PLEASE HELP
Suppose that the functions fand g are defined for all real numbers x as follows.
f(x) = 5x
g(x)=4x-4
Write the expressions for (g.f)(x) and (g-f)(x) and evaluate (g+f)(2).
(g•f)(x) =
(g-f)(x) =
(g+r) (2)=

The computed mean of 52.4 and the actual mean of 52.7 suggest a close relationship in terms of central tendency.

A computed mean is a statistical measure calculated by summing up a set of values and dividing by the number of observations. In this case, the computed mean of 52.4 implies that when the values are averaged, the result is 52.4.

The actual mean of 52.7 refers to the true average of the population or data set being analyzed. Since it is higher than the computed mean, it indicates that the sample used for computation might have slightly underestimated the true population mean.

However, the difference between the computed mean and the actual mean is relatively small, with only a 0.3 unit discrepancy.

Given the proximity of these two values, it suggests that the computed mean is a reasonably accurate estimate of the actual mean.

However, it's important to note that without additional information, such as the sample size or the variability of the data, it is difficult to draw definitive conclusions about the relationship between the computed mean and the actual mean.

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Comparing the characteristics of the two functions, we can conclude that the graph of g(x) = -2² is a reflection of the graph of f(x) = 3x² over the x-axis (option C).

The given functions are f(x) = 3x² and g(x) = -2².

To understand the difference between their graphs, let's examine the characteristics of each function individually:

Function f(x) = 3x²:

The coefficient of x² is positive (3), indicating an upward-opening parabola.

The graph of f(x) will be symmetric with respect to the y-axis, as any change in x will result in the same y-value due to the squaring of x.

The vertex of the parabola will be at the origin (0, 0) since there are no additional terms affecting the position of the graph.

Function g(x) = -2²:

The coefficient of x² is negative (-2), indicating a downward-opening parabola.

The negative sign will reflect the graph of f(x) across the x-axis, resulting in a vertical flip.

The vertex of the parabola will also be at the origin (0, 0) due to the absence of additional terms.

Comparing the characteristics of the two functions, we can conclude that the graph of g(x) = -2² is a reflection of the graph of f(x) = 3x² over the x-axis (option C). This means that g(x) is obtained by taking the graph of f(x) and flipping it vertically. The reflection occurs over the x-axis, causing the parabola to open downward instead of upward.

Therefore, the correct answer is option C: g(x) is a reflection of f(x) over the x-axis.

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Answer:

Step-by-step explanation:

To find the volume of the solid obtained by rotating the region bounded by the graphs y = (x - 4)^3, the x-axis, x = 0, and x = 5 about the y-axis, we can use the method of cylindrical shells.

The formula for the volume of a solid obtained by rotating a region bounded by the graph of a function f(x), the x-axis, x = a, and x = b about the y-axis is given by:

V = 2π ∫[a, b] x * f(x) dx

In this case, the function f(x) = (x - 4)^3, and the bounds of integration are a = 0 and b = 5.

Substituting these values into the formula, we have:

V = 2π ∫[0, 5] x * (x - 4)^3 dx

To evaluate this integral, we can expand the cubic term and then integrate:

V = 2π ∫[0, 5] x * (x^3 - 12x^2 + 48x - 64) dx

V = 2π ∫[0, 5] (x^4 - 12x^3 + 48x^2 - 64x) dx

Integrating each term separately:

V = 2π [1/5 x^5 - 3x^4 + 16x^3 - 32x^2] evaluated from 0 to 5

Now we can substitute the bounds of integration:

V = 2π [(1/5 * 5^5 - 3 * 5^4 + 16 * 5^3 - 32 * 5^2) - (1/5 * 0^5 - 3 * 0^4 + 16 * 0^3 - 32 * 0^2)]

Simplifying:

V = 2π [(1/5 * 3125) - 0]

V = 2π * (625/5)

V = 2π * 125

V = 250π

Therefore, the volume of the solid obtained by rotating the region bounded by the graphs y = (x - 4)^3, the x-axis, x = 0, and x = 5 about the y-axis is 250π cubic units.

Answer:

Step-by-step explanation:

The quadratic formula is y=ax^2+bx+c

If we move everything to the left side of the equation,

-6x^2=-9x+7 becomes

-6x^2+9x-7=0

a=-6, b=9, c=-7, so the third answer choice

Answer:

Step-by-step explanation:

The correct answer is A. A rectangle the same size as the base.

