what is .253 repeating as a fraction

The general solution to the differential equation \(\(y'' - 2y' + y = t^{-1}e^t\)\) is \(\[y(t) = C_1e^t + C_2te^t + (\ln|t| + C_3t + C_4)e^t,\]\) where \(\(C_1\), \(C_2\), \(C_3\), and \(C_4\)\) are arbitrary constants.

One or more terms and the derivatives of one variable (the dependent variable) with respect to the other variable (the independent variable) make up a differential equation. f(x) = dy/dx Here, the independent variable "x" and the dependent variable "y" are both present.

To find the general solution to the differential equation \(\[y'' - 2y' + y = \frac{t^{-1}e^t}{t^2}\]\) using the method of variation of parameters, we can follow these steps:

Step 1: Find the complementary solution (homogeneous solution) to the associated homogeneous equation \(\[y'' - 2y' + y = 0.\]\) The characteristic equation is \(\[r^2 - 2r + 1 = 0,\]\) which factors as \(\[(r - 1)^2 = 0.\]\) Therefore, the complementary solution is \(\[y_c(t) = C_1e^t + C_2te^t,\]\) where \(\(C_1\)\) and \(\(C_2\)\) are arbitrary constants.

Step 2: Assume a particular solution of the form \(\[y_p(t) = u_1(t)e^t,\]\) where \\((u_1(t)\)\) is an unknown function to be determined.

Step 3: Differentiate \(\(y_p(t)\)\) to find \(\(y_p'\)\) and \(\(y_p''\)\), and substitute them into the original differential equation. We have:

\(\[y_p'(t) = u_1'(t)e^t + u_1(t)e^t\]\\y_p''(t) = u_1''(t)e^t + 2u_1'(t)e^t + u_1(t)e^t\]\)

Substitute \(\(y_p(t)\), \(y_p'(t)\)\), and \(\(y_p''(t)\)\) into the differential equation:

\(\[(u_1''(t)e^t + 2u_1'(t)e^t + u_1(t)e^t) - 2(u_1'(t)e^t + u_1(t)e^t) + u_1(t)e^t = \frac{t^{-1}e^t}{t^2}\]\)

Simplify:

\(\[u_1''(t)e^t = \frac{1}{t^2}\]\)

Step 4: Integrate both sides of the equation to solve for \(\(u_1(t)\)\):

\(\[\int u_1''(t)e^t dt = \int \frac{1}{t^2} dt\]\)

\(\[u_1'(t)e^t = -\frac{1}{t} + C_3,\]\) where \(\(C_3\)\) is an arbitrary constant.

Integrate again:

\(\[u_1(t) = \int (-\frac{1}{t} + C_3)e^{-t} dt\]\)

\(\[u_1(t) = \ln|t| + C_3t + C_4,\]\) where \(\(C_4\)\) is an arbitrary constant.

Step 5: The particular solution is \(\(y_p(t) = u_1(t)e^t\)\):

\(\[y_p(t) = (\ln|t| + C_3t + C_4)e^t\]\)

Step 6: The general solution to the original differential equation is the sum of the complementary solution and the particular solution:

\(\[y(t) = y_c(t) + y_p(t)\]\)

\(\[y(t) = C_1e^t + C_2te^t + (\ln|t| + C_3t + C_4)e^t,\] where \(C_1\), \(C_2\), \(C_3\), and \(C_4\)\) are arbitrary constants.

Therefore, the general solution to the differential equation \(\(y'' - 2y' + y = t^{-1}e^t\)\) is \(\[y(t) = C_1e^t + C_2te^t + (\ln|t| + C_3t + C_4)e^t,\]\) where \(\(C_1\), \(C_2\), \(C_3\), and \(C_4\)\) are arbitrary constants.

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The answers are :1. B No2. B No3. B No4. B No5. B No6. B No

Given expressions are:

(x − 3)(x + 5) x + 3 + x + 3 x + 5 x + 3 x + 5 + x − 3 x + 5 (x + 3)(x + 5) x − 5 ÷ x + 5 x − 5

We can solve this by putting the value of x in each expression as x = 5.

The given expression is x - 3. So we will put the value of x as 5. Then we will solve it and compare it with the given expressions as shown below.

1. (x - 3)(x + 5)For x = 5, (x - 3)(x + 5) = (5 - 3)(5 + 5) = 2 x 10 = 20.

Since 20 is not equal to x - 3, the answer is "No". Hence, B is the correct option.

