Find the measure of each angle. Then
classify each angle.
a. b. C. 70 80 90 100 110 120 130 140
150 140 130 120 110 100 90 80 70 60 50 401
30 40 50 60
P
Q²
130 140 150 160 170 180
S
R
10 10
S

The number of terms in the given arithmetic sequence is n = 10. Using the given first, last term, and the common difference of the arithmetic sequence, the required value is calculated.

The general form of the nth term of an arithmetic sequence is

an = a1 + (n - 1)d

Where,

a1 - first term

n - number of terms in the sequence

d - the common difference

The given sequence is an arithmetic sequence.

First term a1 = \(1\frac{1}{2}\) = 3/2

Last term an = \(2\frac{1}{2}\) = 5/2

Common difference d = 1/9

From the general formula,

an = a1 + (n - 1)d

On substituting,

5/2 = 3/2 + (n - 1)1/9

⇒ (n - 1)1/9 = 5/2 - 3/2

⇒ (n - 1)1/9 = 1

⇒ n - 1 = 9

⇒ n = 9 + 1

∴ n = 10

Thus, there are 10 terms in the given arithmetic sequence.

learn more about the arithmetic sequence here:

https://brainly.com/question/503167

#SPJ1

Disclaimer: The given question in the portal is incorrect. Here is the correct question.

Question: If the first and the last term of an arithmetic progression with a common difference are \(1\frac{1}{2}\), \(2\frac{1}{2}\) and 1/9 respectively, how many terms has the sequence?

Answer:

I think its 368.28 cubic inches

Step-by-step explanation:

Answer:

.

Step-by-step explanation:

Answer:

It is given to us that

y =-x-1

put this value in the given equation we will get ouelr answer

x + y =8

x + -x -1 =8

sorry mate we doesn't get our answer because x will be cancelled here

Answer:

4

Step-by-step explanation:

Step-by-step explanation:

a linear function is defined as

y = ax + b

the variable x is only occurring with the exponent of 1.

this represents a straight line in a graphic representation (hence the name "linear").

if the exponent of the variable x is not 1, then it is not a linear function

P : y = 3/x + 2³

it is not linear.

the exponent of x = -1, as 1/x = x^-1. -1 is different to 1, which would be needed as exponent of x to make it linear.

Q : y = (1/3)x² + 3

it is not linear.

the exponent of x = 2. and 2 is different to 1, which would be needed as exponent of x to make it linear.

Answer:

A = 2(7) + (1/2)(4)(4 + 9) = 14 + 26 = 40 m²

Given the state-space model with acceleration being the control input,Let x [t + 1] 1 δ x [t] 0 = + u[t]. v [t + 1] 0 1 v [t] δWhere x[t] = vt is the reference trajectory to track.

The reference trajectory to track is x[t] = vt.The position and speed errors being the state can be found using the following steps. State-space model of the system: {x[t+1]=x[t] + δv[t]v[t+1]=v[t] + δu[t]}Let the position and speed errors be e1[t] = x[t] - v*tand e2[t] = v[t] - v.

From the above state-space model:{x[t+1] = v*t + e1[t] + δv[t]v[t+1] = v + e2[t] + δu[t]}Differentiate e1[t] and e2[t] with respect to time t: {e1[t + 1] = e1[t] + δe2[t + 1] = e2[t] + δNow, we can write the state-space model with errors in state:{e1[t + 1] e2[t + 1] = 1 δ 0 1 e1[t] e2[t] + 0 δ 1 0 δ u[t].

Now, a linear controller that stabilizes the system can be found as below:Let A = [1 δ; 0 1] and B = [0; δ].Let the state-feedback control law be given by u[t] = -K[e1[t]; e2[t]] such that the eigenvalues of the closed-loop system are negative. Therefore,K can be found using the following formulae:

K = (B'PB + R)^{-1}(B'PA)

where,P is a positive definite solution of the algebraic Riccati equationA'PA - P + Q - A'PB(B'PB + R)^{-1}B'PA = 0andR and Q are positive definite matrices.The destabilizing controller can be found by using K = [0 1].Then, the closed-loop system becomes{x[t+1] = (1- δ^2) x[t] + δv[t]v[t+1] = (1- δ^2) v[t] + δu[t]}.

