NEED HELP WITH A MATH QUESTION

Answer:

f(x) = 48(0.5)^n - 1 ⇒ 1st answer

Step-by-step explanation:

* Lets explain how to solve the problem

- The number of alligators changes each week

∵ The number in week 1 is 28

∵ The number in week 2 is 24

∵ The number in week 3 is 12

∵ The number in week 4 is 6

∴ The number of alligators is halved each week

∴ The number of alligators each week = half the number of alligators

   of the previous week

- The number of alligators formed a geometric series in which the

  first term is 48 and the constant ratio is 1/2

∵ Any term in the geometric series is Un = a r^(n - 1), where a is the

  first term and r is the constant ratio

∴ f(n) = a r^(n - 1)

∵ a = 48 ⇒ The number of alligators in the first week

∵ r = 1/2 = 0.5

∴ f(x) = 48(0.5)^n - 1

the answer is f(x) = 48(0.5)^n - 1

1 meter = 1000 mm

so then 5 meters is just 5 * 1000 = 5000 mm.

Answer:

Option 1: {-7,5,18,24,32}

Step-by-step explanation:

Observing the number line we can see that the solution is

x≤18 and x>22

So we will check the options one by one

For {-7,5,18,24,32}

The number set satisfies the solution translated from the number line.

For {-9,7,15,22,26}

As this number set includes 22 which is not included in the solution so this option is not correct.

For {16,17,22,23,24}

This number set also includes 22 so the option is not correct.

For {18,19,20,21,22}

This number set includes 19,20,21,22 which is not a part of the solution. Therefore, this option is also not correct ..

Answer:

-38z

Step by step explanation:

You’d Combine Like Terms:

- 10z + -28z

= (-10z + -28z)

= -38z

Answer: Option A

[tex]x=\frac{3+i}{2}[/tex] or [tex]x=\frac{3-i}{2}[/tex]

Step-by-step explanation:

Use the quadratic formula to find the zeros of the function.

For a function of the form

[tex]ax ^ 2 + bx + c = 0[/tex]

The quadratic formula is:

[tex]x=\frac{-b\±\sqrt{b^2-4ac}}{2a}[/tex]

In this case the function is:

[tex]2x^2-6x+5=0[/tex]

So

[tex]a=2\\b=-6\\c=5[/tex]

Then using the quadratic formula we have that:

[tex]x=\frac{-(-6)\±\sqrt{(-6)^2-4(2)(5)}}{2(2)}[/tex]

[tex]x=\frac{6\±\sqrt{36-40}}{4}[/tex]

[tex]x=\frac{6\±\sqrt{-4}}{4}[/tex]

Remember that [tex]\sqrt{-1}=i[/tex]

[tex]x=\frac{6\±\sqrt{4}*\sqrt{-1}}{4}[/tex]

[tex]x=\frac{6\±\sqrt{4}i}{4}[/tex]

[tex]x=\frac{6\±2i}{4}[/tex]

[tex]x=\frac{3\±i}{2}[/tex]

[tex]x=\frac{3+i}{2}[/tex] or [tex]x=\frac{3-i}{2}[/tex]

Answer:

[tex]1,207.6\ m[/tex]

Step-by-step explanation:

step 1

Find the perimeter of one lap

we know that

The perimeter of one lap is equal to the circumference of a complete circle (two half circles is equal to one circle) plus two times the length of 96 meters

so

[tex]P=\pi D+2(96)[/tex]

we have

[tex]D=35\ m[/tex]

[tex]\pi =3.14[/tex]

substitute

[tex]P=(3.14)(35)+2(96)[/tex]

[tex]P=301.9\ m[/tex]

step 2

Find the total meters of four laps

Multiply the perimeter of one lap by four

[tex]P=301.9(4)=1,207.6\ m[/tex]

Answer:

1207.6

Step-by-step explanation:

step 1

i got it right on the test

step 2

you get it right on the test

Answer:

The coordinates are  (4 , -2) , (0 , -5) , (-2 , -2) , (2 , 1)

Step-by-step explanation:

