Find the value of x in the picture

Answer:

We know that sec(x) = 1/cos(x). Therefore:

7sec(2x) = 7/cos(2x).

The function won't be define at the points where the denomitator equals zero, which is when x=(2n+1)π/2.

Using a graphing calculator, we get that the graph of the function is the one attached.

Answer:

B. 3.64 to the nearest hundredth.

Step-by-step explanation:

3tan1/3theta=8

tan1/3theta = 8/3

1/3 theta =  1.212 radians, 1.212 + π radians.

theta = 1.212 * 3 = 3.636 radians,    3(1.212 + π) radians.

The second value is greater than 2π radians.

The correct answer is C. 1.21, 2.26, 3.31, 4.35, 5.40.

To solve the equation [tex]\( 3 \tan \frac{1}{3}\theta = 8 \)[/tex] in the interval[tex]\( 0 \) to \( 2\pi \)[/tex], we first isolate [tex]\( \tan \frac{1}{3}\theta \):[/tex]

[tex]\[ \tan \frac{1}{3}\theta = \frac{8}{3} \][/tex]

Next, we take the inverse tangent (arctan) of both sides to solve for

[tex]\[ \frac{1}{3}\theta = \arctan\left(\frac{8}{3}\right) \][/tex]

Now, we multiply both sides by 3 to solve for [tex]\( \theta \)[/tex]:

[tex]\[ \theta = 3 \cdot \arctan\left(\frac{8}{3}\right) \][/tex]

Using a graphing calculator, we find the values of [tex]\( \theta \)[/tex] that satisfy the equation within the interval [tex]\( 0 \)[/tex] to[tex]\( 2\pi \)[/tex]. The calculator will give us the principal value and we need to consider all solutions within the given interval, taking into account the periodicity of the tangent function.

The principal value for [tex]\( \arctan\left(\frac{8}{3}\right) \)[/tex] is approximately[tex]\( 1.21 \)[/tex] radians. Since the tangent function has a period of[tex]\( \pi \)[/tex], we add multiples of[tex]\( \pi \)[/tex] to find other solutions within the interval [tex]\( 0 \)[/tex] to [tex]\( 2\pi \).[/tex]

[tex]\[ \theta \approx 1.21 + k\pi \][/tex]

where [tex]\( k \)[/tex] is an integer such that[tex]\( \theta \)[/tex] remains within the interval [tex]\( 0 \)[/tex] to[tex]\( 2\pi \).[/tex]

For[tex]\( k = 0 \):[/tex]

[tex]\[ \theta \approx 1.21 \][/tex]

For [tex]\( k = 1 \):[/tex]

[tex]\[ \theta \approx 1.21 + \pi \approx 4.35 \][/tex]

For[tex]\( k = 2 \):[/tex]

[tex]\[ \theta \approx 1.21 + 2\pi \approx 7.49 \][/tex]

However, this value is outside our interval, so we do not include it.

For[tex]\( k = 3 \):[/tex]

[tex]\[ \theta \approx 1.21 + 3\pi \approx 10.63 \[/tex]]

This value is also outside our interval, so we do not include it.

Since the tangent function is periodic with a period of [tex]\( \pi \),[/tex] we also need to consider the solutions in the second half of the interval[tex]\( 0 \)[/tex] to [tex]\( 2\pi \),[/tex] which are obtained by subtracting the principal value from[tex]\( 2\pi \):[/tex]

[tex]\[ \theta \approx 2\pi - 1.21 + k\pi \][/tex]

[tex]\[ \theta \approx 2\pi - 1.21 + k\pi \][/tex]

For [tex]\( k = 0 \)[/tex]:

[tex]\[ \theta \approx 2\pi - 1.21 \approx 5.40 \][/tex]

For [tex]\( k = 1 \)[/tex]:

[tex]\[ \theta \approx 2\pi - 1.21 + \pi \approx 8.54 \][/tex]

This value is outside our interval, so we do not include it.

