order m × n.
As it is known that [tex](A + B)^t = A^t + B^t[/tex] and [tex](AB)^t = B^t A^t[/tex] for any n × n matrices A and B.
Also, if matrices A and B are symmetric, then
[tex]A^t = A[/tex] and [tex]B^t = B[/tex].
a) Given that
C = A + B
Take the transpose of matrix C,
[tex]C^t = (A + B)^t[/tex]
[tex]= A^t + B^t \\= A + B = C[/tex].
Hence, matrix C is symmetric.
b) Given that
D = A²
Take the transpose of matrix D,
[tex]D = (A^2)^t[/tex]
[tex]= (AA)^t \\= A^t A^t \\= AA \\= A^2 = D[/tex].
Hence, matrix D is symmetric.
c) Given that
E = AB
Let's take an example,
A = [tex]\left[\begin{array}{cc}1&2&2&1\end{array}\right][/tex] and
B = [tex]\left[\begin{array}{cc}1 &-1 &-1&2\end{array}\right][/tex]
So,
E = AB
[tex]=\left[\begin{array}{cc}1&2&2&1\end{array}\right] \times \left[\begin{array}{cc}1 &-1 &-1&2\end{array}\right]\\= \left[\begin{array}{cc}-1&3&1&0\end{array}\right][/tex]
Clearly, matrix E is non-symmetric.
d) Given that
F = ABA
Take the transpose of matrix F,
[tex]F^t = (ABA)^t[/tex]
[tex]= A^t B^t A^t\\ = ABA = F[/tex].
Hence, matrix F is symmetric.
e) Given that
G = AB + BA
Take the transpose of matrix G,
[tex]G^t = (AB + BA)^t[/tex]
[tex]= (AB)^t + (BA)^t \\= B^t A^t + A^t B^t \\= BA + AB = G[/tex].
Hence, matrix G is symmetric.
f) Given that
H = AB-BA
Take the transpose of matrix H,
[tex]H^t = (AB - BA)^t[/tex]
[tex]= (AB)^t - (BA)^t \\= B^t A^t - A^t B^t \\= BA - AB = -H[/tex].
Hence, matrix H is skew-symmetric.
Thus, the matrices C, D, F, and G are symmetric while the rest are not.
Learn more about Matrix here:
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Use the substitution method to solve the system of equations. Choose the
correct ordered pair.
2x + 3y = 29
x = 4
A. (4,7)
B. (3,2)
C. (7,4)
D. (4,11)
Algebra 2 Help! Please help.
Step-by-step explanation:
h(x) =-x-4
h(x)=9
=>9=-x-4
=>x=-13
Answer:
We place 9 in the first expression instead of h (x)
Then we solve the equation
9=-x-4
x=-13
round 737.88 to the nearest tenth place?
Answer:
737.9
Step-by-step explanation:
8 is the hundredth place in 737.88, and 8 rounds up. So, the answer is 737.9
Answer:
737.9
Step-by-step explanation:
When we round something to the nearest ___ place, we want to look to the value to the right of it.
Since we're rounding it to the nearest tenths place, we want to look at the value to the right of it - the hundredths place.
The number in the tens place will be one more if the hundredths place is 5 or greater. It will remain the same if the hundredths place is below 5.
8 is greater than 5. This means the tens place will round up to 9.
So 737.9.
Hope this helped!
if a bag contains 12 quarts 6 dimes 18 nickles what is the part to whole ratio of dimes to all coins
Answer:
I'm not really sure but I think its 6:36
Step-by-step explanation:
12 quarters + 18 nickels + 6 dimes = 36 coins in total
6 dimes in total
6:36
Solve the literal equation 5a + 10b = 2b - 4a for a.
Answer:
A=-8b/9
Step-by-step explanation:
What is 1/5 miles in units to 1/65 hours
Answer:
13/65 miles in 1/65 of an hour, I believe is the answer you're looking for. Hope this helped!
