Determine whether the triangle whose lengths of sides are 3 cm, 4 cm, and 5 cm is a right angled triangle?

The first four terms of the Taylor series for the function (2x) about the point (a=1) are (2x + 2x - 2).

To find the first four terms of the Taylor series for the function (2x) about the point (a = 1), we can use the general formula for the Taylor series expansion:

\(\[f(x) = f(a) + f'(a)(x-a) + \frac{f''(a)}{2!}(x-a)^2 + \frac{f'''(a)}{3!}(x-a)^3 + \ldots\]\)

Let's calculate the first four terms:

Starting with the first term, we substitute

\(\(f(a) = f(1) = 2(1) = 2x\)\)

For the second term, we differentiate (2x) with respect to (x) to get (2), and multiply it by (x-1) to obtain (2(x-1)=2x-2).

\(\(f'(a) = \frac{d}{dx}(2x) = 2\)\)

\(\(f'(a)(x-a) = 2(x-1) = 2x - 2\)\)

Third term: \(\(f''(a) = \frac{d^2}{dx^2}(2x) = 0\)\)

Since the second derivative is zero, the third term is zero.

Fourth term:\(\(f'''(a) = \frac{d^3}{dx^3}(2x) = 0\)\)

Similarly, the fourth term is also zero.

Therefore, the first four terms of the Taylor series for the function (2x) about the point (a = 1) are:

(2x + 2x - 2)

Learn more about taylor series

brainly.com/question/31140778

#SPJ11

Given :

P(-9, -4), Q(-7, -1), R(-2, 5), S(-6, -1).

To Find :

The slope of line PQ.

Solution :

We know , slope is given by :

\(m=\dfrac{y_2-y_1}{x_2-x_1}\\\\m=\dfrac{-9-(-7)}{-4-(-1)}\\\\m=\dfrac{2}{3}\)

Therefore, the slope of line PQ is 2/3.

Hence, this is the required solution.

The result of executing the given code is (B) an array of 6 values, ranging from 0 through 5, will be created and referenced by the variable x.

The code `int[] x = {0, 1, 2, 3, 4, 5};` is initializing an array of integers named `x`. The values inside the curly braces represent the elements of the array. In this case, the values are 0, 1, 2, 3, 4, and 5.

Option (A) is incorrect because the values in the array are not all initialized to 0. Instead, each value corresponds to its respective position in the array.

Option (C) is also incorrect because the variable `x` does not directly store the values 0 through 5. Instead, `x` is a reference to the array that contains those values.

Option (D) is not applicable as the code provided is syntactically correct and will not result in a compiler error.

Therefore, the correct answer is (B) - an array of 6 values, ranging from 0 through 5, will be created and referenced by the variable `x`.

Learn more about array here:

https://brainly.com/question/13261246

#SPJ11

The area of rectangle B is 256 cm²

The area occupied by a rectangle within its boundary is called the area of the rectangle.

Thus, the formula for the area, 'A' of a rectangle whose length and width are 'l' and 'w' respectively is the product

Area of rectangle= length  × width.

It is given that the dimensions of rectangle B are twice times the dimensions of rectangle A.

Let dimensions of rectangle B are l× B.

Area of rectangle is

A= length *  breadth

Area of rectangle A = 128

So, Area of rectangle B

=2( l * B)

= 2l* 2B

=2( l * B)

=2 * 128

= 256 cm²

Hence, the area of rectangle B is 256 cm²

Learn more about this concept here:

https://brainly.com/question/15225905

#SPJ1

Answer:

Explanation: Scott Invested in two banks, and each bank paid 9% and 10% yearly interest. the total amount invested was $6300 and the Interest earned in the first year is $598. We have to find the amount invested in each bank.

Mathematical Formula:

let us say that amount x was invested in the first bank and amount y was invested in the second bank, considering this we can write the following equation for the total money invested:

Similarly, the following is the equation for the total Interest earned in the first year.

Equation (1) and (2) are two linear simultaneous equations:

The graphical solution to the above system is as follows:

Therefore the amount invested in each bank is:

Scott invested $3,100 in the first bank and in the second bank, he invested $3,200.

Answer: 1 to 5

Step-by-step explanation:

The probability that none of the 4 light bulbs work is 2.56%.

As per the given information, the probability that an individual light bulb works is 0.6.

Therefore, the probability that it does not work (i.e., fails) is:

1 - 0.6 = 0.4

Since each light bulb works independently of the other light bulbs, the probability that none of the 4 light bulbs work is the product of the individual probabilities that each light bulb fails.

Calculated as,

P(none work) = P(first fails) × P(second fails) × P(third fails) × P(fourth fails)

P(none work) = 0.4 × 0.4 × 0.4 × 0.4

P(none work) = 0.0256

Therefore, the probability that none of the 4 light bulbs work is 0.0256 or approximately 2.56%.

For similar questions on limit,

brainly.com/question/282767

#SPJ4

The required Matlab code to find the greatest common divisor of a number using the Euclidean algorithm is shown.

To find the greatest common divisor (GCD) of two numbers using the Euclidean algorithm in MATLAB, you can use the following code:

% Replace '12345678' with your actual student number

studentNumber = '12345678';

% Extract the first 4 digits as the first number

firstNumber = str2double(studentNumber(1:4));

% Extract the last 3 digits as the second number

secondNumber = str2double(studentNumber(end-2:end));

% Find the GCD using the Euclidean algorithm

gcdValue = gcd(firstNumber, secondNumber);

% Display the result

disp(['The GCD of ' num2str(firstNumber) ' and ' num2str(secondNumber) ' is ' num2str(gcdValue) '.']);

Make sure to replace '12345678' with your actual student number. The code extracts the first 4 digits as the first number and the last 3 digits as the second number using string indexing. Then, the gcd function in MATLAB is used to calculate the GCD of the two numbers. Finally, the result is displayed using the disp function.

Learn more about Matlab code  here:

https://brainly.com/question/30763780

#SPJ4

Answer:

59

Step-by-step explanation:

The equation is

944 - 5x = 1180 - 9x

Notice what is being said. You start with 944 gallons and take off 5 per week

You also start with 1180 gallons and take on 9 per week.

You want to know when the two are equal. The second tank is larger, but it leaks more. That's what's going to bring about equality.

Add 9x to both sides

944 - 5x + 9x = 1180

944 + 4x = 1180                

Subtract 944 from both sides.

4x = 1180 - 944

4x = 236      

Divide by 4

x = 236/4

x = 59 weeks

The fractions of all the supporters that are male and support the away

team is 1/3

The fractions of all the supporters that are female and support the away

team is 2/9.

A fraction is a value representing a part of a whole.

We have,

Supporters for the Home team = 4/9

Supporting for the away team = 1 - 4/9 = 5/9

Now,

Male supporters from the away team = 3/5 x 5/9 = 1/3

So,

Female supporters from the away team = (1 - 3/5) x  5/9 = 2/5 x 5/9 = 2/9

Thus,

The fractions of all the supporters that are male and support the away

team is 1/3

The fractions of all the supporters that are female and support the away

team is 2/9.

Learn more about fractions here:

https://brainly.com/question/10354322

#SPJ1

Answer:

Ok, our function is:

f(x) = 3*(x - 1)^2 + 2.

First, domain:

We should assume that the domain is all the set of real numbers, and then we see if for some value we have a problem.

In this case we do not see any problem (we can not have a zero in the denominator, and there is no function that has problems with some values of x)

Then the domain is the set of all real numers.

Vertex:

Let's expand our function:

f(x) = 3*x^2 - 3*2*x + 1 + 2

f(x) = 3*x^2 -6*x + 2

The vertex of a quadratic function:

a*x^2 + b*x + c is at:

x = -b/2a

here we have:

a = 3 and b = -6

x = 6/2*3 = 6/6 = 1.

And the value of y at that point is:

f(1) = 3*(1 - 1)^2 + 2 = 2

Then the vertex is at: (1, 2)

Range:

The range is the set of all the possible values of y.

Ok, we can see that the leading coefficient is positive, this means that the arms of our quadratic function will go up.

Then the minimal value of our quadratic function is the value at the vertex, y = 2.

This means that the range can be written as:

R = y ≥ 2

So the range is the set of all real numbers that are larger or equal than 2.

To balance the line by choosing the assignable task with the longest task time first, you need to follow these steps. Determine the task times for each assignable task in the line.

Identify the assignable task with the longest task time. Assign that task to the first station in the line. Calculate the remaining cycle time by subtracting the task time of the assigned task from the total cycle time.
Repeat steps 2-4 for the remaining assignable tasks, considering the updated cycle time after each assignment.

Task A has the longest task time, so it is assigned to the first station. After each assignment, the cycle time is updated by subtracting the task time of the assigned task.  Task B is assigned to the second station, and Task C is assigned to the third station. Since Task C has a task time of 1.2 minutes, the remaining cycle time becomes 0. After that, Task D and Task E are not assigned any task time because the remaining cycle time is already 0. The specific values will depend on the actual task times and cycle time in your scenario.

To know more about assignable visit:

https://brainly.com/question/15106597

#SPJ11

By following these steps, you will be able to balance the line by choosing the assignable task with the longest task time first. The final answer will be the completed table with all the relevant information.

To balance the line by choosing the assignable task with the longest task time first, we need to follow certain steps and fill in the table accordingly.

Step 1: Determine the cycle time.

Given that the cycle time is 2.3 minutes, we will use this value as a reference for balancing the line.

Step 2: List the tasks and their task times.

Create a table with columns for tasks and task times. List all the tasks that need to be performed on the line and their respective task times.

Step 3: Sort the tasks in descending order.

Sort the tasks in descending order based on their task times, with the longest task time at the top and the shortest at the bottom.

Step 4: Calculate the number of operators required for each task.

Starting from the top of the table, divide the task time by the cycle time. Round up the result to the nearest whole number to determine the number of operators needed for each task.

Step 5: Calculate the balance delay.

For each task, calculate the difference between the number of operators required and the number of operators available. This represents the balance delay for each task.

Step 6: Fill in the table.

Fill in the table with the tasks, task times, number of operators required, and balance delay for each task.

Learn more about assignable task

https://brainly.com/question/29772720

#SPJ11

Answer:

false fs

Step-by-step explanation:

The correct answer choice:

The student would be able to afford the in-state cost for one year at a public 2-year college.

The correct option is D.

Multiplication is a mathematical arithmetic operation. It is also a process of adding the same types of expression some number of times.

Example - 2 × 3 means 2 is added three times, or 3 is added 2 times.

Given:

A student is planning to attend college in 5 years.

The student has saved $1,200 and plans to save another $50 per month over the next 60 months.

The total savings,

= 1200 + (50 x 60)

= $4200

That is equivalent to the cost of one year at a public 2-year college.

Therefore, the saving amount is equivalent to the cost of one year at a public 2-year college.

To learn more about multiplication;

https://brainly.com/question/19634536

#SPJ1

The table shows the cost per year of attending different types of colleges.

A student is planning to attend college in 5 years. The student has saved $1,200 and plans to save another $50 per month over the next 60 months.

Based on this information about the student's plan, which statement about the possible choices for a college is true?

Answer choices

The student would be able to afford the cost for one year at a private 4-year college.

The student would be able to afford out-of-state cost for half a year at a 4-year public college.

The student would be able to afford in-state cost for half a year at a public 4-year college.

The student would be able to afford in-state cost for one year at a public 2-year college.

Answer:

explicit  definition: \(a_n=5n-4\)

recursive definition: \(a_n=a_{n-1}+5\)

Step-by-step explanation:

Given arithmetic sequence: 1, 6, 11, 16, 21 ...

Therefore,

Using the general form of arithmetic sequence: \(a_n=a+(n-1)d\)

\(\implies a_n=1+(n-1)5\)

\(\implies a_n=1+5n-5\)

\(\implies a_n=5n-4\)

or \(a_n=a_{n-1}+5\)

The solution to the compound inequality in interval notation is Ø (an empty set).

Let's solve each compound inequality separately and express the solutions in interval notation.

1) (1/4)x - 3 >= -1:

Add 3 to both sides:

(1/4)x >= 2

Multiply both sides by 4 (since 1/4 * 4 = 1):

x >= 8

The solution to the first inequality is x >= 8.

2) -3(x - 2) >= 2:

Distribute -3 to the terms inside the parentheses:

-3x + 6 >= 2

Subtract 6 from both sides:

-3x >= -4

Divide both sides by -3 (note that dividing by a negative number flips the inequality sign):

x <= 4/3

The solution to the second inequality is x <= 4/3.

Combining the two solutions, we have:

x >= 8 and x <= 4/3

However, this is an empty set because there is no number that satisfies both conditions simultaneously. Therefore, the compound inequality has no solution.

In interval notation, we represent an empty set as an interval that doesn't exist. Thus, the solution to the compound inequality in interval notation is Ø (an empty set).

Learn more about interval notation here:

https://brainly.com/question/29184001

#SPJ11

Answer:

\(Solution\)

Here,

\(Principle(p)=$35000\\Rate(r)=2%\\\\Time(t)=9 years\)

\(Now, Interest(I)=\frac{PTR}{100}\)

                            \(=\frac{35000*2*9}{100}\\= $3600\)

A rectangular field with a width of 100 meters and a length of 100 meters would have the same perimeter as the given field (80 meters wide and 120 meters long) but a larger area.

To solve this problem, we need to find another rectangular field with the same perimeter but a larger area compared to the given field. Let's go step by step:

1. Find the perimeter of the given field:

  Perimeter = 2 * (Length + Width)

            = 2 * (120m + 80m)

            = 2 * 200m

            = 400m

2. Determine the area of the given field:

  Area = Length * Width

       = 120m * 80m

       = 9600m²

3. Let's assume the length of the new rectangular field is x meters. Since both fields have the same perimeter, the new field's width can be calculated using the formula for the perimeter:

  Perimeter = 2 * (Length + Width)

  400m = 2 * (x + Width)

  200m = x + Width

4. Now, we need to express the width in terms of x:

  Width = 200m - x

5. The area of the new rectangular field can be calculated using the width and length:

  Area = Length * Width

       = x * (200m - x)

6. To find the dimensions that yield the largest area, we need to find the maximum point of the area function. Let's take the derivative of the area function with respect to x and set it equal to zero:

  d(Area)/dx = 0

  d(x * (200m - x))/dx = 0

  200m - 2x = 0

  2x = 200m

  x = 100m

7. We substitute the value of x back into the equation for the width:

  Width = 200m - x

        = 200m - 100m

        = 100m

8. Therefore, the length and width of the new rectangular field with the same perimeter but a larger area are:

  Width = 100 meters

  Length = 100 meters

In summary, a rectangular field with a width of 100 meters and a length of 100 meters would have the same perimeter as the given field (80 meters wide and 120 meters long) but a larger area.

for more such question on rectangular visit

https://brainly.com/question/2607596

#SPJ8

Answer:

57 miles in 1 hr

Step-by-step explanation:

171/3 = 57

If two triangles are similar, that means their angles are equal and their sides a proportional, so:

          ∠A = ∠D

           \(65 = 2y - 5\\ 65 + 5 = 2y\\ 2y = 65 + 5\\ 2y = 70\\ y = 35\)

Therefore, y = 35, hope that helps!

Answer:

600 boys

Step-by-step explanation:

To find how many boys are at the park, add 360 to 240:

240 + 360

= 600

So, there are 600 boys at the park

Answer:

There are 600 boys at the park.

Step-by-step explanation:

The information we know is that there are already 240 girls at the park, and we also know that there are 360 more boys than girls. So to find out how many boys there are we must add the two values together, 240 and 360.

240 + 360 = 600

So that means there are 600 boys at the park.

Answer:

2 (2/3) Answer Choice C.)

Step-by-step explanation:

Answer:

\(3\frac{2}{3}\)

Step-by-step explanation:

=−1−1/3 +5

−1+5=4

4−1/3 = 3 2/3

Sally's friends took 105 marbles

A word problem  is a math question written as one sentence or more that requires children to apply their math knowledge to a 'real-life' scenario. Solving word problem requires critical thinking.

Let x represents the total number of marble

Sue takes 1/3 of the marble = (1/3)x

remaining marble after sue = x-(1/3)x = (2/3)x

Bill takes 1/4 of the remainder =( 2/3)x × 1/4 =(1/6)x

the remaining marble after Bill is( ⅔-⅙)x = 5x/6

Brian takes 1/2 of the remainder 5x/6 ÷2 = 5x/12

The remainder after Brian = 5x/6-5x/12= 75

multiply through by 12

= 10x-5x = 900

5x = 900

divide both sides by 5

x = 900/5 = 180 marbles

This means the total marble is 180 after all Sally's friends have taken, 75 is left.

Therefore the number of marbles taken by Sally's friends is 180-75 = 105 marbles

Learn more about word problem from: brainly.com/question/21405634

#SPJ1

Answer:

\(\huge\boxed{\bf\: 3:4:2}\)

Step-by-step explanation:

In the given ratio, \(12:16:8\), we can see that all the 3 numbers in ratio are multiples of 4. Hence the lowest common multiple (LCM) of the given ratio = 4.