* Lets revise some transformation

- If point (x , y) rotated about the origin by angle 180°

 ∴ Its image is (-x , -y)

- If the point (x , y) translated horizontally to the right by h units

 ∴ Its image is (x + h , y)

- If the point (x , y) translated horizontally to the left by h units

 ∴ Its image is (x - h , y)

- If the point (x , y) translated vertically up by k units

 ∴ Its image is (x , y + k)

- If the point (x , y) translated vertically down by k units

 ∴ Its image is (x , y - k)

* Now lets solve the problem

∵ ABCD is a parallelogram

∵ Its vertices are A (1 , 1) , B (5 , 4) , C (7 , 1) , D (3 , -2)

∵ The parallelogram rotates about the origin by 180°

∵ The image of the point (x , y) after rotation 180° about the origin

   is (-x , -y)

∴ The images of the vertices of the parallelograms are

  (-1 , -1) , (-5 , -4) , (-7 , -1) , (-3 , 2)

∵ The parallelogram translate after the rotation 5 units to the right

   and 1 unit down

∴ We will add each x-coordinates by 5 and subtract each

   y-coordinates by 1

∴ A' = (-1 + 5 , -1 - 1) = (4 , -2)

∴ B' = (-5 + 5 , -4 - 1) = (0 , -5)

∴ C' = (-7 + 5 , -1 - 1) = (-2 , -2)

∴ D' = (-3 + 5 , 2 - 1) = (2 , 1)

* The coordinates of the parallelograms A'B'C'D' are:

  (4 , -2) , (0 , -5) , (-2 , -2) , (2 , 1)

Answer:

OPTION B.

OPTION C.

Step-by-step explanation:

In order to know which numbers are less than [tex]\frac{9}{4}[/tex], you can convert this fraction into a decimal number. To do this, you need to divide the numerator 9 by the denominator 4. Then:

 [tex]\frac{9}{4}=2.25[/tex]

 Now you need convert the fractions provided in the Options A and B into decimal numbers by applying the same procedure. This are:

Option A→ [tex]\frac{11}{4}=2.75[/tex] (It is not less than 2.25)

Option B→ [tex]\frac{15}{8}=1.875[/tex] (It is less than 2.25)

The number shown in Option C is already expressed in decimal form:

Option C→ [tex]2.201[/tex] (It is less than 2.25)

Answer:

V = 3053.63

Step-by-step explanation:

The volume of a sphere that has a radius of 9 is 3053.63.

V=4

3πr3=4

3·π·93≈3053.62806

Answer is provided in the image attached.

Answer:

5

Step-by-step explanation:

16+24

--------------

30-22

Complete the items on the top of the fraction bar

40

----------

30-22

Then the items under the fraction bar

40

------------

8

Then divide

5

Step-by-step explanation:

First of all, solve the numerator.

16+24=40

Secondly, solve the denominator:

30-22 = 8

So now the fraction appear like this :

[tex] \frac{40}{8} [/tex]

40/8 = 5

Answer:

[tex] D.~ 34.2~cm^2 [/tex]

Step-by-step explanation:

An arc measure of 20 degrees corresponds to a central angle of 20 degrees.

Area of sector of circle

[tex] area = \dfrac{n}{360^\circ}\pi r^2 [/tex]

where n = central angle of circle, and r = radius

[tex] area = \dfrac{20^\circ}{360^\circ}\pi (14~cm)^2 [/tex]

[tex] area = \dfrac{1}{18}(3.14159)(196~cm^2) [/tex]

[tex] area = 34.2~cm^2 [/tex]

Answer:

5/9

Step-by-step explanation:

y = 15 • 3^x

Let x = -3

y = 15 • 3^(-3)

The negative means the exponent goes to the denominator

y = 15 * 1/3^3

  = 15 * 1/27

  =15/27

Divide the top and bottom by 3

 =5/9

Answer:

A

Step-by-step explanation:

The interquartile range is the difference between the upper quartile and the lower quartile, that is

interquartile range = [tex]Q_{3}[/tex] - [tex]Q_{1}[/tex]

The interquartile range (IQR) represents the spread of the middle 50 percent of a data set and is calculated by subtracting the first quartile (Q1) from the third quartile (Q3). It also helps in identifying potential outliers in the data.