Step-by-step explanation:
Which is the best estimate of 47 to the nearest tenth?i
Answer:
47.0Step-by-step explanation:
Answer:
Square Root of 47 to the nearest tenth, means to calculate the square root of 47 where the answer should only have one number after the decimal point. To check that the answer is correct, use your calculator to confirm that 6.92 is about 47.
Step-by-step explanation:
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Which of the following is a value are perfect square
Check all that apply
1
2
55
81
121
Answer:
1, 81, and 121 are correct
Step-by-step explanation:
they are the only ones that do not have a decimal when squared
1=1
81=9
121=11
the sum of a number and 6 is 3
Answer:
x + 6 = 3
-3 + 6 = 3
Step-by-step explanation:
x + 6 = 3
x + 6 - 6 = 3 - 6
x = -3
Express the following vector in the form v vi+V2j+ v3k 3u -v if u (3,5,-8) and v (2,-5,7)
Answer:
7i+20j-31kStep-by-step explanation:
Given the vectors u (3,5,-8) and v (2,-5,7), they can also be written as;
u = 3i+5j-8k
v = 2i-5j+7k
To express the vector 3u - v in vector form, first let us find the vector 3u;
3u = 3(3i+5j-8k)
3u = 3(3i)+3(5j)-3(8k)
3u = 9i+15j-24k
Subtract v from the resulting vector.
Since v = 2i-5j+7k
3u - v = 9i+15j-24k - (2i-5j+7k)
3u-v = 9i+15j-24k -2i+5j-7k
collect the like terms
3u-v = 9i-2i+15j+5j-24k-7k
3u-v = 7i+20j-31k
Hence the vector 3u-v in the form v = vi+V2j+ v3k is 7i+20j-31k
What are the different types of cardinal numbers?
Answer:
Cardinal, Ordinal, and Nominal Numbers
Step-by-step explanation:
Answer:
A Cardinal Number is a number that says how many of something there are, such as one, two, three, four, five. An Ordinal Number is a number that tells the position of something in a list, such as 1st, 2nd, 3rd, 4th, 5th etc
pls help i will mark brainliest......i have a time limit
Answer:
Hey there!
If angle one is congruent to angle two, all of the above is true.
Let me know if this helps :)
John has a 4 litre bottle of water. One mug holds one half of a litre of water. Jane drinks 3 mugs of water, how many mugs would the remaining water fill
Answer:
the answer is 3.5
Step-by-step explanation:
1. the total is 4
2.each mug = .5 of a litre
3.jane drinks 3 mugs which=1.5
4.she drinks 1.5 litres which is 3.5 of the whole bottle
5.so the remaining will be 3.5 which is what remains after she drank 1.5 litres of the whole bottle
As part of their application for a loan to buy Lakeside Farm, a property they hope to develop as a bed-and-breakfast operation, the prospective owners have projected:
Monthly fixed cost (loan payment, taxes, insurance, maintenance) $6000
Variable cost per occupied room per night $ 20
Revenue per occupied room per night $ 75
a. Write the expression for total cost per month. Assume 30 days per month.
b. Write the expression for total revenue per month, first using the general variables, and second including the values of known variables).
c. If there are 12 guest rooms available, can they break even? What would be the profit with 12 rooms?
d. What percentage of rooms would need to be occupied, on average, to break even?
Answer:
Instructions are below.
Step-by-step explanation:
Giving the following information:
Monthly fixed cost= $6,000
Variable cost per occupied room per night= $20
Revenue per occupied room per night= $75
First, we need to structure the total cost formula:
Total cost= 6,000 + 20*x
x= occupied room
Now, we can find the expression for total revenue:
Revenue= selling price per unit*units - fixed cost - unitary variable cost*units
Revenue= 75*x - 6,000 - 20*x
I assume that the 12 rooms will be occupied for the 30 days:
Revenue= 75*(12*30) - 6,000 - 20*(12*30)
Revenue= $13,800
Finally, we need to determine the break-even point in units:
Break-even point in units= fixed costs/ contribution margin per unit
Break-even point in units= 6,000 / (75 - 20)
Break-even point in units= 109 rooms
On percentage= (109/360)*100= 30.28%
Please Help!! Angles A and B are complementary. If the measure of angle A=3x-8 and measure of Angle B =5x+10, what is the measure is each angle?