2. x + 3 + x + 3For x = 5, x + 3 + x + 3 = 5 + 3 + 5 + 3 = 16.

Since 16 is not equal to x - 3, the answer is "No". Hence, B is the correct option.

3. x + 5 For x = 5, x + 5 = 5 + 5 = 10. Since 10 is not equal to x - 3, the answer is "No". Hence, B is the correct option.

4. x + 3 x + 5 + x - 3For x = 5, x + 3 x + 5 + x - 3 = 5 + 3 5 + 5 5 - 3 = 10 + 8 = 18. Since 18 is not equal to x - 3, the answer is "No". Hence, B is the correct option.

5. (x + 3)(x + 5)For x = 5, (x + 3)(x + 5) = (5 + 3)(5 + 5) = 8 x 10 = 80. Since 80 is not equal to x - 3, the answer is "No". Hence, B is the correct option.

6. x - 5 ÷ x + 5 Let's simplify the expression for this one: For x = 5, x - 5 ÷ x + 5 = 5 - 5 ÷ 5 + 5 = 0. Since 0 is not equal to x - 3, the answer is "No". Hence, B is the correct option.

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Answer:

True

Step-by-step explanation:

To convert microseconds to seconds in the programming language C, you can use a simple mathematical expression.

#include <stdio.h>

int main() {

   int microseconds = 1000000;

   double seconds = (double)microseconds / 1000000.0;

   printf("%d microseconds is equivalent to %f seconds\n", microseconds, seconds);

   return 0;

}

A microsecond is a unit of time equal to one millionth of a second, while a second is a unit of time equal to the duration of 9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium-133 atom.

To convert microseconds to seconds in the programming language C, you can use a simple mathematical expression.

A microsecond is a unit of time equal to one millionth of a second, while a second is a unit of time equal to the duration of 9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium-133 atom.

To convert microseconds to seconds in C, you can simply divide the number of microseconds by one million (1,000,000). This can be done using the following code:

c

Copy code

#include <stdio.h>

int main() {

   int microseconds = 1000000;

   double seconds = (double)microseconds / 1000000.0;

   printf("%d microseconds is equivalent to %f seconds\n", microseconds, seconds);

   return 0;

}

In this example, the value of microseconds is set to 1000000, which represents one million microseconds. This value is then divided by one million using the expression (double)microseconds / 1000000.0, which gives the equivalent value in seconds. The result is then displayed using the printf function.

It is important to use the double data type when converting microseconds to seconds, as this data type allows for decimal values, which are necessary for representing fractional units of time.

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Answer:

The probability that the socks picked is not blue is 11/14

Step-by-step explanation:

In this question, we are to calculate that a socks selected from random from the group of socks given in the question is not a blue socks.

This means the socks would either be a black or a white socks

Firstly, we find the total number of socks = 8 + 6 + 14 = 28 socks

Now the probability of picking a blue socks will be 6/28 = 3/14

We must understand that the probability of not picking a blue socks = 1 - the probability of picking a blue socks

Thus, the probability of not picking a blue socks will be 1 - 3/14 = 11/14

Answer:

The probability that a sock chosen at random is not blue P = 11/14 = 0.786

Step-by-step explanation:

Probability is the chances of getting a particular outcome.

Given:

Black socks = 8

Blue socks = 6

White socks = 14

Total = 8+6+14 =28

The probability that a sock chosen at random is not blue P;

P = number of non-blue socks ÷ total number of socks

Number of non blue socks = black + white socks = 8+14 = 22

Substituting the values;

P = 22/28 = 11/14

P = 11/14 = 0.786

Answer:

25

Step-by-step explanation:

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97,

Answer:

25

Step-by-step explanation:

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97

Answer:

n = (1/2)(-1 ± i√2)

Step-by-step explanation:

Among the several ways in which quadratic equations can be solved is the quadratic formula.  Putting to use the coefficients {12, 12, 9}, we obtain the discriminant, b^2 - 4ac:  12^2 - 4(12)(9) = 144 - 432 = -288.  The negative sign of this discriminant tells us that the quadratic has two unequal, complex roots.  These roots are:

      -b ± √(discriminant)

n = ---------------------------------

                 2a

Here we have:

      -12 ± √(-288)           -12 ± i√2√144          -12 ± i12√2

n = ----------------------  =  ------------------------ =  --------------------

            2(12)                             24                           24

or:

n = (1/2)(-1 ± i√2)

