basically the answer is 2n-1 2n comes from the difference to get from 1 to three and the -1 from 2n to get to 1 you need to minus 1 so you get -1
Determine if the table represents a linear function, quadratic function, or exponential function.
Answer:
Quadratic
Step-by-step explanation:
Formula: ax^2+bx+c
variables combining like terms
16. x+3
17. 5y+3
18. x+5y-5
Answer:
16.3x
17. 8y
18.x+y
I thing these are the answers of these equations
This and one more question, it’s now going to be put at much more points
Step-by-step explanation:
Number of stickers Rafael has left
= [tex]100 - 6s[/tex]
Substitute [tex]s = 7[/tex]into the expression.
[tex]100 - 6(7)[/tex]
= [tex]100 - 42[/tex]
= [tex]58[/tex]
Mr. discrete told his students if everyone in the class did at least 35 of the 40 homework assignments for second nine weeks he would add 4% to their final test if he determines the score by doubling the number of correct problems out of 50 and then adding the bonus which inequality would determine the fewest problems a student could answer correctly and still have a A?
A student must answer at least 35 of the 40 homework assignments correctly to get an A.
What is inequality?Inequality is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are not equal.
To determine the fewest number of problems a student could answer correctly and still get an A, we need to set up an inequality that represents the condition for getting an A.
If Mr. Discrete determines the score by doubling the number of correct problems out of 50 and then adding the bonus, then the score for each student can be represented by the equation:
2x + 4% × 50 = 100, where x is the number of correct problems.
If the student needs to get an A, then the score must be at least 90. Therefore, we can set up the inequality:
2x + 4% × 50 ≥ 90
Substituting 4% for 0.04, we get:
2x + 0.0450 ≥ 90
Solving for x, we find:
x ≥ 35
Therefore, to receive an A, a student must complete at least 35 out of the 40 homework assignments.
Learn more about the inequalities here:
brainly.com/question/20383699
#SPJ2
Let A be a given matrix below. First, find the eigenvalues and their corresponding eigenspaces for the following matrices. Then, find an invertible matrix P and a diagonal matrix such that A = PDPâ’1.
(a) [ 3 2 2 3 ]
(b) [ 1 â 1 2 â 1 ]
(c) [1 2 3 0 2 3 0 0 3]
(d) [3 1 1 1 3 1 1 1 3]
It looks like given matrices are supposed to be
[tex]\begin{array}{ccccccc}\begin{bmatrix}3&2\\2&3\end{bmatrix} & & \begin{bmatrix}1&-1\\2&-1\end{bmatrix} & & \begin{bmatrix}1&2&3\\0&2&3\\0&0&3\end{bmatrix} & & \begin{bmatrix}3&1&1\\1&3&1\\1&1&3\end{bmatrix}\end{array}[/tex]
You can find the eigenvalues of matrix A by solving for λ in the equation det(A - λI) = 0, where I is the identity matrix. We also have the following facts about eigenvalues:
• tr(A) = trace of A = sum of diagonal entries = sum of eigenvalues
• det(A) = determinant of A = product of eigenvalues
(a) The eigenvalues are λ₁ = 1 and λ₂ = 5, since
[tex]\mathrm{tr}\begin{bmatrix}3&2\\2&3\end{bmatrix} = 3 + 3 = 6[/tex]
[tex]\det\begin{bmatrix}3&2\\2&3\end{bmatrix} = 3^2-2^2 = 5[/tex]
and
λ₁ + λ₂ = 6 ⇒ λ₁ λ₂ = λ₁ (6 - λ₁) = 5
⇒ 6 λ₁ - λ₁² = 5
⇒ λ₁² - 6 λ₁ + 5 = 0
⇒ (λ₁ - 5) (λ₁ - 1) = 0
⇒ λ₁ = 5 or λ₁ = 1
To find the corresponding eigenvectors, we solve for the vector v in Av = λv, or equivalently (A - λI) v = 0.
