Your friend gives you the right triangle above and to the left and says. "Bisecting an angle is really easy. Take triangle ABC. If I wanted to bisect
(a) Convince your friend that they are wrong. Use what you know about trigonometry to explain why CAD and DAB are not congruent.

(b)locate the point E on that lies on the angle bisector of CAB.How far is point E from point B?Show all your work

The amplitude of subsequent oscillations is 0.093 m.

The spring stiffness is quantified by the spring constant, or k. For various springs and materials, it varies. The stiffer the spring is and the harder it is to stretch, the bigger the spring constant.

Given that,

Mass of a block, m = 1.2 kg

Spring constant of the spring, k = 14.0 N/m

While the block is sitting at rest, a student hits it with a hammer and almost instantaneously gives it a speed of 32.0 cm/s or 0.32 m/s

We need to find the amplitude of the subsequent oscillations.

We can use the conservation of energy here. Initially, the kinetic energy of the block is maximum and then it gets converted to the potential energy of the spring.

Mathematically,

[tex]\frac{1}{2} mv^2=\frac{1}{2}kv^2[/tex]

A is the amplitude of subsequent oscillations.

[tex]A=\sqrt{(\frac{mv^2}{k} )} \\\\A=\sqrt{\frac{(1.2)(0.32)^2}{14} } \\\\A=0.093m[/tex]

So, the amplitude of subsequent oscillations is 0.093 m.

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The amount that should be deposited today is given as follows:

$70,663.15.

The amount of money earned, in compound interest, after t years, is given by:

[tex]A(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]

In which:

The parameters for this problem are given as follows:

t = 15, A(t) = 115000, r = 0.033, n = 1.

Hence the deposit is obtained as follows:

115000 = P(1.033)^15

P = 115000 x (1.033)^(-15)

P = $70,663.15.

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Sally paid $1,043.33 for the leather chair, including tax.

The marked up price of the leather chair is 100% more than the original cost, which means it is twice the original cost.

        $494.47 x 2 = $988.94

       $988.94 x 0.055 = $54.39

        $988.94 + $54.39 = $1,043.33.

Therefore, Sally paid $1,043.33 for the leather chair, including tax.

The calculation provided is applicable for any problem that involves finding the total cost of an item after a percentage markup and the addition of a sales tax. The general formula for calculating the final cost of an item after a markup and sales tax is:

Final cost = (1 + markup percentage) x original cost x (1 + sales tax percentage)

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The linear function that models this scenario is given as follows:

y = -0.25x + 13.

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

In which:

Bridget has 13 gallons of gasoline to use for her lawnmowing business, hence the intercept b is given as follows:

b = 13.

From the graph, when x increases by 20, y decays by 5, hence the slope m is given as follows:

m = -5/20

m = -0.25.

Hence the function is given as follows:

y = -0.25x + 13.

The problem is given by the image presented at the end of the answer.

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Answer:

no it can not so false boiiiiiiiii

Step-by-step explanation:

I think it’s false, maybe

Answer:

21+15+9=45/4=that the answer

Answer:

Step-by-step explanation:

The inequality 5x+12y ≤ 30 represents a shaded region in the xy-plane that includes all the points that satisfy the inequality. To graph this inequality, we can first graph the equation 5x+12y = 30, which is the boundary line of the shaded region.

To graph the boundary line, we can find its x- and y-intercepts:

x-intercept: Set y = 0 and solve for x: 5x + 12(0) = 30, which gives x = 6.

y-intercept: Set x = 0 and solve for y: 5(0) + 12y = 30, which gives y = 2.5.

So the boundary line passes through the points (6, 0) and (0, 2.5).

Next, we can determine which side of the boundary line to shade. One way to do this is to pick a test point that is not on the line and plug it into the inequality. For example, the point (0,0) is a convenient test point. Plugging in x=0 and y=0 into the inequality, we get:

5(0) + 12(0) ≤ 30

which simplifies to 0 ≤ 30. Since this is true, we know that the region containing the point (0,0) is part of the shaded region, and therefore the shaded region is the one that contains the origin.

