Mathematics College

Simple Math Range and domain help Part 2

Answers

Answer 1

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

Here we go ~

Domain : All values of x, for which function is defined.

i.e [tex]\boxed{\sf 0\leqslant x\leqslant 12} [/tex]

Range : All possible values of y, that can be obtained by putting value of x in the equation of function

i.e [tex]\boxed{\sf 0\leqslant y\leqslant 900} [/tex]

Related Questions

8. The number of steps needed to get from one floor to the next in a hotel staircase is 14. The ground level is floor 0.
a. Complete the table.
n(floor number)
s(total steps to reach floor)
1
14
2 3 4 5

Answers

Step-by-step explanation:

0 steps to reach floor 0.

floor 0 to floor 1 = floor 0 + 14 = 0 + 14 = 14

floor 1 to floor 2 = floor 1 + 14 = 14 + 14 = 28

floor 2 to floor 3 = floor 2 + 14 = 28 + 14 = 42

floor 3 to floor 4 = floor 3 + 14 = 42 + 14 = 56

floor 4 to floor 5 = floor 4 + 14 = 56 + 14 = 70

when we look at the calculation for the stairs to floor 1, then we see

floor 1 = floor 0 + 14 = 0 + 14 = 14

and for floor 2

floor 2 = floor 1 + 14 = floor 0 + 14 + 14 = 0 + 14 + 14 = 28

and for floor 3

floor 3 = floor 2 + 14 = floor 0 + 14 + 14 + 14 = 42

and so on.

we see

floor n = s(n) = s(0) + 14×n = 0 + 14×n = 14n

s(n) = 14n

rewrite each expression without using absolute value notation lx-1| if x>1

Answers

we can rewrite:

|x - 1| if x >1

(x - 1) with x > 1.

How to rewrite the expression?

Remember how the absolute value function works:

|x| = x if x ≥ 0.|x| = x if x < 0.

In this case, we have the function:

|x - 1| if x >1

Then the minimum value (not included) that this can take is:

|1 - 1| = 0

So it is only 0 or positive, then we can use the first bullet point only, then we can rewrite:

|x - 1| if x >1

(x - 1) with x > 1.

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Are the red paths in the picture below perpendicular?
A. Yes
B. No

Answers

Answer:

Yes

Step-by-step explanation:

Perpendicular lines form 90-degree angles

Yes it is perpendicular because it is a 90 degree angle

3
25% of the fish in a pond are trout, of the fish are goldfish and
10
the rest of the fish are perch.
Write the ratio of trout to goldfish to perch in this pond in its
simplest form.
< Back to task
Watch video

Answers

The ratio of Trout to Goldfish to Perch in the pond by using ratio and proportion theorem in its simplest form is 5:2:13

As per the question statement, we are supposed to find out the ratio of Trout to Goldfish to Perch in the given pond in its simplest form.

It is given that 25% of the fish in a pond are Trout, 10% are Goldfish and the rest 65% are Perch in the given pond.

Let's suppose there are 100 fishes in the pond so

Number of Trout = 25% of 100 = 25

Number of Goldfish = 10% of 100 = 10

Number of Perch = 65% of 100 = 65

Using ratio and proportion theorem,

Trout : Goldfish : Perch = 25:10:65

Trout : Goldfish : Perch = 5 : 2 : 13

Ratio and Proportion: An ordered pair of numbers a and b, represented as a / b, is a ratio if b is not equal to 0. A proportion is any equation that sets or uses two ratios at the same value.

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Look at this triangle.
B
8 cm
A
22 cm
Work out length AB.

Answers

The length of AB of the given triangle ABC is 23.41cm.

What are triangles?A polygon with three edges and three vertices is called a triangle. It is one of the fundamental geometric shapes. The symbol for a triangle with the vertices A, B, and C is △ABC. In Euclidean geometry, any three points that are not collinear produce a distinct triangle and a distinct plane.

So, Pythagoras's Theorem is used: a²+b² = c²

Where the hypotenuse is c and the sides of the triangle are a and b.

