In this problem, we are given two bases for R2, B = {(1, 2), (-1, -1)} and B' = {(-4, 1), (0, 2)}. We are asked to find the transition matrix P from B' to B, and then use this matrix to find [v]B and [T(v)]B'. Finally, we need to find the inverse of P and the matrix A' for T relative to B', and then use these to find [T(v)]B' in two different ways.
To find the transition matrix P from B' to B, we need to express the vectors in B' as linear combinations of the vectors in B, and then write the coefficients as columns of a matrix. Doing this, we get:
P = [ [1, 2], [-1, -1] ][tex]^-1[/tex] * [ [-4, 0], [1, 2] ] = [ [-2, 2], [1, -1] ]
Next, we are given [v]B' = [4, -1]T and asked to find [v]B and [T(v)]B'. To find [v]B, we use the formula [v]B = P[v]B', which gives us [v]B = [-10, 5]T. To find [T(v)]B', we first need to find the matrix A for T relative to B. To do this, we compute A = [tex][T(1,2), T(-1,-1)][/tex]* P^-1 = [ [6, 3], [-1, -1] ]. Then, we can compute [T(v)]B' = A[v]B' = [-26, 5]T.
Next, we are asked to [tex]find[/tex][tex]P^-1[/tex]and A', the matrix for T relative to B'. To find P^-1, we simply invert the matrix P to get P^-1 = [ [-1/2, 1/2], [1/2, -1/2] ]. To find A', we need to compute the matrix A for T relative to B', which is given by A' = P^-1 * A * P = [ [0, -3], [0, 2] ].
Finally, we are asked to find [T(v)]B' in two different ways. The first way is to use the formula [T(v)]B' = P^-1[T(v)]B, which gives us [T(v)]B' = [-26, 5]T, the same as before. The second way is to use the formula[tex][T(v)]B'[/tex] = A'[v]B', which gives us[tex][T(v)]B'[/tex] = [-26, 5]T
Learn more about transition matrix here:
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How many tons are equal to 36,000 pounds? With work!
Answer:
18 tons
Step-by-step explanation:
1 pound = 0.0005 ton
Therefore,
36,000 pounds
= 36000*0.0005
= 18 tons
What is additive inverse of the check?
please help
7x -3
-7x + 3
-7x - 3
7x - 3
Answer:
pretty sure it would be 7x-3
Alfredo is ordering a taxi from an online taxi service. The taxi charges $3.50 just for
the pickup and then an additional $0.75 per mile driven. How much would a taxi ride
cost if Alfredo is riding for 5 miles? How much would a taxi ride cost that is m miles
long?
Is -50 greater than 2
True or false
FALSE
because negative (-) numbers are always smaller than positive (+) numbers
because negative (-) numbers are always smaller than positive (+) numbers
because negative (-) numbers are always smaller than positive (+) numbers
because negative (-) numbers are always smaller than positive (+) numbers
because negative (-) numbers are always smaller than positive (+) numbers
because negative (-) numbers are always smaller than positive (+) numbers
because negative (-) numbers are always smaller than positive (+) numbers
because negative (-) numbers are always smaller than positive (+) numbers
because negative (-) numbers are always smaller than positive (+) numbers
because negative (-) numbers are always smaller than positive (+) numbers
because negative (-) numbers are always smaller than positive (+) numbers
because negative (-) numbers are always smaller than positive (+) numbers
because negative (-) numbers are always smaller than positive (+) numbers
because negative (-) numbers are always smaller than positive (+) numbers
because negative (-) numbers are always smaller than positive (+) numbers
because negative (-) numbers are always smaller than positive (+) numbers
because negative (-) numbers are always smaller than positive (+) numbers
because negative (-) numbers are always smaller than positive (+) numbers
because negative (-) numbers are always smaller than positive (+) numbers
because negative (-) numbers are always smaller than positive (+) numbers
because negative (-) numbers are always smaller than positive (+) numbers
because negative (-) numbers are always smaller than positive (+) numbers
because negative (-) numbers are always smaller than positive (+) numbers
because negative (-) numbers are always smaller than positive (+) numbers
because negative (-) numbers are always smaller than positive (+) numbers
because negative (-) numbers are always smaller than positive (+) numbers
because negative (-) numbers are always smaller than positive (+) numbers
because negative (-) numbers are always smaller than positive (+) numbers
because negative (-) numbers are always smaller than positive (+) numbers
because negative (-) numbers are always smaller than positive (+) numbers
