Draw three different concave polygons. When you walk around a polygon, at each vertex you need to turn either right (clockwise) or left (counterclockwise). A turn to the left is measured by a positive number of degrees and a turn to the right by a negative number of degrees. Find the sum of the measures of the turn angles of the polygons you drew. Assume you start at a vertex facing in the direction of a side, walk around the polygon, and end up at the same vertex facing in the same direction as when you started.

Answer:

The time at which they will all meet at a place together is 350 minutes

Step-by-step explanation:

The time it takes Faiza to cycle the park = 60 seconds

The time it takes Krish to cycle the park = 14 seconds

The time it takes Joe to cycle the park = 25 seconds

Therefore, the time they will all meet at a place together is given by their Lowest Common Multiple as follows;

LCM = 60 × 14 × 25 = 21,000 seconds

Therefore, the time at which they will all meet at a place together in minutes = 21000 seconds/(60)×minute/second = 350 minutes

Answer:

a

Step-by-step explanation:

To find the key numbers of the inequality x² - 2x - 24 > 0, we need to determine the values of x that make the inequality true. The key numbers are the points where the expression changes sign. In this case, the key numbers are -4 and 6.

To find the key numbers, we can factor the quadratic expression x² - 2x - 24 > 0. The factored form is (x - 6)(x + 4) > 0. The inequality is satisfied when either both factors are positive or both factors are negative.

Setting each factor equal to zero, we get x - 6 = 0 and x + 4 = 0. Solving these equations, we find that x = 6 and x = -4.

Now, we need to determine the intervals on the number line where the inequality is true. We choose test values from each interval and substitute them into the inequality. For example, testing x = -5 gives (-5 - 6)(-5 + 4) > 0, which is true. Similarly, testing x = 0 gives (0 - 6)(0 + 4) < 0, which is false.

By considering the sign changes, we find that the inequality is true for x < -4 and x > 6. Therefore, the key numbers are -4 and 6, which divide the number line into three intervals: (-∞, -4), (-4, 6), and (6, ∞).

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Answer:

steps below but I recommend the graphing calculator on demos

Step-by-step explanation:

y= mx + b.......  y= 1/2x+ 0

our b is 0 so first plot that

our slope is 1/2 so go up one and to the right twice

keep doing that and you will have your line. USE DESMOS

Answer:

25/27

Step-by-step explanation:

because

5/6÷15/3×2/3

in BODMAS =5/6×15/3×2/3

=150/54=25/27

By applying the difference between two cubes formula, the solutions to the equation (x-1) are x = 1 and the complex solutions obtained from solving x² + x + 1 = 0.

The difference between two cubes formula states that a³ - b³ = (a - b)(a² + ab + b²). In this case, we have (x³ - 1³) = 0. By applying the difference between two cubes formula, we get (x - 1)(x² + x + 1) = 0.

To solve for x, we set each factor equal to zero and solve the resulting equations:

x - 1 = 0, which gives x = 1

x² + x + 1 = 0, which can be solved using the quadratic formula or factoring methods.

The equation x² + x + 1 = 0 represents a quadratic equation, and its solutions can be obtained using the quadratic formula:

x = (-b ± √(b² - 4ac)) / (2a)

In this case, a = 1, b = 1, and c = 1. Substituting these values into the quadratic formula, we get:

x = (-1 ± √(1 - 4(1)(1))) / (2(1))

Simplifying further:

x = (-1 ± √(-3)) / 2

Since the discriminant is negative, the quadratic equation does not have real solutions. Therefore, the only solution to the original equation (x - 1) = 0 is x = 1.

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Answer:

1.46

Step-by-step explanation:

Answer:

Solution steps:

Step 1: Locate and underline the whole number place (.) and look to the right (4):

1.456

Step 2: The digit to the right (4) is 4 or below. So, we replace it by a 0 (zero), then we get 1 as the answer.

In short: 1.456 rounded to the nearest whole number is 1.

The volume of the cylinder can be obtained from the calculation as  1356 [tex]cm^3[/tex]

We know that the volume of the cylinder is;

π (pi) is a mathematical constant approximately equal to 3.14159

r is the radius of the cylinder's base (the distance from the center to the edge of the circular base)

h is the height of the cylinder (the distance between the bases)

By substituting the appropriate values for the radius and height into the formula, you can calculate the volume of the cylinder.