The interquartile range (IQR) is a measure of statistical dispersion, which is the spread of the middle 50 percent of a data set. It is calculated by subtracting the first quartile (Q1) from the third quartile (Q3). To elaborate:

If, for example, Q1 is 2 and Q3 is 9, the IQR is calculated as 9 minus 2, resulting in an IQR of 7.

In addition to providing insight into the spread of the central portion of the data set, the IQR can also be used to identify potential outliers. These are values that fall more than 1.5 times the IQR above Q3 or below Q1.

Answer:

x=1

Step-by-step explanation:

So we are talking about parabola functions.

All parabolas (even if they aren't functions) have their axis of symmetry going through their vertex.

For parabola functions, your axis of symmetry is x=a number.

The "a number" part will be the x-coordinate of the vertex.

The axis of symmetry is x=1.

Answer:

x=1

Step-by-step explanation:

The vertex of a parabola is the minimum or maximum of the parabola.

This is the line  where the parabola makes a mirror image.

Assuming the equation for the parabola is ( since this is a function)

y= a(x-h)^2 +k

where (h,k) is the vertex

Then x=h is the axis of symmetry

y = a(x-1)^2+5

when we substitute the vertex into the equation

The axis of symmetry is x=1

Answer:

y = -(2/3)*x - 11

Step-by-step explanation:

To convert a point-slop equation into a linear function, there are certain steps which have to be followed. The primary aim is to make y the subject of the equation. By making sure that y is on the left hand side of the equation and x is on the right hand side of the equation, our goal will be achieved. To do that, first of all do the cross multiplication. This will result in:

3(y+7) = -2(x+6).

Further simplification results in:

3y + 21 = -2x - 12.

Keeping the expression of y on the left hand side and moving the constant on the right hand side gives:

3y = -2x - 33.

Leaving y alone on the left hand side gives:

y = -(2/3)*x - 33/3.

Therefore, y = -(2/3)*x - 11!!!

Answer:

This has one real solution, x=4

Step-by-step explanation:

8 - 4x = 0

Add 4x to each side

8 - 4x+4x = 0+4x

8 =4x

Divide each side by 4

8/4 = 4x/4

2 =x

This has one real solution, x=4

Answer:

This equation has 1 real solution, x=2....

Step-by-step explanation:

8- 4x=0

Move 8 to the R.H.S

-4x=0-8

-4x=-8

Divide both sides by -4

-4x/-4 = -8/-4

x=2

Thus this equation has 1 real solution, x=2 ....

Answer:

Part A) Annual [tex]\$66,480.95[/tex]  

Part B) Semiannual [tex]\$66,862.38[/tex]  

Part C) Monthly [tex]\$67,195.44[/tex]  

Part D) Daily [tex]\$67,261.54[/tex]  

Step-by-step explanation:

we know that    

The compound interest formula is equal to  

[tex]A=P(1+\frac{r}{n})^{nt}[/tex]  

where  

A is the Final Investment Value  

P is the Principal amount of money to be invested  

r is the rate of interest  in decimal

t is Number of Time Periods  

n is the number of times interest is compounded per year

Part A)

Annual

in this problem we have  

[tex]t=5\ years\\ P=\$47,400\\ r=0.07\\n=1[/tex]  

substitute in the formula above  

[tex]A=47,400(1+\frac{0.07}{1})^{1*5}[/tex]  

[tex]A=47,400(1.07)^{5}[/tex]  

[tex]A=\$66,480.95[/tex]  

Part B)

Semiannual

in this problem we have  

[tex]t=5\ years\\ P=\$47,400\\ r=0.07\\n=2[/tex]  

substitute in the formula above  

[tex]A=47,400(1+\frac{0.07}{2})^{2*5}[/tex]  

[tex]A=47,400(1.035)^{10}[/tex]  

[tex]A=\$66,862.38[/tex]  

Part C)