Putting it all together, we can graph the inequality by drawing the line 5x+12y = 30 and shading the region below the line, as shown in the figure below:

    |

 3  |       x

    |      /

 2  |     /

    |    /

 1  |   /  

    |  /  

 0  | /    

    ------------

      0  6

The shaded region includes all the points below the line 5x+12y=30, including the points on the line.

Answer:

Yes, dilation does not change the angle measurements.

Step-by-step explanation:

The solution to the system of equations is (13/3, 16/3).

The graph is given below.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example:

2x + 4 = 8 is an equation.

We have,

y = 14x - 2 _____(1)

y = x + 1 ______(2)

Now,

The graph of the equation is given below.

Now,

From (1) and (2).

14x - 2 = x + 1

14x - x = 1 + 2

13x = 3

x = 13/3

And,

y = x + 1

y = 13/3 + 1

y = 16/3

So,

The solution is (13/3, 16/3)

Thus,

The solution is (13/3, 16/3).

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Considering the expression c^n = d, for n > 1, the number c is the nth root of number d.

The expression for this problem is defined as follows:

c^n = d

To obtain the number that is the nth root to the other, an expression representing the nth root in the problem must appear.

The expression representing the nth root can appear isolating the variable c, as follows:

[tex]c = \sqrt[n]{d}[/tex]

Hence the number c is the nth root of number d.

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The equation that can be used to solve the problem is 66/x + 40/x = 5.3

gage rate of travel on the mountain roads is 20 mph and on the country roads is 48 mph.

A mathematical equation is a formula that uses the equals sign to represent the equality of two expressions. Finding the values of the variables that result in the equality is the first step in solving an equation with variables.

Given that:

In mountain Road

distance = 66 miles ; rate = x mph

⇒ time = d/r = 66/x hrs

In country Road

distance = 96 miles ; rate = 2.4x mph

⇒ time = d/r = 96/(2.4x)

⇒ time = d/r = 40/x hrs.

Equation:

time + time = 5.3 hrs

⇒ 66/x + 40/x = 5.3

⇒ 106/x = 5.3

⇒ 5.3x = 106

⇒ x = 20 mph on mountain Roads

⇒ 2.4x = 2.4*20 mph on country Roads

⇒ 48 mph on country Roads

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The number of hours of television watched and the number of hours of exercise, correct to three decimal places is 3.940.

A decimal is any number expressed in base-10 notation, which includes a decimal point and the numbers 0 through 9. Decimals are used to represent fractions, numbers that are not whole numbers, and numbers that are exceptionally large or tiny.

To calculate the correlation coefficient between hours of television watched and hours of exercise, we will use the formula

r = (∑xy − (∑x)(∑y) / n) /[tex]\sqrt{((2x-x/n)(2y-2/n))}[/tex]

where x is the number of hours of television watched and y is the number of hours of exercise.

Given the data provided, we have

x = 3, 14, 21, 28, 43

y = 38, 27, 36, 15, 30

Therefore,

∑x = 3 + 14 + 21 + 28 + 43 = 109

∑y = 38 + 27 + 36 + 15 + 30 = 156

∑xy = (3)(38) + (14)(27) + (21)(36) + (28)(15) + (43)(30) = 1291

∑x2 = 32 + 142 + 212 + 282 + 432 = 4552

∑y2 = 382 + 272 + 362 + 152 + 302 = 4644

n = 5 (number of members surveyed)

Substituting these values into the formula, we get

r = (1291 − (109)(156) / 5) /[tex]\sqrt{(4552-(109)2/5)(4644-(156)2/5)))}[/tex]

r = (1291 − 17784 / 5) /[tex]\sqrt{(4552-10902/5)(4644-24336/5)}[/tex]

r = (-16493 / 5) / [tex]\sqrt{(3456)(2036)}[/tex]

r = -3298.6 / [tex]\sqrt{695936}[/tex]

r = -3298.6 / 835.2

r = -3.94

Rounded to the nearest thousandth, r = -3.940.

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The following numbers are the result:

22 play trumpet, 11 play trombone, and 8 play saxophone.

Two algebraic expressions having the same value and symbol '=' in between are called an equation.

Given:

There are 41 students in group 2.

Twice as many students play the trumpet as play the trombone,

but 8 students play the saxophone.