• For λ = 1, we have
[tex]\begin{bmatrix}3-1&2\\2&3-1\end{bmatrix}v = \begin{bmatrix}2&2\\2&2\end{bmatrix}v = 0[/tex]
With v = (v₁, v₂)ᵀ, this equation tells us that
2 v₁ + 2 v₂ = 0
so that if we choose v₁ = -1, then v₂ = 1. So Av = v for the eigenvector v = (-1, 1)ᵀ.
• For λ = 5, we would end up with
[tex]\begin{bmatrix}-2&2\\2&-2\end{bmatrix}v = 0[/tex]
and this tells us
-2 v₁ + 2 v₂ = 0
and it follows that v = (1, 1)ᵀ.
Then the decomposition of A into PDP⁻¹ is obtained with
[tex]P = \begin{bmatrix}-1 & 1 \\ 1 & 1\end{bmatrix}[/tex]
[tex]D = \begin{bmatrix}1 & 0 \\ 0 & 5\end{bmatrix}[/tex]
where the n-th column of P is the eigenvector associated with the eigenvalue in the n-th row/column of D.
(b) Consult part (a) for specific details. You would find that the eigenvalues are i and -i, as in i = √(-1). The corresponding eigenvectors are (1 + i, 2)ᵀ and (1 - i, 2)ᵀ, so that A = PDP⁻¹ if
[tex]P = \begin{bmatrix}1+i & 1-i\\2&2\end{bmatrix}[/tex]
[tex]D = \begin{bmatrix}i&0\\0&i\end{bmatrix}[/tex]
(c) For a 3×3 matrix, I'm not aware of any shortcuts like above, so we proceed as usual:
[tex]\det(A-\lambda I) = \det\begin{bmatrix}1-\lambda & 2 & 3 \\ 0 & 2-\lambda & 3 \\ 0 & 0 & 3-\lambda\end{bmatrix} = 0[/tex]
Since A - λI is upper-triangular, the determinant is exactly the product the entries on the diagonal:
det(A - λI) = (1 - λ) (2 - λ) (3 - λ) = 0
and it follows that the eigenvalues are λ₁ = 1, λ₂ = 2, and λ₃ = 3. Now solve for v = (v₁, v₂, v₃)ᵀ such that (A - λI) v = 0.
• For λ = 1,
[tex]\begin{bmatrix}0&2&3\\0&1&3\\0&0&2\end{bmatrix}v = 0[/tex]
tells us we can freely choose v₁ = 1, while the other components must be v₂ = v₃ = 0. Then v = (1, 0, 0)ᵀ.
• For λ = 2,
[tex]\begin{bmatrix}-1&2&3\\0&0&3\\0&0&1\end{bmatrix}v = 0[/tex]
tells us we need to fix v₃ = 0. Then -v₁ + 2 v₂ = 0, so we can choose, say, v₂ = 1 and v₁ = 2. Then v = (2, 1, 0)ᵀ.
• For λ = 3,
[tex]\begin{bmatrix}-2&2&3\\0&-1&3\\0&0&0\end{bmatrix}v = 0[/tex]
tells us if we choose v₃ = 1, then it follows that v₂ = 3 and v₁ = 9/2. To make things neater, let's scale these components by a factor of 2, so that v = (9, 6, 2)ᵀ.
Then we have A = PDP⁻¹ for
[tex]P = \begin{bmatrix}1&2&9\\0&1&6\\0&0&2\end{bmatrix}[/tex]
[tex]D = \begin{bmatrix}1&0&0\\0&2&0\\0&0&3\end{bmatrix}[/tex]
(d) Consult part (c) for all the details. Or, we can observe that λ₁ = 2 is an eigenvalue, since subtracting 2I from A gives a matrix of only 1s and det(A - 2I) = 0. Then using the eigen-facts,
• tr(A) = 3 + 3 + 3 = 9 = 2 + λ₂ + λ₃ ⇒ λ₂ + λ₃ = 7
• det(A) = 20 = 2 λ₂ λ₃ ⇒ λ₂ λ₃ = 10
and we find λ₂ = 2 and λ₃ = 5.