When a rectangular pyramid is sliced parallel to the base, the resulting cross-section is a rectangle that is the same size as the base. The parallel slicing ensures that the cross-section maintains the same dimensions as the base of the pyramid. Therefore, option A, a rectangle the same size as the base, represents the cross-section.

Answer: [tex](-\infty, 0) \cup (0, \infty)[/tex]

Step-by-step explanation:

The graph of [tex]\frac{\sin x}{x}[/tex] is continuous for all real [tex]x[/tex] except [tex]x=0[/tex], and multiplying this by [tex]1/3[/tex] does not change this.

The expression g(x) = f(x) + represents the relationship between the two functions expression for g(x) in terms of f(x).

To express the function g(x) in terms of f(x), we need to understand the relationship between the two functions.

The given expression g(x) = f(x) + indicates that the function g(x) is obtained by adding a certain value or expression to the function f(x). expression for g(x) in terms of f(x).

In general, if we have the function g(x) = f(x) + c, where c is a constant value, then g(x) can be expressed in terms of f(x) as:

g(x) = f(x) + c

In this case, g(x) is obtained by adding the constant value c to the corresponding values of f(x).

It's important to note that without additional information about the specific relationship between f(x) and g(x), such as a functional equation or given values, we cannot provide a more precise expression for g(x) in terms of f(x).

Therefore, the expression g(x) = f(x) + represents the relationship between the two functions expression for g(x) in terms of f(x).

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Answer: 3

Step-by-step explanation: just 3

Edge 2020

HI Your answer is 42

I have calculated it you can trust me

Well you have marked right in the pic

PLEASE MARK AS BRAINLIEST

Answer:

Part A:

The correct expression for how many pencils Ms. Florinda has left after giving them out to her students is:

A. 100 - 2 × (22 - 19)

Part B:

To determine whether Ms. Florinda has enough pencils to give each of her students 2, we can calculate the total number of pencils needed. The total number of students is the sum of the students in both classes, which is 22 + 19 = 41.

If each student needs 2 pencils, then the total number of pencils needed is 2 × 41 = 82.

Comparing this with the initial number of pencils Ms. Florinda bought (100), we can see that she has more than enough pencils to give each of her students 2.

Yes, she has enough pencils to give each of her students 2.

She has 18 more than she needs.

What is needed to be congruent to show that ABC=AXYZ is AC ≅ XZ. option D

Given that in ΔABC and ΔXYZ, ∠X ≅ ∠A and ∠Z ≅ ∠C.

We are to select the correct condition that we will need to show that the triangles ABC and XYZ are congruent to each other by ASA rule..

ASA Congruence Theorem: Two triangles are said to be congruent if two angles and the side lying between them of one triangle are congruent to the corresponding two angles and the side between them of the second triangle.

In ΔABC, side between ∠A and ∠C is AC,

in ΔXYZ, side between ∠X and ∠Z is XZ.

Therefore, for the triangles to be congruent by ASA rule, we must have AC ≅ XZ.

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The z-score for Brazil is given as follows:

Z = 0.87.

The z-score formula is defined as follows:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

In which:

The parameters for this problem are given as follows:

[tex]X = 6.24, \mu = 4.8, \sigma = 1.66[/tex]

Hence the z-score for Brazil is given as follows:

Z = (6.24 - 4.8)/1.66

Z = 0.87.

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The given expression, 10f - 5f + 8 + 6g + 4, simplifies to 5f + 12 + 6g when like terms are combined.

To simplify the expression 10f - 5f + 8 + 6g + 4, we can combine like terms by adding or subtracting coefficients that have the same variables:

10f - 5f + 8 + 6g + 4

Combining the terms with 'f', we have:

(10f - 5f) + 8 + 6g + 4

This simplifies to:

5f + 8 + 6g + 4

Next, we can combine the constant terms:

8 + 4 = 12

Thus, the simplified expression is:

5f + 12 + 6g

This expression is equivalent to 10f - 5f + 8 + 6g + 4.

In summary, the expression 10f - 5f + 8 + 6g + 4 simplifies to 5f + 12 + 6g after combining like terms.