Therefore, the solutions within the interval[tex]\( 0 \)[/tex] to [tex]\( 2\pi \)[/tex], rounded to the nearest hundredth, are: [tex]\[ \boxed{1.21, 2.26, 3.31, 4.35, 5.40} \][/tex]

Note that [tex]\( 2.26 \)[/tex] and [tex]\( 3.31 \)[/tex] are obtained by adding [tex]\( \pi \) to \( 1.21 \)[/tex] and [tex]\( 2.26 \)[/tex]respectively, which are the first two solutions in the first half of the interval. These values are within the interval [tex]\( 0 \) to \( 2\pi \)[/tex] and are also solutions to the original equation.

Answer:

D. (x+8)^2

Step-by-step explanation:

x^2 + 16x  + 64

We are factoring a quadratic trinomial in which the first term is x^2.

We need to find two numbers whose product is 64 and whose sum is 8.

8 * 8 = 64

8 + 8 = 16

The numbers are 8 and 8.

x^2 + 16x + 64 = (x + 8)(x + 8) = (x + 8)^2

Check: If (x + 8)^2 is indeed the correct factorization of x^2 + 16x + 64, then if you multiply out (x + 8)^2, you must get x^2 + 16x + 64.

(x + 8)^2 =

= (x + 8)(x + 8)

= x^2 + 8x + 64

= x^2 + 16x + 64

We get the correct product, so our factorization is correct.

To measure angles within a parallelogram, use a protractor. Align the protractor with the vertex of the angle and read the number where the other side crosses. Repeat for each angle.

To measure the angles within a parallelogram, you can use a protractor. A protractor is a tool that helps measure angles. Here’s how you can use it:

For example, if you want to measure one of the angles in a parallelogram and the protractor shows that the two sides of the angle cross at the 60° mark on the protractor, that means the angle has a measure of 60 degrees.

Answer:

see explanation

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = 3x - 4 ← is in slope- intercept form

with slope m = 3

Given a line with slope m then the slope of a line perpendicular to it is

[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{3}[/tex], hence

y = - [tex]\frac{1}{3}[/tex] x + c ← is the partial equation of the line

To find c substitute (2, 1 ) into the partial equation

1 = - [tex]\frac{2}{3}[/tex] + c ⇒ c = [tex]\frac{5}{3}[/tex]

y = - [tex]\frac{1}{3}[/tex] x + [tex]\frac{5}{3}[/tex] ← equation of line

Answer:

33

Step-by-step explanation:

Using Angela's method, we first multiply, then round.

V = (7.2)(3.5)(8.7)

V = 219.24

V ≈ 219

Using Brian's method, we first round, then multiply.

V = (7.2)(3.5)(8.7)

V ≈ (7)(4)(9)

V ≈ 252

The positive difference between their answers is:

252 − 219 = 33

The positive difference between Angela's and Brian's rounded volumes is 33.

The volume of a cuboid is equal to the product of length, width and height of a cuboid.

According to Angela's method,

V = (7.2)(3.5)(8.7)

V = 219.24

First found the volume, then round.

V ≈ 219

According to Brian's method,

V = (7.2)(3.5)(8.7)

First round, then found the volume,

V ≈ (7)(4)(9)

V ≈ 252

The positive difference between their answers  = 252 − 219 = 33

Hence, the positive difference between Angela's and Brian's rounded volumes is 33

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Answer:

[tex]\huge \boxed{123}[/tex]

Step-by-step explanation:

This question is about the order of operations. The order of operations stands for parenthesis, exponent, multiply, divide, add, and subtract.

Do parenthesis.

[tex]\displaystyle (35+25)=60[/tex]

[tex]\displaystyle 60*2+3[/tex]

Multiply from left to right.

[tex]\displaystyle 60*2=120[/tex]

Add numbers from left to right.

[tex]\displaystyle 120+3=123[/tex]

123 is the correct answer.

Answer:

b. 10x^3 - 6x^2 - 9x + 12

Step-by-step explanation:

A cubic expression has the highest power of the variable to the third power

x^3

b. 10x^3 - 6x^2 - 9x + 12

is the only expression that has the highest power as x^3

a  has x^4  and c and d do not have an x^3 term

Final answer:

The expression that represents a cubic expression is (b) [tex]10x^3 - 6x^2 - 9x + 12[/tex], as it is the only option where the highest power of x is three.

Explanation:

The expression that represents a cubic expression is option (b) [tex]10x^3 - 6x^2 - 9x + 12[/tex]. A cubic expression is one in which the highest degree of any term is three, which means the variable (most commonly x) is raised to the third power. Looking at the options provided:

(a) [tex]19x^4 + 18x^3 - 16x^2 - 12x + 1[/tex] is not a cubic expression because it contains a term with x to the fourth power.

(b) [tex]10x^3 - 6x^2 - 9x + 12[/tex] is a cubic expression because the highest power of x is three.

(c)[tex]-9x^2 - 3x + 4[/tex] is not a cubic expression; it's a quadratic expression since the highest power of x is two.

(d) 4x + 3 is also not a cubic expression; it's linear as the highest power of x is one.

Answer:

a

Step-by-step explanation:

bc its the only one that makes sence to me heheh

Answer: Option D

Step-by-step explanation:

A relationship is a function if and only if for each input value x (domain) only one output value y is assigned (Range)

Option A.

Note that x represents the input values and y represents the output values.

When [tex]x = 3[/tex] then [tex]y = 14[/tex] and [tex]y = 19[/tex].

The input value [tex]x = 3[/tex] has two output values  y assigned.

So the relationship is not a function

Option B.

Note that x represents the input values and y represents the output values.

When [tex]x = 3[/tex] then [tex]y = 0[/tex] and [tex]y = -5[/tex].

The input value [tex]x = 3[/tex] has two output values y assigned.

So the relationship is not a function

Option C

Note that x represents the input values and y represents the output values.

When [tex]x = -1[/tex] then [tex]y = -11[/tex] and [tex]y = 5[/tex].

[tex](-1,-11)[/tex] , [tex](-1, 5)[/tex]

The input value [tex]x = -1[/tex] has two output values y assigned.

So the relationship is not a function

Option D

Note that x represents the input values and y represents the output values  and for each input value x (domain) only one output value y is assigned (Range)

[tex]\{(-5, 3), (-3, 1), (-1, -1), (1, -1), (3, 1), (5, 3)\}[/tex]

So the relationship is a function

Answer:

b. 5x^2 + 9x - 1

Step-by-step explanation:

A quadratic expression had the highest power of the variable at 2

x^2

b. 5x^2 + 9x - 1

a  has the highest power as x

c and d goes higher than x^2

The expression that represents a quadratic expression is 5x^2 + 9x - 1 (option b), which is in the form ax^2 + bx + c, where a, b, and c are constants.

The expression that represents a quadratic expression is option (b), which is 5x^2 + 9x - 1. A quadratic expression is generally in the form ax^2 + bx + c, where a, b, and c are constants, and a is not equal to zero. This type of equation represents a parabola when graphed on a coordinate plane. The examples provided in the question show how various terms relate to the constants a, b, and c in the quadratic equation, and the use of the quadratic formula for solving such equations. Option (a) is linear, option (c) is cubic, and option (d) is quartic, as indicated by the highest powers of x.

Answer:

The area (probability) is: 0.6864.

Step-by-step explanation:

According to the statement, we are in front of a normal distribution with the following parameters:

µ (mean) = 0

σ (Standard deviation) = 1.

Then we need to find the area of the shaded region, which is the area between the points -1.21 < z < 0.84.

And the area (probability) is: 0.6864.

Answer:

A. 0.6864

Step-by-step explanation:

The area of the shaded region between the two z-scores indicated in the diagram is 0.6864.

mean = 0

Standard deviation = 1

Answer:

=1/40

Step-by-step explanation:

=1/8/5

=1/40

Answer:

a) The equation of the total cost is d = a + bc

   The equation for calculating the total is d = 60 + 4(50)

b) The total cost for the job is $260

Step-by-step explanation:

* Lets explain how to solve the problem

- Mr. Gomez owns a carpet cleaning business

- The situation of the job;

# a represents the initial charge (in dollar) for coming to the house

# b represents the number of hours the job takes

# c represents the charge (in dollars) for each hour the  job takes

# d represents the total cost (in dollars) of the job

* Lets make the equation of the total cost

∵ The initial amount of the job is a dollars

∵ The number of hours the job takes is b

∵ The charge per hour is c dollars

∵ The total cost of the job is d

- The total cost is the sum of the initial amount and the product of

 the number of hours the job takes and the charge per hour

∵ The total cost = initial amount + the number of hours × charge

   per hour

∴ d = a + b × c

∴ d = a + bc

a)

* The equation of the total cost is d = a + bc

∵ a = $60 , b = 4 hours , c = $50

∴ d = 60 + 4(50)

* The equation for calculating the total is d = 60 + 4(50)

b)

∵ d = 60 + 4(50)

∴ d = 60 + 200

∴ d = 260

* The total cost for the job is $260

Answer:

Option C and D is correct

Step-by-step explanation:

We need to find the slopes of the given segments.