Monthly

in this problem we have  

[tex]t=5\ years\\ P=\$47,400\\ r=0.07\\n=12[/tex]  

substitute in the formula above  

[tex]A=47,400(1+\frac{0.07}{12})^{12*5}[/tex]  

[tex]A=47,400(1.0058)^{60}[/tex]  

[tex]A=\$67,195.44[/tex]  

Part D)

Daily

in this problem we have  

[tex]t=5\ years\\ P=\$47,400\\ r=0.07\\n=365[/tex]  

substitute in the formula above  

[tex]A=47,400(1+\frac{0.07}{365})^{365*5}[/tex]  

[tex]A=47,400(1.0002)^{1,825}[/tex]  

[tex]A=\$67,261.54[/tex]  

The value of an investment of $47,400 at an interest rate of 7% per year was calculated at the end of 5 years for different compounding methods, reaching slightly different amounts, with the highest value obtained through daily compounding.

The value of the investment at the end of 5 years for different compounding methods would be:

Answer:

9

Step-by-step explanation:

From the diagram:

So, correct option is 9 cases.

Answer:

The correct option is 4. For value 9 both p ∧ r true and q false.

Step-by-step explanation:

The diagram represents three statements: p, q, and r.

We need to find the value for which p ∧ r is true and q false.

p ∧ r true mean the intersection of statement p and r. It other words p ∧ r true means p is true and r is also true.

From the given venn diagram it is clear that the intersection of p and r is

[tex]p\cap r=9+2=11[/tex]

p ∧ r true and q false means intersection of p and r but q is not included.

From the given figure it is clear that for value 2 all three statements are true. So, the value for which both p ∧ r true and q false is

[tex]11-2=9[/tex]

Therefore the correct option is 4.

For this case we have that by definition, the equation of a line of the slope-intersection form is given by:

[tex]y = mx + b[/tex]

Where:

m: It's the slope

b: It is the cutoff point with the y axis

By definition, if two lines are perpendicular then the product of their slopes is -1.

We have the following line:

[tex]y = 2x-6[/tex]

Then[tex]m_ {1} = 2[/tex]

The slope of a perpendicular line will be:

[tex]m_ {1} * m_ {2} = - 1\\m_ {2} = \frac {-1} {m_ {1}}\\m_ {2} = - \frac {1} {2}[/tex]

Thus, the equation of the line will be:

[tex]y = - \frac {1} {2} x + b[/tex]

We substitute the given point and find "b":

[tex]-3 = - \frac {1} {2} (0) + b\\-3 = b[/tex]

Finally the equation is:

[tex]y = - \frac {1} {2} x-3[/tex]

Answer:

[tex]y = - \frac {1} {2} x-3[/tex]

Answer:

[tex]y=-\frac{1}{2}x -3[/tex]

Step-by-step explanation:

The slope-intercept form of the equation of a line has the following form:

[tex]y=mx + b[/tex]

Where m is the slope of the line and b is the intercept with the y axis

In this case we look for the equation of a line that is perpendicular to the line

[tex]y = 2x - 6[/tex].

By definition If we have the equation of a line of slope m then the slope of a perpendicular line will have a slope of [tex]-\frac{1}{m}[/tex]

In this case the slope of the line [tex]y = 2x - 6[/tex] is [tex]m=2[/tex]:

Then the slope of the line sought is: [tex]m=-\frac{1}{2}[/tex]

The intercept with the y axis is:

If we know a point [tex](x_1, y_1)[/tex] belonging to the searched line, then the constant b is:

[tex]b=y_1-mx_1[/tex] in this case the poin is: (0,-3)

Then:

[tex]b= -3 -(\frac{1}{2})(0)\\\\b=-3[/tex]

finally the equation of the line is:

[tex]y=-\frac{1}{2}x-3[/tex]

Answer:

The correct answer is option D.  13

Step-by-step explanation:

From the figure we can see two matrices A and B

To find the sum of a₃₂ and b₃₂

From the given attached figure we get

a₃₂ means that the third row second column element in the matrix A

b₃₂ means that the third row second column element in the matrix B

a₃₂ = 4 and b₃₂ = 9

a₃₂ + b₃₂ = 4 + 9

 = 13

The correct answer is option D.  13

[tex]A={\begin{bmatrix}a_{11}&a_{12}&\cdots &a_{1n}\\a_{21}&a_{22}&\cdots &a_{2n}\\\vdots &\vdots &\ddots &\vdots \\a_{m1}&a_{m2}&\cdots &a_{mn}\end{bmatrix}}[/tex]

So

[tex]a_{32}=4\\b_{32}=9\\\\a_{32}+b_{32}=4+9=13[/tex]

Answer:

y=-(x-3)^2+2

Step-by-step explanation:

since the curve is convex up so the coefficient of x^2 is negative

and by substituting by the point 3 so y = 2

Answer:

B

Step-by-step explanation:

The equation of a parabola in vertex form is

y = a(x - h)² + k

where (h, k) are the coordinates of the vertex and a is a multiplier

here (h, k) = (3, 2), hence

y = a(x - 3)² + 2

If a > 0 then vertex is a minimum

If a < 0 then vertex os a maximum

From the graph the vertex is a maximum hence a < 0

let a = - 1, then

y = - (x - 3)² + 2 → B

Answer:

Step-by-step explanation:

Divide 4378 by 15

From 4378 lets take the first two digits for division:

43/ 15

We know that 43 does not come in table of 15

So we will take 15 *2 = 30

43-30 = 13

The quotient is 3 and the remainder is 13

Now take one more number which is 7 with 13

137/15.

Now 137 does not come in table of 15

15*9 = 135

135-137 = 2

It means quotient is 9 and remainder is 2

Now take one more number which is 8 with 2

28/15

28 does not come in table of 15

15*1 = 15

28-15 = 13/15

Now the quotient is 1 and remainder is 13

Hence, the quotient of 4,378 is 291 and remainder is 13 ....

Answer: (1.5, -5)

Step-by-step explanation: a p e x

Answer:

A (-1,4,1.5)

Step-by-step explanation:

Solve by graphing, the lines intersect near this point.

Answer:

7t^2 + 21t

Step-by-step explanation:

You have 7 tiles of each t by t+3.

One tile has an area of

t * (t+3) = t^2 + 3t

So in total the area is

7* (t^2 + 3t)

7t^2 + 21t

Answer:

= 8.33 inches

Step-by-step Explanation

First add 49 + 16, which equals 65, and subtract that result from 180, since a triangle equals 180 degrees and you find out angle C is equal to 115 degrees.

Now using the formula sinA/a = sinB/b = sinC/c, plug in values and you'd get the equation sin49 x 10/sin115. After solving the equation you'd get about  8.32729886047258 inches.

= 8.33

Answer:

13.2 units

Step-by-step explanation:

∠A = 16°

∠B = 49°

∠C = 180-(16+49)

∠C = 115°

a = 4

Now, from sine rule we get

[tex]\frac{sinA}{a}=\frac{sinB}{b}=\frac{sinC}{c}[/tex]

[tex]\frac{sinA}{a}=\frac{sinC}{c}\\\Rightarrow \frac{sin16}{4}=\frac{sin115}{c}\\\Rightarrow c=\frac{sin115}{ \frac{sin16}{4}}\\\Rightarrow c=13.2[/tex]

∴ c is 13.2 units

Answer:

C

Step-by-step explanation:

note (f - g)(x) = f(x) - g(x)

f(x) - g(x)

= 4x + 1 - (x² - 5) ← distribute by - 1

= 4x + 1 - x² + 5 ← collect like terms

= - x² + 4x + 6 ← in standard form → C

For this case we have the following functions:

[tex]f (x) = 4x + 1\\g (x) = x ^ 2-5[/tex]

We must find [tex](f-g) (x).[/tex] By definition we have to:

[tex](f-g) (x) = f (x) -g (x)[/tex]

So:

[tex](f-g) (x) = 4x + 1- (x ^ 2-5)[/tex]

We take into account that:

[tex]- * + = -\\- * - = +\\(f-g) (x) = 4x + 1-x ^ 2 + 5\\(f-g) (x) = - x ^ 2 + 4x + 6[/tex]