Answer:

57

Step-by-step explanation:

Answer:

x² + (y + 5)² = 61

Step-by-step explanation:

the equation of a circle in standard form is

(x - a)² + (y - b)² = r²

where (a, b ) are the coordinates of the centre and r is the radius

here (a, b ) = (0, - 5 ) and r has to be found

(x - 0)² + (y - (- 5) )² = r² , that is

x² + (y + 5)² = r²

the radius is the distance from the centre to a point on the circle.

using the distance formula to find r

r = \(\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }\)

with (x₁, y₁ ) = (0, - 5 ) and (x₂, y₂ ) = (- \(\sqrt{60}\) , - 6 )

r = \(\sqrt{(-\sqrt{60}-0)^2+(-6-(-5))^2 }\)

 = \(\sqrt{(-\sqrt{60})^2+(-1)^2 }\)

  = \(\sqrt{60+1}\)

  = \(\sqrt{61}\)

then r² = ( \(\sqrt{61}\) )² = 61

the equation of the circle is then

x² + (y + 5)² = 61

The linearly independent solution of the non-homogeneous equation is y = y-c + y-p, y = c1×(x²(-1/2)cos(x)) + c2×(x²(-1/2)sin(x)) + (8/35)×x²(3/2) + (2/35)×x²(-1/2) where c1 and c2 are arbitrary constants.

The associated homogeneous equation is: x²2y'' + xy' + (x²2 - 1/4)y = 0

The complementary solution can be found by assuming y has the form y-c = c1y1 + c2y2, where c1 and c2 are constants, and y1 and y2 are the given linearly independent solutions.

y-c = c1×(x²(-1/2)cos(x)) + c2×(x²(-1/2)sin(x))

Now, the particular solution, denoted as y-p, of the non-homogeneous equation.

y-p has the form:

y-p = Ax²(3/2) + Bx²(-1/2)

where A and B are constants to be determined.

The first and second derivatives of y-p:

y-p' = A×(3/2)x²(1/2) - (1/2)Bx²(-3/2)

y-p'' = A(3/4)×x²(-1/2) + (3/4)Bx²(-5/2)

Substituting these into the non-homogeneous equation:

x²2y_-p'' + xy-p' + (x²2 - 1/4)×y-p = x²(3/2)

x²2×(A×(3/4)x²(-1/2) + (3/4)Bx²(-5/2)) + x(A×(3/2)x²(1/2) - (1/2)Bx²(-3/2)) + (x^2 - 1/4)(Ax²(3/2) + Bx²(-1/2)) = x²(3/2)

Simplifying and collecting like terms:

(3A/4)x²(3/2) + (3B/4)x²-1/2) + (3A/2)x²(3/2) - (1/2)Bx²(3/2) + (A - (1/4))x²(5/2) + (B/4)x²(1/2) - (A/4)x²(-1/2) + Bx²(-3/2) = x²(3/2)

Matching the coefficients of like powers of x:

[(3A/4) + (3A/2) - (1/2)B]x²(3/2) + [(3B/4) + (B/4)]x²(-1/2) + [(A - (1/4))]x²(5/2) + [(-A/4) + B]x²(-1/2) + [B/4]x²(-3/2) = x²(3/2)

Equating the coefficients of x²(3/2) on both sides:

(3A/4) + (3A/2) - (1/2)B = 1

(9A/4) - (1/2)B = 1

Equating the coefficients of x²(-1/2) on both sides:

[(3B/4) + (B/4)] - (A/4) = 0

(4B/4) - (A/4) = 0

Simplifying the equations:

(9A - 2B) = 4

4B - A = 0

Solving these equations simultaneously ,A = 8/35 and B = 2/35.

Therefore, the particular solution is: y-p = (8/35)×x²(3/2) + (2/35)×x²(-1/2)

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The largest possible assigned cycle time for the production line is 2.7 minutes, while the smallest possible assigned cycle time is 0.9 minutes.

In line balancing, the goal is to allocate the tasks evenly across the production line to achieve maximum efficiency. The largest possible assigned cycle time is determined by the task with the longest duration. In this case, the task with a duration of 2.7 minutes sets the upper limit for the cycle time. If all tasks were assigned the same cycle time, it would take at least 2.7 minutes to complete one cycle of the production line.

On the other hand, the smallest possible assigned cycle time is determined by the sum of the task durations. In this case, the sum of all task times is 6.4 minutes. By dividing this total time by the number of workstations or operators in the production line, we can determine the smallest possible assigned cycle time.

Since there are no constraints mentioned about the number of operators, we assume a single operator. Therefore, the smallest possible assigned cycle time would be 6.4 minutes divided by 1, which equals 6.4 minutes. However, it is worth noting that this cycle time is not realistic or practical for an operator to achieve.

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The point of intersection with x - axis is (5/3,0) and the point of intersection with y - axis is (0,5).  

Any point on AB's perpendicular bisector, P(x,y), shall be considered. Then, PA = PB.

√(x-3)²+(y-6)² = √(x+3)²+(y-4)²

(x-3)²+(y-6)² = (x+3)²+(y-4)²

x² -6x+ 9 + y²- 12y + 36 = x² +6x+ 9 + y²- 8y + 16

12x + 4y -20 = 0

3x+ y-5 =0 ---(1)  

Consequently, 3x+y-5=0 is the equation for the perpendicular bisector of AB.

We know that the coordinates of any point on x-axis are of the form (x,0). In other words, any point on the x-axis has a y-coordinate of zero. Thus, if we enter y = 0 in (1), we get

3x -5 = 0

x = 5/3

Thus, the x-axis is cut by the perpendicular bisector of AB at (5/3, 0).

(ii) Any point's y-axis coordinates have the following format: (0,y). When we enter x = 0 in (1), we obtain

y − 5 = 0

⇒ y = 5

Thus, the y-axis is where the perpendicular bisector of AB intersects (0,5).

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Step-by-step explanation:

a^2-b^2+2a+2b

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

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

Answer:

(8+8)=16 + (5x3)=15

Step-by-step explanation:

so 16+15=31 all you have to do is parenthesis first then do whatever is in the middle last

Answer:

Step-by-step explanation:

x ≤ -4  and x> 0

So,

0 > x ≤ -4

Answer:

(multiply both sides by 6)

6×\(\frac{4h+4}{6}\)-10×6=-2h×6

(simplify)

4h+4-60=-12h

4h-56=-12h

(move constant to the right side and variable to the left)

4h+12h=56

16h=56

(divide both sides by 16)

h=7/2

Answer:

1/196

Step-by-step explanation:

Answer: 28

Step-by-step explanation:

Based on the calculations, the rate of change for the function is equal to 5.

Mathematically, the rate of change for the function can be calculated by using this expression;

Rate of change = [½ ÷ ⅒]/[0 - (-1)]

Rate of change = 5/1

Rate of change = 5.

Rate of change = [5/2 ÷ ½]/[1 - 0]

Rate of change = 5/1

Rate of change = 5.

Rate of change = [125/2 ÷ 25/2]/[3 - 2]

Rate of change = 5/1

Rate of change = 5.

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Answer: 23

Step-by-step explanation:

The number of times the last passenger who boarded the ride make a complete loop on the Ferris wheel is 22.

A trigonometric equation is one that involves one or more of the sixs sine, cosine, tangent, cotangent, secant, and cosecant. Some trigonometric equations, like x = cos x, can be solved only numerically, through successive approximations.

Given that, Sine function model: h=-82.5cos3π(t)+97.5 where h is the height of the passenger above the ground measure in feet and t is the time of operation of the ride in minutes.

The duration of the ride is 15 min.

Let the period be T, then we can write:

h=-82.5.cos(2πt/T)+97.5

So, we must have 2π/T =3π or T=2/3 minutes

Number of complete periods

Floor(15/T)=22

Therefore, the number of times the last passenger who boarded the ride make a complete loop on the Ferris wheel is 22.

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"Your question is incomplete, probably the complete question/missing part is:"

The Colossus Ferris wheel debuted at the 1984 New Orleans World’s Fair. The ride is 180 ft tall, and passengers board the ride at an initial height of 15 ft above the ground. The height above ground, h, of a passenger on the ride is a periodic function of time, t. The graph displays the height above ground of the last passenger to board over the course of the 15 min ride.

The duration of the ride is 15 min.

How many times does the last passenger who boarded the ride make a complete loop on the Ferris wheel.

(a) The expected length of the queue, not including the vehicle being served, is 0.625 vehicles.

(b) The probability that there are no more than 5 cars at the gate, including the vehicle being served, is approximately 0.0176.

(c) The average waiting time of a vehicle at the ticket gate is 1.5 minutes or 0.025 hours.