I'll omit the details for finding the eigenvector associated with λ = 5; I ended up with v = (1, 1, 1)ᵀ.
• For λ = 2,
[tex]\begin{bmatrix}1&1&1\\1&1&1\\1&1&1\end{bmatrix}v = 0[/tex]
tells us that if we fix v₃ = 0, then v₁ + v₂ = 0, so that we can pick v₁ = 1 and v₂ = -1. So v = (1, -1, 0)ᵀ.
• For the repeated eigenvalue λ = 2, we find the generalized eigenvector such that (A - 2I)² v = 0.
[tex]\begin{bmatrix}1&1&1\\1&1&1\\1&1&1\end{bmatrix}^2 v = \begin{bmatrix}3&3&3\\3&3&3\\3&3&3\end{bmatrix}v = 0[/tex]
This time we fix v₂ = 0, so that 3 v₁ + 3 v₃ = 0, and we can pick v₁ = 1 and v₃ = -1. So v = (1, 0, -1)ᵀ.
Then A = PDP⁻¹ if
[tex]P = \begin{bmatrix}1 & 1 & 1 \\ 1 & -1 & 0 \\ 1 & 0 & -1\end{bmatrix}[/tex]
[tex]D = \begin{bmatrix}5&0&0\\0&2&0\\0&2&2\end{bmatrix}[/tex]
Two parallel chords PQ and MN are 3 cm apart on the same side of a circle where PQ = 7 cm
and MN = 14 cm. Calculate the radius of the circle.
https://www.algebra.com/algebra/homework/Circles/Circles.faq.question.407869.html
To form a hyperbola what is the relationship between the base of the cone and the angle of the plane that intersects the cone
A. The plane is a parallel to the base of the cone
B. The plane may be perpendicular to the base of the cone
C. the plane must be at a 45 degree angle to the base of the cone
D. The plane is at an angle that is neither parallel nor perpendicular to the base of the cone
What is 13% of 50% of 329,500,000
Answer:
21417500
Step-by-step explanation:
Calculate 50% of the given amount then 13% of result
50% of 329500000
= [tex]\frac{50}{100}[/tex] × 329500000
= 0.5 × 329500000
= 164750000
Then
13% of 164750000
= [tex]\frac{13}{100}[/tex] × 164750000
= 0.13 × 164750000
= 21417500
I wmat to sleep been doing work for an hour help me out
Answer:
A. 23, 37.....
B. 26, 42......
Step-by-step explanation:
have a great day!
1.
Identify the vertex and the y-intercept of the graph of the function.
y = 0.5(x – 3)^2
A. vertex, (3, 0); y-intercept 4.5
B. vertex, (–3, 0); y-intercept, 4.5
C. vertex, (–3, 0); y-intercept, 1.5
D. vertex, (3, 0); y-intercept, 1.5
Answer:
A. vertex, (3, 0); y-intercept 4.5
Step-by-step explanation:
Rewrite in vertex form and use this form to find the vertex
( h , k ) . ( 3 , 0 )
To find the x-intercept, substitute in 0 for y and solve for x . To find the y-intercept, substitute in 0 for x and solve for y .
x-intercept(s):
( 3 , 0 )
y-intercept(s):
( 0 , 4.5 )
write an equation of the line slope intercept form that is parallel to Y= 1/2 X +3 and through the point (2, -1)
Answer:
y=1/2x
Step-by-step explanation:
I first did point-slope form which is
y+1=1/2(x-2)
Then, I converted it into slope-intercept form which is
y=1/2x
reflect the co ordinate (7,-5) in the y-axis
Answer:
(-7, -5)
Step-by-step explanation:
Hope this helps!
I rlly need help it’s due tmrw
Answer:
3.Top: |-80| + |50| = 80 + 50 = 130m
Bottom: same as top
Left: |50| + |-20| = 50 + 20 = 70m
Right: same as left
4.