Let x be the number of students playing the trombone.

So, according to the question,

x + 2x + 8 = 41

3x = 33

x = 11

Hence, 22 play trumpet, 11 play trombone, and 8 play saxophone.

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The weight of the robot is within the error limit of 0.3%.

Given is that a robot building club organizes competitions by weight categories called classes each class permit a percent error of 0.3%. In the 5 kg class one robot weighs 4.925 kg.

Let -

{x} = 0.3% of 5

{x} = 0.3/100 x 5

{x} = 3/1000 x 5

{x} = 15/1000

{x} = 3/200

{x} = 0.015                                                                            .... Eq { 1 }

Now -

For the weight of the robot to be under the weight limit -

4.925 ≤ (5 - x)

4.925 ≤ (5 - 0.015)

4.925 ≤ 4.985                                                       ..... Eq { 2 }

which is true.                              

Therefore, the weight of the robot is within the error limit of 0.3%.

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The p-value (rounded to four decimal places) is 0.2709.

Probability refers to a possibility that deals with the occurrence of random events.

The probability of all the events occurring need to be 1.

The formula of probability is defined as the ratio of a number of favorable outcomes to the total number of outcomes.

P(E) = Number of favorable outcomes / total number of outcomes

We are given that;

p = 477/1000 = 0.477

p = 0.48

n = 1000

Now,

The test statistic for a hypothesis test for a proportion is given by:

z = (pi - p) / sqrt(p * (1 - p) / n)

where p is the sample proportion, p is the hypothesized proportion under the null hypothesis, n is the sample size, and sqrt is the square root function.

Substituting these values into the formula, we get:

z = (0.477 - 0.48) / sqrt(0.48 * 0.52 / 1000) ≈ -0.61

We find that the area to the left of z = -0.61 is approximately 0.2709 This means that the probability of getting a test statistic as extreme or more extreme than -0.61, assuming the null hypothesis is true, is 0.2709

Therefore, by probability the answer will be 0.2709

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We can show that any field IF is a vector space over itself, with the field addition used as vector addition and the field multiplication used as scalar multiplication.

A field is a set of elements, denoted by IF, that satisfies the following axioms:

Commutativity of addition

Associativity of addition

Existence of additive identity

Existence of additive inverse

Commutativity of multiplication

Associativity of multiplication

Distributivity of multiplication over addition

Existence of multiplicative identity

Existence of multiplicative inverse

Given these axioms, we can show that IF is a vector space over itself.

Closure under addition: For any a, b in IF, their sum a + b is also in IF.

Commutativity of vector addition: For any a, b in IF, a + b = b + a.

Associativity of vector addition: For any a, b, c in IF, (a + b) + c = a + (b + c).

Existence of additive identity: The additive identity 0 in the field IF can also be used as the additive identity in the vector space.

Existence of additive inverse: For any a in IF, its additive inverse -a in the field IF can also be used as the additive inverse in the vector space.

Distributivity of scalar multiplication over vector addition: For any a in IF and any u, v in IF, a * (u + v) = a * u + a * v.

Distributivity of scalar multiplication over field addition: For any a, b in IF and any u in IF, (a + b) * u = a * u + b * u.

Existence of multiplicative identity: The multiplicative identity 1 in the field IF can also be used as the multiplicative identity in the vector space.

Therefore, we have shown that any field IF is a vector space over itself, with the field addition used as vector addition and the field multiplication used as scalar multiplication.

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Using the Divergence Theorem, we get the flux of F across the closed surface S is π/2 (27√2 - 27).

To apply the Divergence Theorem, we will first compute the divergence of F as follows -

div(F) = ∂Fx/∂x + ∂Fy/∂y + ∂Fz/∂z

= 1 + 1 + 1

= 3

Now we will calculate the flux of F across the closed surface S that completely surrounds T. By the Divergence Theorem, this is equal to the triple integral of the divergence of F over the region T and is given by -

∫∫S F•n dS = ∭T div(F) dV

We can describe the region T using cylindrical coordinates:

0 ≤ r ≤ 2

-π/2 ≤ θ ≤ π/2

0 ≤ z ≤ √(9 - r sin θ)

The bounds on r and θ come from the fact that the half cylinder is contained within the plane x = 2, and the plane y = ±3. The bounds on z come from the equation of the half cylinder.