In order to stabilize the system, a linear controller has been found using the reformulated model. The destabilizing controller can also be found.  Thus, this is how the state-space model can be reformulated and linear controllers can be found to stabilize or destabilize the system.

To know more about Riccati equation :

brainly.com/question/31476486

#SPJ11

1. Definition of a correspondence: A correspondence is a mathematical concept that defines a relation between two sets, where each element in the first set is associated with one or more elements in the second set. It can be thought of as a rule that assigns elements from one set to elements in another set based on certain criteria or conditions.

2. Definition of a fixed point of a correspondence: In the context of a correspondence, a fixed point is an element in the first set that is associated with itself in the second set. In other words, it is an element that remains unchanged when the correspondence is applied to it.

3. Set of (mixed strategy) best replies in normal form games: In a normal form game, the set of (mixed strategy) best replies for a given player i is the collection of strategies that maximize the player's expected payoff given the strategies chosen by the other players. It represents the optimal response for player i in a game where all players are using mixed strategies.

Best reply correspondence: The "best reply correspondence," denoted by B in class, is a correspondence that assigns to each mixed strategy profile the set of best replies for each player. It maps a mixed strategy profile to the set of best responses for each player.

4. Nash equilibrium and fixed point of best reply correspondence: A mixed strategy profile α∗ is a Nash equilibrium if and only if it is a fixed point of the best reply correspondence. This means that when each player chooses their best response strategy given the strategies chosen by the other players, no player has an incentive to unilaterally change their strategy. The mixed strategy profile remains stable and no player can improve their payoff by deviating from it.

5. Brower's fixed point theorem: Brower's fixed point theorem states that any continuous function from a closed and bounded convex subset of a Euclidean space to itself has at least one fixed point. In other words, if a function satisfies these conditions, there will always be at least one point in the set that remains unchanged when the function is applied to it.

6. Proving Brower's theorem using Kakutani's fixed point theorem: Kakutani's fixed point theorem is a more general version of Brower's fixed point theorem. By using Kakutani's theorem, we can prove Brower's theorem as a corollary.

Kakutani's theorem states that any correspondence from a non-empty, compact, and convex subset of a Euclidean space to itself has at least one fixed point. Since a continuous function can be seen as a special case of a correspondence, Kakutani's theorem can be applied to prove Brower's theorem.

7. Conditions for Kakutani's fixed point theorem: Kakutani's fixed point theorem requires several conditions to hold in order to guarantee the existence of a fixed point. These conditions include non-emptiness, compactness, convexity, and upper semi-continuity of the correspondence.

If any of these conditions are not satisfied, the conclusion of Kakutani's theorem does not hold, and there may not be a fixed point.

8. Example without a fixed point: An example without a fixed point can be a correspondence that does not satisfy the condition of closedness in the relative topology of S², where S is the set where the correspondence is defined. This means that there is a correspondence that maps elements in S to other elements in S, but there is no element in S that remains unchanged when the correspondence is applied.

This is a valid counterexample because it shows that even if all other conditions of Kakutani's theorem are satisfied, the lack of closedness in the relative topology can prevent the existence of a fixed point.

To know more about correspondence here

https://brainly.com/question/12454508

#SPJ11

A homogeneous system in parametric vector form:

(x1,x2,x3) = (s,s,-0.25s)

Parametric vector Form:

Any equation expressed as a parameter is a parametric equation. The general equation y = mx + b (where m and b are parameters) of a straight line in the form of a slope intersection is an example of a parametric equation. Example: one of the variables to t(x = t). Then we can rewrite this equation as y = t²+5.

So the set of parametric equations is x = t and y=t²+5.

According to the Question:

We are to solve them in parametric form.

X₁ + 2X₂ + 12X₃ = 0     ----------------------- (1)

2X₁ + X₂ + 12X₃ = 0     ----------------------- (2)

-X₁ + X₂ = 0                  ----------------------- (3)

From equation 3 we get

x₁ = x₂

Substitute in 1 and 2 to get

3x₁ + 12x₃ = 0 and

3x₁ + 12x₃ = 0

Thus, we find these two equations are dependent.  So we can have infinite solutions in parametric form only.