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Step-by-step explanation:

a linear relationship or function is described in general as

y = f(x) = ax + b

Because the variable term has the variable x only with the exponent 1, this makes this a straight line - hence the name "linear".

here f(x) is P(x) :

P(x) = ax + b

now we are using both given points (ordered pairs) to calculate a and b :

20 = a×170 + b

2820 = a×220 + b

to eliminate first one variable we subtract equation 1 from equation 2 :

2800 = a×50

a = 2800/50 = 280/5 = 56

now, we use that in any of the 2 original equations to get b :

20 = 56×170 + b

b = 20 - 56×170 = 20 - 9520 = -9500

so,

P(x) = 56x - 9500

The expression (3√2) / (3√6) with a rationalized denominator is 3√9 / 6. Option C is the correct answer.

To rationalize the denominator in the expression (3√2) / (3√6), we can multiply both the numerator and denominator by the conjugate of the denominator. The conjugate of √6 is -√6, so we multiply the expression by (-√6) / (-√6):

(3√2 / 3√6) * (-√6 / -√6)

This simplifies to:

-3√12 / (-3√36)

Further simplifying, we have:

-3√12 / (-3 * 6)

-3√12 / -18

Finally, we can cancel out the common factor of 3:

- 3√9 / - 6.

Simplifying further, we get:

3√9 / 6.

Option C is the correct answer.

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The given statement "An event with probability 3/4 is more likely to happen than an event with probability 4/5" is true.

The reason why we say an event with a higher probability is more likely to happen is because probability is the measure of how often an event will occur during a large number of trials.

Therefore, when we compare the probabilities of two events, we can expect that the one with the higher probability will occur more often and therefore is more likely to happen.For instance, in the context of a coin flip, the probability of getting heads is 1/2 while the probability of getting tails is also 1/2.

Therefore, both events are equally likely to happen. On the other hand, if we were to compare the probability of rolling a six-sided die and getting a 1, which has a probability of 1/6, with the probability of rolling the die and getting a number less than or equal to 4, which has a probability of 4/6 or 2/3, we can say that the latter is more likely to happen since it has a higher probability.

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The data set has two outliers, namely the points (2, 225) and (8, 75).

Based on the given information about the scatterplot, we can observe that most of the points are grouped closely together and show a slight increase.

There are two points that lie outside of this cluster, specifically (2, 225) and (8, 75).

To determine if these points are outliers, we need to consider their deviation from the general pattern exhibited by the majority of the data points.

If these points deviate significantly from the overall trend, they can be considered outliers.

In this case, since (2, 225) and (8, 75) lie outside of the cluster of closely grouped points and do not follow the general pattern, they can be considered outliers.

These points are noticeably different from the majority of the data points and may have influenced the overall trend of the scatterplot.

The data set has two outliers, namely the points (2, 225) and (8, 75).

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[tex]\qquad\displaystyle \rm \dashrightarrow \: let \: \: Sydney's \: \: age \: \: be \: \: 'y'[/tex]

[tex]\qquad\displaystyle \tt \dashrightarrow \: Devaughn's \: \: age \: \: will \: \: be \: \: 3y[/tex]

Sum up ;

[tex]\qquad\displaystyle \tt \dashrightarrow \: 3y + y = 80[/tex]

[tex]\qquad\displaystyle \tt \dashrightarrow \: 4y = 80[/tex]

[tex]\qquad\displaystyle \tt \dashrightarrow \: y = 80 \div 4[/tex]

[tex]\qquad\displaystyle \tt \dashrightarrow \: y = 20[/tex]

So, Sydney's age is 20 years, n that of Devaughn is 20 × 3 = 60 years

Answer:

Sydney= 20, Devaughn= 60

Step-by-step explanation:

Let Sydney's age be 'x'

Devaughn's age = 3 times x = 3x

We Know That

The sum of their ages is 80.

So,

3x + x = 80

4x = 80

If we shift the 4 to the 80 side

x = 80/4

x = 20

So, Sydney's age is 20

Therefore, Devaughn's age =

3x = 3 times x

= 3 times 20

= 60

Answer:

AB = √3

Step-by-step explanation:

Since ABCD is a rectangle, all angles are 90°

∠CDA = 90°

⇒ ∠CDB + ∠BDA = 90

⇒ ∠BDA = 60

In ΔABD,

sin(∠BDA) = opposite/ hypotenuse = AB / BD

⇒ sin(60) = AB/2

⇒ AB = 2 sin(60)

⇒ AB = 2 (√3)/2

AB = √3

Answer:

Step-by-step explanation:

To solve these problems, we can use the Poisson probability formula:

P(x; λ) = (e^(-λ) * λ^x) / x!

Where:

P(x; λ) is the probability of x events occurring

e is the base of the natural logarithm (approximately 2.71828)

λ is the average rate of events occurring in the given time period

x is the number of events

(a) Probability of exactly 4 orders arriving in 30 minutes:

The average rate of orders is given as 5 orders per hour. To find the average rate of orders in 30 minutes, we divide it by 2 (since 30 minutes is half an hour):

λ = 5 orders/hour / 2 = 2.5 orders/30 minutes

Using the Poisson probability formula:

P(x = 4; λ = 2.5) = (e^(-2.5) * 2.5^4) / 4!

Calculating this:

P(x = 4; λ = 2.5) ≈ (0.082 * 39.0625) / 24

P(x = 4; λ = 2.5) ≈ 3.22265625 / 24

P(x = 4; λ = 2.5) ≈ 0.134

Therefore, the probability that exactly 4 orders will arrive in 30 minutes is approximately 0.134, or 13.4%.

(b) Probability of at least 2 orders arriving in an hour:

To find the probability of at least 2 orders, we need to calculate the probabilities of having 0 and 1 order and subtract it from 1 (since it's the complement).

Using the Poisson probability formula:

P(x = 0; λ = 5) = (e^(-5) * 5^0) / 0! = e^(-5) ≈ 0.0067

P(x = 1; λ = 5) = (e^(-5) * 5^1) / 1! ≈ 0.0337

P(at least 2 orders) = 1 - P(x = 0) - P(x = 1) ≈ 1 - 0.0067 - 0.0337 ≈ 0.9596

Therefore, the probability of at least 2 orders arriving in an hour is approximately 0.9596, or 95.96%.

The box plot that best represents the numerical data is: A. A box plot using a number line from 3 to 12.25 with tick marks every one-fourth unit. The box extends from 6.25 to 9.25 on the number line. A line in the box is at 7.5. The lines outside the box end at 4.5 and 11. The graph is titled Shoe Sizes, and the line is labeled Size of Shoe.

In order to determine the five-number summary for the survey, we would arrange the data set in an ascending order:

4.5,6,6,6.5,7,7,7.5,8,8.5,9,9.5,10,11

Based on the information provided about the list of shoe sizes for a group of 13 people, we would use a graphical method (box plot) to determine the five-number summary for the given data set as follows:

Minimum (Min) = 4.5.

First quartile (Q₁) = 6.25.

Median (Med) = 7.5.

Third quartile (Q₃) = 9.25.

Maximum (Max) = 11.

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Answer:

Hope this helps and have a nice day

Step-by-step explanation:

To find the value of x, we can use the formula:

Time = Distance / Speed

Let's calculate the time taken to travel from Q to P and back to Q.

From Q to P:

Distance = 12 km

Speed = 6 km/h

Time taken from Q to P = Distance / Speed = 12 km / 6 km/h = 2 hours

From P to Q:

Distance = 12 km

Speed = (6 + x) km/h

Time taken from P to Q = Distance / Speed = 12 km / (6 + x) km/h

Given that the total time taken for the round trip is 3 hours 20 minutes, we can convert it to hours:

Total time = 3 hours + (20 minutes / 60) hours = 3 + (1/3) hours = 10/3 hours

According to the problem, the total time is the sum of the time from Q to P and from P to Q:

Total time = Time taken from Q to P + Time taken from P to Q

Substituting the values:

10/3 hours = 2 hours + 12 km / (6 + x) km/h

Simplifying the equation:

10/3 = 2 + 12 / (6 + x)

Multiply both sides by (6 + x) to eliminate the denominator:

10(6 + x) = 2(6 + x) + 12

60 + 10x = 12 + 2x + 12

Collecting like terms:

8x = 24

Dividing both sides by 8:

x = 3

Therefore, the value of x is 3.

Answer:

x = 3

Step-by-step explanation:

speed  = distance / time

time = distance / speed

Total time from P to Q to P:

T = 3h 20min

P to Q :

s = 6 km/h

d = 12 km

t = d/s

= 12/6

t = 2 h

time remaining t₁ = T - t

= 3h 20min - 2h

=  1 hr 20 min

= 60 + 20 min

= 80 min

t₁ = 80/60 hr

Q to P:

d₁ = 12km

t₁ = 80/60 hr

s₁ = d/t₁

[tex]= \frac{12}{\frac{80}{60} }\\ \\= \frac{12*60}{80}[/tex]

= 9

s₁ = 9 km/h

From question, s₁ = (6 + x)km/h

⇒ 6 + x = 9

⇒ x = 3

Answer:

f(3r - 1) = -6r + 6

Step-by-step explanation:

To find f(3r - 1), we substitute 3r - 1 for x in the expression for f(x) and simplify:

f(x) = 4 - 2x

f(3r - 1) = 4 - 2(3r - 1)

= 4 - 6r + 2

= -6r + 6

So, f(3r - 1) = -6r + 6.

The tax charged on Omari's monthly earning of Ksh 24,200 is Ksh 3,340.

To calculate the tax charged on Omari's monthly earning, we need to consider the tax brackets and rates applicable in the specific tax system or country. Since you haven't specified a particular tax system, I will provide a general explanation.

Assuming we have a simplified progressive tax system with three tax brackets:

For the first tax bracket, let's say income up to Ksh 10,000 is taxed at a rate of 10%.

For the second tax bracket, income between Ksh 10,001 and Ksh 20,000 is taxed at a rate of 15%.

For the third tax bracket, income above Ksh 20,000 is taxed at a rate of 20%.

To calculate the tax charged on Omari's monthly earning of Ksh 24,200, we can divide it into the respective tax brackets:

Ksh 10,000 falls in the first tax bracket. So, the tax for this portion is 10% of Ksh 10,000, which is Ksh 1,000.

Ksh 20,000 - Ksh 10,000 = Ksh 10,000 falls in the second tax bracket. The tax for this portion is 15% of Ksh 10,000, which is Ksh 1,500.

The remaining amount, Ksh 24,200 - Ksh 20,000 = Ksh 4,200, falls in the third tax bracket. The tax for this portion is 20% of Ksh 4,200, which is Ksh 840.

Now, we can sum up the taxes for each bracket:

Total Tax = Tax in the first bracket + Tax in the second bracket + Tax in the third bracket

Total Tax = Ksh 1,000 + Ksh 1,500 + Ksh 840

Total Tax = Ksh 3,340

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The proposal is as follows

Part III  -  The distance between buoys A and B is 12.8 kilometers.

Part IV  -  The length of the other two triangle legs are 10.2 kilometers and 8.4 kilometers.

Part V  - The total length of the race course is 31.4 kilometers.

Part VIII  - The winner's speed during last year's race was 10.8 knots.

See the proposal attached.

Dear Sponsor,

I'm seeking sponsorship for the San Francisco sailboat race.

With a proven track record and the determination to win, your investment of $5,500 covers travel costs and potential hazards.

By associating your brand with a winning sailor, you'll gain significant exposure to thousands of spectators. Join me in this thrilling race for success.

Sincerely,

[Your Name]

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The domain of f(x) is (0, +∞), and the range is (0, +∞). The graph of the function will have a vertical asymptote at x = 0 and will continuously increase as x approaches positive infinity.

To graph the given logarithmic function f(x) based on the table, we can use the information provided. The table presents pairs of values (x, y), where x represents the input and y represents the output of the function.

From the table, we can observe that the input values (x) are positive and non-zero. This indicates that the domain of the function is x > 0, meaning x is greater than zero. In interval notation, the domain would be written as (0, +∞).

Looking at the output values (y) in the table, we see that they are all positive. This suggests that the range of the function is y > 0, meaning y is greater than zero. In interval notation, the range would be expressed as (0, +∞).

Graphically, the function f(x) is logarithmic and will have a vertical asymptote at x = 0. As x approaches positive infinity, the function increases without bound. The graph starts at y = 125 when x = 1, and it intersects the y-axis at y = 5 when x = 1.5. The graph of the function will resemble a curve that approaches but never touches the x-axis.

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Answer:

We don't need to worry about the displaystyle- {3} −3 anyway, because we dcided in the first step that displaystyle {x}ge- {2} x ≥ −2. So the domain for this case is displaystyle {x}ge- {2}, {x}ne {3} x≥ −2,x≠ 3, which we can write as displaystyle {left [- {2}, {3}right)}cup {left ({3},inftyright)} [−2,3)∪(3,∞).