130m+130m+70m+70m=400m
The perimeter is 400 meters
What is the measure of ZPRQ?
P
O
A. 172°
1020
B. 70°
70"
s
C. 86°
D. 1020
Answer: should be 86°, not sure.
Step-by-step explanation:
what is the answer??????
Answer:
1) ⅓
2) ⅓
Step-by-step explanation:
1) The repeating decimal, 0.333333.., is the same as ⅓ when simplified.
If we express 0.333333... as a fraction to the nearest hundreths: [tex]\frac{33}{100}[/tex], and 33 is a third of a hundred, which is ⅓.
Therefore, the fraction form of 0.333333... is ⅓.
2) In order to determine the product of 4/6 and 2/4, simply multiply the numerator of both fractions together. Similarly, do the same for both denominators.
[tex]\frac{4}{6}[/tex] × [tex]\frac{2}{4}[/tex] = [tex]\frac{4 * 2}{6 * 4} = \frac{8}{24}[/tex]
Next, simplify [tex]\frac{8}{24}[/tex] by dividing it with [tex]\frac{8}{8}[/tex]:
[tex]\frac{8}{24}[/tex] ÷ [tex]\frac{8}{8}[/tex] = ⅓
Therefore, the product of [tex]\frac{4}{6}[/tex] and [tex]\frac{2}{4}[/tex] is ⅓.
-2x=-2x+8
i need help asap
step by step please
Answer:
0=8
Step-by-step explanation:
Transform y = cot(x) to get the graph of. Which type of transformation is not performed? vertical shift horizontal shift vertical stretch horizontal stretch.
Transformation involves changing the form of the function
The transformation that is not performed is (a) vertical shift
The function is given as:
[tex]\mathbf{y = cot(x)}[/tex]
From the complete question, the transformed function is:
[tex]\mathbf{y=3cot[\frac 15(x+2)]}[/tex]
On y = cot(x); start by translating the function 2 units left.
The rule of this transformation is:
[tex]\mathbf{(x,y) \to (x +2,y)}[/tex]
So, we have:
[tex]\mathbf{y = cot(x + 2)}[/tex]
Next, stretch the function horizontally by a factor of 1/5
The rule of this transformation is:
[tex]\mathbf{(x,y) \to (\frac 15x,y)}[/tex]
So, we have:
[tex]\mathbf{y=cot[\frac 15(x+2)]}[/tex]
Lastly, stretch the function vertically by a factor of 3
The rule of this transformation is:
[tex]\mathbf{(x,y) \to (x,3y)}[/tex]
So, we have:
[tex]\mathbf{y=3cot[\frac 15(x+2)]}[/tex]
From the above transformations, we have:
Horizontal shift Vertical stretch Horizontal stretchHence, the transformation that is not performed is (a) vertical shift
Read more about transformations at:
https://brainly.com/question/13801312
Answer:
vertical shift
Step-by-step explanation:
edge
4x+3+3=-2
help asappl
Answer:
x = − 2
Step-by-step explanation:
n/4 = -11
what does the N =
Answer:
N = -44
Step-by-step explanation:
have a great day! :)
Answer:
n=44
Step-by-step explanation:
n/4=11/1
crossmultiply
n=4×11=44
40.185 + 0.01
Round your answer to the nearest
hundredth.
Answer:
40
Step-by-step explanation:
Answer:
40.20 luv:)
Step-by-step explanation:
The question is written on the image
Answer:
I have attached the answer below.
Step-by-step explanation:
The diagram which has red ink cannot take a perfect feeding path.
Hopefully this helps.
$75 to $25 show your work
Answer:
decrease
Step-by-step explanation:
the percent change measures FROM the first value. A change from 50 to 75 is a change of 50% (25 is the difference between the two numbers, and 25 is 50% of 50). A change from 75 to 50 is a change of -33.3% (25 is still the difference between the two. 25 is 33.3% of 75
STATION 5 ! GIVING BRAINLIEST TO WHOEVER ANSWER W AN GREAT EXPLNATION<3
Answer:
a.
Step-by-step explanation:
Answer:
A, B, E
Step-by-step explanation:
I just put the number of fiction books over the number of nonfiction books. Then I plugged it into a calculator and if the answer was the same as 15/22, then it was right!
2385/3498=15/22
3945/5786=15/22
2340/3588≠15/22
2480/3410≠15/22
4650/6820≠15/22
2310/3696=15/22
Evaluate.
3.23
+52
- 18 ÷6 A.25 B.31 C.40 D.46
Answer:
d
Step-by-step explanation:
plzzzz help me!!!
Plz don't steal my points or add a link
Answer: What do you mean? if you till me i can help you
Step-by-step explanation:
You can wash a car 1.5 times as fast as your friend. Working together, the two of you can wash 1 car in 6 minutes. How long does it take each of you to wash the car when working alone? Leave your answer as a fraction!
If the two of you can wash 1 car in 6 minutes:
It will take you 10 minutes to wash the car alone
take your friend 15 minutes to wash the car alone
Let the duration you can work be represented by y
Let the duration your friend can work be represented by x
You can wash a car 1.5 times as fast as your friend
That is, y = 1.5x
Working together, the two of you can wash 1 car in 6 minutes
This can be represented by the equation
[tex]\frac{1}{x}+\frac{1}{y} = \frac{1}{6}[/tex]
Substitute x = 1.5y into the equation above
[tex]\frac{1}{1.5y}+\frac{1}{y} = \frac{1}{6}\\\\\frac{1+1.5}{1.5y} = \frac{1}{6}\\\\\frac{2.5}{1.5y} = \frac{1}{6}\\\\1.5y=2.5(6)\\\\1.5y=15\\\\y=\frac{15}{1.5} \\\\y=10[/tex]
It will take you 10 minutes to wash the car alone
Substitute y = 10 into x = 1.5y
x = 1.5(10)
x = 15 minutes
It will take your friend 15 minutes to wash the car alone
Learn more here: https://brainly.com/question/25547756
2x=x-4
solve for x
step by step please
2x = x - 4
2x - x = - 4
x = - 4
________
Hope it helps ⚜
Answer:
x=-4
Step-by-step explanation:
2x=x-4
2x-x=-4
x=-4
Proof
2*(-4)=-4-4
-8=-8
in a certain game, a fair die is rolled and a player gains 20 points if the die shows a 6. if the die does not show a 6, the player loses 3 points. if the die were to be rolled 100 times, what would be the expected total gain or loss for the player?
The expected gain or loss is an illustration of mean and expected values.
The expected total gain is 83 points
The given parameters are:
Addition of 20 points for rolling a 6Removal of 3 points for not rolling a 6The probability of rolling a 6 in a fair die is 1/6.
The probability of not rolling a 6 in a fair die is 5/6.
So, the expected gain in each game is:
[tex]\mathbf{E(x) = 20 \times \frac 16 - 3 \times \frac 56}[/tex]
[tex]\mathbf{E(x) = \frac{20}6 - \frac{15}6}[/tex]
Take LCM
[tex]\mathbf{E(x) = \frac{5}6}[/tex]
[tex]\mathbf{E(x) = 0.83}[/tex]
The number of games is 100.
So, the expected gain is:
[tex]\mathbf{Gain = 100 \times 0.83}[/tex]
[tex]\mathbf{Gain = 83}[/tex]
Hence, the expected total gain is 83 points
Read more about expected value at:
https://brainly.com/question/13499496
A leaky pipe drips 2 fluid ounces of water per hour. How many cups of water does it leak in 2 days? Remember that 8 fluid ounces = 1 cup
Answer:
12 cups
Step-by-step explanation:
There are 48 hours in two days.
48 · 2 = 96 ( 2 being fluid ounces per hour )
96 ÷ 8 = 12 ( 8 being fl oz in each cup )
I hope that this helped!!!
How would I solve [tex]-2 \frac{1}{2} - -2 \frac{1}{2}[/tex]