because negative (-) numbers are always smaller than positive (+) numbers
because negative (-) numbers are always smaller than positive (+) numbers
because negative (-) numbers are always smaller than positive (+) numbers
because negative (-) numbers are always smaller than positive (+) numbers
because negative (-) numbers are always smaller than positive (+) numbers
because negative (-) numbers are always smaller than positive (+) numbers
because negative (-) numbers are always smaller than positive (+) numbers
because negative (-) numbers are always smaller than positive (+) numbers
because negative (-) numbers are always smaller than positive (+) numbers
because negative (-) numbers are always smaller than positive (+) numbers
because negative (-) numbers are always smaller than positive (+) numbers
because negative (-) numbers are always smaller than positive (+) numbers
because negative (-) numbers are always smaller than positive (+) numbers
because negative (-) numbers are always smaller than positive (+) numbers
because negative (-) numbers are always smaller than positive (+) numbers
because negative (-) numbers are always smaller than positive (+) numbers
because negative (-) numbers are always smaller than positive (+) numbers
because negative (-) numbers are always smaller than positive (+) numbers
because negative (-) numbers are always smaller than positive (+) numbers
because negative (-) numbers are always smaller than positive (+) numbers
because negative (-) numbers are always smaller than positive (+) numbers
Which number line shows all the values of that make the inequality -3 +1 < 7 true?
Answer:
Number line D is true
Step-by-step explanation:
Given
[tex]-3x + 1 < 7[/tex]
See attachment for number lines
Required
Which number line makes the inequality true
First, we solve for x in [tex]-3x + 1 < 7[/tex]
[tex]-3x < 7 - 1[/tex]
[tex]-3x < 6[/tex]
Divide through by -3
[tex]\frac{-3x}{-3} < \frac{6}{-3}[/tex]
[tex]x > -2[/tex]
The inequality means x is greater than -2.
This means that, the line must point to the right of -2 and the "greater than" means that the circle must be opened
Number line D is true
need help , ill give a brainlist to the best answer
Answer:
-7, 7
Step-by-step explanation:
A coin lands on heads 300 times. The relative frequency of heads is 0.6. How many times was the coin flipped?
Answer: Number of times the coin is flipped =500
Step-by-step explanation:
Relative frequency of head = [tex]\dfrac{\text{Number of times heads occur}}{\text{Total number of times coin is flipped}}[/tex]
Let x= Number of times the coin is flipped, then
[tex]0.6=\dfrac{300}{x}\\\\\Rightarrow\ x=\dfrac{300}{0.6}\\\\\Rightarrow\ x=\dfrac{3000}{6}\\\\\Rightarrow\ x=500[/tex]
Hence, Number of times the coin is flipped =500
PLSSSSSSSS HELP CORRECT ANSWER GETS BRAINLIEST
Answers
A.2 bags
B.3 bags
C.4 bags
D.5 bags
Answer:
A. 2 bags
Step-by-step explanation:
12x5=60
60 divided by 2 = 30
30 divided by 15 equals 2 bags
Please tell me if this is correct or incorrect
Hope this helps
Step-by-step explanation:
what are the dimensions of the flower bed
otherwise you can solve it by 151515/area of the flower bed
HELP meeeeeeeeeeeeeeeeeeeee
Answer:
first:
a)
second:
b)
Step-by-step explanation:
In AJKL.m._J = 40and m K = 55°. In AMNP, m M = 40° and m P = 85 A student concludes that the triangles are not similar. Do you agree or disagree? Why? (1 point)
O Disagree, by the Interior Angles Theorem, m N = 55°, so the triangles are similar by the AA similarity criterion
O Disagree, by the Interior Angles Theorem, mZN = 45°, so the triangles are similar by the AA similarity criterion
O Agree by the interior Angles Theorem, m_N = 45 Togo the triangles are not similar by the AA
O Agree, since m_K #m_P, the triangles are not similar by the AA similarity criterion
Answer: A
Step-by-step explanation:
Source: trust me bro
10 - 4 (3-2y) = 8y -5
Answer:
No Solutions
Step-by-step explanation:
10 - 4(3-2y) = 8y - 5
Distribute:
10 - 12 + 8y = 8y - 5
Simplify:
-2 + 8y = 8y - 5
Same to both sides
-2 + 5 = 8y - 8y
3 = 0y
No Solutions
Let me know if you have any questions
3 unit right
3 unit left
3 unit up
3 unit down
8 unit right
8 unit left
8 unit up
8 unit down
Help me plz., ,, ,, ,, ,,,
Answer:
1. 100000
2. 16777216
3. x7
4.64
5.1/64 (Decimal: 0.015625)
Step-by-step explanation:
5= h/1.25 help me plz
Answer:
Step-by-step explanation:
5=h/1.25
h=6.25
On solving for the value of {h}, we get -
{h} = 6.25.
What is function?A function is a relation between a dependent and independent variable. We can write the examples of functions as -
y = f(x) = ax + b
y = f(x, y, z) = ax + by + cz
Given is the expression as -
5 = h/1.25
We can solve for the value of {h} as -
5 = h/1.25
{h} = 5 x 1.25
{h} = 5 x 125/100
{h} = 125/20
{h} = 6.25
Therefore, on solving for the value of {h}, we get -
{h} = 6.25.
To solve more questions on functions, visit the link below-
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Szklanka ma pojemnóść 250ml czyli 250cm³. Ile szklanek można napełnić wodą z litrowej butelkki
Answer:
75cm
Step-by-step explanation:
When a new TV became available in a store, the number sold in the first week was high. Sales
decreased over the next two weeks and then they remained steady over the next two weeks. The
following week, the total number sold by the store increased slightly. Sketch the graph of this function
over the six weeks.
Answer:
The way you would sketch the graph is slowly increasing, staying about the same, and then go up a little bit.
Good luck!
Can someone help me please
Answer:
height of b = 280
Step-by-step explanation:
candle b has a height of 280 - 5t, when it comes out of the mold then t=0 so the initial height of b is 280
candle b's height drops by 5 every hour (that's what the -5t part means)
candle a started at 216 and dropped to 192 in 3 hours, so it dropped by 24 in 3 hours so it drops 8 each hour
so candle b starts out taller (280 v. 216) and candle b burns slower (a at 8 per hour and b at 5 per hour), so b will never 'catch up' with a... candle a will be burned out while candle b is still burning
is a rectangle a plane shape
Answer:
A plane shape with four straight sides and four right angles for corners is called a rectangle.
Step-by-step explanation:
1/3a = -5. Solve each equation
Answer:
1/3a = -5
1=3a×-5
1=-15a
a=-1/15
Answer:
a=-15
Step-by-step explanation:
1/3a = -5
1/3(*3)a=-5*3
a=-15
A local aquarium purchased a new turtle tank for their giant turtle exhibit. What is the volume of the turtle tank?
Answer:
[tex]Volume = 1440m^3[/tex]
Step-by-step explanation:
Given
Missing dimensions:
[tex]Length = 15m[/tex]
[tex]Width = 8m[/tex]
[tex]Height = 12m[/tex]
Required
Determine the volume
Volume is calculated as:
[tex]Volume = Length * Width * Height[/tex]
This gives:
[tex]Volume = 15m * 8m * 12m[/tex]
[tex]Volume = 1440m^3[/tex]
please help me on this will give you brainliest
Answer:
2,010,000
Step-by-step explanation:
3 x 10^5
10^5= 100000
3 x 100000 = 300000
300000 x 6.7 = 2,010,000
Hope this helps
Answer:
Im not 100% sure but i think its 44,776.1194
Step-by-step explanation: What you do is multiply 3 x 100,000 because 10 to the 5th power is 100,000. Then you divide 300,000 by 6.7 and get your answer of 44,776.1194. Sorry if its incorrect
A student solves the inequality −5v>55. Each step in the student's solution is shown below. Identify where the student made any errors.
Note: Steps of student are not given. So, the proper steps of the solution are provided below.
Given:
The inequality is
[tex]-5v>55[/tex]
To find:
Where the student made any errors?
Solution:
We have,
[tex]-5v>55[/tex]
On dividing both sides -5 change the sign of equality because -5 is a negative number.
[tex]\dfrac{-5v}{-5}<\dfrac{55}{-5}[/tex]
[tex]v<-11[/tex]
Therefore, the solution of given inequality is [tex]v<-11[/tex].
A quantity with an initial value of 720 decays continuously at a rate of 9% per hour. What is the value of the quantity after 69 hours, to the nearest hundredth?
Answer:
1.45
Step-by-step explanation:
f(t)=720e^rt
f(t)=720e
rt
Continuously uses Pe^(rt)
r\text{: decays }9\% \
r: decays 9%→−0.09
per hour
f(t)=720e^{-0.09t}
f(t)=720e
−0.09t
(where t is in hours)
69\text{ hours: no time conversion necessary}
69 hours: no time conversion necessary
hours are the only units in the problem.
\text{Plug in }t=69
Plug in t=69
f(69)=720e^{-0.09(69)}
f(69)=720e
−0.09(69)
1.44665097413
1.44665097413
\approx 1.45
≈1.45
Round to the nearest hundredth
Rewrite this division expression a an equivalent multiplication expression: 5/8 divided by 2/3
Please help me I’m not very smart lol
Answer:
Step-by-step explanation:
Dividing by a fraction is the same as multiplying by the upside-down fraction.
(5/8) ÷ (2/3) = (5/8) ⋅ (3/2) = 15/16
Connections Academy Sample Work Pre Calc
Please Help!!!
I believe
y (theta) = 3 sin t
and
a(theta) = 3 cos t
but that might be wrong because I'm so confused. Please Please help!
Step-by-step explanation:
sintheta=y/3"theta=sin-¹(y/3")
cos theta=a/3"
theta=cos-1(a/3)
sin beta=y/7"
beta=sin-¹(y/7")
b=√{y²+7" ²}
sorry last one I don't know
Answer:
sinθ = y/3 ⇒ y(θ) = 3 sinθcosθ = a/3 ⇒ a(θ) = 3 cosθsin β = y/7 = 3 sinθ / 7 ⇒ β(θ) = arcsin (3/7sinθ)b(θ) = √(7²-y²) = √(49-9sin²θ)p(θ) = a(θ) + b(θ) = 3 cosθ + √(49-9sin²θ)The graph is attached
---------------------------------------
p.s.
b(θ) can be put in different way:
cos β = b/7 ⇒ b(θ) = 7 cos β = 7cos(arcsin(3/7sinθ))Then
p(θ) = a(θ) + b(θ) = 3 cosθ + 7cos(arcsin(3/7sinθ))This doesn't change the function or the graph
The Value that you insert into a function is know as the?
Answer:
Step-by-step explanation:
Most commonly, that value would be the "independent variable."
We evaluate the function at that particular value of the independent variable.
if there are 10 birds for 4 dogs,what is the ratio of birds to dogs?
Answer:
10:4 ( Answer )
I hope it helps you
There are 6 balls. Half of the balls are blue. One ball is red. The rest are green. Write the fraction for the green balls.
Answer:
1/3 (Minimized) 2/6
Step-by-step explanation:
Write an equation of the parabola in intercept form that passes through (-2, 0.05) with x-intercepts of -7 and -3
Important things you need to know:
1. x intercept = solution of the equation
2. parabola = the highest power is x²
3. "passes through" is important because you have the y intercept (it is the c in ax² + bx + c = 0)
The intercept form is y = a(x-r)(x-s), where r and s are the x intercepts (solutions) of the graph
Substitite the numbers and values you know:
y = a(x-r)(x-s)
0.05 = a(-2-(-7)) × (-2-(-3))
Then you should find a.
Rewrite the equation in the form of y = a ( x+7 )( x+3 ) where the value of a is found.
Suppose that the function f(x)=3x+10 represents the cost to rent a movie for a month. Kim has $15. How many more dollars does she need to rent 8 movies?
Answer:
$19
Step-by-step explanation:
Given data
Cost of movie
f(x)=3x+10
Hence the cost of 8 movies is
f(x)=3(8)+10
f(x)=24+10
f(x)=$34
Hence the cost of 8 movies is $34, Kim needs extra
=34-15
=$19