Step-by-step explanation:

The height of a person whose length of forearm is 24.5 cm is equal to 163.38 centimeters.

In this exercise, we would plot the length of forearm on the x-axis of a scatter plot while height would be plotted on the y-axis of the scatter plot through the use of Microsoft Excel.

On the Microsoft Excel worksheet, you should right click on any data point on the scatter plot, select format trend line, and then tick the box to display a linear equation for the line of best fit on the scatter plot;

y = 3.01x + 89.63

Based on the equation of the line of best fit above, the height of a person whose length of forearm is 24.5 cm can be determined as follows;

y = 3.01x + 89.63

y = 3.01(24.5) + 89.63

y = 163.375 ≈ 163.38 centimeters.

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The midpoint of AB is M(-4,2). If the coordinates of A are (-7,3), and the coordinates of B is (-1, 1).

To find the coordinates of point B, we can use the midpoint formula, which states that the coordinates of the midpoint between two points (A and B) can be found by averaging the corresponding coordinates.

Let's denote the coordinates of point A as (x1, y1) and the coordinates of point B as (x2, y2). The midpoint M is given as (-4, 2).

Using the midpoint formula, we can set up the following equations:

(x1 + x2) / 2 = -4

(y1 + y2) / 2 = 2

Substituting the coordinates of point A (-7, 3), we have:

(-7 + x2) / 2 = -4

(3 + y2) / 2 = 2

Simplifying the equations:

-7 + x2 = -8

3 + y2 = 4

Solving for x2 and y2:

x2 = -8 + 7 = -1

y2 = 4 - 3 = 1

Therefore, the coordinates of point B are (-1, 1).

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Answer:

[tex]\dfrac{\sqrt{2}-\sqrt{6} }{4} }[/tex]

Step-by-step explanation:

Find the exact value of cos(105°).

The method I am about to show you will allow you to complete this problem without a calculator. Although, memorizing the trigonometric identities and the unit circle is required.    

We have,

[tex]\cos(105\°)[/tex]

Using the angle sum identity for cosine.

[tex]\boxed{\left\begin{array}{ccc}\text{\underline{Angle Sum Identity for Cosine}}\\\\\cos(A+B)=\cos(A)\cos(B)-\sin(A)\sin(B)\end{array}\right}[/tex]

Split the given angle, in degrees, into two angles. Preferably two angles we can recognize on the unit circle.

[tex]105\textdegree=45\textdegree+60\textdegree\\\\\\\therefore \cos(105\textdegree)=\cos(45\textdegree+60\textdegree)[/tex]

Now applying the identity.

[tex]\cos(45\textdegree+60\textdegree)\\\\\\\Longrightarrow \cos(45\textdegree+60\textdegree)=\cos(45\textdegree)\cos(60\textdegree)-\sin(45\textdegree)\sin(60\textdegree)[/tex]

Now utilizing the unit circle.

[tex]\boxed{\left\begin{array}{ccc}\text{\underline{From the Unit Circle:}}\\\\\cos(45\textdegree)=\dfrac{\sqrt{2} }{2}\\\\\cos(60\textdegree)=\dfrac{1}{2}\\\\\sin(45\textdegree)=\dfrac{\sqrt{2} }{2}\\\\\sin(60\textdegree)=\dfrac{\sqrt{3} }{2} \end{array}\right}[/tex]

[tex]\cos(45\textdegree)\cos(60\textdegree)-\sin(45\textdegree)\sin(60\textdegree)\\\\\\\Longrightarrow \Big(\dfrac{\sqrt{2} }{2}\Big)\Big(\dfrac{1 }{2}\Big)-\Big(\dfrac{\sqrt{2} }{2}\Big)(\dfrac{\sqrt{3} }{2}\Big)[/tex]

Now simplifying...

[tex]\Big(\dfrac{\sqrt{2} }{2}\Big)\Big(\dfrac{1 }{2}\Big)-\Big(\dfrac{\sqrt{2} }{2}\Big)(\dfrac{\sqrt{3} }{2}\Big)\\\\\\\Longrightarrow \Big(\dfrac{\sqrt{2} }{4} \Big)-\Big(\dfrac{\sqrt{6} }{4} \Big)\\\\\\\therefore \cos(105\textdegree)= \boxed{\boxed{\frac{\sqrt{2}-\sqrt{6} }{4} }}[/tex]