In a recent year, a university had an enrollment of 15,363 male and 19,512 female undergraduate students. The total number of full-time instructional faculty was 1,849. Find the ratio of students to full-time instructional faculty as a unit ratio. Round to the nearest whole number.

The expression sec x csc x cot x  in terms of sin x and cos x is

1/ (sin x)^2.

According to the given question.

We have an expression sec x csc x cot x.

Here, we have to write the above expression in terms of sinx and cosx.

As we know that,

sec x = 1/cos x

csc x = 1/sin x

cot x = cos x/ sin x

Thereofore, the expression sec x csc x cot x  in terms of sin x and cos x is given by

sec x csc x cot x

= (1/cos x) (1/sinx) (cosx/ sinx)

= 1/ (sin x)^2

Hence, the expression sec x csc x cot x  in terms of sin x and cos x is

1/ (sin x)^2.

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the standard form equation is y=ax²+bx+c where a is the quadratic coefficient, b is the linear coefficient, and c is the constant coefficient.

therefore, for y =  5/16x² - 5x/4 -35/4

Quadratic coefficient = 5/16, linear coefficient = 5/4, constant term = -35/4

What are zeros ?

zeros denotes the factors of the given equation in other words the zeros of the function are the values that make the factors zero. The factors need to multiply out to give the original standard-form equation.

Polynomial roots are the same as polynomial zeros, so they can be found by factoring the quadratic equation into two linear factors, after which they can be equating to zero.

Its easiest to first start out with a vertex form equation because it can then be converted to a standard quadratic equation.

given a vertex at (2,-10) , and point of intersection at (6,-5), the equation can be set up like this in the form of :

y = a(x-h)²+ k

y = a(x-2)^2-10, as we know h and k from the vertex.

We also know y and x from the given point of intersection so a can be solved by substituting the values of x and y to get value of a.

y = a(x-2)²-10

-5 = a(6-2)² - 10

16a = 10-5

a = 5/16

a = 5/16 which is also known as the quadratic coefficient because it is part of a second degree quantity and a Trinomial as a whole(quadratic).

since all the variables are known, you can expand the equation and set it to standard form :

y = 5/16(x-2)²-10

y = 5/16(x-2)² - 10

y = 5/16(x²+4-4x) -10

y = 5/16x² + 5/4 - 5x/4 - 10

y =  5/16x² - 5x/4 -35/4

For reference, the standard form equation is y=ax²+bx+c where a is the quadratic coefficient, b is the linear coefficient, and c is the constant coefficient.

In this instance, 5/16x² - 5x/4 -35/4 = ax²+bx+c

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Answer:

72

Step-by-step explanation:

let's begin by restating what we already know,

360 bottles of juice in 5 minutes

for goodness's sake let's abbreviate this

360 boj in 5 mins

RATIO TIME!

360 : 5

pay attention how I put the BOJ (bottles of juice) first and the time last

now to find how many boj per min. we will say

[tex]\frac{1}{5} (360: 5)[/tex]

72:1

so, we now know that the factory of juice produces 72 bottles of juices per minute ( that's ALOT of juices per minute imo)

^_^ hope this helps, happy learning

Answer:

2x – 4y = 6

x3 – y = –2

Step-by-step explanation:

When graphing these two are linear.

Answer:

2x - 4y = –2

x3 – y = –2

Step-by-step explanation:

'cause they both have two unknown digits and this can be worked out with 3 methods;

1. substitution method

2. elimination method

3. grahical method

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Answer: $2.50

Step-by-step explanation: To find the tax rate, you need to divide 1.50 by 30

1.5/30 = .05, which is the percent taxed. To find the tax amount for a $50 item, you just need to multiply $50 by the tax rate, which is .05, to get $2.50

Based on the results of the physical fitness test, the reason why we are unable to calculate the mean number of pull-us done by the students in each class is that we don't have the exact number of pull-ups done by each student.

To calculate the simple mean of a distribution of numbers, we would need the value of all the numbers to be known. These numbers will then be summed up and divided by the number of the distribution.

In this case of the physical fitness test, the number of pull-ups is not known for all the students as there are some that either did below 5 or above 10 and we don't know the exact number of pull-ups done.

As a result, we are unable to calculate the mean.

Question is:
Explain why we are unable to calculate the mean number of pull-ups done by the students in each class.

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Taking into account the definition of a system of linear equations, 178 children, 62 students and 89 adults attended to the movie theater.

A system of linear equations is a set of two or more equations of the first degree, in which two or more unknowns are related.

Solving a system of equations consists of finding the value of each unknown so that all the equations of the system are satisfied. That is to say, the values ​​of the unknowns must be found, with which when are replaced in the equations, they must give the solution proposed.

In this case, a system of linear equations must be proposed taking into account that:

On the other hand, you know:

So, the system of equations to be solved consists of the following equations:

Equation 1: C + S + A= 329

Equation 2: 5C + 7S + 12A= 2392

Equation 3: A= C÷2= 1/2C

There are several methods to solve a system of equations, it is decided to solve it using the substitution method, which consists of clearing one of the two variables in one of the equations of the system and substituting its value in the other equation.

Replacing equation 3 in equation 1 and isolating the variable S you get:

C + S + 1/2C= 329

3/2C + S= 329

S= 329 - 3/2C

Replacing this expression and equation 3 in equation 2 you get:

5C + 7(329 - 3/2C) + 12×1/2C= 2392

Solving:

5C + 7×329 - 7×3/2C + 12×1/2C= 2392

5C + 2303 - 21/2C + 6C= 2392

5C - 21/2C + 6C= 2392 -2303

1/2C= 89

C= 89÷ 1/2

C= 178

Remembering that S= 329 - 3/2C, you get S= 329 - 3/2×178 → S= 62

Finally, substituting the value of C in Equation 3: A= 1/2C= 1/2×178 → A=89

In summary, 178 children, 62 students and 89 adults attended to the movie theater.

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Answer:

23% or 23/100

Step-by-step explanation:

Since there are 23 in 100 is is 23/100 or 23%

Answer:

4.348%

Step-by-step explanation:

blue marbles = 19

yellow marbles = 23

probably of getting yellow = 23/100

= 4.34782608696

then you round then number to three decimal places and there you go

Answer:From the given table, we have that:

1. The relation of the situation is: (20,2), (22.5, 5), (25,4), (27.5, 4), (29,4), (29,5), (30,1), (30,2), (30,3), (30,4), (30,5), (32.5, 1), (32.5, 3), (35,4), (40,2), (42.5, 3).

2. The domain is {20, 22.5, 25, 27.5, 29, 30, 32.5, 35, 40, 42.5} and the range is {1, 2, 3, 4, 5}.

3. There are inputs such as 25, 29, 30 and 32.5 that are mapped to multiple outputs, hence the relation does not represent a function.

What is the relation of this situation?

To build the relation, we look at the graph, and write all pairs of (Age, Finishing Place), as follows:

(20,2), (22.5, 5), (25,4), (27.5, 4), (29,4), (29,5), (30,1), (30,2), (30,3), (30,4), (30,5), (32.5, 1), (32.5, 3), (35,4), (40,2), (42.5, 3).

What are the domain and the range?

The domain of a relation is the set that contains all possible input values for the values, that is, the values of x.

The range of a relation is the set that contains all possible output values for the values, that is, the values of y.

Hence, for the given relation:

The domain is {20, 22.5, 25, 27.5, 29, 30, 32.5, 35, 40, 42.5} and the range is {1, 2, 3, 4, 5}.

When does a relation represents a function?

A relation represents a function if each value of the input is mapped to only one value of the output.

For this problem, we have that:

There are inputs such as 25, 29, 30 and 32.5 that are mapped to multiple outputs, hence the relation does not represent a function.

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Step-by-step explanation:

Coordinates of P is 8

Since 3+2 = 5, we are dividing line segment AB into 5 congruent parts with point P 3/5 of the way from A to B.  

x-coordinate of P = x-coordinate of A + (3/5)(change in x from A to B) = -4 + (3/5)(20) = 8

y-coordinate of P = y-coordinate of A + (3/5)(change in y from A to B) = 8 + (3/5)(-10) = 2

P = (8,2)

In each axis, find the distance from A to B, apply the ratio to get the distance from A to P, and add that value to A.

Note the ratio:   We are given the ratio of AP to PB as 3/2.  This means that the ratio of AP to AB is 3/5

Here is is for the X-axis:

AB = 20

AP = 20 *3/5 = 12

So P = -4 + 12 = 8

It is one of the branches of geometry where the position of a point is defined using coordinates.

Coordinates are a set of values which helps to show the exact position of a point in the coordinate plane.

A coordinate plane is a 2D plane which is formed by the intersection of two perpendicular lines known as the x-axis and y-axis.

It is used to divide any line into two parts, in m:n ratio

The number line which is also known as a Cartesian plane is divided into four quadrants by two axes perpendicular to each other, labelled as the x-axis (horizontal line) and the y-axis(vertical line).

The four quadrants along with their respective values are represented in the graph below-

Quadrant 1 : (+x, +y)

Quadrant 2 : (-x, +y)

Quadrant 3 : (-x, -y)

Quadrant 4 : (+x, -y)

The point at which the axes intersect is known as the origin. The location of any point on a plane is expressed by a pair of values (x, y) and these pairs are known as the coordinates.

How To Find Coordinates of a Point on Graph With Examples

A set of values that shows the exact position of a point in a two-dimensional coordinate plane are called the coordinates. These represent the exact location of a point on a coordinate graph having both x, y axes. You can check the definition of coordinates, step by step detailed procedure to find the coordinates of a point with solved examples.

Coordinates Definition

A pair of numbers that describe the exact position of a point on a cartesian plane by using the horizontal and vertical lines called the coordinates. Usually represented by (x, y) the x value and y value of the point on a graph. Every point or an ordered pair contains two coordinates. The first one is the x coordinate or abscissa and the second is the y coordinate or ordinate. The values of the coordinates of a point can be any positive or negative real number.

The other types of coordinates are map coordinates (north/south, east/west), three-dimensional coordinates, polar coordinates (distance, angle), etc. Detailed information about x coordinate, y coordinate of a point follows:

x‐coordinate (Abscissa): The first number or the number which is located to the left side of a comma in the point is the x coordinate of the ordered pair. It represents the amount of movement along the x-axis from the origin. The movement is to the right side if the number is positive and to the left side of the origin if the number is negative.

y‐coordinate (Ordinate): The number which is located to the right side of the comma in the ordered pair or the second number is known as the y coordinate of the ordered pair. This ordinate indicates the amount of movement along the y-axis. If the number is positive, then the movement is above the origin and the movement is below the origin if the number is negative.

Point on x-axis: A point on the x-axis means its movement along the horizontal line is always zero and the y-coordinate of all points on the x-axis is zero. Therefore, the coordinates of a point on the x-axis are of the form (x, 0).

Point on y-axis: A point on the y-axis means the distance from the y-axis is zero and the x coordinate of every point on the y-axis is zero. Hence, the coordinates of a point on the y-axis are (0, y).

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Answer:
The cost that Kaleb would spend at McDonalds if he ordered 3 McGriddles would be 11.50.

Step-by-step explanation:

We know this is the answer because, when solving for c(3), we would get c(3)=2.3(3)+2.50=11.50.

Answer: 31 Minutes

Step-by-step explanation:

Minus 0.80 from 7.93, and then divide 7.13 by 0.23 and you get 31

Here we go ~

[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]

[tex]\qquad \sf  \dashrightarrow \: (1 - \tan {}^{4} (a) ) \cos {}^{4} (a) [/tex]

[tex]\qquad \sf  \dashrightarrow \: (1 + \tan {}^{2} (a) )(1 - { \tan}^{2} (a)) \cos {}^{4}(a ) [/tex]

[ a² - b² = (a + b)(a - b) ]

[tex]\qquad \sf  \dashrightarrow \: ( \sec {}^{2} (a) )(1 - ( \sec{}^{2} (a) - 1) )\cos {}^{4} (a) [/tex]

[ sec² a = 1 + tan² a, so : tan² a = sec²a - 1 ]

[tex]\qquad \sf  \dashrightarrow \: \bigg( \dfrac{1}{{}cos^{2} (a)} \bigg)(2 - \sec{}^{2} (a) ) \cos {}^{4} (a) [/tex]

[tex]\qquad \sf  \dashrightarrow \: \bigg(2 - \dfrac{1}{ \cos {}^{2} (a) } \bigg) \cos {}^{2} (a) [/tex]

[tex]\qquad \sf  \dashrightarrow \: \dfrac{2 \cos {}^{2} (a) - 1}{ \cos {}^{2} (a) } \times \cos {}^{2} (a) [/tex]

[tex]\qquad \sf  \dashrightarrow \: 2 \cos {}^{2} (a) - 1[/tex]

[tex]\qquad \sf  \dashrightarrow \: 2(1 - \sin {}^{2} (a) ) - 1[/tex]

[ sin²a + cos² a = 1, hence sin²a = 1 - cos²a ]

[tex]\qquad \sf  \dashrightarrow \: 2 - 2 \sin {}^{2} (a) - 1[/tex]

[tex]\qquad \sf  \dashrightarrow \: 1 - 2 \sin {}^{2} (a) [/tex]

Answer:

See proof below

Step-by-step explanation:

Prove [tex]\left(\:1\:-\:tan^4A\right)cos^4A\:=\:1\:-\:2\:sin^2A[/tex]

[tex]\left(1-\tan ^4\left(A\right)\right)\cos ^4\left(A\right)[/tex]  can be expressed in sin, cos terms

Use the trigonometric identity [tex]\tan \left(x\right)=\frac{\sin \left(x\right)}{\cos \left(x\right)}[/tex]

[tex]\left(1-\tan ^4\left(A\right)\right)\cos ^4\left(A\right) = \left(1-\left(\frac{\sin \left(A\right)}{\cos \left(A\right)}\right)^4\right)\cos ^4\left(A\right)[/tex]

[tex]\mathrm{Simplify}\:\left(1-\left(\frac{\sin \left(A\right)}{\cos \left(A\right)}\right)^4\right)\cos ^4\left(A\right)[/tex]

[tex]\mathrm{Apply\:exponent\:rule}:\quad \left(\frac{a}{b}\right)^c=\frac{a^c}{b^c}[/tex]

= [tex]\left(1-\frac{\sin ^4\left(A\right)}{\cos ^4\left(A\right)}\right)\cos ^4\left(A\right)[/tex]

Multiplying the expression in parentheses by [tex]\cos ^4\left(A\right)[/tex] we get

[tex]\frac{\cos ^4\left(A\right)-\sin ^4\left(A\right)}{\cos ^4\left(A\right)}\cos ^4\left(A\right)[/tex]

Cancel the common factor [tex]\cos ^4\left(A\right)[/tex]

This gives us

[tex]\cos ^4\left(A\right)-\sin ^4\left(A\right)[/tex]

Now,

[tex]\sin ^4\left(A\right)=\left(\sin ^2\left(A\right)\right)^2[/tex]

[tex]\cos ^4\left(A\right)=\left(\cos ^2\left(A\right)\right)^2[/tex]

[tex]\:\cos ^4\left(A\right)-\sin ^4\left(A\right)[/tex] = [tex]\left(\cos ^2\left(A\right)\right)^2-\left(\sin ^2\left(A\right)\right)^2[/tex]

[tex]\mathrm{Apply\:Difference\:of\:Two\:Squares\:Formula:\:}x^2-y^2=\left(x+y\right)\left(x-y\right)[/tex]

[tex]\left(\cos ^2\left(A\right)\right)^2-\left(\sin ^2\left(A\right)\right)^2=\left(\cos ^2\left(A\right)+\sin ^2\left(A\right)\right)\left(\cos ^2\left(A\right)-\sin ^2\left(A\right)\right)[/tex]

= [tex]\cos ^2\left(A\right)-\sin ^2\left(A\right)[/tex]   [tex]\textrm{ since }\cos ^2\left(A\right)+\sin ^2\left(A\right)[/tex] = 1

Using the fact that [tex]\cos ^2\left(A\right)=1-\sin ^2\left(A\right)[/tex]

we get

[tex]\cos ^2\left(A\right)-\sin ^2\left(A\right) = 1-\sin ^2\left(A\right)-\sin ^2\left(A\right)\\\\= 1-2\sin ^2\left(A\right)[/tex]

Proved

Using the Empirical Rule, it is found that 16% of men over 20 have upper arm lengths greater than 44.2 cm.

It states that, for a normally distributed random variable:

For the distribution in this problem, we have that:

Hence, 44.2 is one standard deviation above the mean, as 44.2 = 39.1 + 1 x 5.1.

The normal distribution is symmetric, meaning that 50% of the measures are above the mean and 50% are below. Of those measures above the mean, 68% are less than 44.2 and 32% are more than 44.2 cm, hence:

0.5 x 32 = 16%.

16% of men over 20 have upper arm lengths greater than 44.2 cm.

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If Wilson produces only one 1 bag, then his profit starts decreasing

Given the function;

Let  f ( x ) = [tex]2x^4 - 4x^3 + 7[/tex]

Where;

x is  the number of bags of cereal produced

[tex]f'x = 2x^4 - 4x^3 + 7[/tex]

[tex]f'(x) = 8x^3 - 12x^2[/tex]

Factorize the expression

[tex]f'(x) = 4x^2(2x - 3)[/tex]

If the value of x is decreasing, we have;

f ′ ( x ) ≤ 0

4x² (2x - 3) ≤ 0

If x² ≥ 0, then;

2x - 3  ≤ 0

x ≤ 3/ 2

With x as the number of bags

x ∈ N

x = 1 is the only possibility

Thus, if Wilson produces only one 1 bag, then his profit starts decreasing

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The complete question:

Wilson hires a financial analyst to analyse costs and profits for his cereal production business. The analyst determines that Wilson’s eventual profit function is given as: pi = 2x ^ 4 - 4x ^ 3 + 7,  where x is the number of bags of cereal produced. At what point or number of bags of cereal will Wilson’s profit start decreasing

Answer:

(-6, 7)

Step-by-step explanation:

90 degrees counterclockwise / 270 degrees clockwise:

(x,y) -> (-y,x)
180 degrees counterclockwise / 180 degrees clockwise:

(x,y) -> (-x,-y)

270 degrees counterclockwise / 90 degrees clockwise:

(x,y) -> (y,-x)

Answer:

n(AuB)=15

n(AnB)=8 is the answer!

Answer:

5<x<7

Step-by-step explanation:

Hey there !

firstly, in inequality; we must know that we should put the x alone.

so, in order to put the x alone; we should do the following process,

1</2x-9/<5

here,

adding +9 in all sides, we get;

=1+9<2x-9+9<5+9

=10<2x<14

dividing it by 2;we get

=10/2<2x/2<14/2

=5<x<7

This is the following answer. hope it helps!

Thank you!

Answer:

Minimum = (-3, -2)

Step-by-step explanation:

Standard form of a quadratic function:

[tex]f(x)=ax^2+bx+c[/tex]

If a > 0 the parabola opens upwards and the curve has a minimum point.

If a < 0 the parabola opens downwards and curve has a maximum point.

Given function:

[tex]f(x)=x^2+6x+7[/tex]

As a > 0, the parabola opens upwards and so the curve has a minimum point.

The minimum/maximum point of a quadratic function is its vertex.

Vertex form of a quadratic function:

[tex]f(x)=(x-h)^2+k[/tex]

Where (h, k) is the vertex.

To rewrite the given function in vertex form, complete the square.

Add and subtract the square of half the coefficient of the term in x:

[tex]\implies f(x)=x^2+6x+7 +\left(\dfrac{6}{2}\right)^2-\left(\dfrac{6}{2}\right)^2[/tex]

[tex]\implies f(x)=x^2+6x+7 +9-9[/tex]

[tex]\implies f(x)=x^2+6x+9+(7 -9)[/tex]

[tex]\implies f(x)=x^2+6x+9-2[/tex]

Factor the perfect square trinomial formed by x²+6x+9:

[tex]\implies f(x)=(x+3)^2-2[/tex]

Compare with the vertex form:

Therefore, the vertex is (-3, -2) and so the minimum value of the given function is (-3, -2).

Answer:

B

Step-by-step explanation:

using the rule of exponents

[tex]a^{m}[/tex] ÷ [tex]a^{n}[/tex] = [tex]a^{(m-n)}[/tex] , then

[tex]6^{9}[/tex] ÷ 6³ = [tex]6^{(9-3)}[/tex] = [tex]6^{6}[/tex]

Answer:

200mm

Step-by-step explanation:

200mm can be rewritten as 20 cm

a womans hand is on average 17.3 cm

this is the closest estimate out of the three

4 x + 8 = negative 24 , 9 x + 18 = negative 24 are  equations have the same value of x .

What in mathematics is a linear equation?

A - 4 x + 8 = negative 24

E - 4 x = negative 32

ARE CORRECT ON EDGE.

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The complete question is-

Which equations have the same value of x as Two-thirds (6 x + 12) = negative 24? Select two options.

4 x + 8 = negative 24

9 x + 18 = negative 24

4 x = negative 16

StartFraction 18 x + 36 over 2 EndFraction = negative 24

4 x = negative 32

Answer: 29/21

Quotient: 1

Reminder: 8

Step-by-step explanation:

Add up the amount of 7th graders playing instruments (not including drums) total and put that number under the amount of 8th graders playing a instrument.

Use the 1st  digit 2 from dividend 29

21 & 29 squared root

Since 2 is less than 21, use the next digit 9 from dividend 29 and add 0 to the quotient. Find the closest multiple of 21 to 29.

1×21=21 is the nearest. Now subtract 21 from 29 to get reminder 8. Add 1 to quotient.

Since 8 is less than 21, stop the division. The reminder is 8. The topmost line 01 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 1.

The elements that will be coming in the set D∪E will be {12, 14, 15, 16, 17}.

A set may be defined as a collection of letters or numbers that are written in order to depict a certain value or entity. A set is always represented by a capital letter symbol and is always written in curly brackets { }. Union of two sets may be defined as a new set which has the collection of all the elements of the two individual sets. Union of two sets is represented by the symbol '∪'. Union of two Indvidual sets, set A and set b is written as A∪B.

Now, according to the question set D is = {12, 15, 17} and set E is = {12, 14, 15, 16}.

The union of the two sets contains all the elements of the sets D and E.

Thus, D∪E will be given by {12, 14, 15, 16, 17}.

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[tex] \sqrt{12.25 } = 3.5[/tex]

Answer:

1.29 x [tex]10^{9}[/tex]

Step-by-step explanation:

{(1.8 x 10^-6) x (4.3 x 10^8)}  / [(8 x 10^-5) x (7.5 x 10^-3)]

[(1.8 x 4.3)x(10^-6 x 8)] / [(8 x 7.5) x(10^-5 x 10^ -3)]

(.129 x 10^[2-(-8)]

.129 x 10^10

1.29 x 10^-1 x 10^10

1.29 10^9

Answer:

16

Step-by-step explanation: This is because when we look at the square we realize by definition it is a 4-sided shape with 4 equal side lengths this means that if one side is 4 all the 4 sides of a square are also 4 and in this case, we would do length times width and get an answer of an area of 16 units.

The layout of the fast-food restaurant of dimensions 6 by 8 5 feet squares is presented in the attached table created with Sheets.

The dimensions of the facility are;

Horizontal = 6 squares

Vertical = 8 squares

The side length of each square = 5 feet

Therefore;

Area of each square = 5² ft.² = 25 ft.²

Number of squares, n, required by each dependent are therefore;

CB department, n = 300 ÷ 25 = 12 squares

CF department, n = 200 ÷ 25 = 8 squares

PS department, n = 8 squares

DD department, n = 8 squares

CS department, n = 12 squares

A layout for the fast-food restaurant is therefore;

Please see the attached table layout created using Sheets.

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Answer:

A. The expression is in its simplest form.

Step-by-step explanation:

Answer:

i tried this i think the answer is 11a plus 2a subract3b ppus 5