The system of equation that describes the relation between the total cost (Y) and the number of tickets purchased (X) in a single visit to the park is Y = 3X + 20 i.e, option (C)
Define System of Equation
A set of simultaneous equations, also known as a system of equations or an equation system, is a finite set of equations for which common solutions are sought.
Given,
Cost of theme park is = $20
Tickets for each ride and attraction are = $3 a piece
Number of tickets purchased = X
So, total cost of tickets is = 3 * X
Total cost of visit to the theme park is = Y
So, the equation we get
Y = 3X + 20
Hence, the system of equation that describes the relation between the total cost (Y) and the number of tickets purchased (X) in a single visit to the park is Y = 3X + 20 i.e, option (C).
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How many four-letter words can be formed by using the letters in facetious? There are nine letters
available, and each one can be used at most once per word.
Answer:
Step-by-step explanation:
To find the number of four-letter words that can be formed using the letters in facetious, you can use the combination formula:
nCr = n! / (r! (n - r)!)
In this case, n is the total number of letters available (9) and r is the number of letters per word (4). Therefore, the number of four-letter words that can be formed is:
nCr = 9! / (4! (9 - 4)!) = 9! / (4! 5!) = (9 x 8 x 7 x 6) / (4 x 3 x 2 x 1) = 126
Therefore, there are 126 four-letter words that can be formed using the letters in facetious.
A 6 -sided die with the numbers 1 to 6 on its faces is rolled and a ticket is drawn from a bag of 7 tickets labelled 1 to 7 . How many different ways can you roll a 1 on the die and draw a 7 from the bag of tickets?
The no. ways roll a 1 on the die and draw a 7 from the bag of tickets is 1 And the probaility is [tex]\frac{1}{42}[/tex]
What is Probability?Probability is the ratio of favorable outcomes to all other potential outcomes of an event. The symbol x can be used to signify how many positive findings there are in an experiment with 'n' results. The following formula can be used to determine the likelihood of an event:
Probability (event) equals a favorable result/the total of outcomes divided by n.
The no. ways roll a 1 on the die and draw a 7 from the bag of tickets is 1
And the probaility is -
[tex]\frac{1}{6} X \frac{1}{7}[/tex]
[tex]= \frac{1}{42}[/tex]
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It is given § = {x: 1 ≤ x ≤ 10, x is an integer); P= {odd numbers); Q= {prime numbers) and R= {1,2,3,4,5} List the elements of each of the following sets. (a) (PNQ)UR (b) (RNP)'UQ (c) Q'N(PUR) (d) (PUQUR)' (POR)
The elements of the required sets would be:
(a) (P∩Q)∪R = {1, 2, 3, 4, 5, 7}
(b) (R∩P)'∪R = {2, 3, 4, 5, 6, 7, 8, 9, 10}
(c) Q'∩(P∪R) = {2, 3, 5, 7}
(d) (P∪Q∪R)'∩(P∩R) = ∅
What are sets?A set, denoted by the curly brackets , is a grouping of items, numbers, elements or objects.
A set of numbers, for instance, is 1, 2, 3, 4.
Solution:
P' = {2, 4, 6, 8, 10}
Q' = {1, 4, 6, 8, 9, 10}
R' = {6, 7, 8, 9, 10}
P∩Q = {3, 5, 7}
R'∪P' = {2, 4, 6, 7, 8, 9, 10}
P∪R = {1, 2, 3, 4, 5, 7, 9}
P∩R = {1, 3, 5}
P∪Q∪R = {1, 2, 3, 4, 5, 7, 9}
P'∩Q'∩R' = S - P∪Q∪R
= {6, 8, 10}
Now we can find the elements of the required sets:
(a) (P∩Q)∪R = {1, 2, 3, 4, 5, 7}
(b) (R∩P)'∪R = {2, 3, 4, 5, 6, 7, 8, 9, 10}
(c) Q'∩(P∪R) = {2, 3, 5, 7}
(d) (P∪Q∪R)'∩(P∩R) = ∅
Hence, the elements of the required sets would be
(a) (P∩Q)∪R = {1, 2, 3, 4, 5, 7}
(b) (R∩P)'∪R = {2, 3, 4, 5, 6, 7, 8, 9, 10}
(c) Q'∩(P∪R) = {2, 3, 5, 7}
(d) (P∪Q∪R)'∩(P∩R) = ∅
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A ramp goes from a doorway of a building to the ground. The end of the ramp connected to the doorway is 1 foot above the ground. The horizontal distance from the bottom of the ramp to the building is 10 feet. What is the angle of elevation of the ramp to the nearest degree?
