WORD PROBLEM:
You have 200 meters of fencing to enclose two adjacent rectangular pens for livestock. The total area of the enclosed region is 1400 square meters. What are the dimensions of each pen?

The solutions to the equations using function machine are x = 7, x = 5, b = 10, b = 5, n = 7, w = -4, k = 8 and h = 3

From the question, we have the following equations that can be used in our computation:

Using a function machine, we have:

Equation (a)

3x + 4=25

This becomes

x  ⇒ [  ] ⇒ [  ]  = [  ]

So, we have

x  ⇒ [ 21 ] ⇒ [ +4 ]  = [ 25 ]

This means that

x = 21/3

x = 7

Equation (b)

3x - 4 = 11

This becomes

x  ⇒ [  ] ⇒ [  ]  = [  ]

So, we have

x  ⇒ [ 15 ] ⇒ [ -4 ]  = [ 11 ]

This means that

x = 15/3

x = 5

Equation (c)

4b - 10 = 30

This becomes

b  ⇒ [  ] ⇒ [  ]  = [  ]

So, we have

b  ⇒ [ 40 ] ⇒ [ -10 ]  = [30]

This means that

b = 40/4

b = 10

Equation (d)

4b + 10 = 30

This becomes

b  ⇒ [  ] ⇒ [  ]  = [  ]

So, we have

b  ⇒ [ 20 ] ⇒ [ +10 ]  = [30]

This means that

b = 20/4

b = 5

Equation (e)

5n + 2 = 37

This becomes

n  ⇒ [  ] ⇒ [  ]  = [  ]

So, we have

n  ⇒ [ 35 ] ⇒ [ +2 ]  = [37]

This means that

n = 35/5

n = 7

Equation (f)

2w + 10 = 2

This becomes

w  ⇒ [  ] ⇒ [  ]  = [  ]

So, we have

w  ⇒ [ -8 ] ⇒ [ +10 ]  = [2]

This means that

w = -8/2

w = -4

Equation (g)

3k + 4 = 28

This becomes

k  ⇒ [  ] ⇒ [  ]  = [  ]

So, we have

k  ⇒ [ 24 ] ⇒ [ +4 ]  = [28]

This means that

k = 24/3

k = 8

Equation (h)

6h - 7 = 11

This becomes

h  ⇒ [  ] ⇒ [  ]  = [  ]

So, we have

h  ⇒ [ 18 ] ⇒ [ -7 ]  = [11]

This means that

h = 18/6

h = 3

Hence, the value of h is 3

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The domain of the given function is z<0 or z>0

The entire range of independent variable values is the domain of a function.

According to this definition, it means:

The collection of all x-values that can cause the function to "work" and produce actual y-values is known as the domain.

Keep these things in mind when locating the domain:

A fraction's denominator (bottom) cannot be 0.

In this section, the integer following a square root symbol must be positive.

The domain of a function is a set of input of argument values for which the function is real or defined.

1) Finding the singularity point:

Taking the denominator 4×[tex]z^{2}[/tex] = 0 ⇒ z = 0

∴The following function will not be defined if z = 0

So the function domain is z>0 or z<0

The domain of the given function is z<0 or z>0

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The area of regular hexagon in simplest radical form is [tex]600\sqrt{3}[/tex] m².

There are many different types of hexagons. The most common type is a regular hexagon, which is a hexagon that has sides of equal length and angles of equal measure. The perimeter is the total length or distance around a two dimensional shape. In the figure below, the perimeter of each shape is the sum of the lengths of each side, shown in red. The perimeter of a circle or ellipse is called the circumference. For a polygon, the perimeter is the sum of its side lengths.

The given polygon is a regular hexagon with perimeter 120 m.

Thus, the length of each side,

s = 120/6 = 20 m.

The area, A, of a regular hexagon can be found given only its side length, s, with the formula:

[tex]A = \frac{3\sqrt{3} }{2} s^{2}[/tex]

Substitute s = 120 m in above formula:

[tex]A = \frac{3\sqrt{3} }{2} (20)^{2} \\A = \frac{3\sqrt{3} }{2}(400)\\A = 600 \sqrt{3}[/tex]

Thus, the area of regular hexagon in simplest radical form is [tex]600\sqrt{3}[/tex] m².

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The expression given as 89 ∛9 cannot be further simplified

From the question, we have the following parameters that can be used in our computation:

89 ∛9

The above expression is a radical expression

And the radicand is ∛9

The radicand ∛9 implies that the cube root of 9

The cube root of  9 is a decimal number

So, it is better to leave the expression without changing its form

Hence. 89 ∛9 cannot be further simplified

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Answer:

A

Step-by-step explanation:

A box plot shows the five-number summary of a set of data.

Five-number summary:

Therefore, from inspection of the given box plot:

The median of a set of data is the middle value when all data values are placed in order of size.

Therefore, the only answer option that has a maximum value of 34 and a median of 31 is answer option A.

The given division will give the result as (x-3) + [2/(x+3)].

Polynomial are mathematical expressions involving variables raised with non negative integers and coefficients(constants who are in multiplication with those variables) and constants with only operations of addition, subtraction, multiplication and non negative exponentiation of variables involved.

The given division of the two of the polynomial can be carried out as shown below,

[tex]\dfrac{x^2-7}{x+3}\\\\=x+\dfrac{-3x-7}{x+3}\\\\=x-3+\dfrac{2}{x+3}\\\\=(x-3)+\dfrac{2}{x+3}[/tex]

Hence, [tex]\dfrac{x^2-7}{x+3}=(x-3)+\dfrac{2}{x+3}[/tex].

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The slope of the line that passes through the points (-6,1) and (-6,-4) is Undefined.

The slope(m) of the line passing through two points is X1,Y1 and X2, Y2 is

m=[tex]\frac{y2-y1}{x2-x1}[/tex]

we have (x1,y1) and (x2,y2) is (-6,1) and (-6,-4) respectively substitute the values in m=[tex]\frac{y2-y1}{x2-x1}[/tex],

we get m=[tex]\frac{-4-1}{-6-(-6)}[/tex] = -5/0 which is Undefined.

Whenever the slope of the line is undefined then the line must be vertical. Because the slope of the vertical line cannot be defined.

The slope of the line that passes through the points (-6,1) and (-6,-4) is Undefined.

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The value of hypotenuse will be;

⇒ Hypotenuse = 132.35

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The values are,

⇒ θ = 20° opposite = 45

Now,

Since, The values are,

⇒ θ = 20° opposite = 45

We know that;

⇒ sin θ = Opposite / Hypotenuse

⇒ sin 20° = 45 / Hypotenuse

⇒ Hypotenuse = 45 / sin 20°

⇒ Hypotenuse = 45 / 0.34

⇒ Hypotenuse = 132.35

Thus, The value of hypotenuse will be;

⇒ Hypotenuse = 132.35

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Answer: To find out how many seconds it will take for the egg to hit the ground, we need to find the value of x when the height of the egg is 0 feet. We can do this by setting the height of the egg equal to 0 in the equation 27 - 16x^2 and solving for x.

The equation for the height of the egg in feet x seconds after being dropped is given as:

27 - 16x^2 = 0

Subtracting 27 from both sides of the equation gives us:

-16x^2 = -27

Dividing both sides of the equation by -16 gives us:

x^2 = 27/16

Taking the square root of both sides of the equation gives us:

x = sqrt(27/16)

Plugging this value into the equation for the height of the egg gives us:

27 - 16(sqrt(27/16))^2 = 0

Simplifying this equation gives us:

27 - 16(27/16) = 0

Which simplifies to:

27 - 27 = 0

This equation is true, so the value of x that we found is a solution to the equation. This means that the egg will hit the ground after sqrt(27/16) seconds.

I hope this helps! Let me know if you have any other questions.

By using fraction, it can be calculated that

30 boards are required to cover a floor of width 205 inches wide

What is fraction?

Suppose there is a collection and a part of collection has to be taken.

The part which is taken is called fraction. In other words part of a whole is called fraction.

The upper part of the fraction is the numerator and the lower part of the fraction is the denominator.

This is a word problem on fraction

Width of each board = [tex]6\frac{5}{6}[/tex] inches = [tex]\frac{41}{6}[/tex] inches

Total width of floor = 205 inches

Number of boards required = [tex]205 \div \frac{41}{6}[/tex] = [tex]205 \times \frac{6}{41}[/tex] = 30

30 boards are required

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3) The rate of change on the interval [1, 7] is -1, so the correct option is A.

4) By using the rate of change formula, we will see that h(9) = 40

We know that for a function f(x), the average rate of change on the interval [a, b] is:

r = ( f(b) - f(a))/(b - a)

Here the interval is [1, 7]

Using the graph we can see that:

f(1)= 6

f(7) = 0

Then the average rate of change is:

r = ( f(7) - f(1))/(7 - 1)

r = (0 - 6)/6 = -1

The correct option is A.

4) Which will be value of h(9)?

We know that the average rate of change of h(x) is 7 on the interval [5, 9]

Then we can write:

7 = ( h(9) - h(5))/(9 - 5)

We know that h(15) = 12, then we have the equation:

7 = (h(9) - 12)/4

Now we can solve that for h(9), we will get:

7 = (h(9) - 12)/4

7*4 = h(9) - 12

28 = h(9) - 12

28 + 12 = h(9)

40 = h(9)

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The change in the  angular velocity and number of revolutions  is given as,

when the angular velocity decreases the number of revolutions also decreases.

The rotation rate, which refers to how quickly an item rotates or circles in relation to another point, is measured vectorially by angular velocity.

Angular velocity can be defined as the speed at which an item rotates or revolves around an axis. The Greek letter omega stands for angular velocity. The SI unit of angular velocity is radians per second because it is measured in angle per unit time.

The only distinction between revolution and rotation is that the axis of rotation in a revolution is located outside the body. Both motions of an item or body in space are circular.

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The value of k in which a line is has a slope 1/4 passing through the points (4,6) and (12,k) is 8.The option is A.8

Slope of straight line(m) which is passing through the point is y=mx+c, where m= slope of the line c is the intercept and x and y are distance from the respective x-axis and y-axis.

The line is passing through the 2 points say ([tex]x_{1}[/tex],[tex]y_{1}[/tex]) and ([tex]x_{2}[/tex], [tex]y_{2}[/tex]) then m=[tex]\frac{y_{2} -y_{1} }{x_{2}-x_{1} }[/tex]we are having the points (4,6) and (12,k)( [tex]x_{1}[/tex],[tex]y_{1}[/tex]) and ([tex]x_{2}[/tex],[tex]y_{2}[/tex])and slope m=1/4.

Now substitute the values of( [tex]x_{1}[/tex],[tex]y_{1}[/tex]) and ([tex]x_{2}[/tex],[tex]y_{2}[/tex]) in m=[tex]\frac{x_{2}-x_{1} }{y_{2}-y_{1} }[/tex].

[tex]\frac{1}{4}[/tex]= [tex]\frac{k-6}{12-4}[/tex],

4(k-6)= 8

4k-24=8

4k=32

k=[tex]\frac{32}{4}[/tex]

k=8

The value of k in which a line is has a slope 1/4 passing through the points (4,6) and (12,k) is 8.The option is A.8

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She earned 0.91 pounds for every $1 US dollar when a visitor traded $1,000 US dollars for 910 British pounds.

A proportion is an equation that sets two ratios equal to each other. For example, if there is one guy and three girls, the ratio may be written as 1: 3. (for every one boy there are 3 girls) One-quarter are males and three-quarters are girls. 0.25 are males (by dividing 1 by 4). According to the notion of proportion, two ratios are in proportion when they are equivalent. It is a formula or statement that shows that two ratios or fractions are equivalent.

Here,

For 910 pounds, she spent $1000 US dollars.

For $1,

=910/1000 pound

=0.91 pounds

For each $1 US dollar, she received 0.91 pounds as tourist exchanged $1,000 US dollars for 910 British pounds.

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The unit rate or the number of miles run in one hour is 12 miles thus, 4 miles in 1/3 hour will be the faster.

The rate of change is the change of a quantity over 1 unit of another quantity.

Most of the time the rate of change is the change with respect to time.

For example the speed 3meter/second.

As per the given,

4 miles in 1/3 hour ⇒ 4 x3/1 = 21 miles/hour

1.3 miles in 4 hours ⇒ 1.4/4 mile/hour

1/2 mile in hours ⇒ 0.5 miles/hour

Hence "The unit rate or the number of miles run in one hour is 12 miles thus, 4 miles in 1/3 hour will be the faster".

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Answer:

NO

Step-by-step explanation:

Two fourths =

[tex] \frac{2}{4} = 0.5[/tex]

Two thirds =

[tex] \frac{2}{3} = 0.66667[/tex]

Therefore

0.66667 > 0.5

[tex] \frac{2}{3} > \frac{2}{4} [/tex]

or

0.5 < 0.66667

[tex] \frac{2}{4} < \frac{2}{3} [/tex]

i hope this helped

Answer: No, 2/4 is not greater than 2/3

Step-by-step explanation: To find an easy way to calculate their values we have 2 options. So, the 1st option is to turn them into a decimal. I already calculated their values which are:

2/4 = 0.5

2/3 = 0.667

Then, we compare the two decimal numbers to get the answer.

0.5 is not greater than 0.667.

The 2nd way is to find a common denominator, which would look like this:

2/4 =  6/12

2/3 =  8/12

8/12 is greater than 6/12, so that also proves that 2/4 is not greater than 2/3.

The pressure of 28 inches of mercury occurs about 6 miles from the eye of the hurricane. We get this from the given algebraic expression.

An expression is formed by variables, constants, and algebraic operations. Since the operation among them is an algebraic or arithmetic operation, it is said to be an algebraic expression.

It is given that the algebraic expression that relates the barometric pressure and the eye of the hurricane as

f(x) = 0.48 ln(x+2) + 27

Here x is the distance in miles from the eye of the hurricane.

f(x) is the pressure of the mercury in a barometer in inches

So, the required distance from the eye of the hurricane when the pressure of 28 inches of mercury in the meter is

(Here f(x) = 28)

f(x) = 0.48 ln(x+2) + 27

⇒ 28 = 0.48 ln(x+2) + 27

⇒ 0.48 ln(x+2) = 28 - 27

⇒ ln (x+2) = 1/0.48

⇒ ln(x+2) = 2.0833

Applying exponential base "e" on both sides, we get

(x+2) = [tex]e^{2.0833}[/tex]

⇒ x + 2 = 8.0309

⇒ x = 8.0309 - 2 = 6.0309

When the result is rounded to the nearest whole number, we get x = 6 miles.

Thus, for the pressure of 28 inches of mercury, the eye of the hurricane is 6 miles far from the barometer.

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Answer:

(x-3)²+(y-1)²=50

Step-by-step explanation:

we know,

general eqn of circle passing through a point is

r²=(x-h)²+(y-k)²------($)

then,at (-4,2) the eqn becomes

r²=(-4-h)²+(2-k)²----(1)

at (-2,6),

r²=(-2-h)²+(6-k)²-----(2)

at (4,8),

r²=(4-h)²+(8-k)²-------(3)

Now,

from (1) and(2),

(-4-h)²+(2-k)²=(-2-h)²+(6-k)²

or,16+8h+h²+4-4k+k²=4+4h+h²+36-12k+k²

or,h²-h²+8h-4h+k²-k²-4k+12k+16+4-4-36=0

or,4h+8k-20=0

or,4(h+2k)=20

or,h+2k=5------(4)

also,from (2) and (3),

(-2-h)²+(6-k)²=(4-h)²+(8-k)²

or,4+4h+h²+36-12k+k²=16-8h+h²+64-16k+k²

or,h²-h²+4h+8h+k²-k²-12k+16k+4+36-64-16=0

or,12h+4k-40=0

or,4(3h+k)=40

or,3h+k=10-------(5)

Now,multiplying eqn (5)by 2 then subtracting from (4),we get

h+2k=5

6h+2k=20

- - -

_________

-5h=-15

.:h=3

putting value of h in (4),we get

3+2k=5

or,2k=2

.:k=1

Now,putting value of k and h in eqn(1),

r²=(-7)²+(1)²

or,r²=49+1

.:r²=50

Now putting value of h,k and r² in eqn($),we get

(x-3)²+(y-1)²=50,which is required eqn of circle

Answer:

hi

Step-by-step explanation:

Answer:

Below

Step-by-step explanation:

log x = 2 log 6 + log 3    using properties of logs, this becomes

log x = log 6^2 + log 3

       = log (6^2 * 3 ) = log (108)

x = 108

A) The break-even sales level in shillings XYZ Company needs to achieve is Shs.1,096,443.

B) The break-even sales level in units XYZ Company needs to achieve is 27,444 units to make a profit of Shs.195,000.

The break-even point is the sales level when total revenue equals total costs (fixed and variable).

At the break-even point, there is no profit or loss.

Selling price per unit = Shs.66

Variable production cost per unit  = Shs.44

Variable selling cost per unit = Shs.4

Total variable cost per unit = Shs.48 (Shs.44 + Shs.4)'

Contribution margin per unit = Shs.18 (Shs.66 - Shs.48)

Contribution margin ratio = 27.27% (Shs.18/Shs.66 x 100)

Fixed production cost (total)  = Shs.200,000

Fixed selling and administrative cost (total) Shs.99,000

Total fixed costs = Shs. 299,000 (Shs.200,000 + Shs.99,000)

Target profit = Shs.195,000

a) Break-even sales in shillings = Fixed costs/Contribution margin ratio

= Shs.1,096,443 (Shs.299,000/27.27%)

b) Break-even sales in units to achieve target profit = (Fixed costs + Target profit)/Contribution margin per unit

= (Shs.299,000 + Shs.195,000/Shs.18)

= Shs.494,000/Shs.18

= 27,444 units

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XYZ Company manufactures a product called "PERMA". Pertinent cost and revenue data relating to the manufacture of this product are given below:

Selling price per unit = Shs.66

Variable production cost per unit  = Shs.44

Variable selling cost per unit = Shs.4

Fixed production cost (total)  = Shs.200,000

Fixed selling and administrative cost (total) Shs.99,000

Required:

a) Calculate the break-even sales level in shillings;

b) Suppose the company desires to make a profit of shs.195,000, what should be the output in units?

In the triangle below, ΔABE≅ΔCBD. Reason (AAS)

We should know that the postulates talk about the proofs about the given diagram or flowchart

There is an attached diagram to support our answer

Below gives the correct explanations

S/n         Statement                                     Reason

1               <ABE≅<CDE                             Given in the diagram

2            <AEB≅CED           The theory of vertical angles  are      equal        3             BE≅ED                                 Also given in the diagram

4          ΔABE≅ΔCDE            The rule of Angle, Side Angle proof

In conclusion the triangle below, ΔABE≅ΔCBD. Reason (AAS)

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Complete question:

Given AC 1 BD, complete the flowchart proof below. Note that the last statement and reason have both been filled in for you

Step-by-step explanation:

f(x)=3x²-x-2

a) (2,8)

f(2)=3(2²)-2-2

f(2)=3(4)-4

f(2)=12-4

f(2)=8

Hence, the point (2,8) is on the graph of f(x)

b) x=-1

f(-1)=3((-1)²)-(-1)-2

f(-1)=3(1)+1-2

f(-1)=3-1

f(-1)=2

c) x=-2

f(-2)=3((-2)²)-(-2)-2

f(-2)=3(4)+2-2

f(-2)=12+0

f(-2)=12

[tex]d)\ f(x)\in(-2\frac{1}{12} ,\infty)[/tex]

e) y=0

3x²-x-2=0

3x²-x-2=0

3x²-3x+2x-2=0

3x(x-1)+2(x-1)-0

(x-1)(3x+2)=0

x-1=0

x=1

3x+2=0

3x=-2

Divide both parts of the equation by 3:

x=-2/3

f) x=0

f(x)=3(0²)-0-2

f(x)=3(0)-2

f(x)=0-2

f(x)=-2

Answer: 6.

Step-by-step explanation: We can solve this problem by using the combination formula:

C(n, r) = n! / (r! * (n - r)!)

In this case, n is the number of choices (the digits 2, 3, 4, 5, 6, and 9) and r is the number of items in each combination (4 digits).

Plugging in the values, we get:

C(6, 4) = 6! / (4! * 2!) = (6 * 5 * 4 * 3) / (4 * 3 * 2) = 30

Therefore, there are 30 four-digit odd numbers that can be formed using the digits 2, 3, 4, 5, 6, and 9. However, not all of these numbers will be less than 5000, so we need to further filter the list to only include those that meet this requirement.

The four-digit odd numbers that can be formed using these digits are:

2359, 2395, 2539, 2593, 2935, 2953, 3259, 3295, 3529, 3592,

3925, 3952, 5239, 5293, 5329, 5392, 5923, 5932, 9235, 9253,

9352, 9523, 9532

Out of these numbers, only 2359, 2539, 2935, 3925, 5239, and 9523 are less than 5000. Therefore, there are 6 four-digit odd numbers less than 5000 that can be formed using the digits 2, 3, 4, 5, 6, and 9.

Therefore, the final answer is 6.

Answer: 19/36

Step-by-step explanation:

First the LCM (Least Common Denominater) must be found, the LCM of 9 and 4 is 36

Since 9 x 4 is 36, the numerator and denominator of 7/9 will be multiplied by 4 making it 28/36

Since 4 x 9 equals 36, the numerator and denominator of 1/4 will be multiplied by 4 making it 9/36

Now that they have common denominators the numerators can be subtracted from each other as well as the denominators

28/36 - 9/36 = 19/36

19/36 cannot be simplified therefore 7/9 - 1/4 = 19/36

The balance in the account after 4 years as interest is compounded monthly is $9,066.02.

The formula accrued amount in a compounded interest is expressed as;

A = P( 1 + r/n )^( n × t )

Where A is accrued amount, P is principal, r is interest rate and t is time.

Given the data in the question;

Plug the given values into the above formula and solve for A.

A = P( 1 + r/n )^( n × t )

A = 8600( 1 + 0.0132/12 )^( 12 × 4 )

A = 8600( 1 + 0.0011 )^( 48 )

A = 8600( 1.0011 )^( 48 )

A = $9,066.02.

Therefore, the accrued amount after 4 years is $9,066.02.

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After solving the equation, the value of y obtained is equal to 10°.

An angle results from the intersection of two lines at a point. The term "angle" describes the width of the "gap" that exists between these two rays. It's represented by the symbol ∠.

Angles are most frequently measured in degrees and radians, a measurement of roundness or rotation. Angles are a part of everyday existence.

As per the information obtained from the given figure,

Angle, C = 4y

Angle, E = 180 - 116 = 64 and,

Angle, D = 7y + 6

As we know, the sum of the angles of a triangle is 180°.

Then,

4y + 64 + 7y + 6 = 180

11y = 180 - 70

11y = 110

y = 110/11

y = 10°

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The standard quadratic equation is (c) y = x² + 5x - 66

From the question, we have the following parameters that can be used in our computation:

Zeros  -11 and 6

This means that

x = -11 and x = 6

The quadratic equation can then be calculated as

y = (x - 6) * (x + 11)

Evaluate the products

y = x² - 6x + 11x - 66

Evaluae the like terms

y = x² + 5x - 66

Hence, the equation is y = x² + 5x - 66

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