The lines are parallel if there slopes are equal.

A) = RS, where R is at (1, 3) and S is at (4, 2)

[tex]Slope\,\,of\,\,RS =\frac{y_{2}-y_{1}}{x_{2}-x_{1}} \\Slope\,\,of\,\,RS=\frac{2-3}{4-1}\\Slope\,\,of\,\,RS=\frac{-1}{3}[/tex]

Option A is incorrect because Slope of MN = -3 while slope of RS = -1/3

B)= PQ, where P is at (5, 6) and Q is at (8, 7)

[tex]Slope\,\,of\,\,PQ =\frac{y_{2}-y_{1}}{x_{2}-xx_{1}} \\Slope\,\,of\,\,PQ=\frac{7-6}{8-5}\\Slope\,\,of\,\,PQ=\frac{1}{3}[/tex]

Option B is incorrect because Slope of MN = -3 while slope of PQ = 1/3

C)= TU, where T is at (8, 1) and U is at (5, 10)

[tex]Slope\,\,of\,\,TU=\frac{y_{2}-y_{1}}{x_{2}-xx_{1}} \\Slope\,\,of\,\,TU\,\,=\frac{10-1}{5-8}\\Slope\,\,of\,\,TU\,\,=\frac{9}{-3} \\Slope\,\,of\,\,TU=-3[/tex]

Option C is correct because Slope of MN = -3 while slope of TU = -3

D)= WX, where W is at (2, 6) and X is at (4, 0)

[tex]Slope\,\,of\,\,WX\, =\frac{y_{2}-y_{1}}{x_{2}-xx_{1}} \\Slope\,\,of\,\,WX\,=\frac{0-6}{4-2}\\Slope\,\,of\,\,WX\,=\frac{-6}{2} \\Slope\,\,of\,\,WX\,=-3[/tex]

Option D is correct because Slope of MN = -3 while slope of WX = -3

Segments TU and WX have the slope -3, which is the same as line MN's slope, making them parallel to segment MN.

The question asks which line segments are parallel to a line MN with a slope of
-3. To determine if two segments are parallel, they must have the same slope. The slope of a line through two points (x1, y1) and (x2, y2) is calculated with the formula
m = (y2 - y1) / (x2 - x1).

Let's find the slopes for each segment:

Therefore, the segments parallel to MN are TU and WX.

To find the inverse of a function switch the place of y (aka f(x) ) with x. Then solve for y.

Original equation:

y = 4x + 5

Switched:

x = 4y + 5

Solve for y by isolating it:

x - 5 = 4y + 5 - 5

x - 5 = 4y

(x - 5)/4 = 4y/4

[tex]\frac{1}{4}x-\frac{5}{4} = y[/tex]

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:

Option B

center (3,2)

radius 3

Step-by-step explanation:

Given:

x^2+y^2-6x+4y+4=0

x^2+y^2-6x+4y=-4

Now completing square of x^2-6x by introducing +9 on both sides:

x^2-6x+9+y^2+4y=-4+9

(x-3)^2+y^2+4y=5

Now completing square of y^2+4y by introducing +4 on both sides:

(x-3)^2+y^2+4y+4=5+4

(x-3)^2 + (y-2)^2= 9

Now comparing with the circle equation:

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

where

r= radius of circle

h= x-offset from origin

k= y-offset from origin

In given case

r=3

h=3

k=2

Hence, option B is correct with radius =3 and center =(3,2)!

Answer:

Center (3,-2); radius 3

Answer:

The value of x is 4

Step-by-step explanation:

we know taht

The intersecting chords theorem  states that the products of the lengths of the line segments on each chord are equal.

so

In this problem

[tex](12)(x)=(8)(x+2)[/tex]

solve for x

[tex]12x=8x+16[/tex]

[tex]12x-8x=16[/tex]

[tex]4x=16[/tex]

[tex]x=4[/tex]

Answer:

Alex investment = $ 23,800

Step-by-step explanation:

The statement is Alex and Rachel are forming partnership. According to the agreement Alex invest $3000 more than Rachel's two-third investment and the total capital is $55,000.Find out Alex investment.

Let x be the investment of Rachel. Lets make an equation to find the value of x.

x+2/3x +$3000=$55,000

Combine the like terms:

x+2/3x = 55,000 - 3000

x+2/3x = $52000

Now take the L.C.M of L.H.S

3x+2x/3 = $52000

Now Add the values of x.

5x/3 = $52000

Multiply both the terms by 3.

5x/3 *3 = 3* $52000

5x= 156000

Now divide both the sides by 5.

5x/5 = 156000/5

x= 31200

Now calculate Alex investment. According to the statement Alex invest $3000 more than 2/3 of Rachel.

We have found the Rachel investment which is $31200. Therefore we can write 2/3 of Rachel investment as 2/3(31200).

=2/3(31200)+$3000

=2*10400+3000

=20,800+3000

=$23,800

Rachel investment = $31200

Alex investment = $ 23,800

If you want to check whether the investments are correctly determined or not. You can add both the investments and the result will be the partnership's capital amount.

$31200+$ 23,800 = $55,000 ....

Answer:

Step-by-step explanation:

(x^3 + 2x − 3)(x^4 − 3x^2 + x)

Multiply each value of 2nd bracket with 1st bracket:

=x^4(x^3 + 2x − 3) - 3x^2(x^3 + 2x − 3) +x(x^3 + 2x − 3)

=x^7+2x^5-3x^4-3x^5-6x^3+9x^2+x^4+2x^2-3x

Now combine the terms with same power:

=x^7-x^5-2x^4-6x^3+11x^2-3x

You can also  take the common from the expression:

x(x^6-x^4-2x^3-6x^2+11x-3)....

The product of (x^3 + 2x − 3)(x^4 − 3x^2 + x) is x(x^6-x^4-2x^3-6x^2+11x-3)....

So,

[tex]4^{-x}[/tex]

When [tex]x=-3[/tex]

Becomes,

[tex]4^{-(-3)}=4^3=\boxed{64}[/tex]

Hope this helps.

r3t40

Answer:

Answer is x>3

Step-by-step explanation:

The last step is: divide -2 to both sides and since the 2 is negative the sign flips so it would be x>3.

Hope my answer has helped you and if not i'm sorry.

Answer:

A.

Step-by-step explanation:

Now since the degree is odd (3 in this case) and the leading coefficient is positive (1), then the end behavior is going to be:

for left-end behavior, it is down

for right-end behavior, it is up

We are going to definitely have some increasing action going on because it goes from down to up reading from left to right.

Let's graph it in our ti-84's or whatever you have.

This is a very rough graph but you can see it is just increasing on the entire domain.  This means reading the graph from left to right, there is only rise.

I can give you an answer with calculus in it if you prefer.

[tex]\bf \textit{surface area of a cylinder}\\\\ SA=2\pi r(h+r)~~ \begin{cases} h=height\\ r=radius\\ \cline{1-1} h=16\\ r=7 \end{cases}\implies SA=2\pi (7)(16+7) \\\\\\ SA=14\pi (23)\implies SA=322\pi[/tex]

The surface area of the right circular cylindrical container that has a radius of 7 cm and a height of 16 cm in terms of π is 322π.  This is obtained by using the formula for surface area of cylinder.

Surface area of cylinder is, S = 2πrh+2πr², where S is the surface area, r is the radius and h is the height of the cylinder.

Given that r =7 cm, h =16 cm,

S = 2πrh+2πr²

  = 2π(7)(16)+2π(7)²

  = 224π+98π

  = 322π

Hence the surface area of the right circular cylindrical container that has a radius of 7 cm and a height of 16 cm in terms of π is 322π.

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Answer:

A'(0, -8), B'(6, 0), C'(0, 8), D'(-6, 0)

Step-by-step explanation:

Whenever you are doing a 90° clockwise rotation ABOUT THE ORIGIN, it is in the form of [y, -x], meaning you take the y and make it your x, then take your original x and put its OPPOSITE.

90° counterclockwise rotation → [-y, x]

90° clockwise rotation → [y, -x]

I hope this helps, and as always, I am joyous to assist anyone at any time.

Answer:

x = 18.

Step-by-step explanation:

x + 9.5 = 27.5

Subtract 9.5 from both sides:

x = 27.5 - 9.5

x = 18 (answer).

wassup the answer is 18 have fun get that A+

Answer:

A

Step-by-step explanation:

Alright so in the graph we can see the highest y that is reach is at x=3 which is y=6.  The maximum of the graph g(x) is 6.

Now we have to be a bit more algebraic and messy when comes to finding a maximum (the vertex of the parabola) of f(x)=-2x^2+4x+3.

First step, I'm going to find the x-coordinate of the vertex.  Once we do that we can find the y that corresponds to it by using y=-2x^2+4x+3.

So the x-coordinate of the vertex can be found by computing -b/(2a).

a=-2 and b=4 so we are going to plug that in giving us -4/(2*-2)=-4/-4=1.

So the x-coordinate of the vertex is 1 and we are going to find the y that corresponds to that using y=-2x^2+4x+3.

So let's plug in 1.

This gives us:

y=-2(1)^2+4(1)+3

y=-2(1)+4+3

y=-2+4+3

y=2+3

y=5

So the maximum of graph f is 5.

6 is higher than 5

So g has the higher maximum

So the answer is A.

Answer:

A.) g(x)

Step-by-step explanation:

:p

Answer:

Step-by-step explanation:

When you divide by 100, the decimal moves 2 places to the left.

847.8

When you have moved the decimal 3 places to the left, you have divided by 1000

To reverse the effects of 847.8 by dividing by 10000 you need to multiply by 10000

847.8 * 10000 = 8478000 Try this on your calculator to confirm it.

Same with the last one. To get 847.8 when you have divided by 1 million, you movie the decimal in the answer 6 places.

847.8 * 1000000 = 847800000

Answer:

[tex](q \circ r)(7)=22[/tex]

[tex](r \circ q)(7)=8[/tex]

Step-by-step explanation:

1st problem:

[tex](q \circ r)(7)=q(r(7))[/tex]

r(7) means to replace x in [tex]\sqrt{x+9}[/tex] with 7.

[tex]r(7)=\sqrt{7+9}=\sqrt{16}=4[/tex]

[tex](q \circ r)(7)=q(r(7))=q(4)[/tex]

q(4) means replace x in [tex]x^2+6[/tex] with 4.

[tex]q(4)=4^2+6=16+6=22[/tex].

Therefore,

[tex](q \circ r)(7)=q(r(7))=q(4)=22[/tex]

2nd problem:

[tex](r \circ q)(7)=r(q(7))[/tex]

q(7) means replace x in [tex]x^2+6[/tex] with 7.

[tex]q(7)=7^2+6=49+6=55[/tex].

So now we have:

[tex](r \circ q)(7)=r(q(7))=r(55)[/tex].

r(55) means to replace x in [tex]\sqrt{x+9}[/tex] with 55.

[tex]r(55)=\sqrt{55+9}=\sqrt{64}=8[/tex]

Therefore,

[tex](r \circ q)(7)=r(q(7))=r(55)=8[/tex].

[tex]a_1=1\\d=2\\a_n=1+(n-1)\cdot 2=1+2n-2=2n-1[/tex]

Answer:

Zack and bo

Step-by-step explanation:

A and B is where the circles intersect so zack and bo are the only names I see there.

The elements {Zack, Bo} are in A and B.

The element that is present in both set A and set B i.e. at the common area of set A and set B in Venn diagram is called set A intersection set B.

Here In Venn diagram set A is green colored which contains the element {Kalie, Noah, Zack, Bo}

Set B is orange colored which contains the element {Julia, Zack, Bo}.

The elements which are present in both A and B are the intersection of set A and set B.

These elements are available at the common joint area of set A and set B.

Here, dark color represents the area that contains the element present in A and B.

In that dark-colored region, the elements present are {Zack,Bo}.

Therefore The elements {Zack, Bo} are in A and B.

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