If we swap the values,

B= 8 cmA= 22 cm

Then,

22²+8² = c²484 + 64= c²√548 = cC= 23.41

Therefore, the length of AB of the given triangle ABC is 23.41cm.

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What was the vertical distance, d, of his jump, rounded to the nearest tenth?

Answers

The vertical distance of the jump is 4.8 feet.

What was the vertical distance, d, of his jump, rounded to the nearest tenth?

We know that the equation that relates the vertical distance of the jump and the time is:

t = √d/2

In this case, we know that the time is t = 1.09 seconds, replacing that in the equation we get:

1.09 = √d/2

Now we can solve that equation for d.

1.09*2 = √d

Now we apply an exponent of 2 in both sides to remove the square root:

2.18^2 = d = 4.8 ft

The vertical distance of the jump is 4.8 feet.

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The engineering department of a large company has 25 members. The members must select a chair person, a vice chairperson, a secretary, and a 4-person advisory committee. Determine the number of different ways this can be done.

Answers

Using permutations and combinations, The number of different ways this can be done is 316250 ways.

What exactly are combinations and permutations?

A permutation is an orderly arrangement of the items or numbers. Combinations are a means to choose items or numbers from a collection or set of items without regard for the items' chronological sequence.

We will solve it using permutations and combinations

a. The number is ²⁵P₄= 25! / (25 - 4)!

25! / 21! = 25 × 24 × 23 × 22 = 303600 ways.

b. The number is ²⁵C₄= 25! / 4! . (25 - 4)!

= 25! / 4! . 21! = 25 × 24 × 23 × 22 / 4 × 3 × 2

= 12650 ways

Total number of ways to select persons are =

303600 + 12650

= 316250

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Serenity's car used 1/50 of a gallon to travel 5/8 of a mile. At what rate does the car use gas, in miles per gallon? On the double number line below, fill in the given values, then use multiplication to find the missing value.

Answers

Using proportions, it is found that the car uses gas at a rate of 31.25 miles per gallon.

What is a proportion?

A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct(when both increase or both decrease) or inverse proportional(when one increases and the other decreases, or vice versa), can be built to find the desired measures in the problem, or equations to find these measures.

The gas consumption of the car is given by the proportion of number of miles divided by the number of gallons, hence:

(5/8)/(1/50).

To divide two fractions, we multiply the numerator by the inverse of the denominator, hence:

5/8 x 50 = 31.25.

The car uses gas at a rate of 31.25 miles per gallon.

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Paisley is deciding between two parking garages. Garage A charges an initial fee of $5 to park plus $3 per hour. Garage B charges an initial fee of $11 to park plus $2 per hour. Let A A represent the amount Garage A would charge if Paisley parks for t t hours, and let B B represent the amount Garage B would charge if Paisley parks for t t hours. Write an equation for each situation, in terms of t , t, and determine the interval of hours parked, t , t, for which Garage A is cheaper than Garage B.

Answers

Considering the definition of an inequality, the interval of hours parked for which Garage A is cheaper than Garage B is 6 hours.

Definition of inequality

An inequality is the existing inequality between two algebraic expressions, connected through the signs:

greater than >.less than <.less than or equal to ≤.greater than or equal to ≥.

An inequality contains one or more unknown values called unknowns, in addition to certain known data.

Solving an inequality consists of finding all the values of the unknown for which the inequality relation holds.

Interval of hours parked for which Garage A is cheaper than Garage B

In this case, you know that:

Garage A charges an initial fee of $5 to park plus $3 per hour. Garage B charges an initial fee of $11 to park plus $2 per hour.

Being "t" the time parked, in hours. If you want to determinate the interval of hours parked for which Garage A is cheaper than Garage B, the inequality that expresses the previous relationship is

5 + 3t < 11 + 2t

Solving:

3t - 2t < 11 -5

t < 6

Finally, the interval of hours parked for which Garage A is cheaper than Garage B is 6 hours.

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5 boxes of books in the room . Each box has 36 books . How many books in all

Answers

just multiply 36 by 5 = 180

Find the formula for the nth term of the following sequence:

648, 108, 18, 3...

Include "n=" in your answer, and do not use any spaces.

Answers

The nth term of the sequence is Tn = 3888^n - 1

What is a geometric sequence?

A geometric sequence can be defined as a sequence in which each term is determined by multiplying the preceding term in the sequence by the same value.

The formula for the nth term of a geometric sequence is expressed as;

Tn = ar^n - 1

Where;

Tn is the nth terma is the first termr is the common ratio

From the given sequence, we have that;

a = 648

r = 6

Substitute into the formula

Tn = 648 × 6^n - 1

Tn = 3888^n - 1

Thus, the nth term of the sequence is Tn = 3888^n - 1

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Two of the dozen eggs in a carton are cracked. About what percent of the carton is cracked?

Answers

The most appropriate choice of percentage will be given by-

16.67 % of carton is cracked

What is Percentage?

Percentage is a ratio expressed as a percentage of 100.

Here,

Number of eggs cracked = 2

Total number of eggs = 12

Percentage of carton cracked = [tex]\frac{2}{12} * 100[/tex]

= 16.67 %

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Which is the graph of y ≤ 1 – 3x?

Answers

Step-by-step explanation:

To graph an equation using the slope and y-intercept, 1) Write the equation in the form y = mx + b to find the slope m and the y-intercept (0, b). 2) Next, plot the y-intercept. 3) From the y-intercept, move up or down and left or right, depending on whether the slope is positive or negative.

Evaluate each expression for the given values of the variables

-3[(w-6)^2+x]^2 ; w=5, x=6

Answers

The solution to the above question is -147

-3[(w-6) ^2+x] ^2 where the value of w = 5 and x amounts to 6

Using algebraic identity: (a-b) ^2 = (a^2 -2ab+b^2)

= -3 [(w^2 -2w*6 +6^2) + x] ^2

= -3 [(w^2 -12w+36) + x] ^2

now substitute the value of w = 5

= -3 [(5^2 -12*5+36) + x] ^2

= -3 [(25 -60+36) + x] ^2

= -3 [1+ x] ^2

Using algebraic identity: (a+ b) ^2 = a^2 +2ab + b^2

= -3 [1^2+2x*1+ x^2]

= -3 [1+2x+ x^2]

now substitute the value of x = 6

= -3 [1+2*6+ 6^2]

= -3 [1+12+ 36]

= -3 [49]

= -147

The above answer can be derived through direct substitution also. Both the methods will any way give the same answer.

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I NEED HELP. I NEED TO SOLVE THIS BUT I DONT KNOW HOW TO! I NEED TO TURN IT IN BEFORE THE 29TH!

Answers

Answer: 1: $27.92

Step-by-step explanation: Multiply the amount of goodie bags (8) by how much they cost individually ($3.49) and you should come out with the answer $27.92.

Answer: 2 : $37.5

Step-by-step explanation: This would be considered not using long division but this should be the only practical answer. Using long division you would come up with 37 with a remainder of 2, which doesn't seem to be correct.

Answer: 3 : $177.92

Step-by-step explanation: Adding the cost of both the goodie bags and the 4 hours worth of the bounce house the total should have came out to be, $177.92

PLEASE HELP MEEE.....

Answers

im not sure sry man....... delete this answer bc im not sure how to

The midpoint of AB is M(-2, -6). If the coordinates of A are (1,−4), what are the coordinates of B?

Answers

Applying the midpoint formula, the coordinates of B are: (-5, -8).

How to Apply the Midpoint Formula?

The midpoint formula is:

M(x, y) = [(x1 + x2)/2, (y1 + y2)/2].

Given the following:

M(x, y) = (-2, -6)

A(x1, y1) = (1,−4)

B(x2, y2) = (?, ?)

Plug in the values

M(-2, -6) = [(1 + x2)/2, (-4 + y2)/2]

Isolate each coordinate

-2 = (1 + x2)/2

(-2)(2) = 1 + x2

-4 = 1 + x2

-4 - 1 = x2

-5 = x2

x2 = -5

-6 = (-4 + y2)/2

(-6)(2) = -4 + y2

-12 = -4 + y2

-12 + 4 = y2

-8 = y2

y2 = -8

Therefore, applying the midpoint formula, the coordinates of B are: (-5, -8).

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You are shopping for a new car. The dealer is offering a special deal whereby you can finance the car for 5 years at 0% interest. You can afford monthly payments of $225 with an absolute deviation of no more than $35. Write an absolute value inequality that represents the range of monthly car payments that you can afford. Use the absolute value button and use the variable x.

Answers

The absolute value inequality that represents the range of monthly car payments that you can afford is 52 < | x | ≤ 60.

What is absolute value inequality?

An absolute value inequality is an inequality that has an absolute value sign with a variable inside.

Example: | x + 2 | > 4

We have,

Financing a car for 5 years.

Monthly payment = $225

Since 5 years = 5 x 12 months = 60 months.

The cost of the car:

= 60 x $225

= $13500

Absolute deviation = $35

This means monthly payments can be increased maximum up to $35.

So if the monthly payment is increased maximum we have the monthly payment as:

= $225 + $35

= $260

If $260 is the monthly payment then,

The number of months the car finance can be done is:

= $13500 / $260

= 51.9 months

The absolute value inequality for the range of months is:

52 < | x | ≤ 60

Where x is the number of months to finance the car.

Thus the absolute value inequality that represents the range of monthly car payments that you can afford is 52 < | x | ≤ 60.

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lee is traveling by train. he has 270 miles left to travel.after 2 hours,he has 180 miles remaining.the train travels at a constant rate for the entire trip.what is the speed of the train and the distance of the trip?

Answers

270-180= 90 the distance of the trip is 90 miles and the speed of the train is 45 miles per an hr

In item 16, how many bacteria will there
be after 5 splittings?
(1) 2
(2) 4
(3) 8
(4) 16
(5) 32

Answers

Answer: 32 i think

Step-by-step explanation:

assuming there was one original bacteria, then multiplying it by two, or splitting it in two five times means 32

5 is going to be your answer for this question. Have a great day my dude.

Wendell mailed four packages. Each weighed 1 and 3/8 pounds. What was the total weight of the four packages?

Answers

The total weight of 4 packets will be equal to 5 and 1 / 2 pounds.

We are given that:

The total number of packages = 4

Weight of each of the package is given as 1 and 3 / 8 pounds

Weight of 1 package = 1 and 3 / 8 pounds.

Weight of 1 package = 11 / 3 pounds

Now, we need to calculate the total weight of 4 packets.

We will do this my multiplying 4 with the weight of each packet.

So, we get that:

Total weight of 4 packets = 4 × 11 / 8 pounds.

Total weight of 4 packets = 11 / 2 pounds

Total weight of 4 packets = 5 and 1 / 2 pounds.

Therefore, the total weight of 4 packets will be equal to 5 and 1 / 2 pounds.

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Will give brainliest for a detailed solution to ALL PARTS to this probability problem! Thank you!
The time to failure of a typical household refrigerator has the following PDF:
f(t)=t/a 0≤t≤4 yr
a.) What is the value of a?
b.) What is the reliability of the refrigerator for the first year?
c.) What is the probability that a refrigerator will fail during the first month?

Answers

Using integrals and probabilities, it is found that:

a) The value of a is of a = 8.

b) The reliability of the refrigerator for the first year is of 93.75%.

c) There is a 0.0004 = 0.04% probability that a refrigerator will fail during the first month.

What is the distribution?

The distribution is given as follows:

f(t) = t/a, 0≤t≤4.

The cumulative distribution function(cdf) is of 1, hence:

[tex]\int_{0}^{4} f(t) dt = 1[/tex]

[tex]\int_{0}^{4} \frac{t}{a} dt = 1[/tex]

[tex]\left(\frac{t^2}{2a}\right)_{t = 0}^{t = 4} = 1[/tex]

Applying the Fundamental Theorem of Calculus:

8/a = 1

a = 8.

Hence:

The value of a is of a = 8.

The probability that the refrigerator lasts more than one year is:

[tex]P(t > 1) = \int_{1}^{4} \frac{t}{8} dt[/tex]

[tex]P(t > 1) = \left(\frac{t^2}{16}\right)_{t = 1}^{t = 4}[/tex]

P(t > 1) = 1 - 1/16

P(t > 1) = 15/16

P(t > 1) = 0.9375 = 93.75%.

The reliability of the refrigerator for the first year is of 93.75%.

For item c, the probability that a refrigerator will fail during the first month is:

[tex]P\left(t < \frac{1}{12}\right) = \int_{0}^{\frac{1}{12}} \frac{t}{8} dt[/tex]

[tex]P\left(t < \frac{1}{12}\right) = \left(\frac{t^2}{16}\right)_{t = 0}^{t = \frac{1}{12}}[/tex]

Hence:

P(t < 1/12) = 1/(144 x 16) = 0.0004.

There is a 0.0004 = 0.04% probability that a refrigerator will fail during the first month.

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Which ordered pair is a solution to the inequality 4x - 3y < 16?

Answers

The ordered pair (3, -1) that is a solution is the one which makes the inequality TRUE when the value of the ordered pairs are substitute into the inequality 4x - 3y < 16

What is a solution set to an inequality or an equation?

If the equation or inequality contains variable terms, then there might be some values of those variables for which that equation or inequality might be true. Such values are called solution to that equation or inequality. Set of such values is called solution set to the considered equation or inequality.

WE have been given an inequality as 4x - 3y < 16.

Here, we need to get the ordered pair solution to the system of linear equations.

Then Substitute x = 3 and y = -1 into 4x - 3y < 16

4(3) - 3(-1) < 16

12 + 3 < 16

15 < 16

(TRUE)

Therefore, the ordered pair, (3, -1) is the solution because it is the only given ordered pair which makes the inequality true.

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What are the coordinates of the point on the directed line segment from (2, -1) to (9, 6) that partitions the segment into a ratio of 5 to 2?

Answers

Answer:

Fill in the blanks to declare sum equal to a + b (int _ = a __b)Which of the following is not a valid variable name in python?What shape represents the start and end of a flowchart?Which of the following is not a valid variable name in python?An integer data type can hold decimal values.Which of the following is not a valid variable name in python?An integer data type can hold decimal values.Which of the following is not a valid variable name in python?Fill in the blanks to declare sum equal to a + b (int _ = a __b)Variables must be defined with a name and a data type before they

can be usedAn integer data type can hold decimal values.Which of the following is not a valid variable name in python?Fill in the blanks to declare sum equal to a + b (int _ = a __b)Variables must be defined with a name and a data type before th

PLEASE ANSWER ASAP!!!! FULL ANSWER!! NO BEGGING FOR BRAINLIEST!!

Bob can row 9 mph in still water. The total time to travel downstream and return upstream to the starting point is 6 hours. If the total distance downstream and back is 30 miles, determine the speed of the river (current speed).

Current Speed = __________

Answers

If the total time to travel downstream and return upstream to the starting point is 6 hours. If the total distance downstream and back is 30 miles, the speed of the river (current speed) is 6.

Current speed

Time = Distance/speed

Time taken to row upstream:

(30/2) /(9 - x)

15/(9-x)

Time taken to row downstream:

15/(9 + x)

Total time spent is 6 hours hence,

15/(9- x) + 15/(9 + x) = 6

Cross multiplying

15(9 + x) + 15(9 - x) = 6(9+ x)(9 - x)

= 135 + 15x + 135- 15x =6(81 -9x + 9x - x²)

=270 = 6(81 - x²)

270/6 = 81- x²

45 = 81- x²

x² = 81- 45

x²= 36

x =√36

x = 6

Therefore If the total time to travel downstream and return upstream to the starting point is 6 hours. If the total distance downstream and back is 30 miles, the speed of the river (current speed) is 6.

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An air traffic controller is tracking two planes.To start Plane A was at an altitude of 990 meters and plane B was at an altitude of 1476 meters.plane A is loosing altitude at 18 meters per second and plane b is loosing altitude at 27 meters per second.write an equation to show when the two planes would be at the same altitude

Answers

The equation representing when the two planes would be at the same altitude is 9x=486

In terms of mathematics, what is an equation?

Equation: A declaration that two expressions with variables or integers are equal. In essence, equations are questions, and attempts to systematically identify the solutions to these questions have been the driving forces behind the creation of mathematics.

From (a) we get that: Altitude of Plane A = 990-18x

Altitude of Plane B = 1476-27x

make 890 - 18x = 1476-27x

-18x+27 x = 1476-890

9x=486

X= 54

so pass 54 seconds will the two plane at the same altitude.

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You have a canteen that holds 32 fluid ounces and weighs 0.25 pounds when empty. Water weighs 0.065 pound per fluid ounce. You begin a hike with a full canteen of water. Write and simplify an expression for the weight of the canteen and water after you drink x fluid ounces.

Answers

The simplification of the expression for the weight of the canteen after drinking is 2.33 lbs

How to write the expression

The total weight can be gotten as:

weight of empty canteen + ( 32 - x ) of the water x weight of water

This would be represented by

total weight = 0.25 + 0.065 * (32-x)

We have to open up the expression

weight = 0.25 + 2.08 - 0.065x

When the weight is 0 we would have

0.25 + 2.08 - 0.065x0

= 2.33 lbs

Hence the simplification of the expression for the weight of the canteen after drinking is 2.33 lbs

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The junior varsity football
team scored 23 points in last Saturday’s
game. They scored a combination of 7-
point touchdowns and 3-point field goals.
How many touchdowns and how many
field goals did they score?

Answers

Answer:

2 touchdowns, 3 field goals

Step-by-step explanation:

The number of touchdowns cannot be more than 3, so it is relatively easy to find the solution by trial and error.

23 is not divisible by 3, so 0 touchdowns is not a solution

23 -7 = 16 is not divisible by 3, so 1 touchdown is not a solution

23 -14 = 9 is divisible by 3, so 2 touchdowns and 3 field goals is a solution

21 -21 = 2 is not divisible by 3, so there is only one solution.

Answer:

1 touchdown and 3 field goals

points B (-6, 0) and C(-1, -5) are translated to B' and C', respectively.
What are the coordinates of B' and C'?

Answers

Answer: The answer would be for "B" that it's 6 units to the left and 0 units down and for "C" It would 1 to the left and -5 units down!

Step-by-step explanation: I used a graph to help me determine these coordinates :D

1. f(x)=5x^2-80x+69

2. f(x)=-9x^2+81x+6

Answers

The roots of f(x)=5x^2-80x+69, f(x)=-9x^2+81x+6 is mathematically given as

[tex]x=\frac{40+\sqrt{1255}}{5}, \frac{40-\sqrt{1255}}{5}[/tex]x=9.07347, -0.07347

This is further explained below.

What are the roots of f(x)=5x^2-80x+69 f(x)=-9x^2+81x+6?

Generally, the equation for the function is mathematically given as

f(x)=5x^2-80x+69

Therefore

Set5 x^2-80 x+69 equal to 0 .

5 x^2-80 x+69=0

Solve for x.

Use the quadratic formula to find the solutions.

[tex]\frac{-b+\sqrt{b^2-4(a c)}}{2 a}[/tex]

Substitute the values a=5, b=-80, and c=69 into the quadratic formula and solve for x.

[tex]\frac{80 \pm \sqrt{(-80)^2-4 \cdot(5 \cdot 69)}}{2 \cdot 5}[/tex]

[tex]x=\frac{40 \pm \sqrt{1255}}{5}[/tex]

The final answer is the combination of both solutions.

[tex]x=\frac{40+\sqrt{1255}}{5}, \frac{40-\sqrt{1255}}{5}[/tex]

In conclusion, we implore the same format to solve for

f(x)=-9x^2+81x+6

Roots

x=9.07347, -0.07347