No unique solution is possible

Let x₁ = x₂ = s

Since 3x₁ +12x₃ = 0

x₁ = -4x₃

Or x₃ = -0.25s

So solution in parametric form is

(x1,x2,x3) = (s,s,-0.25s) for all real values.

Learn more about Homogeneous System:

https://brainly.com/question/30504189

#SPJ4

not sure how the format is for the question but i think its

for the second column: y=2+2, y=6+2, y=7+2

for third column: 4, 8, 9

for the fourth column: (2,4), (6,8), (7,9)

for the according to the table:

(6,8), when his brother is 6 he is 8

for the graph: graph out the points (2,4), (6,8), (7,9)

another solution can be when he is 5 his brother is 3

(these should be right)

Answer:

8) Table

2...

6...

7...

According to table 6, the point (6,8) means when his brother is 8 Trisjohn is 6

For the graph plot points at (2,4) (6,8) and (7,9) and connect with a straight line

When Kimarius is 5 his brother is 3

Have a lovely day :)

Answer:

Answer: LCM of 3 and 15 is 15. 2.

Step-by-step explanation:

Hope this helps

Answer: no it does matter because it just the same numbers repeating

Step-by-step explanation:

Answer:

To me its A but i fully dont know im sorry if you get this wrong :(

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

Answer:

169.641

Step-by-step explanation:

Calculator

Answer:

18.3 x 9.27

= Use the multiplication method.

= 169.641

Answer:

\(d=\sqrt{73}\approx8.54\)

Step-by-step explanation:

So we have the two points (10,-4) and (2,-7).

And we want to find the distance between them using the Distance Formula and the Pythagorean Theorem. Let's do each one individually.

1) Distance Formula.

The distance formula is:

\(d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2\)

Let's let (10,-4) be (x₁, y₁) and let's let (2,-7) be (x₂, y₂). So:

\(d=\sqrt{((2)-(10))+((-7)-(-4))^2\)

Simplify:

\(d=\sqrt{(2-10)^2+(-7+4)^2\)

Subtract:

\(d=\sqrt{(-8)^2+(-3)^2\)

Square:

\(d=\sqrt{64+9}\)

Add:

\(d=\sqrt{73}\)

Approximate:

\(d\approx8.54\)

So, the distance between (10,-4) and (2,-7) is approximately 8.54 units.

2) Pythagorean Theorem

Please refer to the graph.

So, we want to find the distance. This will be the length of the red line, or the hypotenuse.

First, let's find the length of the two legs.

The longer leg will be the difference between the two x-coordinates. So, the length of the longer leg is:

\((10-2)=8\)

Note: It doesn't matter if we do 2-10, which gives -8, since we are going to square anyways. Also, distance is always positive, so 8 would be our answer.

And the shorter leg is the difference between the two y-coordinates. Namely:

\((-7-(-4))=-3=3\)

So, the shorter leg is 3 units.

So now, we can use the Pythagorean Theorem, which is:

\(a^2+b^2=c^2\)

Substitute 8 for a and 3 for b. So:

\((8)^2+(3)^2=c^2\)

Square:

\(64+9=c^2\)

Add:

\(c^2=73\)

Take the square root:

\(c=\sqrt{73}\approx8.54\)

This is the same as our previous answer, so we can confirm that it's correct.

So, using both the distance formula and the Pythagorean Theorem, the distance between the two points is approximately 8.54.

And we're done!

Distance formula: d = √(x2-x1)²+(y2-y1)²

= √(2-10)²+(-7-(-4))²

= √-8²+(-3)²

= √64+9

= √73

≈ 8.54

Best of Luck!

Answer:

206

Step-by-step explanation:

replace n in the sequence with 12 to find the 12th term

T 12 = (12)^2 + 5(12) + 2 = 206

To provide Logical Proofs with line-by-line justifications for the following arguments,

Let's use the first 4 rules of inference.

Given below is the justification for each step of the proof with the applicable rule of Inference.

E > M1. A > (E > ~F) Premise2. H v (~F > M) Premise3. A Premise4. ~H  Premise5. A > E > ~F 1, Hypothetical syllogism6.

E > ~F 5,3 Modus Ponens 7 .

~F > M 2,3 Disjunctive Syllogism 8.

E > M 6,7 Hypothetical SyllogismIf

A is true, then E must be true because A > E > ~F.