Answer:
Step-by-step explanation:
3x - 8 + 5x + 10 = 90
8x + 2 = 90
8x = 88
x = 11
3(11) - 8 = 33 - 8 = 25 for <A
5(11) + 10 = 55 + 10 = 65 for<B
Find the missing exponent
Answer:
-6
Step-by-step explanation:
When an exponent is outside and inside the parenthesis you need to add them to get rid of the the parenthesis. The answer is -6 because -6*2 is -12.
Hope this helps. If you have questions put them in the comments.
Answer:-6
Step-by-step explanation:
When an exponent is outside and inside the parenthesis you need to add them to get rid of the the parenthesis. The answer is -6 because -6*2 is -12.
Anjali spent half of her weekly allowance
at the movies. To earn more money her
parents let her weed the garden for $10.
What is her weekly allowance if she ended
with $19?
A woman making $3000 per month has her salary reduced by 10% because of sluggish sales. One year later, after a dramatic improvement in sales, she is given a 20% raise over her reduced salary. Find her salary after the raise.
Answer:
$3240 a month
Step-by-step explanation:
First, find her reduced salary:
3000(0.9)
= 2700
Then, find her salary after the raise:
2700(1.2)
= 3240
So, her salary after the raise is $3240 a month
Which inequality is true?
O A n-3>1
B. 9n> 27
c. 9/3n> 1
O D. N+7<10
Answer:
c.
Step-by-step explanation:
3. Two fair dice are thrown once, find the probability of getting a total score greater than 5
Answer:
26/36
Step-by-step explanation:
The probability of something = the amount of favourable outcomes/total possible outcomes.
The total number of dice combinations is 36 (6x6).
In this case there are more outcomes more than 5 than less than 5 so for the sake of simplicity we are going to find the number of outcomes less than 5 and then find the inverse.
There are only 10 possible dice combos which add to totals 5 or under:
1,1 1,2 2,1 1,3 3,1 1,4 4,1 2,2 2,3 and 3,2
That means there is a 10/36 probability of getting a total score less than 5 so to get the probability of getting more than 5, we just do 36/36 - 10/36 (because all probabilities add to 1)
Therefore there is a 26/36 probability that the toatals will add to greater than 5.
Alternatively you could also draw up a possibilities table and count the favourable outcomes.
Hope this helped!
Answer:
13/18.
Step-by-step explanation:
The favourable outcomes are (1,5) (1,6) (2,4) (2,5) (2,6) (3,3) (3,4) (3,5) (3,6) (4,2)(4,3) (4,4) 4,5) (4,6) 5,1) (5,2) 5,3) (5,4) (5,5) (5,6 )(6,1) to (6,6).
= total of 26.
As the total of all possible outcomes is 36 the answer is 26/36
= 13/18.
If (42)P = 414, what is the value of p?
7 8 12 16
Answer:
c
Step-by-step explanation:
what number does a Roman numerals MDC XL IX represent
Answer:
the answer is 1649
Help i dont understand this someone help me pls :(
Answer:
10
Step-by-step explanation:
Sally hopes to buy a 10 - kayak for $15,000. Describe all the numbers that when round to the nearest hundred are 15,000
Answer:
All the numbers ranging from 14,500 to 15444 would be rounded to 15000
Step-by-step explanation:
All the numbers ranging from 14,500 to 15444 would be rounded to 15000.
How this is possible.
1) all the numbers from 0-4 are not counted as the next number when rounded off.