Now, let's divide the 3 numbers by 4.

\(12:16:8\\= \frac{12}{4}:\frac{16}{4}:\frac{8}{4}\\=\boxed{\bf\: 3:4:2}\)

This ratio cannot be further simplified as they don't have any common multiples except for 1.

So, the simplified ratio = \(\boxed{\bf\: 3:4:2}\)

\(\rule{150pt}{2pt}\)

Answer:

1436.76

Step-by-step explanation:

I think so

Answer: V≈1436.76

\(V=\frac{4}{3} \pi r^3\)

4/3×π=4.1887902047863909846168578443727

r=7

7^3=343

4.1887902047863909846168578443727×343=1,436.7550402417321077235822406198

1,436.7550402417321077235822406198=1436.76

I hope this is good enough:

x = -1 and y = 3 in equations (i) and (ii):x + y = 2-1 + 3 = 2 (satisfied)3x + y = 0-3 + 3 = 0 (satisfied)

a) Solving the system using substitution:

We know that: x+y=2 (i)3x+y=0 (ii)We will solve equation (i) for y:y=2-x

Now, substitute this value of y in equation (ii):3x + (2-x) = 03x+2-x=0 2x = -2 x = -1

Substitute the value of x in equation (i):x + y = 2-1 + y = 2y = 3b)

Solving the system using elimination (linear combination) :

We know that: x+y=2 (i)3x+y=0 (ii)

We will subtract equation (i) from equation (ii):3x + y - (x + y) = 0 2x = 0 x = 0

Substitute the value of x in equation (i):0 + y = 2y = 2c)

Solving the system by graphing:We know that: x+y=2 (i)3x+y=0 (ii)

Let us plot the graph for both the equations on the same plane:

                                graph{x+2=-y [-10, 10, -5, 5]}

                                 graph{y=-3x [-10, 10, -5, 5]}

From the graph, we can see that the intersection point is (-1, 3)d)

We calculated the value of x and y in parts a, b, and c and the solutions are as follows:

Substitution: x = -1, y = 3

Elimination: x = 0, y = 2

Graphing: x = -1, y = 3

We can see that the value of x is different in parts a and b but the value of y is the same.

The value of x is the same in parts a and c but the value of y is different.

However, the value of x and y in part c is the same as in part a.

Therefore, we can say that the solutions of parts a, b, and c are not the same.

However, we can check if these solutions satisfy the original equations or not. We will substitute these values in the original equations and check:

Substituting x = -1 and y = 3 in equations (i) and (ii):x + y = 2-1 + 3 = 2 (satisfied)3x + y = 0-3 + 3 = 0 (satisfied)

Therefore, the values we obtained for x and y are the correct solutions.

Learn more about equations

brainly.com/question/29538993

#SPJ11

Answer:

  33°

Step-by-step explanation:

You want angle M in the congruent triangles XYZ and MNL with angle N marked 124° and angle X marked 33°.

The congruence statement tells you corresponding (and congruent) angle pairs are ...

  X and M (33°)

  Y and N (124°)

  L and Z

The measure of angle M is 33°.

__

Additional comment

The measures of angles L and Z are 180° -124° -33° = 23°.

The area of the rectangle 81 square units and the perimeter of the rectangle is 36 units.

In this question, we have been given the rectangle with coordinates (3,7), (3,-2), (-6.-2) and (-6,7)

We need to find the perimeter and area of the rectangle.

Using distance formula we find the length and width of the rectangle.

d1 = √(-2 - 7)² + (3 - 3)²

d1 = √(-9)²

d1 = 9

And d2 = √(-2 + 2)² + (-6-3)²

d2 = √(-9)²

d2 = 9

d3 = √(7 + 2)² + (-6 + 6)²

d3 = 9

This means, the length and width of rectangle are equal i.e., 9 units.

So, perimeter would be,

P = 4 * 9

P = 36 units

And the area would be,

A = 9 * 9

A = 81 square units

Therefore, the area of the rectangle 81 square units and the perimeter of the rectangle is 36 units.

Learn more about the rectangle here:

https://brainly.com/question/20693059

#SPJ1

Answer:

It's segment CA = segment FD if they're actually segments because I'm not sure if they are. They don't have the line at the top, so yeah but good luck.

Step-by-step explanation: