Which equation would best represent the equation of the line T.

The system of linear equations using the Gauss-Jordan elimination method has infinitely many solutions involving the parameter t, with x = 128/15, y = 2t - (11/5), and z = t.

To solve the given system of linear equations using the Gauss-Jordan elimination method, we'll perform row operations to transform the augmented matrix into reduced row-echelon form. Let's go through the steps:

Write the augmented matrix representing the system of equations:

| 3 -2 4 | 30 |

| 2 1 -2 | -1 |

| 1 4 -8 | -32 |

Perform row operations to eliminate the coefficients below the leading 1s in the first column:

R2 = R2 - (2/3)R1

R3 = R3 - (1/3)R1

The augmented matrix becomes:

| 3 -2 4 | 30 |

| 0 5 -10 | -11 |

| 0 6 -12 | -42 |

Next, eliminate the coefficient below the leading 1 in the second row:

R3 = R3 - (6/5)R2

The augmented matrix becomes:

| 3 -2 4 | 30 |

| 0 5 -10 | -11 |

| 0 0 0 | 0 |

Now, we can see that the third row consists of all zeros. This implies that the system of equations is dependent, meaning there are infinitely many solutions involving one parameter.

Expressing the system of equations back into equation form, we have:

3x - 2y + 4z = 30

5y - 10z = -11

0 = 0 (redundant equation)

Solve for the variables in terms of the parameter:

Let's choose z as the parameter (let z = t).

From the second equation:

5y - 10t = -11

y = (10t - 11) / 5 = 2t - (11/5)

From the first equation:

3x - 2(2t - 11/5) + 4t = 30

3x - 4t + 22/5 + 4t = 30

3x + 22/5 = 30

3x = 30 - 22/5

3x = (150 - 22)/5

3x = 128/5

x = 128/15

Therefore, the solution to the system of linear equations is:

x = 128/15

y = 2t - (11/5)

z = t

If t is any real number, the values of x, y, and z will satisfy the given system of equations.

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The coordinates of the midpoint of the line segment are (-1, 1)

The coordinates of the endpoints of the line segment are:

(4, -2) and ( -6, 4)

That is x₁ = 4, y₁ = -2, x₂ = -6, y₂ = 4

The formulae for finding the coordinates the coordinates of the midpoint of a line given the endpoints are:

Substituting the necessary parameters into the equation:

Therefore, the coordinates of the midpoint of the line segment are (-1, 1)

The given problem has been proved below using the rules of Congruence.

The given problem can be solved easily if we apply the basic rules of Congruence on the question properly as they are required. Congruence is when two given figures have the same shape and size.

Given that,

3AB=7AD

3AC=7AE

So, by re-arranging them we get the same ratio that is,

AB/AD=7/3

AC/AE=7/3

Hence, we can conclude that,

AB/AD=AC/AE

Also, we can show that ∠BAC and ∠DAE by the property of vertical angles.

But ∠BAC ≌ ∠DAE is also true by the vertical angle theorem in this diagram.

So, SAS property ∆ABC~∆ADE is proved in the end.

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\(f(x) = 4tan(8\pi) + 4sec^2(8\pi)(x - 8\pi) + 8sec^2(8\pi)tan(8\pi)(x - 8\pi)^2/2!\)

This expression represents the first three nonzero terms of the Taylor series expansion for f(x) = 4tan(x) centered at c = 8π.

What is the trigonometric ratio?

the trigonometric functions are real functions that relate an angle of a right-angled triangle to ratios of two side lengths. They are widely used in all sciences that are related to geometry, such as navigation, solid mechanics, celestial mechanics, geodesy, and many others.

To find the first three nonzero terms of the Taylor series for the function f(x) = 4tan(x) centered at c = 8π, we can use the definition of the Taylor series expansion.

The general formula for the Taylor series expansion of a function f(x) centered at c is:

\(f(x) = f(c) + f'(c)(x - c)/1! + f''(c)(x - c)^2/2! + f'''(c)(x - c)^3/3! + ...\)

Let's begin by calculating the first three nonzero terms for the given function.

Step 1: Evaluate f(c):

f(8π) = 4tan(8π)

Step 2: Calculate f'(x):

f'(x) = d/dx(4tan(x))

= 4sec²(x)

Step 3: Evaluate f'(c):

f'(8π) = 4sec²(8π)

Step 4: Calculate f''(x):

f''(x) = d/dx(4sec²(x))

= 8sec²(x)tan(x)

Step 5: Evaluate f''(c):

f''(8π) = 8sec²(8π)tan(8π)

Step 6: Calculate f'''(x):

f'''(x) = d/dx(8sec²(x)tan(x))

= 8sec⁴(x) + 16sec²(x)tan²(x)

Step 7: Evaluate f'''(c):

f'''(8π) = 8sec⁴(8π) + 16sec²(8π)tan²(8π)

Now we can write the first three nonzero terms of the Taylor series expansion for f(x) centered at c = 8π:

f(x) ≈ f(8π) + f'(8π)(x - 8π)/1! + f''(8π)(x - 8π)²/2!

Simplifying further,

Hence, \(f(x) = 4tan(8\pi) + 4sec^2(8\pi)(x - 8\pi) + 8sec^2(8\pi)tan(8\pi)(x - 8\pi)^2/2!\)

This expression represents the first three nonzero terms of the Taylor series expansion for f(x) = 4tan(x) centered at c = 8π.

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Answer:

\(4^{8}\)

Step-by-step explanation:

Whenever multiplying the same values with exponentials, they add up. So, 3+5 = 8.

\(4^{3} . 4^{5} = 4^{8}\)

Answer:

Step-by-step explanation:

the top one... which is I am assuming asking for the diameter?

Formula = d=2r  

so 2x4 which is 8

But if you were wanting number 6

the formula is A=πr2

which would be 3.14 x 1^1 = 3.14

you take the diameter and square it and then multiply it by pi

Answer:

-2/4 then 5/16 then 3/8 then 1/2 plz mark brainiest :)

Answer:

-2/4 , -3/8 , 5/16 , 1/2

Step-by-step explanation:

Using the given inputs:

-3/8 5/16 -2/4 1/2

The least common denominator (LCD) is: 16.

Rewriting as equivalent fractions with the LCD:

-3/8 5/16 -2/4 1/2

-6/16 5/16 -8/16 8/16

Sorting this table by the numerators of the equivalent fractions in order from least to greatest:

-2/4   -3/8   5/16   1/2

-8/16 < -6/16 < 5/16 < 8/16

Therefore, the sorted inputs in order from least to greatest is:

-2/4 < -3/8 < 5/16 < 1/2

It is more likely that the distance across a circular field is the diameter rather than the circumference.

To determine whether the distance across a circular field is the diameter or the circumference, we can use some formulas that relate these parts of a circle. The formulas are:

Circumference = π * diameter

Diameter = 2 * radius

Radius = diameter / 2

If we plug in the given distance of 98.638 meters into these formulas, we can see which one gives a reasonable value for the other parts of the circle. For example, if we assume that the distance is the diameter, then we can find the radius and circumference as follows:

Radius = diameter / 2

Radius = 98.638 / 2

Radius = 49.319 meters

Circumference = π * diameter

Circumference = π * 98.638

Circumference ≈ 310.05 meters

These values seem reasonable for a circular field. However, if we assume that the distance is the circumference, then we can find the diameter and radius as follows:

Diameter = circumference / π

Diameter = 98.638 / π

Diameter ≈ 31.39 meters

Radius = diameter / 2

Radius = 31.39 / 2

Radius ≈ 15.695 meters

These values seem too small for a circular field. Therefore, it is more likely that the distance across a circular field is the diameter rather than the circumference.

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Complete question:

The distance across a circular field is 98.638 meters. Is it a diameter, a radius or a circumference?

Hi ;-)

\(\frac{2xy}{5ac}:\frac{4xy^2}{15a^2c}=\frac{2xy}{5ac}\cdot\frac{15a^2c}{4xy^2}=\frac{3a}{2y}\\\\Answer: \ \text{D}\)

Answer:

\({ \underline{ \sf{D. \: \: \frac{3a}{2y} }}}\)

Step-by-step explanation:

\({ \sf{ \frac{2xy}{5ac} \div \frac{ {4xy}^{2} }{15 {a}^{2} c} }}\)

find the reciprocal :

\({ \sf{ = \frac{2xy}{5ac} \times \frac{15 {a}^{2}c }{4 {xy}^{2} } }} \\ \\ = { \sf{( \frac{2xy}{4 {xy}^{2} }) \times ( \frac{15 {a}^{2}c }{5ac} ) }} \\ \\ = { \sf{ \frac{1}{2y} \times 3a}} \\ \\ = { \sf{ \frac{3a}{2y} }}\)

The final number remaining in this sequence is the number 2.

We start with the first 300 natural numbers written in ascending order. We remove the numbers at odd places, which means we remove all the numbers at positions 1, 3, 5, and so on.

After the first removal, we are left with the numbers at even positions: 2, 4, 6, and so on.

Now, we repeat the process and remove the numbers at odd positions again. We remove numbers at positions 1, 3, 5, and so on from the remaining sequence.

After the second removal, we are left with the numbers at even positions again: 4, 8, 12, and so on.

We can observe that in each removal, the sequence reduces to half its size, and we are left with the numbers at even positions.

Continuing this process, we will eventually reach a point where we have only one number left.

Since we start with 300 numbers, after the first removal, we have 150 numbers. After the second removal, we have 75 numbers. After the third removal, we have 38 numbers. After the fourth removal, we have 19 numbers. After the fifth removal, we have 10 numbers. After the sixth removal, we have 5 numbers. After the seventh removal, we have 3 numbers. After the eighth removal, we have 2 numbers. Finally, after the ninth and last removal, we are left with a single number.

Therefore, the final number remaining in this sequence is the number 2.

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In the given research scenario, the dependent variable is the average number of pounds lost.

The dependent variable is the variable that is being measured or observed in an experiment. It is the outcome or response variable that is expected to change as a result of manipulating the independent variable(s). In this case, the independent variable is the type of diet (low-carb or high-carb), and the dependent variable is the average number of pounds lost by the participants.

The researchers are comparing the average weight loss between the two groups: one following a low-carbohydrate diet and the other following a high-carbohydrate diet with the same number of calories. They are interested in determining whether the type of diet has an effect on weight loss. Hence, the dependent variable is the average number of pounds lost, as it is the variable that is expected to vary based on the diet type.

If you would like to represent the dependent variable using LaTeX code, you can use the following snippet:

\(\text{Dependent Variable: Average number of pounds lost}\)

I hope this explanation clarifies the concept of the dependent variable in the given research scenario. Let me know if you have any further questions.

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The measured density for pure water (0% sugar solution) may be higher or lower than 1.00 g/mL due to factors such as temperature and impurities.

The density of water is usually quoted as 1.00 g/mL at 4°C. However, this precise value may vary depending on the temperature and the presence of impurities. At temperatures higher than 4°C, the density of water decreases due to thermal expansion. Conversely, at temperatures lower than 4°C, the density of water increases due to the formation of hydrogen bonds, resulting in a lattice-like structure.

Additionally, impurities in water can also affect its density. For example, dissolved substances such as salts or sugars can increase the density of water. In the case of a 0% sugar solution, if the measured density is higher than 1.00 g/mL, it could indicate the presence of impurities or experimental error. On the other hand, if the measured density is lower than 1.00 g/mL, it could suggest that the water sample is purer than the standard value.

Overall, the measured density of pure water can deviate from the commonly quoted value of 1.00 g/mL due to factors like temperature and impurities.

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Step-by-step explanation:

no.

15/20 = 3/4

10/15 = 2/3

This problem involves the concept of direct proportion. This means that as the amount of gas increases, the distance the car can travel also increases at the same rate.

To solve the problem, we can set up a proportion:

25 miles / 1 gallon = x miles / 5.5 gallons

To solve for x, we can cross-multiply:

25 miles * 5.5 gallons = 1 gallon * x miles

137.5 miles = x

Therefore, the car can travel 137.5 miles with 5 1/2 gallons of gas.

It's important to note that this problem assumes a constant rate of fuel efficiency for the car. In other words, the car will always travel 25 miles on 1 gallon of gas. If the car's fuel efficiency changes, the distance it can travel on a given amount of gas will also change. This is an example of inverse proportion, where the amount of gas needed to travel a certain distance increases as the car's fuel efficiency decreases.

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On one side of the square, it is 4.5 units long. The formula in finding the area of a square is A = s^2, where s is for side. The formula can also be A = s * s in which both formulas are the same and will result in the same answer. So overall, the area of the square is 20.25 or 20 ¼ square units. Hope this helps!

Answer:

16

Step-by-step explanation:

16+4x = 10 +14

-16             -16

4x = 8

/4      /4

x=2

8x=8(2)

=16

Answer:

4%

Step-by-step explanation:

4% percent of 625 is 25 and the price used to 635 and now  its 650 which means there was a $25 increase which means 4% is correct

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True. Exception reports show a greater level of detail than is included in routine reports.

Exception reports are reports that help in identifying data that does not conform to expected patterns. Exception reports show information about an exception in the data set.

This helps to identify irregularities or anomalies in data or system operations.Exception reports are used to analyze system performance, monitor resource consumption, and to detect unusual activity.

This type of report is important to identify issues or errors, where the routine reports or standard reports would not provide enough detail or insight to do so.

It provides detailed information on any unusual event or anomaly that occurred beyond the usual course of events or processes.Exception reports are generated and distributed when the data is not expected or when an event occurs that is outside of what is considered typical.

For example, a financial system might generate an exception report if a transaction is entered that exceeds the maximum allowed amount. This report would show the details of the transaction and highlight the exception.

The purpose of exception reports is to provide users with a higher level of detail than they would find in routine reports. Exception reports are used to highlight significant data, which will be used for further analysis or action.

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(a) The concentration of the product X at any time t is given by the explicit expression x(t) = (αß / (α + ß)) * (1 - e^(-k(α+ß)t)).

(b) The expression for the velocity constant k can be determined by substituting the given concentration n at t = 1 into the equation and solving for k. The expression for k is k = -ln(1 - n/(αß)) / (α + ß).

(c) With α = 250, ß = 40, and n = 25, the concentration of the product at the end of 5 minutes can be calculated using the expression x(t) from part (a).

(d) The Euler method can be used to approximate the concentration of the product at the end of five minutes by taking smaller time steps and comparing the approximate solution with the exact solution.

(a) To solve the differential equation dx/dt = k(α - x)(ß - x), we can separate variables and integrate. Rearranging the equation gives

dx/[(α - x)(ß - x)] = k dt.

Integrating both sides with respect to x, we obtain:

∫(1/[(α - x)(ß - x)]) dx = ∫k dt.

We can use partial fraction decomposition to integrate the left side of the equation. Assuming α and ß are distinct values, we can express

1/[(α - x)(ß - x)] as A/(α - x) + B/(ß - x), where A and B are constants.

Multiplying both sides by (α - x)(ß - x), we have:

1 = A(ß - x) + B(α - x).

Setting x = α, we get 1 = A(ß - α), which gives A = 1/(α - ß).

Setting x = ß, we get 1 = B(α - ß), which gives B = 1/(ß - α).

Substituting the values of A and B back into the partial fraction decomposition, we have:

1/[(α - x)(ß - x)] = 1/(α - ß)(α - x) - 1/(ß - α)(ß - x).

Integrating both sides with respect to t, we get:

∫dx/[(α - x)(ß - x)] = (1/(α - ß))∫dt - (1/(ß - α))∫dt.

Simplifying, we have:

(1/(α - ß)) ln|(α - x)/(ß - x)| = (1/(α - ß))t + C.

Multiplying both sides by (α - ß), we obtain:

ln|(α - x)/(ß - x)| = t + C.

Taking the exponential of both sides, we have:

|(α - x)/(ß - x)| = e^t * e^C.

Since e^C is a constant, we can write:

|(α - x)/(ß - x)| = Ce^t,

where C is a constant.

Taking the positive and negative cases separately, we have two expressions:

(α - x)/(ß - x) = Ce^t,

and

(x - α)/(x - ß) = Ce^t.

Solving these equations for x, we can find the explicit expressions representing the concentration x(t) of the product X at any time t.

(b) At time t = 1, the concentration of the product is n moles per litre, which means x(1) = n. We can substitute this into the equation x(t) = (αß / (α + ß)) * (1 - e^(-k(α+ß)t)) and solve for k.

Substituting t = 1 and x(1) = n, we have:

n = (αß / (α + ß)) * (1 - e^(-k(α+ß))).

Solving for k, we get:

k = -ln(1 - n/(αß)) / (α + ß).

This gives us the expression for the velocity constant k in terms of the given concentration n.

(c) With α = 250, ß = 40, and n = 25, we can substitute these values into the expression for x(t) obtained in part (a) to find the concentration of the product at the end of 5 minutes. Substituting t = 5, α = 250, ß = 40, and n = 25, we have:

\(x(5) = (250 * 40 / (250 + 40)) * (1 - e^{-k(250+40)*5}).\)

By evaluating this expression, we can find the concentration of the product at the end of 5 minutes.

(d) To approximate the concentration of the product at the end of five minutes using the Euler method, we can divide the time interval into smaller steps (e.g., one minute). Starting with the initial condition x(0) = 0, we can use the formula:

x(t + h) ≈ x(t) + h(dx/dt),

where h is the time step (in this case, one minute) and dx/dt is given by the differential equation dx/dt = k(α - x)(ß - x). We repeat this approximation every one minute until we reach 5 minutes and compare the approximate solution with the exact solution obtained in part (a).

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The upper bound of 206.264 to 3 decimal places would be 206.265.

What is upper bound?

In mathematics, an upper bound is a value that is greater than or equal to all of the values in a set. For example, if we have a set of numbers {1, 2, 3}, then 3 is an upper bound of this set because it is greater than or equal to all the numbers in the set.

An upper bound can be either a member of the set or not. If the upper bound is a member of the set, then it is called a maximum element of the set. If the upper bound is not a member of the set, then it is called a strict upper bound of the set.

In the context of rounding, the upper bound refers to the next highest value that a number could be rounded to. For example, if we are rounding a number to the nearest integer, the upper bound would be the next integer greater than the original number.

The upper bound of 206.264 to 3 decimal places would be 206.265.

This is because the third decimal place of the original number is 4, and any number greater than or equal to 5 in the next decimal place would round the number up to the next value. Therefore, rounding 206.264 to 3 decimal places gives 206.265.

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Answer:

x = 8.5

Step-by-step explanation:

In this question, we are to calculate the value of x.

To calculate this, we shall be utilizing one of the important properties of parallelogram.

This property is that opposite angles of a parallelogram are equal.

This means that mQSR = mSPQ = 4x + 90

Now to finally calculate x, we make use of another important parallelogram property which is that angles of parallelogram which faces each other are supplementary.

This means that they add up to be 180

Since mQSR faces mQRS

This means that;

4x + 90 + 9x -20 = 180

13x + 70 = 180

13x = 110

x = 110/13 which is approximately 8.5

a. Null hypothesis: The population means credit card charges for groceries and dining out are equal.

Alternative hypothesis: The population means credit card charges for groceries and dining out are not equal.
b. Using a level of significance of 0.05, we can conclude that the population means differ since the calculated p-value is less than 0.05.
c. The point estimate of the difference between the population means is also not provided in the question. Therefore, we cannot calculate the confidence interval estimate of the difference between the population means.

a. To formulate the null and alternative hypotheses, you can use the following notation:

H0 (null hypothesis): μ1 - μ2 = 0 (There is no difference between the population mean credit card charges for groceries and the population mean credit card charges for dining out)

Ha (alternative hypothesis): μ1 - μ2 ≠ 0 (There is a difference between the population mean credit card charges for groceries and the population mean credit card charges for dining out)

b. To determine if the population means differ at a given level of significance (let's say α), you would need to perform a hypothesis test using the sample mean difference, sample standard deviation, and sample sizes for both populations. Unfortunately, you didn't provide these values, so I cannot perform the test or calculate the p-value.

c. To determine which category has a higher population mean annual credit card charge, you would need to compare the point estimate of the difference between the population means. Since you didn't provide the sample mean difference, I cannot determine which category has a higher population mean annual credit card charge.
We cannot determine which category, groceries or dining out, has a higher population mean annual credit card charge without additional information such as the sample mean credit card charges for each category. The point estimate of the difference between the population means is also not provided in the question.

Additionally, to calculate the confidence interval estimate of the difference between the population means, you would need the sample mean difference, sample standard deviation, and sample sizes. Without this information, I cannot provide the confidence interval estimate.

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You are correct that the slope of line AB is 2. To find the slope of the line CD, we can apply the slope formula again (like I assume you did with AB).

\(m=\frac{15-7}{4-0}=\boxed{2}\)

Therefore, since the slopes of lines AB and CD are equal, they are parallel

It will take approximately 12 years and 9 months for Sienna Rose's money to grow to $7000.

What is compound interest?

Compound interest is interest that is calculated not only on the original principal amount of a loan or investment but also on any accumulated interest from previous periods. In other words, the interest earned on an investment or the interest charged on a loan is added to the principal, and then the interest for the next period is calculated on the new total amount.

For example, if you invest $1,000 at an annual interest rate of 5%, and the interest is compounded annually, you would earn $50 in interest at the end of the first year. Instead of receiving that $50, it would be added to your principal, so your new balance would be $1,050. The following year, you would earn 5% interest on $1,050, which would be $52.50. This process would continue for each year of the investment.

Compound interest can be very beneficial for long-term investments, as the interest earned on the accumulated interest can significantly increase the total return. However, it can also work against you in the case of loans, as the interest charged on the accumulated interest can quickly increase the total amount owed.

We can use the formula for compound interest to solve this problem:

\(A= P (1+\frac{r}{n} )^{nt}\)

where

A is the amount of money after t years,

P is the principal (starting amount),

r is the annual interest rate (as a decimal),

n is the number of times the interest is compounded per year, and

t is the time (in years).

In this case,

P = $4000,

r = 0.036 (since the interest rate is given as 3.60% per year),

n = 12 (since the interest is compounded monthly), and

we want to find t when A = $7000.

Substituting these values into the formula, we get:

$7000 = $4000(1 + 0.036/12)^(12t)

Dividing both sides by $4000 and taking the natural logarithm of both sides, we get:

ln(1.75) = 0.003 t

Solving for t, we get:

t = ln(1.75)/(0.003)

t ≈ 153.71 months

Therefore, it will take approximately 153 months, or 12 years and 9 months (since there are 12 months in a year), for Sienna Rose's money to grow to $7000.

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Answer:

False because both 2 and 8, and 3 and 5 are alternate interior angles

When variables compete to explain the same effects, they are sometimes called "colliders".

Variables are units of measure that may take on various values and affect the outcome of the analysis. As a result, the effect size of one variable might alter the effect size of another, which can cause problems in correctly evaluating the influence of one variable on the outcome variable.

In science, an effect refers to the impact of one event, process, or object on another, and it can be positive or negative.

Effects can be evaluated to determine their degree and impact, as well as the causes that underlie them.

In some instances, one variable (V1) might influence another variable (V2), which in turn affects a third variable (V3). When the two variables are related but are not directly connected, this situation is known as a collider.

In summary, when variables compete to explain the same effects, they are referred to as "colliders."

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The probability that the sum of the two is even and at least one of the dice shows 5 is 1/18.

There are a total of 36 possible outcomes when you roll two dice, since each die has 6 possible outcomes.

To find the number of outcomes where the sum of the dice is even, we can divide the 36 outcomes into two groups: outcomes where the sum is even, and outcomes where the sum is odd. There are 18 even sums (2, 4, 6, 8, 10, 12) and 18 odd sums (1, 3, 5, 7, 9, 11). So the probability that the sum of the dice is even is 18/36, or 1/2.

Now, we need to find the number of outcomes where at least one of the dice shows 5. There are 4 outcomes where the first die shows 5 (5,5; 5,1; 5,2; 5,3) and 4 outcomes where the second die shows 5 (1,5; 2,5; 3,5; 4,5). There are also 4 outcomes where both dice show 5. However, we have counted each of these outcomes twice (once as an outcome where the first die shows 5, and once as an outcome where the second die shows 5). So we need to subtract these 4 outcomes from our total. This leaves us with a total of 8 outcomes where at least one of the dice shows 5.

So the probability that at least one of the dice shows 5 is 8/36, or 2/9.

Finally, we want to find the probability that the sum of the dice is even and at least one of the dice shows 5. Since these two events are independent (the fact that the sum is even does not affect the probability that one of the dice shows 5, and vice versa), we can find the probability of both events occurring by multiplying the probabilities of the individual events.

So the probability that the sum of the dice is even and at least one of the dice shows 5 is (1/2) * (2/9) = 1/18.

Therefore the answer is: 1/18.

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Let's start on Friday's temperature, the problem says that it was -7°F and it was half of the temperature on Thursday, which means on Thursday is was:

-7*2 °F = -14°F.

On Thursday, the temperature was 8°F higher than on Wednesday, then on Wednesday it was:

-14°F - 8°F = -22°F.

On Wednesday the temperature was twice as low as for Tuesday, then on Tuesday it was:

-22°F/2 = -11°F.

On Tuesday, the temperature was 6°F colder than on Monday, then on Monday it was:

-11°F + 6°F = -5°F.

Therefore, the recorded temperature for Monday was -5°F.