can someone please answer this question? thank you! (assignment due today)
15. Find the values of x and y.
(10x – 61)º
(18y + 5)º
(r + 10)º

As per the points A, B, and C are colinear points and the point C lies between points A and B on the line.

Let's begin by finding the distance between points A and B. Using the distance formula equation, we can substitute the values of the x and y coordinates of A and B:

AB = √((0 - 5)² + (5 - (-5))²)

= √(25 + 100)

= √125

= 5√5

Therefore, the distance between points A and B is 5√5.

Similarly, we can find the distance between points B and C:

BC = √((2 - 0)² + (1 - 5)²)

= √4 + 16

= √20

= 2√5

Finally, we can find the distance between points A and C:

AC = √((2 - 5)² + (1 - (-5))²)

= √9 + 36

= √45

= 3√5

Alternatively, we can use the equation of the line passing through any two of these points and check if the third point lies on that line.

Let's use the points A and B to find the equation of the line passing through them:

y - (-5) = ((5 - (-5)) / (0 - 5))(x - 5)

y + 5 = (10 / (-5))(x - 5)

y + 5 = -2(x - 5)

y + 5 = -2x + 10

y = -2x + 5

Now, let's check if point C lies on this line by substituting its coordinates into the equation:

1 = -2(2) + 5

1 = 1

Since the equation is true, we can conclude that points A, B, and C are collinear. Moreover, since point C lies between points A and B on the line, we can say that C lies on segment AB.

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Complete Question:

Given points A, B, and C. Find AB, BC, and AC. Are A, B, and C collinear? If so, which point lies between the other two? A(5, −5), B(0,5), C(2, 1)

To solve this problem we need to apply the average speed formula, which is shown below:

We need to find the time, therefore we will arrange the equation in order to isolate the time on the left side as shown below:

Applying the data from the problem:

Answer:

18

Step-by-step explanation:

The radius is half of the diameter, so we would multiply 9 x 2 and get 18.

Hope this helps!

The roots of the indicial equation associated with the regular singular point x0=0 are r=1 and r=3.

To find the roots of the indicial equation associated with the regular singular point x0=0 of the differential equation:

x^2y" + 3x(x+1)y' + (x^2 - 3)y =0

We can assume a solution of the form:

y(x) = x^r * sum_(n=0)^infinity (a_n * x^n)

where r is the root of the indicial equation and a_n are constants to be determined.

Substituting y(x) into the differential equation, we get:

x^2 * [r(r-1)x^(r-2) + 2rx^(r-1) + x^r * sum_(n=0)^infinity ((n+r)(n+r-1)a_n*x^(n-1))]

3x(x+1) * [rx^(r-1) + x^r * sum_(n=0)^infinity ((n+r)a_n * x^(n-1))]

(x^2 - 3) * [x^r * sum_(n=0)^infinity (a_n * x^n)] = 0

Collecting terms and setting the coefficient of each power of x to zero, we obtain the following recurrence relation for the coefficients a_n:

a_(n+2) = [(3-r-n)a_(n+1) - (n+r-2)a_n]/[(n+2)(n+r+1)]

The indicial equation is obtained by substituting y(x)=x^r into the differential equation and solving for r. In this case, we get:

r(r-1) + 3r - 3 = 0

Simplifying and factoring, we have:

(r-1)(r-3) = 0

Therefore, the roots of the indicial equation associated with the regular singular point x0=0 are r=1 and r=3.

So, the two roots of the indicial equation are 1 and 3.

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1. The outcomes in the sample space of choosing a letter from the word STARK are: S, T, A, R, K.

2. Number of outcomes in the sample space = 6 (from THANKS) × 5 (from STARK) = 30.

3. The Probability of choosing the letters AA is 0, as there are no occurrences of the letter A in both words together.

1. The outcomes in the sample space of choosing a letter from the word THANKS are: T, H, A, N, K, S.

  The outcomes in the sample space of choosing a letter from the word STARK are: S, T, A, R, K.

2. To find the number of outcomes in the sample space, we multiply the number of outcomes for each word.

  Number of outcomes in the sample space = Number of outcomes for the first word × Number of outcomes for the second word

  Number of outcomes in the sample space = 6 (from THANKS) × 5 (from STARK) = 30.

3. The probability of choosing the letters AA would be the number of favorable outcomes (which is 0 in this case) divided by the total number of outcomes in the sample space.

  Probability of choosing AA = Number of favorable outcomes / Total number of outcomes

  Probability of choosing AA = 0 / 30 = 0.

Therefore, the probability of choosing the letters AA is 0, as there are no occurrences of the letter A in both words together.

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Let's simplify each expression shown in the exercise:

Option a

Given:

You can apply the Product of powers property. This states the following:

Where "b" is the base and "n" and "m" are exponents.

Then, you get:

By definition:

Therefore:

The expression given in Option a is equal to 1.

Option b

Knowing that any number or expression with exponent zero is equal to 1, you get that:

The expression given in Option b is equal to 1.

Option c

Given:

You can notice that the numerator and the denominator are equal, then:

The expression given in Option c is equal to 1.

Option d

Given:

You can simplify it using the Quotient of powers property, which states that:

Then, you get:

The expression given in Option d is not equal to 1.

The answer is: Option d.

Answer:

1.-2x+4y=17

if you want me to solve for x : x=-17/2 +2y

If you want me to solve for y: y=17/4+x/2

2. If you want me to solve for x: x=-1+10y/3

If you want me to solve for y: y=3/10+3x/10

3. If you want me to do it all together it would be:

x=-79/4, y=-45/8

Step-by-step explanation:

Assume a stick of length 1 is randomly broken into two portions. The smaller piece's estimated length is 0.25.

The random variable L (the length for the shorter stick) has a uniform distribution.

Thus the probability density function for L is as follows:

This means 2 for all length in the range 0 - 0.5

Now, we calculate the expected value for random variable L as seen on the attachment. Based on the calculation, 0.25 is the smaller piece's estimated length for the randomly broken stick.

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Answer:

x=101

Step-by-step explanation:

∠1 + 79° = 180° (linear pair)

∠1 = 180°-79°

∠1 = 101

x = ∠1 = 101 (corresponding angles)

hope you understood!

The number of full revolutions that Liz's front wheel completed is  16,037 full revolutions.

First, we need to find the circumference of the wheel. The formula for the circumference of a circle is C = 2πr, where r is the radius of the circle. In this case, the radius of the wheel is 54 cm, so we can plug that into the formula:

C = 2π(54 cm) = 108π cm

Next, we need to convert the total distance traveled from kilometers to centimeters, so that we can divide by the circumference of the wheel in centimeters.

There are 100,000 centimeters in a kilometer, so we can multiply the distance traveled in kilometers by 100,000 to get the distance in centimeters:

54.82 km * 100,000 cm/km = 5,482,000 cm

Now we can divide the total distance traveled by the circumference of the wheel to find the number of full revolutions:

5,482,000c m / 108π cm = 16,037.35

So, Liz's front wheel completed approximately 16,037 full revolutions.

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Answer:

Let's assume that the total distance of the trip is D miles. Jorge has already covered half of the distance i.e. D/2 miles at an average speed of 20 mph. Let's call the time taken to cover this distance T1.

We can use the formula: Average speed = Total Distance / Total Time

We know that the overall average speed for the entire trip is 40 mph. So, for the remaining half of the trip, Jorge needs to cover another D/2 miles at an average speed of 40 mph. Let's call the time taken to cover this distance T2.

Now we can write two equations:

1. 20 mph = (D/2) / T1  => T1 = (D/2) / 20

2. 40 mph = (D/2) / T2  => T2 = (D/2) / 40

We need to find out the average speed in the second half of the trip. Let's call it S2.

We know that the total time taken for the entire trip is T1 + T2.

Total time = T1 + T2 = (D/2) / 20 + (D/2) / 40 = D/30

We can again use the formula: Average speed = Total Distance / Total Time

So, we have:

D = D

Total time = D/30

Total distance = D/2 + D/2 = D

Average speed = Total distance / Total time

40 mph = D / (D/30)

40 mph = 30

This is not possible as the average speed cannot be higher than the maximum speed (which is 40 mph in this case). So, it means that there is no way for Jorge to achieve an average speed of 40 mph for the entire trip.

Step-by-step explanation:

ANSWER:

A.

B.

C.

D.

STEP-BY-STEP EXPLANATION:

We must bear in mind that when a value increases or decreases in percentage form, the form of the equation is exponential, while when it increases or decreases in a fixed manner, the form of the equation is linear.

Starting from the equation, the equations would then be:

A.

B.

C.

D.

Answer:

(D) 72

Step-by-step explanation:

A factor is an integer that divides into a whole number without a remainder.

In this case, both 4 and 9 need to be the result of a division of 72 by some number. 4 is a factor of 8, since 8 divided by 2 is 4, but 9 isn't. 9 is a factor of 18, but 4 isn't. Neither 4 nor 9 is a factor of 49. If you divide 72 by 18, you get 4. If you divide 72 by 8, you get 9.

4 and 9 are factors of 72.

Answer:

The answer is D

72

Step-by-step explanation:

Factors of 72 are 8,9

8=2×2×2

8=4×2

1,2 3,4,6,8,9.........72

Answer:

C.48

Step-by-step explanation:

90° is horizontal.

42+48=90

The arm gate still has to rotate by 48°.

We have the arm of a crossing gate that moved 42° from a vertical position.

We have to determine how many more degrees does the arm have to move so that it is in horizontal position.

The arm of the crossing gate can rotate to a maximum position of 90° when it is in vertical position and to a minimum position of 0° when it is in horizontal position.

According to the question -

Angle by which arm of a crossing gate moved from the vertical position = 42°.

Then, the arm gate still has to rotate = 90° - 42° = 48°

Hence, the arm gate still has to rotate by 48°.

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The probability that a student chosen randomly from the class passed the test or completed the homework is 20/27.

The probability that a student chosen randomly from the class passed the test or completed the homework is calculated as follows:

Let the probability that a student completed the homework be P(B).

Also, let the probability that a student passed the test be P(A)

P(A or B) = P(A) + P(B) - P(A * B)

From the data table:

The number of students who passed the test = 18

The number of students who completed the homework = 17

The number of students who both passed the test and completed the homework = 15.

Total number of students = 27

P(A) = 18/27

P(B) = 17/27

P(A*B) = 15/27

Therefore,

P(A or B) = 18/27 + 17/27 - 15/27

P(A or B) = 20/27

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Answer:

The correlation has no unit of measurement; it is just a number.

Correlation requires both variables to be quantitative.

Step-by-step explanation:

Correlation refers to the measure of the relationship between two variables. The correlation between two variables is measured using the correlation Coefficient which may take any value between - 1 and 1 ; the closer the correlation Coefficient is to either 1 or - 1, the greater the relationship with negative depicting a negative association and positive depicting a positive relationship between the variables. The correlation Coefficient requires that both variables are numeric (quantitative). The correlation Coefficient has no unit of measurement.

Answer:

Proved below!

Step-by-step explanation:

Start by multiplying both sides by 2 (as said in the question):

\(\implies 4c + 10a = 388\)

\(\implies 2(4c + 10a) = 2(388)\)

\(\implies 8c + 20a = 776\)

Substitute the solution(s) in the equation:

\(\implies 8(52) + 20(18) = 776\)                                                                   (c = 52; a = 18)

\(\implies 416 + 360 = 776\)

\(\implies \bold{776 = 776 \ \ \ (Proved)}\)

Answer:

Let c = number of children's tickets sold

Let a = number of adults tickets sold

Given:

⇒ 4c + 10a = 388

Multiply both sides of the equation by 2:

⇒ 2(4c + 10a) = 2 × 388

⇒ 8c + 20a = 776

If c = 52 and a = 18, substitute these values into the equation and solve:

⇒ 8(52) + 20(18)

⇒ 416 + 260

⇒ 776

As 776 = 776, this proves that c = 52 and a = 18 is a solution to this equation.

Answer:

answer = 19.2

Step-by-step explanation:

48 = 24 + 1.25x

48 - 24 = 1.25x

24 = 1.25x

24/1.25 = x

19.2 = x

The value of tensions are:

T₁ = 231/74

T₂ = -329/66

T₃ = 8/33

We can use Gaussian elimination to solve the system of equations:

5T₁ + 3T₂ + 5T₃ = 70

T₁ + 2T₂ + 4T₃ = 24

4T₁ + 2T₂ = 40

First, we'll use the third equation to eliminate T₂ from the first two equations:

4T₁ + 2T₂ = 40   (equation 3)

T₁ + 2T₂ + 4T₃ = 24   (equation 2)

Multiplying the third equation by 2 and subtracting it from the second equation:

T₁ + 2T₂ + 4T₃ = 24   (equation 2)

- 8T₁ - 4T₂ = -80   (2 × equation 3)

------------------------

-7T₁ + 4T₃ = -56

Now we have two equations:

5T₁ + 3T₂ + 5T₃ = 70   (equation 1)

-7T₁ + 4T₃ = -56   (from previous step)

Multiplying the first equation by 7/5 and adding it to the second equation:

5T₁ + 3T₂ + 5T₃ = 70   (equation 1)

-7T₁ + 4T₃ = -56   (from previous step)

------------------------

T₁ + 7T₃ = 14

Now we can use the third equation to eliminate T₂ from the first equation:

4T₁ + 2T₂ = 40   (equation 3)

5T₁ + 3T₂ + 5T₃ = 70   (equation 1)

Multiplying the third equation by 3/2 and subtracting it from the first equation:

4T₁ + 2T₂ = 40   (equation 3)

-11T₁ - T₃ = -35   (3 × equation 3 - 5 × equation 1)

Now we have two equations:

T₁ + 7T₃ = 14   (from previous step)

-11T₁ - T₃ = -35   (from this step)

Multiplying the second equation by -7 and adding it to the first equation:

T₁ + 7T₃ = 14   (from previous step)

74T₁ = 231

Therefore, T₁ = 231/74.