2) all the numbers from 5-9 are counted as the next number when rounded off.
Example Suppose we have numbers from 15- 19.
These numbers can be rounded off to 20
But numbers from 10-14 would never be rounded off to 20 instead they are rounded as 10.
Same happens in the hundreds case.
If we have numbers from 450 - 499 they can be rounded as 500
And numbers from 400 - 444 cannot be rounded as 500 but the number 445 may be rounded as 450 . When we carry 5 from units place and replace it as 450 then again 450 can be rounded to 500.
Same happens with 15000 but when are rounding nearest hundred not ten.
Thus all the numbers ranging from 14,500 to 15444 would be rounded to 15000.
If a package of gift cards has a total value of $1050 how much does the average set of 2 gifts card price at if there are 15 in a group?
Answer:
$140
Step-by-step explanation:
If a package of gift cards has a total value of $1050, the total price for 2 gift cards will be 2×$1050 = $2100
If there are 15 in an average set of 2 gift cards, the average cost of the two gift cards will be expressed as;
Total price of 2gift cards/amount of card per group.
Average cost of of 2 gift cards = $2100/15
= $140
Hence the average cost of 2gift cards if there are 15 in a group is $134
OLGA went on an 82 mile bike trip last week by Thursday night she travel 64 miles of the total distance which president is reasonable estimate of how much of the trip OLGA completed by Thursday
Answer:Note: This symbol ≈ means approximately.
629 ≈ 600
215 ≈ 200
111 ≈ 100
588 ≈ 600
Now, we add the simplified numbers up: 600 + 200 + 100 + 600 = 1500. So, your answer is D or 1,500.
Step-by-step explanation:PLZZZ GIVE BRAINLYEST HOPE IT HELPS
Find an expression for the number of colored border tiles needed for any N x N square center.
Answer:
8N - 4 border tiles.
Step-by-step explanation:
There are 4 border tiles in each corner and between the tiles there are N-2 tiles along the 4 sides.
So the number of border tiles
= 4+ 4(N - 2)
= 4 + 4N - 8
= 8N - 4.
What’s the answer to 1.9m + 14 = 2m?
Answer:
[tex] \boxed{ \bold{ \huge{ \boxed{ \sf{m = 140}}}}}[/tex]
Step-by-step explanation:
[tex] \sf{1.9m + 14 = 2m}[/tex]
Move 2m to right hand side and change it's sign
Similarly, move 14 to left hand side and change it's sign
[tex] \dashrightarrow{ \sf{1.9m - 2m = - 14}}[/tex]
Collect like terms
[tex] \dashrightarrow{ \sf{ - 0.1m = - 14}}[/tex]
Divide both sides by -0.1
[tex] \dashrightarrow{ \sf{ \frac{ - 0.1m} { - 0.1} = \frac{ - 14}{ - 0.1}}} [/tex]
Calculate
[tex] \dashrightarrow{ \sf{m = 140}}[/tex]
Hope I helped!
Best regards! :D
Jamie invests part of $10,000 at 9% annual interest and the rest at 8%. If his annual income from
these investments is $860, how much does he invest at 8%?
Answer:
$4000
Step-by-step explanation:
Assuming a = money invested at 9%
Assuming b = money invested at 8%
then we can form am equation from the question given
1) a + b = $10000, also
0.09a + 0.08b = $860 -> multiply by 100
2) 9a + 8b = $86000
Next we try to solve both equations simultaneously. We multiply both the left hand side and the right hand side of the first equation by 8. We have
3) 8a + 8b = $80000, now we subtract 3 from 2
9a + 8b = $86000
-8a - 8b = -$80000
a = $6000.
Then, we plug this in any of the first 2 equations, to get b
9 * $6000 + 8b = $86000
$54000 + 8b = $86000
8b = $86000 - $54000
8b = $32000
b = $32000/8
b = $4000.
Therefore, he invested $4000 at 8%