V = π[tex]r^2[/tex]h

V = 3.14 *[tex](12/2)^2[/tex] * 12

h = 1356 [tex]cm^3[/tex]

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Answer:

An arithmetic sequence has first term 4 and common difference 8

Step-by-step explanation:

Answer: the answer is X=-6

Step-by-step explanation:

5x-14=8x+4 - move variable to the left-hand side and change its sign

5x-8x-14=4  - first switch it you are going to have a better understanding

5x-8x= 4=14 move constant to the right-hand side and change its sign

-3x=4+14 collect like term

-3x=18 add the numbers/ then divide both sides of the equation by -3

x=-6

Answer:

(2x - 1)(2x + 1)

Step-by-step explanation:

Difference of Squares: (ax + b)(ax - b) = (ax² - b²)

Answer:

4×^2-1=(2× +1)(2× -1)

Step-by-step explanation:

using a^2 - b^2 =(a+b)(a-b)

Answer:

2.5 times taller

Step-by-step explanation:

6+6=12 3+3=6 12+6=18  so the streetlight is 18 ft

1. The eigenvalues of matrix A are 2 and 3.

2. The bases for the eigenspaces of A are {(1, -1)} and {(3, 1)}.

3. A is diagonalizable because it has distinct eigenvalues and the sum of the dimensions of its eigenspaces is equal to the dimension of the matrix.

4. The matrix P is [1, 3; -1, 1], and the diagonal matrix D is [2, 0; 0, 3], such that P^(-1)AP = D.

5. A^23 is equal to 2^23, which can be written as 223.

6. The system of differential equations can be solved using the matrix equation X' = PX, where X is the vector [x1; x2] and P is the matrix [1, 2; 2, 1].

1. To find the eigenvalues of matrix A, we solve the characteristic equation det(A - λI) = 0, where λ is the eigenvalue. By calculating the determinant, we get (2-λ)(2-λ) - 1 * 1 = 0, which simplifies to λ^2 - 4λ + 3 = 0. Solving this quadratic equation, we find the eigenvalues λ = 2 and λ = 3.

2. To find the eigenspaces of A, we solve the equations (A - λI)X = 0, where X is a non-zero vector in the eigenspace corresponding to eigenvalue λ. For eigenvalue λ = 2, we have (A - 2I)X = 0, which gives the equation [0, 1; -1, 0]X = 0. The solution is X = [1, -1]. Similarly, for eigenvalue λ = 3, we have (A - 3I)X = 0, which gives the equation [-1, 1; -1, 1]X = 0. The solution is X = [3, 1].

3. A matrix is diagonalizable if it has a complete set of eigenvectors. In this case, since A has distinct eigenvalues and the sum of the dimensions of its eigenspaces (2) is equal to the dimension of the matrix (2x2), A is diagonalizable.

4. To find the matrix P and diagonal matrix D, we need to find the eigenvectors corresponding to the eigenvalues of A. The matrix P is formed by taking the eigenvectors as its columns, i.e., P = [1, 3; -1, 1]. The diagonal matrix D is formed by placing the eigenvalues on its diagonal, i.e., D = [2, 0; 0, 3]. Then, we can verify that P^(-1)AP = D.

5. A^23 means raising the matrix A to the power of 23, which is equivalent to raising each element of A to the power of 23. Since A is a 2x2 matrix, A^23 is represented as 223.

6. The system of differential equations can be solved using the matrix equation X' = PX, where X is the vector [x1; x2], X' is the derivative of X with respect to t, and P is the matrix [1, 2; 2, 1]. By solving this equation, we can find the solution for x1 and x2 as functions of t.

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Answer:

15

Step-by-step explanation:

Its y2 - y1 over x2-x1

Given that the graph of f(x) = ax² + 3 passes through the point (1,1). We are supposed to find the value of a.Since the point (1, 1) lies on the graph of the function, we can say thatf(1) = 1That is:a(1)² + 3 = 1a + 3 = 1a = 1 - 3a = -2

Therefore, the value of a is -2. Thus, the graph of the function f(x) = -2x² + 3 passes through the point (1, 1).The solution is done in 88 words.

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Answer:

Probably y=2x+60

Step-by-step explanation:

It seemed to fit best, dont count on my answer tho, not 100% sure :(

When I put the line through the points, the y intercept was around 50/60 and the slope is positive so it eliminated a few answers. then I chose y=2x+60 since that slope seemed more correct than a slop of 8.

Answer:

all are functions

Step-by-step explanation:

a function is when each x has a y

a relation is when 1 x has more than 1 y which makes it invalid therefore not a function

Answer:

x=11/18 or 0.61

Step-by-step explanation:

Let x represent the blank

[tex]As\ x:11::1/3:6\ form\ a\ proportion,\ we\ may\ use\ the\ ratio\ method\ to\ find\ x.\\\\Hence,\\x:11::1/3:6\\6x=1/3*11\\x=11*1/3*1/6\\x=11*1/18\\x=11/18[/tex]

Answer:

The answer is $97.35

Step-by-step explanation:

This because you would need to multiply 75x1.298 to get your answer and your conversion method is multiplying so your answer is $97.35

Hope this helps and have a great day!!