Answer:

[tex](f-g) (x) = - x ^ 2 + 4x + 6[/tex]

Option C

Answer: 1) (x - 7)(x - 8)

               2) 2x(2x-7)(x + 2)

               3) (4x + 7)²

               4) (9ab² - c³)(9ab² + c³)

Step-by-step explanation:

1) x² - 15x + 56  → use standard form for factoring

                    ∧

                -7 + -8 = -15

  (x - 7) (x - 8)

************************************

2) 4x³ - 6x² - 28x      → factor out the GCF (2x)

2x(2x² - 3x - 14)         → factor using grouping

2x[2x² + 4x    - 7x - 14]    

2x[ 2x(x + 2)   -7(x + 2)]

2x(2x - 7)(x + 2)

*************************************

3) 16x² + 56x + 49     → this is the sum of squares

√(16x²) = 4x      √(49) = 7

              (4x + 7)²

******************************************************

4) 81a²b⁴ - c⁶          → this is the difference of squares

√(81a²b⁴) = 9ab²       √(c⁶) = c³

       (9ab² - c³)(9ab² + c³)

Answer:

[tex]\boxed{\vphantom{\dfrac{\sqrt{2}}{2}}\quad \cos(x+y)\quad }\longleftrightarrow \boxed{\quad \dfrac{-(\sqrt{6}+\sqrt{2})}{4}\quad }[/tex]

[tex]\boxed{\vphantom{\dfrac{\sqrt{2}}{2}}\quad \sin(x+y)\quad }\longleftrightarrow \boxed{\quad\dfrac{\sqrt{6}-\sqrt{2}}{4}\quad }[/tex]

[tex]\boxed{\quad \tan(x+y)\quad }\longleftrightarrow \boxed{\quad\sqrt{3} -2\quad }[/tex]

[tex]\boxed{\vphantom{\sqrt{3}}\quad \tan(x-y)\quad }\longleftrightarrow \boxed{\quad-(2+\sqrt{3})\quad }[/tex]

Step-by-step explanation:

To find the values of the given trigonometric identities, we first need to find the values of cos x and sin y using the Pythagorean identity, sin²x + cos²x ≡ 1.

Given values:

[tex]\sin x = \dfrac{\sqrt{2}}{2}\qquad \textsf{Angle $x$ is in Quadrant I}\\\\\\\cos y=-\dfrac{1}{2}\qquad \textsf{Angle $y$ is in Quadrant II}[/tex]

Find cos(x):

[tex]\sin^2 x+\cos^2 x=1\\\\\\\left(\dfrac{\sqrt{2}}{2}\right)^2+\cos^2 x=1\\\\\\\dfrac{1}{2}+\cos^2 x=1\\\\\\\cos^2 x=1-\dfrac{1}{2}\\\\\\\cos^2 x=\dfrac{1}{2}\\\\\\\cos x=\pm \sqrt{\dfrac{1}{2}}\\\\\\\cos x=\pm \dfrac{\sqrt{2}}{2}[/tex]

As the cosine of an angle is positive in quadrant I, we take the positive square root:

[tex]\cos x=\dfrac{\sqrt{2}}{2}[/tex]

Find sin(y):

[tex]\sin^2 y + \cos^2 y = 1 \\\\\\ \sin^2 y + \left(-\dfrac{1}{2}\right)^2 = 1 \\\\\\ \sin^2 y + \dfrac{1}{4} = 1 \\\\\\ \sin^2 y = 1-\dfrac{1}{4} \\\\\\ \sin^2 y = \dfrac{3}{4} \\\\\\ \sin y =\pm \sqrt{ \dfrac{3}{4}} \\\\\\ \sin y = \pm \dfrac{\sqrt{3}}{2}[/tex]

As the sine of an angle is positive in quadrant II, we take the positive square root:

[tex]\sin y = \dfrac{\sqrt{3}}{2}[/tex]

The tangent of an angle is the ratio of the sine and cosine of that angle. Therefore:

[tex]\tan x=\dfrac{\sin x}{\cos x}=\dfrac{\frac{\sqrt{2}}{2}}{\frac{\sqrt{2}}{2}}=1[/tex]

[tex]\tan y=\dfrac{\sin y}{\cos y}=\dfrac{\frac{\sqrt{3}}{2}}{-\frac{1}{2}}=-\sqrt{3}[/tex]

Now, we can use find the sum or difference of two angles by substituting the values of sin(x), cos(x), sin(y), cos(y), tan(x) and tan(y) into the corresponding formulas.

[tex]\dotfill[/tex]

[tex]\cos(x+y)=\cos x \cos y - \sin x \sin y \\\\\\ \cos(x+y)=\left(\dfrac{\sqrt{2}}{2}\right) \left(-\dfrac{1}{2}\right) - \left(\dfrac{\sqrt{2}}{2}\right) \left(\dfrac{\sqrt{3}}{2}\right) \\\\\\ \cos(x+y)=-\dfrac{\sqrt{2}}{4} - \dfrac{\sqrt{6}}{4} \\\\\\ \cos(x+y)=\dfrac{-\sqrt{2}-\sqrt{6}}{4} \\\\\\ \cos(x+y)=\dfrac{-(\sqrt{2}+\sqrt{6})}{4} \\\\\\ \cos(x+y)=\dfrac{-(\sqrt{6}+\sqrt{2})}{4}[/tex]

[tex]\dotfill[/tex]

[tex]\sin(x+y)=\sin x \cos y + \cos x \sin y \\\\\\\sin(x+y)=\left(\dfrac{\sqrt{2}}{2}\right) \left(-\dfrac{1}{2}\right) + \left(\dfrac{\sqrt{2}}{2}\right) \left(\dfrac{\sqrt{3}}{2}\right) \\\\\\\sin(x+y)=-\dfrac{\sqrt{2}}{4} + \dfrac{\sqrt{6}}{4} \\\\\\ \sin(x+y)=\dfrac{-\sqrt{2}+\sqrt{6}}{4} \\\\\\ \sin(x+y)=\dfrac{\sqrt{6}-\sqrt{2}}{4}[/tex]

[tex]\dotfill[/tex]

[tex]\tan(x+y)=\dfrac{\tan x + \tan y}{1-\tan x \tan y} \\\\\\ \tan(x+y)=\dfrac{1 + (-\sqrt{3})}{1-(1) (-\sqrt{3})} \\\\\\ \tan(x+y)=\dfrac{1 -\sqrt{3}}{1+\sqrt{3}} \\\\\\ \tan(x+y)=\dfrac{(1 -\sqrt{3})(1 -\sqrt{3})}{(1+\sqrt{3})(1-\sqrt{3})} \\\\\\ \tan(x+y)=\dfrac{1-2\sqrt{3}+3}{1-\sqrt{3}+\sqrt{3}-3} \\\\\\ \tan(x+y)=\dfrac{4-2\sqrt{3}}{-2} \\\\\\ \tan(x+y)=-2+\sqsrt{3} \\\\\\ \tan(x+y)=\sqrt{3} -2[/tex]

[tex]\dotfill[/tex]

[tex]\tan(x-y)=\dfrac{\tan x - \tan y}{1+\tan x \tan y} \\\\\\\tan(x-y)=\dfrac{1 - (-\sqrt{3})}{1+(1) (-\sqrt{3})} \\\\\\\tan(x-y)=\dfrac{1 +\sqrt{3}}{1-\sqrt{3}} \\\\\\\tan(x-y)=\dfrac{(1 +\sqrt{3})(1 +\sqrt{3})}{(1-\sqrt{3})(1+\sqrt{3})} \\\\\\ \tan(x-y)=\dfrac{1+2\sqrt{3}+3}{1+\sqrt{3}-\sqrt{3}-3} \\\\\\ \tan(x-y)=\dfrac{4+2\sqrt{3}}{-2} \\\\\\ \tan(x-y)=-2-\sqrt{3}\\\\\\\tan(x-y)=-(2+\sqrt{3})[/tex]

Answer:

Hey, You have chosen the correct answer.

the correct answer is C.