(a) To find the expected length of the queue at the ticket gate, we need to calculate the expected number of vehicles waiting in the queue at any given time. This can be found by using the Little's Law, which states that the expected number of customers in a stable system is equal to the arrival rate multiplied by the average time spent in the system.

In this case, the arrival rate is 25 vehicles per hour, and the average time spent in the system is the time it takes to buy the tickets, which is 1.5 minutes or 0.025 hours. Therefore, the expected number of vehicles waiting in the queue is

E[N] = λW = 25 x 0.025 = 0.625 vehicles

So the expected length of the queue, not including the vehicle being served, is 0.625 vehicles.

(b) To find the probability that there are no more than 5 cars at the gate, including the vehicle being served, we need to use the Poisson distribution with a mean of 25 vehicles per hour. Let X be the number of vehicles arriving in an hour, then X Poisson(25).

P(X ≤ 5) = ∑ P(X = k) for k = 0 to 5

= ∑ (e^(-λ) × λ^k / k!) for k = 0 to 5

= e^(-25) × (25^0 / 0!) + e^(-25) × (25^1 / 1!) + ... + e^(-25) × (25^5 / 5!)

Using a calculator or software, this probability is found to be approximately 0.0176.

(c) The average waiting time of a vehicle can be found by dividing the expected number of vehicles waiting in the queue by the arrival rate. From part (a), we know that the expected number of vehicles waiting in the queue is 0.625 vehicles. The arrival rate is 25 vehicles per hour. Therefore, the average waiting time of a vehicle is

W = E[N] / λ = 0.625 / 25 = 0.025 hours or 1.5 minutes

So the average waiting time for a vehicle at the ticket gate is 1.5 minutes.

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The quadratic equation is `8x² - 18x - 5 = (8x - 5)(x - 1)`.Explanation: Here's how to factor the quadratic equation completely: 8x² - 18x - 5 is a quadratic equation.

Step 1: Multiply 8 and -5 together to get -40.Step 2: Find two numbers that have a product of -40 and a sum of -18. Since -20 and 2 have a product of -40 and a sum of -18, they're the two numbers we need.Step 3: Break the -18x term into -20x + 2x. Step 4: Rewrite the quadratic equation as follows: 8x² - 20x + 2x - 5 Step 5: Group the first two terms and the last two terms: 4x(2x - 5) + 1(2x - 5)Step 6: Factor out the (2x - 5) factor:(2x - 5)(4x + 1).

Therefore, the quadratic equation is factored completely into (8x - 5)(x - 1)

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The total number of intervals in a frequency distribution for a numerical variable can vary depending on the range and nature of the data, typically ranging from a minimum of 5 to a maximum of 20 intervals.

A frequency distribution is a representation of data that organizes values into intervals or bins and shows the number of occurrences or frequencies within each interval. The choice of the number of intervals depends on the characteristics of the data and the desired level of detail in the distribution. Generally, it is recommended to have at least five intervals to capture the overall pattern of the data. Too few intervals may oversimplify the distribution, while too many intervals may result in excessive detail and difficulty in interpretation.

The maximum number of intervals, often around 20, is determined by the data range and the desired level of granularity. When the range of values is large or the data contains outliers, more intervals may be needed to capture the variations accurately. On the other hand, if the range is small or the data is relatively homogenous, a smaller number of intervals may suffice. Balancing the level of detail with the readability and interpretability of the distribution is essential to effectively communicate the information contained in the data.

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A frequency distribution for a numerical variable is a statistical tool that groups the data into intervals and counts the frequency of observations within each interval. The total number of intervals typically ranges from 5 to 20. However, the choice of how many intervals to use depends on the total number of observations in the dataset and the need to balance detail with complexity.

In the realm of statistics, creating a frequency distribution for a numerical variable is a common task. In a frequency distribution, data is grouped into intervals or classes, and the frequency of observations within each interval is counted. When determining the number of intervals, it often depends on the total number of observations in the dataset.

Typically, the total number of intervals in a frequency distribution may range from 5 to 20. These are rough guidelines though, and the number of intervals you decide upon should best represent the data and make it easier to interpret.  

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There are 7 degrees of freedom.

In performing the pooled-variance t test, the degrees of freedom can be calculated using the formula:
df = (n1 - 1) + (n2 - 1)

Substituting the given values:
df = (4 - 1) + (5 - 1)
df = 3 + 4
df = 7

Therefore, there are 7 degrees of  freedom.