Substituting this value back into the equation T₁ + 7T₃ = 14, we get:

(231/74) + 7T₃ = 14

7T₃ = (74/231) × 20

T₃ = 8/33

Finally, substituting T₁ = 231/74 and T₃ = 8/33 into the equation -11T₁ - T₃ = -35, we get:

-11(231/74) - (8/33) = -329/66

Therefore, T₂ = -329/66.

So, the tensions are: T₁ = 231/74 T₂ = -329/66 T₃ = 8/33

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The pirate has gone into debt by $38,979 in base 10 due to his encounter with Captain Rusczyk.

To determine the amount of debt, we need to calculate the difference between the value of the goods the pirate stole and the amount demanded by Captain Rusczyk. The pirate initially stole $2345_6, which means it is in base 6. Converting this to base 10, we have $2\times6^3 + 3\times6^2 + 4\times6^1 + 5\times6^0 = 2\times216 + 3\times36 + 4\times6 + 5\times1 = 432 + 108 + 24 + 5 = 569$.

Captain Rusczyk demanded $41324_5, which means it is in base 5. Converting this to base 10, we have $4\times5^4 + 1\times5^3 + 3\times5^2 + 2\times5^1 + 4\times5^0 = 4\times625 + 1\times125 + 3\times25 + 2\times5 + 4\times1 = 2500 + 125 + 75 + 10 + 4 = 2714$.

Therefore, the pirate has gone into debt by $569 - 2714 = -2145$. Since the pirate owes money, we consider it as a negative value, so the pirate has gone into debt by $38,979 in base 10.

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Of course it is a rational number.

Whole number are numbers without fractions or decimals, integers too but what is the difference then ? Integers include also negative numbers without fractions or decimals.

Obviously -5.41 is neither an integer, nor a whole number.

-5.41 is not an irrational too since irrational have infinite sequence of numbers after the comma.

-5.41 is in fact a rational number.

Good luck

Answer:

a=56,   a=199

Step-by-step explanation:

1)a/8=7

a=7×8   a=56

2)194=a-5

194+5=a   199=a

The annual rate of decline is 5.3%.

What is exponential ?

Exponential refers to a mathematical function where the variable is in the exponent. Exponential functions have the general form:

\(f(x) = a^{x}\)

here "a" is a constant called the base, and "x" is the variable. When the base "a" is a positive number greater than 1, the function grows exponentially as "x" increases. When the base "a" is a number between 0 and 1, the function decays exponentially as "x" increases.

We can start by using the formula for exponential decay:

\(N(t) = N0 * (1 - r)^{t}\)

where N(t) is the population after t years, N0 is the initial population, r is the annual rate of decay (as a decimal), and t is the time in years.

We are given that the initial population is 670, so N0 = 670. After 4 years, the population has reduced to 557, so N(4) = 557. We can plug these values into the formula and solve for r:

\(557 = 670 * (1 - r)^{4}\)

\((557/670)^{1/4} = 1 - r\)

\(0.947 = 1 - r\)

\(r = 0.053\)

So the annual rate of decline is 5.3%.

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Answer:

175

Step-by-step explanation:

since 1 was 152 you have to add more to get number 8

Answer:

4.6 feet

Step-by-step explanation:

The answer to the question is C, which is integers 4,5 or -4,-3.

Let's call the first integer x and the second integer x+1 (since they are consecutive).
According to the problem, we can set up the following equation:
x(x+1) = x + (x+1) + 19
We can simplify this equation by expanding the left side and combining like terms on the right side:
x^2 + x = 2x + 20
Now we can move all the terms to one side and get a quadratic equation:
x^2 - x - 20 = 0
We can factor this equation as (x-5)(x+4) = 0, which means the solutions for x are 5 and -4.
Therefore, the two consecutive integers are either 4,5 or -4,-3.
The long answer includes all the steps of solving the quadratic equation:
x^2 - x - 20 = 0
We can use the quadratic formula to solve for x:
x = (-b ± √(b^2 - 4ac)) / 2a
In this case, a=1, b=-1, and c=-20.
x = (1 ± √(1 - 4(1)(-20))) / 2(1)
x = (1 ± √81) / 2
x = (1 ± 9) / 2

The two solutions for x are 5 and -4.
Therefore, the two consecutive integers are either 4,5 or -4,-3.
The product of two consecutive integers is 19 more than their sum. To find the integers, let's represent them as x and x+1.

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Answer:

Yes, negative 2 is bigger than negative six.

Answer:

(-2 is greater than -6 )it is the lower the it is such as -2 the way you know which is greater is by whatever negative is closer to 0 or to the positive numbers.

Step-by-step explanation:

Hope this heped!