Also, if ~H is true, then ~F must be true because H v (~F > M). And if ~F is true,

Then M must be true because ~F > M. Therefore, E > M is a valid  based on the given premises using the first four rules of inference.

to know more about Modus Ponens visit :

brainly.com/question/27990635

#SPJ11

Answer:

75.6 miles

Step-by-step explanation:

Multiply 4.2 by 18

Nastya's annual payments on the loan will be approximately $7,350.68 (rounded to the nearest cent).

To find Jean's equity as a percent of the house value, we need to calculate the equity and divide it by the house value, then multiply by 100 to get the percentage.

Jean's equity is the difference between the house value and the mortgage amount. So, the equity is $792078.31 - $600,000 = $192,078.31.

To calculate the percentage, we divide the equity by the house value and multiply by 100: ($192,078.31 / $792078.31) * 100 = 24.26%.

Therefore, Jean's equity as a percent of the house value is 24.26%.

Now, let's move on to Nastya's question.

To calculate Nastya's annual payments on a fully amortizing loan, we need to use the formula for calculating the monthly payment:

P = r * PV / (1 - (1 + r)^(-n))

Where:
P = Monthly payment
r = Monthly interest rate (annual interest rate / 12)
PV = Present value of the loan
n = Total number of payments

Given:
PV = $622,422
Annual interest rate = 5.2%
n = 10 years

First, we need to convert the annual interest rate to a monthly interest rate: 5.2% / 12 = 0.43333%.

Next, we substitute the values into the formula and solve for P:

P = (0.0043333 * 622422) / (1 - (1 + 0.0043333)^(-10))

Using a calculator, we get P ≈ $7,350.68.

To learn more about annual payments

https://brainly.com/question/18958209

#SPJ11

17 is the integer expressed in base 10.

Given that,

The base 7 representation of a positive integer is AB and its base 5 representation is BA, where A and B are digits from 1 to 4, inclusive.

We have to find what is the integer expressed in base 10.

We know that,

Base 7 representation of a positive integer AB.

Can be written as 7A+B in base 10.

Base 5 representation of BA can be written as 5B+A in base 10.

So, 7A+B= 5B+A

6A=4B

A=2/3B

Now, A and B must be in 1 to 4.

The digits between 1 and 4 who are 2/3 of another is 2 and 3.

A=2 and B=3

So,

Base 7 is 23

And Base 5 is 32

Base 7 is 23 is 17 of base 10.

And Base 5 is 32 is 17 of base 10.

A=17

Therefore, 17 is the integer expressed in base 10.

To learn more about integer visit: https://brainly.com/question/15276410

#SPJ4

Answer:

5.95

Step-by-step explanation:

Answer:

(5z + 4) + (3z - 6) = 8z - 2

Step-by-step explanation:

(5z + 4) + (3z - 6)

Combine them by their like terms.

(5z + 3z) + (4 + (-6))

Add 5z and 3z.

8z + (4 + (-6))

Add 4 and -6.

8z + (-2)

Simplify.

8z - 2

Any number ending with a even number is even

B. 41680

C. 55822

D. 87318

E. 93256

Answers are B, C, D, E

Answer:

$650

Step-by-step explanation:

You need to get at least $65 in savings to make the card worthwhile

10% of x is 65

multiply both sides by 10

100% of 10x is 65

get rid of 10x since we don't need that

100% of our answer is 650

The remainder when f(x) = x³ - 5x² + 4x - 10 is divided by (x + 5) is (b) -280

The functions are given as

f(x) = x3 − 5x2 + 4x − 10 is divided by (x + 5)

Rewrite them as

f(x) = x³ - 5x² + 4x - 10 is divided by (x + 5)

Set the divisor to 0

So, we have

x + 5 = 0

Determine the value of x

This gives

x = -5

By the remainder theorem

Substitute x = -5 in the function f(x)

So, we have

f(-5) = (-5)³ - 5(-5)² + 4(-5) - 10

Evaluate the expression

f(-5) = -280

By the remainder theorem, this represents the remainder

Read more about remainder at

brainly.com/question/14130807

#SPJ1

Answer:

The jeweler made 4 bracelets and 3 necklaces!

Proof:

Bracelets : 4 * 6 = 24 grams

Necklaces: 3 * 16 = 48 grams

24 g + 48 g = 72 g