Now we can write the triple integral as follows -

∭T div(F) dV = ∫0^2 ∫-π/2^π/2 ∫0^√(9 - r sin θ) 3 r dz dθ dr

Evaluating this integral, we get,

∭T div(F) dV = π/2 (27√2 - 27)

Therefore, the flux of F across the closed surface S is π/2 (27√2 - 27).

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The derivative of the function y = tan⁻¹ x which is expressed in terms of x will be 1 / (1 + x²).

The rate of change of a function with respect to the variable is called differentiation. It can be increasing or decreasing.

The function is given below.

x = tan y

Get the equation for y, then we have

x = tan y

y = tan⁻¹ x

Differentiate the function with reprect to 'x', then we have

y' = (d/dx) tan⁻¹ x

y' = 1 / (1 + x²)

The derivative of the function y = tan⁻¹ x which is expressed in terms of x will be 1 / (1 + x²).

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On x-axis where |x|>0 is located at point E on the coordinate plane.

What does a math definition of a coordinate plane mean?

A surface with two dimensions known as the coordinate plane is created by two number lines. The x-axis is the name given to one horizontal number line. The y-axis is the name given to the vertical number line that is the other number line. A place known as the origin is where the two axes collide.

                        To graph points, lines, and other things, we can utilize the coordinate plane. The Y-axis and the X-axis cross to create a two-dimensional plane known as a coordinate plane, also referred to as a rectangular coordinate plane grid.

on x-axis except at the origin

or on x-axis where |x|>0

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Step-by-step explanation:

a probability is always the ratio

desired cases / totally possible cases.

if 2 non-overlapping events should occur, the probability of both events happening is the product of both individual probabilities.

e.g. the probability to roll two 6 with 2 dice (or in 2 consecutive rolls with 1 die) is 1/6 × 1/6 = 1/36

if 1 of 2 possible non-overlapping events should occur, the probability of one of the events happening is the sum of the individual probabilities.

e.g. the probability to roll a 1 or a 2 with a die is

1/6 + 1/6 = 2/6 = 1/3

both students are dual-enrolled.

in our case, for the first selection we have the totally possible cases of 27.

the desired cases (dual-enrolled) are 17.

so, the probabilty to select a dual-enrolled student is

17/27

for the second selection (without replacement of the first pull) the totally possible cases are now 26 (because we pulled one student from the general pool of candidates in the first selection).

the desired cases are now 16 (because for our case we pulled a dual-enrolled student from the general pool).

the probabilty to select a dual-enrolled student in the second selection is

16/26 = 8/13

the overall probability to select two dual-enrolled students in 2 selections is

17/27 × 8/13 = 136/351 = 0.387464387... ≈ 0.387

the first student is dual-enrolled, the second is not.

for the first selection the totally possible cases are 27.

the desired cases are again 17.

the probability of the first dejection is again

17/27

for the second selection the totally possible cases are 26 (see above).

the desired cases are still 10.

the probably for this second selection is

10/26 = 5/13

the overall probability to select first a dual-enrolled student and then a not-dual-enrolled student is

17/27 × 5/13 = 85/351 = 0.242165242... ≈ 0.242

Answer:

The First question's answer is AngleW = 77 degrees

The Second question's answe is x = 2

Step-by-step explanation:

First Question:

AngleW = 7x

AngleY = 6x + 11

Since Opposite Angles in a parallelogram are equal,

AngleW = AngleY

or

7x = 6x + 11

7x - 6x = 11

x = 11

Now that we know the value of x, we can find the value of angleW

AngleW = 7x

AngleW = 7(11)

Angle W = 77

Second Question:

LN = 20

UN = 5x

Since LN and KM are diagonals of the parallelogram, they bisect each other at point of contact, so, UN = 1/2LN

or

5x=1/2 × 20

5x = 10

x = 2

Answer:

y = -110x + 1,600

Step-by-step explanation:

Zachary purchased a computer for $1,600 on a payment plan. Four months after he purchased the computer, his balance was $1,160. Five months after he purchased the computer, his balance was $1,050. What is an equation that models the balance y after x months?

1,160 - 1,050 = $110 change from month 5 to 4

Double check if the rate of decrease is steady over time:

1,600 - ($110 * 4 months) = 1,160

1,600 - ($110 * 5 months) = 1,050

This means, Zachary is paying $110 per month for his computer.

SO:

remaining payment plan balance = initial balance - 110 per month

This can be modeled by the algebraic equation:

y = 1,600 - 110x

rearrange right side:

y = -110x + 1,600

Answer:

[tex]y=-110x+1600[/tex]

Step-by-step explanation:

Given information:

Define the variables:

Therefore:

[tex]\boxed{\begin{minipage}{8cm}\underline{Slope Formula}\\\\Slope $(m)=\dfrac{y_2-y_1}{x_2-x_1}$\\\\where $(x_1,y_1)$ and $(x_2,y_2)$ are two points on the line.\\\end{minipage}}[/tex]

Determine if the equation is linear by calculating the slope between each pair of (x, y) points:

[tex]\implies \text{Slope}\;(m)=\dfrac{1050-1160}{5-4}=-110[/tex]

[tex]\implies \text{Slope}\;(m)=\dfrac{1160-1600}{4-0}=-110[/tex]

As the slope is the same, the equation is linear.

[tex]\boxed{\begin{minipage}{6.3 cm}\underline{Slope-intercept form of a linear equation}\\\\$y=mx+b$\\\\where:\\ \phantom{ww}$\bullet$ $m$ is the slope. \\ \phantom{ww}$\bullet$ $b$ is the $y$-intercept.\\\end{minipage}}[/tex]

As the initial purchase price of the computer was $1,600, the y-intercept is 1600.  We have already calculated the slope. Therefore, substitute the found slope and y-intercept into the slope-intercept formula to create an equation that models the balance y after x months:

The instructor chose to use the highest score now mode, hence the score of the second attempt would be used that is 10/10.

In statistics, the value that consistently appears in a particular set is referred to as the mode. The mode or modal value in a data set is sometimes referred to as the value or number that occurs most frequently in the data set. In addition to mean and median, it is one of the three measures of central tendency.

The scores at different attempts are:

First attempt: 2/10 = 0.2

Second attempt: 10/10 = 1

Third attempt: 3/10 = 0.3

The instructor chose to use the highest score now mode, hence the score of the second attempt would be used that is 10/10.

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B. Theorem is the term that refer to true statements.

According to the definitions of the terms we have:

A confirmed factual assertion is referred to as a theorem.

• Proposition: A truthful assertion that's less significant but nonetheless intriguing.

• Lemma: A true statement that serves as an example of another true statement.

significant theorem that aids in the validation of other findings).

• Corollary: A true statement that can be inferred directly from a premise or theorem.

• Proof: The justification for why a claim is accurate.

• Conjecture: An assertion that is deemed true but for which there is no supporting evidence. (An assertion that is being put forth as being true).

• Axiom: A fundamental presumption regarding a mathematical scenario. (a premise we take to be true)

Hence, B. Theorem is the term that refer to true statements.

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The percent change of an object is the ratio of its final value to its initial value.

The percentage of an item's final value versus its starting value is its percent change. By dividing the difference in data by the starting value, you can get the percent change.

"Rate" simply refers to the quantity divided by another number, typically 100, 1,000, or another multiple of 10. A rate per 100 is known as a percentage.

Percentage Change is the difference that results from deducting the old value from the new value, dividing by the old value, and multiplying the result by 100 to represent it as a percentage. In most cases, multiplying a fraction by 100 results in a percent conversion.

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Answer:

So, Donna served 9, Alonzo served 19 and kevin served 57 orders.

Step-by-step explanation:

Let orders be :

Donna - x, Alonzo - y, Kevin - z

x = y - 10 - eqn i

z = 3y - eqn ii

Now, By the question,

x + y + z = 85

we know from eqn i and eqn ii,

y - 10 + y + 3y = 85

or, 5y = 95

so, y = 19

Now,

z = 3(19) = 57

x = 19 - 10 = 9

Based on the information given the rate of increase is 55%.

Rate of increase:

Using this formula

Rate of increase=Stock value per share/Number of shares of stock×100

Where:

Stock value per share=$55 per share

Number of shares of stock=100 shares

Let plug in the formula

Rate of increase=$55/100×100

Rate of increase=55%

Inconclusion the rate of increase is 55%

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According to the information, it can be inferred that Rebecca spent 31 minutes and 25 seconds on her phone from Monday to Thursday

To calculate the time Rebecca spent on her phone from Monday through Thursday we must add the number of minutes (and seconds) she used her phone during this period. For this we must rely on the information in the table:

According to the table, Rebecca made two calls each day, and each call was delayed:

Monday

call 1: 2 minutes 15 seconds

call 2: 4 minutes 23 seconds

Tuesday

call 1: 5 minutes 53 seconds

call 2: 1 minute 20 seconds

Wednesday:

call 1: 6 minutes 40 seconds

call 2: 3 minutes

Thursday:

call 1: 4 minutes 12 seconds

call 2: 3 minutes 42 seconds

Based on the above, we need to add the time in minutes and seconds and then calculate how much time in total she used her phone:

So finally we must divide the number of seconds into 60 (number of seconds that a minute has) and calculate how many minutes they are:

205 / 60 = 3.4

This equates to 3 minutes and 25 seconds. In total, Rebeca spent 31 minutes and 25 seconds on her phone from Monday to Thursday.

Note: This information is incomplete. Here is the complete information:

Monday

call 1: 2 minutes 15 seconds

call 2: 4 minutes 23 seconds

Tuesday

call 1: 5 minutes 53 seconds

call 2: 1 minute 20 seconds

Wednesday:

call 1: 6 minutes 40 seconds

call 2: 3 minutes

Thursday:

call 1: 4 minutes 12 seconds

call 2: 3 minutes 42 seconds

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Answer: The trigonometric identity for the tangent of a sum of angles can be used to simplify the expression:

tan (480° + 300°) = (tan 480° + tan 300°) / (1 - tan 480° tan 300°)

Using the identity for the tangent of half an angle, the tangent of 480° can be expressed as follows:

tan 480° = tan (450° + 30°) = (tan 450° + tan 30°) / (1 - tan 450° tan 30°) = (1 + tan 30°) / (1 - tan 30°) = (1 + √3/3) / (1 - √3/3) = (1 + √3) / (√3 - 1)

Using the identity for the sine and cosine of a multiple of 30°, the tangent of 300° can be expressed as follows:

tan 300° = tan (30° * 10) = tan 30° / (1 - tan 30°) = √3 / (1 - √3) = √3 / (-1 - √3)

Plugging these values back into the expression for tan (480° + 300°), we get:

tan (480° + 300°) = (tan 480° + tan 300°) / (1 - tan 480° tan 300°) = ( (1 + √3) / (√3 - 1) + √3 / (-1 - √3) ) / (1 - (1 + √3) / (√3 - 1) * √3 / (-1 - √3) )

Expanding the denominator and simplifying, we get:

tan (480° + 300°) = ( (1 + √3) / (√3 - 1) + √3 / (-1 - √3) ) / ( (√3 - 1) / (-1 - √3) - (1 + √3) / (-1 - √3) )

Using the identity for the sine and cosine of a sum of angles, the sine and cosine of 480° + 300° can be expressed as follows:

sin (480° + 300°) = sin 480° cos 300° + cos 480° sin 300°

Finally, using the identity for the tangent of an angle in terms of sine and cosine, we get:

tan (480° + 300°) = sin (480° + 300°) / cos (480° + 300°) = sin 780° / cos 780°

The other trigonometric functions in the expression can be simplified using similar techniques, but the final result may be complex. However, it can be verified that the expression is equal to 3/2 by using a calculator or numerical methods.

Step-by-step explanation:

Answer:

A: 5

Step-by-step explanation:

Using the side-splitter theorem (parallel lines and similar triangle ratios).

[tex]\frac{16}{4x} = \frac{28}{35}[/tex]

Through cross mutliplying, we get 112x = 560

x = 5