Answer:

r u indian??

Step-by-step explanation:

wow bro m an indian too

Answer:

we use BODMAS

-4 x 4 /5÷ 4=-16/5÷4

=-16÷1[tex]1/4[/tex]

=-16 ÷ 5/4

=-16 x 4/5

=-64/5

=12[tex]4/5[/tex]

Step-by-step explanation:

Step-by-step explanation:

To solve for x, we can begin by simplifying both sides of the equation:

0.06(10000) + 0.08x = 0.072(10000 + x)

600 + 0.08x = 720 + 0.072x

0.08x - 0.072x = 720 - 600

0.008x = 120

x = 120 / 0.008

x = 15,000

Therefore, the value of x is 15,000.

A. The arrival rate per hour must increase to at least 10 customers per hour to justify a second telephone boothe.

B. The arrival rate per hour must increase by at least 1.6 customers per hour to justify a second telephone booth under the new criterion.

To get the how much arrival rate must increase, we must get the expected waiting time for a customer.

Assuming;

X is the number of customers who arrive per hour

Y is the length of a phone call in minutes.

Then, X follows a Poisson distribution with λ = 4 (since 4 customers per hour use the phone on average)

Y follows a negative exponential distribution with mean μ = 5 (since the mean length of a phone call is 5 minutes).

Total time is given as sum of waiting time and length of call;

T = W + Y

The waiting time W is the difference between the time a customer arrives and the time that the phone becomes available. waiting time follows a uniform distribution where mean= 1/λ (since the arrivals follow a Poisson process);

Then we have;

E(W) = 1/(2λ) = 1/8 hours

The expected total time T that a customer spends at the phone booth is:

E(T) = E(W) + E(Y) = 1/8 + 5/60 = 11/48 hours

For a second telephone booth to be justifiable, new customer that arrives must wait 3 minutes or longer for the phone.

E(W) ≥ 1/20

To get λ,

1/(2λ) ≥ 1/20

λ ≤ 10

This means that, the arrival rate per hour must increase to at least 10 customers per hour to justify a second telephone booth.

b. Getting how much the arrival rate per hour must increase to justify a second telephone booth under the new criterion,

we need to find the probability that a customer has to wait at all.

Let P(W > 0) be the probability that a customer has to wait.

P(W > 0) = 1 - P(W = 0)

The waiting time W follows a uniform distribution with mean 1/λ, so we have:

P(W = 0) = 1 - λ/4

The length of a phone call Y follows a negative exponential distribution with mean 5 minutes = 1/12 hours, so we have:

P(Y > t) = e^(-μt) = e^(-t/12)

The probability that a customer has to wait is given as;

P(W > 0) = 1 - P(W = 0) = λ/4

To justify a second telephone booth, the probability of having to wait at all must exceed 0.6. so we have;

P(W > 0) > 0.6

λ > 2.4

The arrival rate per hour must increase by at least 2.4 - 4 = 1.6 customers per hour to justify a second telephone booth under the new criterion.

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Answer:

situation a and she bought 3 pounds

Step-by-step explanation:

Answer: I would say A because $10 per pound seems to much and laundry detergent to turn out as $16

To determine the price per unit at which the quantity supplied equals 6 units, we need additional information such as the supply function or the relationship between price and quantity supplied.  The price and quantity relationship in the supply function can vary depending on various factors such as production costs, market conditions, and technology.

Therefore, it is crucial to have more context or data to determine the specific price per unit required for the quantity supplied to be 6 units.  In summary, without the supply function or more information, it is not possible to determine the exact price per unit at which the quantity supplied equals 6 units.

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Answer:

$90.00

Step-by-step explanation:

The equation would be 150-3(20), or 150-60, which equals $90.00

Answer:

she will have $90 after 20 days

Step-by-step explanation:

3 times 20 = 60

60-150=90

Answer:

-10a-15b

Hope this helps!!!!

Answer:

Step-by-step explanation:

[tex] - 5(2a + 3b)[/tex]

Expand : Use -5 to open the bracket

[tex] - 5 \times 2a = - 10a \\ - 5 \times 3b = - 15b \\ \\ - 10a - 15b[/tex]

Answer:

What kind of proof do you need?

M, Q, and N are collinear, with Q between M and N.

Triangle QPM is isosceles (PM=PQ).

That makes PN greater than PQ.

If you need a formal proof, it looks as if you can use trigonometry and the law of sines.

If you need a formal two-column proof using Euclidean geometry, I'm not sure how you would do it....

Step-by-step explanation: