Find the tenth term in each sequence.
-14, -6, -2, 0, 1, ...

Answer:

y = -5/4x -4

Step-by-step explanation:

slope(m)= -5/4

x1=-4,y1=1

using the formula for one point form

y-y1=m(x-x1)

y-1= -5/4(x-(-4))

y-1 = -5/4x + -5/4 × +4

y - 1 = -5/4x -5

y=-5/4x -5 + 1

y = -5/4x -4.

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A) the limit of the difference quotient at x0 = 3 for f(x) is  lim(h → 0) (f(3+h) - f(3) )/h = 3² + 3(3) - 6 = 12

B) the expression of a line passing through the same point that f(x) passes through at x = 3 with a slope equal to the limit you found in part is y = 12x - 29.

C) See graph attached.

Part A ) The difference quotient of a function f(x) at x0 is given by:

(f(x0+h) - f(x0)) /h

To calculate the limit of the difference quotient at x0 = 3 for f(x) we need to find the limit of the above expression as h approaches 0.

f(x) = x³ - 4x² + 2

(f(3+h) - f(3))/h

= ( (3+h)³ - 4(3+h)² + 2 - (3³ - 4(3)² + 2) )/h

 = (27 + 27h +   9h² + h³ - 4(9 + 6h + h²) + 2 - 19)/h

= (h³ + 3h² - 6h)/h

= h² + 3h - 6

Therefore, the limit of the difference quotient at x0 = 3 for f(x) is:

lim(h → 0) (f(3+h) - f(3))/h

= 3² + 3(3) - 6 = 12

Part B)  To find the equation of a line passing through the point (3, f(3)) with a slope equal to the limit found in part A, we can use the point-slope form of the equation of a line...

y - y1 = m (x - x1)

where m is the slope and (x1, y 1) is the given point.

Substituting the values

y - f(3) = 12(x - 3)

Expanding and simplifying

y = 12x - 29

so this means that the equation of the line passing through the point (3, f(3)) with a slope equal to the limit found in part A is y = 12x - 29.


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Full Question:

Part A

Consider the function f(x) = x3 − 4x2 + 2. Calculate the limit of the difference quotient at x0 = 3 for f(x).

Part B

Find the equation of a line passing through the same point that f(x) passes through at x = 3 with a slope equal to the limit you found in part A.

Part C

Graph the function f(x) and the line you identified in part B. How do the graphs relate to each other? What does the slope of the line represent about the function at the given point?

9514 1404 393

Answer:

  4a. ∠V≅∠Y

  4b. TU ≅ WX

  5. No; no applicable postulate

  6. see below

Step-by-step explanation:

a. When you use the ASA postulate, you are claiming you have shown two angles and the side between them to be congruent. Here, you're given side TV and angle T are congruent to their counterparts, sides WY and angle W. The angle at the other end of segment TV is angle V. Its counterpart is the other end of segment WY from angle W. In order to use ASA, we must show ...

  ∠V≅∠Y

__

b. When you use the SAS postulate, you are claiming you have shown two sides and the angle between them are congruent. The angle T is between sides TV and TU. The angle congruent to that, ∠W, is between sides WY and WX. Then the missing congruence that must be shown is ...

  TU ≅ WX

__

The marked congruences are for two sides and a non-included angle. There is no SSA postulate for proving congruence. (In fact, there are two different possible triangles that have the given dimensions. This can be seen in the fact that the given angle is opposite the shortest of the given sides.)

  "No, we cannot prove they are congruent because none of the five postulates or theorems can be used."

__

The first statement/reason is always the list of "given" statements.

1. ∠A≅∠D, AC≅DC . . . . given

2. . . . . vertical angles are congruent

3. . . . . ASA postulate

4. . . . . CPCTC

Answer:

t = d/r; t = 5

Step-by-step explanation:

Hi there!

1) Isolate t

d = rt

Divide both sides by r

d/r = rt/r

d/r = t

t = d/r

2) Solve for t when distance is 40 and the rate is 8

t = d/r

Replace d with 40 and rate with 8

t = 40/8

t = 5

I hope this helps!

Answer:

3.6 is the sales tax in dollars

Step-by-step explanation:

Together, the entire price, is 90+0.04, or 4%, which equals $93.6

The probability is closer to one than zero.

Probability theory is used to analyze and predict the likelihood of events happening in various fields such as statistics, gambling, physics, finance, and more. It allows us to make informed decisions based on the likelihood of different outcomes. In probability theory, the total number of possible outcomes is important to determine the probability of a single event occurring. By comparing the favorable outcomes to the total outcomes, we can calculate the probability of an event happening.

Probability is a measure of the likelihood of an event to occur. Many events cannot be predicted with total certainty. We can predict only the chance of an event to occur i.e., how likely they are going to happen, using it. Probability can range from 0 to 1, where 0 means the event to be an impossible one and 1 indicates a certain event. Probability for Class 10 is an important topic for the students which explains all the basic concepts of this topic. The probability of all the events in a sample space adds up to 1.For example, when we toss a coin, either we get Head OR Tail, only two possible outcomes are possible (H, T). But when two coins are tossed then there will be four possible outcomes,  i.e {(H, H), (H, T), (T, H), (T, T)}.

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Step-by-step explanation:

Based on the information given, we have a diagram with two sides labeled as 13.3 mm and 5.5 mm, and another side labeled as X mm.

To find the length of X, we can use the fact that the sum of the lengths of the sides of a triangle is equal to the perimeter.

Perimeter = 13.3 mm + 5.5 mm + X mm

The perimeter is the total distance around the triangle. Since we have three sides, the perimeter is the sum of the lengths of those sides.

To find X, we can subtract the sum of the known sides from the perimeter:

X mm = Perimeter - (13.3 mm + 5.5 mm)

Since the value of X is not given, we cannot calculate it without the perimeter value. If you provide the perimeter value, I can help you find the length of X.

Answer:

There are two types of hypotheses tests. null and alternative

They are complements.

Step-by-step explanation:

There are two types of hypotheses tests. null and alternative

the table shows the summary of both tests.

True Situation                              DECISION

                                  Accept H0             Reject H0

                                                               (or accept Ha)

H0 is true          Correct decision       Wrong Decision

                            (no error)                     type I error          

H0 is false          Wrong Decision           Correct decision

                             type II error                 ( no error)    

The probability of making a type I error is conventionally denoted by alpha and that of committing a type II error is indicated by beta.

∝ = P ( type I error) = P (reject H0 / H0 is true)

β = P (type II error) = P (accept H0 / H0 is false)

When ∝ becomes larger, β tends to become smaller . There is inverse relationship between ∝ and β.

When H0 is true Ha is false when Ha is false H0 is true. So they are compliments of each other.

The given diagram implies that the triangle $ABC$ is an isosceles triangle with angles of $24^\circ$. This can be verified by computing the length of the hypotenuse and using the Pythagorean Theorem.

Equation is a mathematical expression that consists of variables, symbols, and numbers, and shows the relationship between different quantities. An equation can involve one or more unknowns, and can be represented as an equality or as an inequality. Solving an equation requires understanding the relationship between the different elements in the equation, and manipulating the equation to isolate the unknowns. Common types of equations include linear equations, quadratic equations, and polynomial equations.

From this diagram, we can conclude that $\angle ABC$ is an isosceles triangle. This is because the angles opposite equal sides of a triangle must be equal. Since $\angle BAC=24^\circ$, $\angle ABC$ must be $24^\circ$. Furthermore, the sides $AB$ and $AC$ are equal, so $ABC$ is an isosceles triangle.

This conclusion can be verified by using the Pythagorean Theorem. If $AB=AC$, then it follows that $BC = \sqrt{AB^2 + AC^2} = \sqrt{2AB^2}$. Since $AB=3$, it follows that $BC=\sqrt{2*3^2}=6$. Therefore, the triangle $ABC$ is a right triangle with legs of length 3 and hypotenuse of length 6. Since $\angle BAC = 24^\circ$, it follows that $\angle ABC = 24^\circ$, verifying that the triangle is isosceles.

In conclusion, the given diagram implies that the triangle $ABC$ is an isosceles triangle with angles of $24^\circ$. This can be verified by computing the length of the hypotenuse and using the Pythagorean Theorem.

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Answer:

78

Step-by-step explanation:

Answer:6/5 or 1.2

Step-by-step explanation:

4/5 divided by 2/3

=4/5 *3/2

=12/10

=6/5

=1.2

Answer:

D is correct

Step-by-step explanation:

the left side of the graph is negative so it's -5

up is positive so it's positive 2

Answer:

option d) is correct

Step-by-step explanation:

in the graph left side is (-) and up it is (+).

So, the value of x=-5

and y=2

Answer: Suppose there exists a positive rational number r such that r^2 < 2. Then we have 2 - r^2 > 0. Let h = (2 - r^2)/4. Then h > 0 because r^2 < 2.

Consider the number rh = r + h. We have:

(rh)^2 = (r + h)^2 = r^2 + 2rh + h^2 = r^2 + 2(2 - r^2)/2 + (2 - r^2)/16

= r^2 + 2 + (2 - r^2)/16

< 2 + 2 + (2 - 2)/16 = 2.

Thus, for any positive rational number r such that r^2 < 2, there exists a larger positive rational number rh = r + h such that (rh)^2 < 2.

Step-by-step explanation:

Answer:

Step-by-step explanation:

i am working on the assumption that nobody does all three of them

i got 4 because including the people that do swimming and park, the total number of people that do swimming is 22.

the same logic goes for cycling: including the people that do swimming and visit the national park, the total is 23.

so that means that find how many people do swimming and cycling, we have to add the people doing only swimming, with the people doing both swimming and park and then subtract that answer from 22 which gives you 4

Answer:

See attachment for what the graph looks like.

Step-by-step explanation:

When you graph these equations, convert 4x+8y=16 into slope-intercept form, which should be y= -1/2x+2.

In this case, 2 is the y-intercept, the part of the line that intercepts with the y-axis, with a negative (goes downward) slope of 1/2.

The line should intersect at (0,2) and have a slope of -1/2.

The x-intercept of the line is at 4 and the y-intercept of the line is at 2. Then the graph is sketched below.

A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.

The linear equation is given as,

x/a + y/b = 1

Where 'a' is the x-intercept of the line and 'b' is the y-intercept of the line.

The equation of the line is given below.

4x + 8y = 16

Convert the general form of the line into an intercept form. Then we have

4x + 8y = 16

x/4 + y/2 = 1

The x-intercept of the line is at 4 and the y-intercept of the line is at 2. Then the graph is sketched below.

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The simplified form of -20/2(7 2/3) is -230/3.

To solve the expression -20/2(7 2/3), we need to follow the order of operations, which states that we should perform the operations inside parentheses first, then any multiplication or division from left to right, and finally any addition or subtraction from left to right.

First, let's convert the mixed number 7 2/3 to an improper fraction.

7 2/3 = (7 * 3 + 2) / 3 = 23/3

Now, let's substitute the value back into the expression:

-20/2 * (23/3)

Next, we simplify the multiplication:

-10 * (23/3)

To multiply a fraction by a whole number, we multiply the numerator by the whole number:

-10 * 23 / 3

Now, we perform the multiplication:

-230 / 3

Therefore, the simplified form of -20/2(7 2/3) is -230/3.

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Answer:

Rounded down to the nearest foot, the length of the garden is nine feet.

Step-by-step explanation:

We're told that the length of the chicken coop, 3x + 12 feet, is equal to the length of the garden, 6x - 16 feet.  Let's put them together then and solve for x:

3x + 12 = 6x - 16

First, we'll subtract 6x from both sides

3x - 6x + 12 = 6x - 6x - 16

-3x + 12 = -16

Now we subtract 12 from both sides:

-3x + 12 - 12 = -16 - 12

-3x = -28

Finally divide both sides by -3

-3x / -3 = -28 / -3

x = 28/3

x = 9 and 1/3

As the question asks for the number of feet only (not inches), the answer is nine feet.

A third of a foot though is four inches, so the more exact answer is nine feet and four inches, or 9'4"

Hey there! I'm happy to help!

Let's look at all of the perfect squares (numbers with integer square roots) so that we can see where the square root of 12 lies.

√1=1

√4=2

√9=3

√16=4

√25=5

√36=6

√49=7

√64=8

√81=9

√100=100

We see that √12 would be in between √9 and √16 (3 and 4), so the square root of 12 is in between 3 and 4.

I hope that this helps! Have a wonderful day! :D

The square root of 12 lies between the whole numbers 3 and 4.

The value of a number's power 1/2 is the number's square root. It is the number whose product by itself yields the original number, to put it another way.

Let's look at all of the perfect squares (numbers with integer square roots) so that we can see where the square root of 12 lies.

√1=1

√4=2

√9=3

√16=4

√25=5

√36=6

√49=7

√64=8

√81=9

√100=100

We see that √12 would be in between √9 and √16 (3 and 4), so the square root of 12 is in between 3 and 4.

Therefore, the square root of 12 lies between the whole numbers 3 and 4.

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The matching expressions are:

\(i) 3a x 4 = C (12a)\\ii) a^2 x a = A (a^3)\\iii) 6 × 1/2 a^2 = D (3a^2)\)

i) 3a x 4 can be represented as C (12a) since multiplying 3a by 4 gives 12a.

ii) a^2 x a can be represented as A (a^3) since multiplying a^2 by a gives a^3.

iii) \(6 \times 1/2 a^2\) can be represented as D (3a^2) since multiplying 6 by 1/2 and then by a^2 gives 3a^2.

To understand the matching expressions, let's break down each one:

i) 3a x 4:

This expression represents multiplying a variable, 'a', by a constant, 4. The result is 12a, which matches with C (12a).

ii) a^2 x a:

This expression represents multiplying the square of a variable, 'a', by 'a' itself. This results in a^3, which matches with A (a^3).

iii) 6 × 1/2 a^2:

This expression involves multiplying a constant, 6, by a fraction, 1/2, and then multiplying it by the square of 'a', a^2. The final result is 3a^2, which matches with D (3a^2).

Therefore, the matching expressions are:

i) 3a x 4 = C (12a)

ii) a^2 x a = A (a^3)

iii) 6 × 1/2 a^2 = D (3a^2)

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The alternative hypothesis is Ha : μa ≠ μb Ha : μa - μb ≠ 0

Since they want to find out if the difference in the mean times spent studying by the students of the two schools is statistically significant, it means that it is a two directional test. Also called a two tailed test. The hypothesis would be as follows:

Null Hypothesis: There is no difference in the mean times spent by the schools' students.

Alternative Hypothesis: There is at least some difference in the mean times spent by the schools' students.

By using the appropriate symbols, it becomes

The null hypothesis is

H0 : μa = μb H0 : μa - μb = 0

The alternative hypothesis is

Ha : μa ≠ μb Ha : μa - μb ≠ 0

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Answer:

-9-9x=27+9

-9x=36÷(-9)

x=-4

Step-by-step explanation:

prove me wrong

Answer:

=2x+4

Step-by-step explanation:

Let's simplify step-by-step.

5x+4−3x

=5x+4+−3x

Combine Like Terms:

=5x+4+−3x

=(5x+−3x)+(4)

=2x+4

Answer:

2x+4...

Step-by-step explanation:

Hopefully it helps

The value of x that makes quadrilateral ABCD a rectangle if BE = 3x+1 and ED = 5x-3 is x = 2.

A quadrilateral with parallel sides that are equal to one another and four equal vertices is known as a rectangle. It is also known as an equiangular quadrilateral for this reason.

Rectangles can also be referred to as parallelograms because their opposite sides are equal and parallel.

There are four vertices and four sides.

Every vertex has an angle of 90 degrees.

Equal and parallel opposed sides are bisected by a diagonal.

We know that the diagonals of a rectangle bisect each other.

Thus, for the quadrilateral to be a rectangle we have:

BE = ED

3x + 1 = 5x - 3

1 + 3 = 5x - 3x

4 = 2x

x = 2

Hence, the value of x that makes quadrilateral ABCD a rectangle if BE = 3x+1 and ED = 5x-3 is x = 2.

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Answer:

x is 28

Step-by-step explanation:

When two lines intersected in a point, then they formed two pairs of vertically opposite angles. The vertically opposite angles are equal in measures

Let us solve our question

∵ AB and CD are straight lines intersected at O

∴ ∠AOC and ∠DOB are vertically opposite angles

∴ ∠AOD and ∠COB are vertically opposite angles

→ The vertically opposite angles are equal in measures

∴ m∠AOC = m∠DOB

∴ m∠COB = m∠AOD

→ ∠ COB is formed from ∠COE, ∠EOF, and ∠FOB

∵ m∠COB = m∠COE + m∠EOF + m∠FOB

∵ m∠COE = 3x, m∠EOF = x, m∠FOB = x + 12

∴ m∠COB = 3x + x + x + 12

→ Add the like terms

∴ m∠COB = 5x + 12

∵ m∠AOD = 152°

∵  m∠COB = m∠AOD

∴ 5x + 12 = 152

→ Subtract 12 from both sides

∴ 5x + 12 - 12 = 152 - 12

∴ 5x = 140

→ Divide both sides by 5

∴ \(\frac{5x}{5}=\frac{140}{5}\)

∴ x = 28

→ To justify the solution substitute x by 28 in m∠COB the answer must

   be 152°

∵ m∠COB = 5x + 12

∵ x = 28

∴ m∠COB = 5(28) + 12

∴ m∠COB = 140 + 12

∴ m∠COB = 152°

∴ The value of x is correct

Answer:

8200 * 100 = 820,00

820,000 ÷ 10 = 82,000

820 * 10 = 8200

82,000 ÷ 1,000 = 82

Step-by-step explanation:

Love your username btw

Arithmetic operations contain operations such as Addition, Subtraction, Multiplication, and Division.

Arithmetic operations exist as a branch of mathematics, that concerns the analysis of numbers and operation of numbers that exist valid in all the other constituents of mathematics. It essentially contains arithmetic operations such as Addition, Subtraction, Multiplication, and Division.

8200 \(*\)100 = 8,20,000

820000 ÷ 10 = 82,000

820 \(*\) 10 = 8,200

82000 ÷ 1000 = 82

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The probability that the random sample of 100 male students has a mean gpa greater than 3. 42 is 0.9452.

A statistic known as the standard deviation is used to describe how volatile or dispersed a group of numerical values is. While a big standard deviation denotes that the values are scattered across a wider range, a low standard deviation indicates that the values tend to be close to the set mean.

From the given information, a scores random sample of 100 male students is selected and the GPA for each student is calculated which follows approximately normal with a mean of 3.5 and standard deviation of 0.5. That is,

µ = 3. 5 and σ = 0. 5

and the random sample of 100 male students has a mean GPA 3.42 is considered.

The z-score value is,

Z=( 3.42-3.5)/ (0.5/√100)

Z= -0.08/0.05

Z=-1.6

The value of z-score is obtained by taking the difference of x and µ. Then the resulting value is divided with the standard deviation by sample size.

The probability that the random sample of 100 male students has a mean GPA greater than 3.42 is obtained below:

The required probability is,

P(X>3.42)=P(z>-1.6)

= 1- P(Z≤-1.6)

From the “standard normal table”, the area to the left of Z=-1.6 is 0.0548.

P(X>3.42)= 1- P(Z≤-1.6)

=1-0.0548

=0.9452

The probability that the random sample of 100 male students has a mean GPA greater than 3.42 is 0.9452.

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The true statements about the polynomial function graphed are:

Its leading coefficient is positive.

It has an odd degree.

None of the zeroes have even multiplicity.

From the given options, the true statements about the polynomial function graphed are:

Its leading coefficient is positive.

It has an odd degree.

None of the zeroes have even multiplicity.

Let's analyze each statement:

Its leading coefficient is positive:

The leading coefficient of a polynomial is the coefficient of the term with the highest degree.

From the graph, if the polynomial is going upwards on the right side, it indicates that the leading coefficient is positive.

It has an odd degree: The degree of a polynomial is the highest power of the variable in the polynomial expression.

If the graph has an odd number of "turns" or "bumps," it indicates that the polynomial has an odd degree.

None of the zeroes have even multiplicity:

The multiplicity of a zero refers to the number of times it appears as a factor in the polynomial.

In the given graph, if there are no repeated x-intercepts or no points where the graph touches and stays on the x-axis, it implies that none of the zeroes have even multiplicity.

The other statements (its leading coefficient is negative, it has an even degree, it has exactly two real zeroes, it has exactly three real zeroes, and none of the zeroes have odd multiplicity) cannot be determined based solely on the information given.

Therefore, the true statements about the polynomial function graphed are:

Its leading coefficient is positive.

It has an odd degree.

None of the zeroes have even multiplicity.

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Answer:

the question isnt clear

Step-by-step explanation:

Answer:

a) 0.16

b) 100.00

c) 0.001

d) 16.00

Using the formula of volume of a sphere and hemisphere, the volume of the figures are given as;

1. 2144.57 m³

2. 696.6 m³

3. 20569.1m³

4. 2637ft³

5. 56.5km³

6. 6381.79 in³

The volume of a sphere is given as 4/3πr³

Where π is a constant whose value is equal to 3.14 approximately. “r” is the radius of the hemisphere.

1. The volume of the sphere is;

v = 4/3 * 3.14 * 8³ = 2144.57m³

2. The volume of the sphere is;

v = 4/3 * 3.14 * (11/2)³ = 696.6m³

3. The volume of the sphere is;

v = 4/3 * 3.14 * 17³ = 20569.1m³

4. The volume of the hemisphere is;

v = 2/3 * 3.14 * 10.8³ = 2637ft³

5. The volume of the hemisphere is;

v = 2/3 * 3.14 * 3³ = 56.5km³

6. The volume of the hemisphere is;

v = 2/3 * 3.14 * (29/2)³ = 6381.79in³

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The Vertex is : (-6, -30)

The X-intercepts are : Approximately (-10.89, 0) and (-1.11, 0)

The Y-intercept is : (0, 6)

The Axis of symmetry is : x = -6

The functions Domain: is All real numbers

The Range is : All real numbers greater than or equal to -30.

To sketch the graph of the quadratic function \(f(x) = x^2 + 12x + 6,\) we can start by identifying the vertex, x-intercepts, y-intercept, axis of symmetry, domain, and range.

To find the vertex, we can use the formula x = -b/2a, where a, b, and c are the coefficients of the quadratic equation in standard form\((ax^2 + bx + c).\)

In this case, a = 1, b = 12, and c = 6.

Applying the formula, we get x = -12/(2 \(\times\) 1) = -6.

To find the y-coordinate of the vertex, we substitute this x-value into the equation:\(f(-6) = (-6)^2 + 12(-6) + 6 = 36 - 72 + 6 = -30.\)

So, the vertex is (-6, -30).

To determine the x-intercepts, we set f(x) = 0 and solve for x. In this case, we need to solve the quadratic equation \(x^2 + 12x + 6 = 0.\)

Using factoring, completing the square, or the quadratic formula, we find that the solutions are not rational.

Let's approximate them using decimal values: x ≈ -10.89 and x ≈ -1.11. Therefore, the x-intercepts are approximately (-10.89, 0) and (-1.11, 0).

The y-intercept is obtained by substituting x = 0 into the equation: \(f(0) = 0^2 + 12(0) + 6 = 6.\)

Thus, the y-intercept is (0, 6).

The axis of symmetry is the vertical line that passes through the vertex. In this case, it is the line x = -6.

The domain of the function is all real numbers since there are no restrictions on the possible input values of x.

To determine the range, we can observe that the coefficient of the \(x^2\) term is positive (1), indicating that the parabola opens upward.

Therefore, the minimum point of the parabola occurs at the vertex, (-6, -30).

As a result, the range of the function is all real numbers greater than or equal to -30.

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