The angle of elevation of the ramp to the nearest degree will be 5.71°.
What is trigonometry?The branch of mathematics that sets up a relationship between the sides and the angles of the right-angle triangle is termed trigonometry. The trigonometric functions, also known as a circular, angle, or goniometric functions in mathematics, are real functions that link the angle of a right-angled triangle to the ratios of its two side lengths.
Given that a ramp goes from a doorway of a building to the ground. The end of the ramp connected to the doorway is 1 foot above the ground. The horizontal distance from the bottom of the ramp to the building is 10 feet.
The angle of elevation will be calculated as,
tanθ = ( 1 / 10)
θ = tan⁻¹(1/10)
θ = 5.7°
Therefore, the angle of elevation of the ramp to the nearest degree will be 5.71°.
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Alex can earn $15 an hour mowing neighborhood lawns on weekends. If Alex decides to spend an hour mowing rather than watching a football game, his opportunity cost of mowinf lawns is:
a. The $15 he earns
b. The enjoyment he would have received from watching the football game during that time.
c. The $15 he earns minus the enjoyment he would have received from watching the football game during that time.
d. The $15 he earns plus the enjoyment he would have received from watching the football game during that time.
e. Nothing because he would have received $15 worth of enjoyment from watching the football game during that time
The opportunity cost of mowing the lawn is The $15 he earns minus the enjoyment he would have received from watching the football game during that time.
Opportunity costs are the possible advantages that a person, investor, or company forgoes while deciding between two options. Opportunity costs are by definition invisible, making it simple to ignore them. Making smarter decisions requires an understanding of the possible opportunities lost when a company or person selects one investment over another.
Opportunity Cost =FO−CO where:
FO=Return on best-forgone option
CO=Return on the chosen option
The formula for calculating an opportunity cost is simply the difference between the expected returns of each option.
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Value Rent-A-Car rents a luxury car at a daily rate of $40.49 plus 5 cents per mile. A business person is allotted $120 for car rental each day. How many miles can the business person
travel on the $120?
The business person can travel miles.
(Type an integer or a decimal.)
When renting a car for $40.49 with a fixed mileage charge of $0.05, a businessperson can go 1590.2 miles.
What is expression?An expression, often known as a mathematical expression, is a finite collection of symbols that are well-formed in accordance with context-dependent principles. Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. An expression in mathematics is made up of numbers, variables, and functions (such as addition, subtraction, multiplication or division etc.) You can think of expressions as being comparable to phrases.
Here,
The cost of car rent=$40.49
Cost for per mile=$0.05
Let him travel x miles,
40.49+0.05x=120
0.05x=120-40.49
0.05x=79.51
x=79.51/0.05
x=1590.2 miles
The business person can travel 1590.2 miles when the rent of car cost $40.49 fixed and $0.05 for every mile travelled.
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How deep is a valley if it takes a rock 5.2 seconds to strike the bottom and it is traveling at 25 m/s?
Answer:
[tex]\huge\boxed{\sf h = 130\ m}[/tex]
Step-by-step explanation:
Given data:Time = t = 5.2 s
Velocity = v = 25 m/s
Required:Height = h = ?
Formula:h = vt
Solution:h = 25(5.2)
h = 130 m[tex]\rule[225]{225}{2}[/tex]
Answer:
The valley is 130 m deep.
Step-by-step explanation:
Formula we use,
→ Height = Time × Speed
Now the height will be,
→ Time × Speed
→ 5.2 × 25
→ 130 metres
Thus, valley is 130 m deep.
I need help with this Question
Step-by-step explanation:
Just Substitute in place of X
Use properties to rewrite the given equation. Which equations have the same solution as 2.3p – 10.1 = 6.5p – 4 – 0.01p? Select two options. 2.3p – 10.1 = 6.4p – 4 2.3p – 10.1 = 6.49p – 4 230p – 1010 = 650p – 400 – p 23p – 101 = 65p – 40 – p 2.3p – 14.1 = 6.4p – 4
The equation which have the same solution as 2.3p – 10.1 = 6.5p – 4 – 0.01p is 230p – 1010 = 650p – 400 –p
What is an expression?Expression in mathematics is combination of variables with the use of operations and given rules. It can be in the form of equation, numbers etc.
Given that an expression;
2.3p – 10.1 = 6.5p – 4 – 0.01p
Firstly we will simplify the above expression by removing decimals.
For that,
(23 / 10)p – (101 / 10) = (65 / 10)p – 4 – (1 / 100)p
Now we will take LCM,
{ (23 - 101) / (10) }p = {650p - 400 - p} / 100
230p – 1010 = 650p – 400 –p
Therefore The equation which have the same solution as 2.3p – 10.1 = 6.5p – 4 – 0.01p is 230p – 1010 = 650p – 400 –p.
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What is volume of a cone that has a radius of 6cm and height of 18c
Answer:
136
Step-by-step explanation:
The formula of the volume of a cone is v=b*h.First you need to find the diameter, simple, 6*2=12, you get the 12 because the diameter is always twice as large as the radius. Next you multiply 18*12 which gives you 136!
Which statement about 199° is correct?
A. sin 199°> 0
B. tan 199° < 0
C. cos 199° < 0
The cosine of the angle 199° will be less than zero that is cos 199° < 0. Then the correct option is C.
What is trigonometry?Trigonometric functions examine the interaction between the dimensions and angles of a triangular form.
In the first quadrat, the angle is from 0° to 90°.In the second quadrat, the angle is from 90° to 180°.In the third quadrat, the angle is from 180° to 270°.In the fourth quadrat, the angle is from 270° to 360°.The angle of 199° lies in the third quadrant.
In the third quadrant, the sine and cosine of the angle are negative and the tangent of an angle is positive.
The cosine of the point 199° will be under zero that is cos 199° < 0. Then, at that point, the right choice is C.
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Kim ran a 26-mile marathon.
She ran 1/7 of the marathon during
the first hour. How many miles did
Kim run during the first hour?
Answer:
3.714
Step-by-step explanation:
26 x ⅐ = 26 / 7
= 3.714 or [tex] 3 \frac{5}{7} [/tex]
Let D be a region bounded by a simple closed path C in the xy-plane. The coordinates of the centroid x, y of D are x = 1 2A x2 dy C y = ? 1 2A y2 dx C where A is the area of D. Find the centroid of a quarter-circular region of radius a.
If D be a region bounded by a simple closed path C in the xy-plane, then the centroid of the quarter circle is (4a/3π , 4a/3π) .
In the question ,
it is given that D is the region bounded by a simple closed path C in the xy-plane .
the radius of the circle is = "a" ,
let the equation of the circle be x² + y² = a² ,
So , the area of the quarter circle is (A) = (1/4)*πa²
The coordinate of the centroid x will be :
x = [tex]\frac{1}{2A} \int\limits x^{2} dy[/tex]
x = [tex]\frac{1}{2(\frac{\pi a^{2} }{4})} \int\limits^a_0 {a^{2} -y^{2} } \, dy[/tex]
Simplifying further ,
we get ,
x = 2/πa² [{a²(a) - a³/3} - 0 ]
x = 2/πa² [a³ - a³/3 ]
x = 4a/3π
The coordinate of the centroid y will be :
y = [tex]\frac{1}{2A} \int\limits y^{2} dx[/tex]
y = [tex]\frac{1}{2(\frac{\pi a^{2} }{4})} \int\limits^a_0 {a^{2} -x^{2} } \, dx[/tex]
Simplifying further ,
we get ,
y = 2/πa² [{a²(a) - a³/3} - 0 ]
y = 2/πa² [a³ - a³/3 ]
y = 4a/3π
Therefore , the coordinates of the centroid is (4a/3π , 4a/3π) .
The given question is incomplete , the complete question is
Let D be a region bounded by a simple closed path C in the xy-plane. The coordinates of the centroid x, y of D are x = [tex]\frac{1}{2A} \int\limits x^{2} dy[/tex] , y = [tex]\frac{1}{2A} \int\limits y^{2} dx[/tex] ?
Find the centroid of a quarter-circular region of radius a.
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Use the slope formula to find the slope of the line through the points (−10,2) and (−4,−4).
The slope of the line passing through the points (10) 2, and (14), is -9/-13.
What is slope?A line's steepness and direction are measured by the line's slope.
Without actually using a compass, determining the slope of lines in a coordinate plane can assist in forecasting whether the lines are parallel, perpendicular, or none at all
Any two different points on a line can be used to calculate the slope of any line.
A line's slope is determine by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively.
Two locations located on a straight line can be used to determine a line's slope. We can use the slope of line formula if we know the two spots' coordinates. These two points' coordinates should be-
P1 = (x1, y1) and P2 = (x2, y2)
Hence, The slope of the line passing through the points (10) 2, and (14), is -9/-13.
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how do you solve 5/13y+25=0
Answer:
y = -100/13
Step-by-step explanation:
To solve this equation, we can first get all the terms containing the variable y on one side of the equation and all the constant terms on the other side. We can do this by subtracting 25 from both sides of the equation:
5/13y + 25 - 25 = 0 - 25
This gives us:
5/13y = -25
Next, we can divide both sides of the equation by 5/13 to get rid of the fraction:
(5/13y) / (5/13) = (-25) / (5/13)
This simplifies to:
y = -100/13
Therefore, the solution to the equation is y = -100/13.
what do 17, 19, 46 and 55 have in common?
Answer:
They are all prime numbers
Explanation:
17, 19, 46, and 55 are all prime numbers. A prime number is a whole number greater than 1 that is only divisible by 1 and itself. Since 17, 19, 46, and 55 are all prime numbers, they have no other factors besides 1 and themselves, which means they cannot be divided evenly by any other number.
A park has two sprinklers that are used to fill a fountain. One sprinkler can fill the
fountain in 3 h, whereas the second sprinkler can fill the fountain in 6 h. How long will
it take to fill the fountain with both sprinklers operating?
It takes 2 hrs to fill the fountain with both sprinklers operating
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Given,
A park has two sprinklers that are used to fill a fountain
One sprinkler can fill the fountain in 3 h
second sprinkler can fill the fountain in 6 h
We need to find the time required to fill the fountain by two sprinklers.
Let t = time required with both sprinklers working
t/3+t/6=1
2t+t/6=1
3t/6=1
Apply cross multiplication
3t=6
Divide both sides by 3
t=2
Hence, it takes 2 hrs to fill the fountain with both sprinklers operating
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Write the equation of the circle with center (2, -3) and a radius of 4.
es ))
A)
B)
9)
D)
(x + 2)² + (y - 3)² = 4
(x - 2)² + (y + 3)² = 4
(x + 2)² + (y - 3)² = 16
(x - 2)² + (y + 3)² = 16
[tex]\textit{equation of a circle}\\\\ (x- h)^2+(y- k)^2= r^2 \hspace{5em}\stackrel{center}{(\underset{2}{h}~~,~~\underset{-3}{k})}\qquad \stackrel{radius}{\underset{4}{r}} \\\\[-0.35em] ~\dotfill\\\\ ( ~~ x - 2 ~~ )^2 ~~ + ~~ ( ~~ y-(-3) ~~ )^2~~ = ~~4^2\implies {\large \begin{array}{llll} (x-2)^2+(y+3)^2=16 \end{array}}[/tex]
6. What is the reflection image of (5, –3) across the line y = –x? (–3, 5) (–3, –5) (3, –5) (3, 5)
Check the picture below.
STATISTICS - please please help ASAP!! This is for my final exam! I will give brainliest to the correct answer!
Below is a list of wait times at the Disney World ride “It’s a Small World.” You will use this data to fill in a table.
5 5 5 5 5 10 10 10 10 15
15 15 15 15 15 15 20 20 20 20
20 20 20 20 25 25 25 25 25
25 30 30 30 30 30 35 35 35 35
40 40 40 45 45 50 60 60 60 75
Fill in the Frequency table below in the Frequency column and the Relative Frequency column (in percents, example 12%, not a decimal.)
Fill in the blanks in the Frequency column and the Relative Frequency column.
(columns pictured)
Step-by-step explanation: To fill in the table, we will need to first count the number of times each wait time appears in the given data. We can then use these counts to fill in the Frequency column of the table. We will also need to calculate the relative frequency of each wait time, which is the number of times it appears in the data divided by the total number of data points. We can then use these relative frequencies to fill in the Relative Frequency column of the table, expressed as a percentage.
Here is the completed table:
Wait Time (minutes) Frequency Relative Frequency (%)
5 5 11.36
10 4 9.09
15 7 15.91
20 6 13.64
25 7 15.91
30 4 9.09
35 5 11.36
40 3 6.82
45 2 4.55
50 1 2.27
60 2 4.55
75 1 2.27
Note that the total number of data points is 44, so each relative frequency is calculated as the corresponding frequency divided by 44.
I hope this helps! Let me know if you have any other questions.
There are 11 freshmen and 6 sophomores in a class. If three students are selected at random, find the probability that two are freshmen and one is a sophomore. (See Example 6. Round your answer to three decimal places.)
Jonathan has a points card for a movie theater. He receives 25 rewards points just for signing up. He earns 13.5 points for each visit to the movie theater. He needs at least 135 points for a free movie ticket. What is the least number of visits he needs to make in order to earn a free movie ticket?
Answer:
9
Step-by-step explanation:
You want to know the least number of visits Jonathan must make to a movie theater to have at least 135 points if he has 25 points and earns 13.5 for each visit.
PointsAfter x visits to the theater, Jonathan will have earned 13.5x points in addition to the signing bonus. His total will be ...
13.5x +25
VisitsJonathan wants that total to be at least 135:
13.5x +25 ≥ 135
13.5x ≥ 110 . . . . . . . subtract 25
x ≥ 110/13.5 ≈ 8.148
The smallest integer greater than 8.148 is 9.
Jonathan needs to make at least 9 visits to earn a free movie ticket.
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Solve 15x - 10y = -30 and 5x - 9y = 7 using elimination. Show Steps. Put answer in coordination form (x,y)
An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
The coordinates are (0, 3) or (34/5, 3)
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
We have,
15x - 10y = -30 _____(1)
5x - 9y = 7 ______(2)
Multiply 3 on (2)
15x - 27y = 21 _____(3)
Using the elimination method we get,
From (1) and (3) we get,
15x - 10y = -30
15x - 27y = 21
(-) (+) (-)
17y = 51
This means,
y = 51/17
y = 3
Now,
Put y = 3 in (1) we get,
15x - 10y = -30
15x- 10 x 3 = -30
15x - 30 = -30
15x = 0
x = 0
Put y = 3 in (2) we get,
5x - 9y = 7
5x - 9 x 3 = 7
5x - 27 = 7
5x = 7 + 27
5x = 34
x = 34/5
Thus,
The coordinates are (0, 3) or (34/5, 3)
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The area of a circle is 0.2826 square inches. What is the circle's diameter?
Use 3.14 for .
Submit
inches
Answer:
0.6 inches
Step-by-step explanation:
The equation to find the area of a circle is:
[tex]{a} = \pi {r}^{2} [/tex]
however the problem requires you replace π with 3.14.
Using inverse operations you can find the variable r.
Step 1:
Plug in variables.
[tex]0.2826 = 3.14{r}^{2} [/tex]
Step 2:
Solve for r.
[tex]0.2826 \div 3.14 = 3.14 \div 3.14 \times {r}^{2} \\ \sqrt{0.09} = \sqrt{ {r}^{2} } \\ r = 0.3[/tex]
Step 3:
Find diameter from radius.
[tex]0.3 \times 2 = 0.6[/tex]
The diameter of the circle is 0.6 inches.
A rectangular pool has an area of 30 sq. ft. One side is 1 more than the other side. How long are the sides?
In 1992, there were 285 alligators in Orange County, Florida. The number of alligators increased by 75% per year after 1992. How many alligators were there in Orange County, Florida in 2001?
The number of alligators was there in Orange country, Florida in 2001 is equal to 43872.
What is the Percentage?The Latin term "per centum," which signifies "by the hundredth," was the source of the English word "percentage." Segments with a denominator of 100 are considered percentages. In other words, it is a relationship where the worth of the entire is always considered 100.
As per the given information provided in the question,
Total number of alligators 1992 = 285
Percent increase of alligators every year = 75%
Total number of years from 1992 to 2001,
2001 - 1992 = 9 years
The population of alligators in 2001,
= 285 × (175/100)⁹
= 285 × (7/4)⁹
= 43871.98 or,
= 43872 alligators.
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what is the slope for (1, -5) and (4, 1)?
Diego has 48 chocolate chip cookies, 64 vanilla cookies and 100raisin cookies for a bake sale. He wants to make bags that have all three cookie flavors and the same number of each flavor per bag.
A. How many bags can he make without having any cookies left over?
B. Find another solution to this problem
Answer:
Step-by-step explanation:
The number of bags he can make without having any cookies left over is 4 bags.
Number of chocolate chips = 48
Number of vanilla cookies = 64
Number of raisin cookies = 100
a service station on the interstate changes $2.29 per gallon of
gasoline and $1.89 per quart for oil. What would be a recourable
amount to pay for 10 gallons of gasoline and 2 quarts of oil ?
A) $20
B) $23
C) $25
D) $27
Answer:
D) $27
Step-by-step explanation:
You want an estimate of a reasonable amount to pay for 10 gallons of gas at $229 per gallon, and 2 quarts of oil at $1.89 per quart.
EstimateFor estimating purposes, we like to round numbers to 1 or 2 significant figures.
The cost of 10 gallons of gas is about 10 × $2.30 = $23.
The coast of 2 quarts of oil is about 2 × $2 = $4.
So, the total cost of the gas and oil is about $23 +4 = $27.
You expect the total to be near $27.
__
Additional comment
Part of estimating is estimating the error in your estimate. Here the error is $0.01 per gallon of gas, or $0.10 for 10 gallons. The error is $0.11 per quart of oil, so $0.22 for 2 quarts. The final estimate of $27 is $0.10 +0.22 = $0.32 too high. $27 is different from the next answer choice by $2, so is still the best answer choice.
Select all of the following equation(s) that are quadratic in form. x4 – 6x2 – 27 = 0 3x4 = 2x 2(x + 5)4 + 2x2 + 5 = 0 6(2x + 4)2 = (2x + 4) + 2 6x4 = -x2 + 5 8x4 + 2x2 – 4x = 0
The equation that is quadratic in all the equations is 6(2x+4)²=(2x+4)+2
How to Identify a quadratic equation?A quadratic equations defined as any equation that can be rearranged in standard form as ax²+bx+c=0 or -b±[tex]\frac{\sqrt{} b^{2}-4ac }{2a}[/tex]
From the list of equations the one that carries the standard form for a quadratic equation is
6(2x+4)²=(2x+4+)+2
Expand the brackets to have
6[(2x+4)(2x+4)=(2x+4)+2
6[4x²+8x+8x+16]=(2x+4)+2
Collecting like terms and opening the brackets further;
6[4x²+16x+16]=2x+4+2
=24x²+96x+96=2x+6
Collecting like terms we have
24x²+96x-2x+96-6=0
⇒24x²94x+90=0
In conclusion, the equation carries 2 as its highest power therefore, it is a quadratic equation.
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