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There are 7 degrees of freedom for the pooled-variance t-test.

To perform a pooled-variance t-test, we need to calculate the degrees of freedom. The formula for degrees of freedom in a pooled-variance t-test is:

\(\[\text{{df}} = n_1 + n_2 - 2\]\)

where \(\(n_1\)\) and \(\(n_2\)\) are the sample sizes of the two independent samples.

In this case, \(\(n_1 = 4\)\) and \(\(n_2 = 5\)\). Substituting these values into the formula, we get:

\(\[\text{{df}} = 4 + 5 - 2 = 7\]\)

In a pooled-variance t-test, we combine the sample variances from two independent samples to estimate the population variance. The degrees of freedom for this test are calculated using the formula \(df = n1 + n2 - 2\), where \(n_1\)and \(n_2\) are the sample sizes of the two independent samples.

To understand why the formula is \(df = n1 + n2 - 2\), we need to consider the concept of degrees of freedom. Degrees of freedom represent the number of independent pieces of information available to estimate a parameter. In the case of a pooled-variance t-test, we subtract 2 from the total sample sizes because we use two sample means to estimate the population means, thereby reducing the degrees of freedom by 2.

In this specific case, the sample sizes are \(n1 = 4\) and \(n2 = 5\). Plugging these values into the formula gives us \(df = 4 + 5 - 2 = 7\). Hence, there are 7 degrees of freedom for the pooled-variance t-test.

Therefore, there are 7 degrees of freedom for the pooled-variance t-test.

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Answer: 90 degrees.

Step-by-step explanation:

Step 1: The smallest angle must be 90/2 = 45 degrees.

Step 2: The largest angle is twice the size of the smallest angle, so it is 90 degrees.

Answer:

1. measure of angle E is 90 degrees

2. Measure of angle F + measure of angle G is 90 degrees

Step-by-step explanation:

Angle E is 90 degrees because it is marked as a right angle (the square)

A triangle has 180 degrees so if E is 90 degrees then the other 2 also have to equal 90 degrees

By Quadratic Formula factors of \(a^2+4b^2\) are \((a+2bi),(a-2bi)\).

The quadratic formula in elementary algebra is a formula that gives the solution(s) to a quadratic equation. In addition to the quadratic formula, there are various methods for solving quadratic equations, including factoring (direct factoring, grouping, and the AC technique), completing the square, graphing, and others.

The following general quadratic equation is given:

\(ax^2+bx+c=0\)

The quadratic formula is:

\(x=\frac{-b+\sqrt{b^2-4ac} }{2a}, \frac{-b-\sqrt{b^2-4ac} }{2a}\);

where x stands for an unknown, a, b, and c are constants, and a≠0.

Each of these two answers is also referred to as a quadratic equation root (or zero). These roots, which are clearly stated as \(y = ax^2 + bx + c\), are the x-values at which any parabola crosses the x-axis geometrically.

Given;

\(y=a^2+4b^2;\\\)

By comparing this with general equation \(x=a,a=1,b=0,\)\(c=4b^2\)

By substituting in the formula;

\(x=\frac{-0+\sqrt{(0)^2-4(1)(4b^2)} }{2(1)} =2bi\\(or) x=\frac{-0-\sqrt{(0)^2-4(1)(4b^2)} }{2(1)} =-2bi\)

That gives us;

\(y=(a+2bi)(a-2bi)\)

By Quadratic Formula factors of \(a^2+4b^2\) are \((a+2bi),(a-2bi)\).

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The variable associated with the interior and exterior angles in the triangle is equal to 56.

The value of the exterior angle is equal to 116°.

This question presents the case of a geometric system formed by a triangle and a semirray that includes two interior angles and a exterior angle. Please notice that the sum of the measures of interior angles in a triangle equals 180° and the sum of two supplementary angles equals 180°.

First, derive the equation of the missing interior angles in triangle PQR:

m ∠ R = 180° - 60° - x

m ∠ R = 120° - x

Second, obtain the equation for the two supplementary angles:

(120° - x) + (2 · x + 4°) = 180°

124° + x = 180°

x = 56

Third, determine the value of the exterior angle:

θ = 2 · x + 4

θ = 2 · 56 + 4

θ = 116°

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Answer:

-5, - 2, 3

Step-by-step explanation:

y=2x+3, y=-7, x=-5; y=-1, x=-2, y=9, x=3