Answer:
red cubes = 99, plastic cubes = 462
Step-by-step explanation:
total number of cubes/total ratio
= 560/17
= 33 (approximately)
red cubes
= 33 × 3
= 99
plastic cubes
= 33 × 14
= 462
Though 462 + 99 equals 561 rather than 560, I had to approximate the values because if not, the result will be 461 which is a prime number.
17. Represent and Connect The expression
-120 + 13.4m represents a submarine that
began at a depth of 120 feet below sea level and
ascended at a rate of 13.4 feet per minute. What
was the depth of the submarine after 6 minutes?
Please help me
the function that models the percent of children taking antidepressants from 2004 to 2009 is f(x)=-0.086x+2.92, where x is the number of years after 2000.
a. find the inverse of this function. what do the outputs of the inverse function represent?
b. use the inverse function to find when the percentage is 2.3%.
The evaluation of the inverse of the function, f(x) = -0.086·x + 2.92 are;
a. The inverse of the function is f⁻¹(x) = -11.63·x + 33.95
B. The inverse function gives the number of year after 2000 when the percentage of children taking antidepressants is equal to x
b. The percentage of children taking antidepressant is 2.3% in 2007
What is the inverse of a function?The inverse of a function is a function that gives the input from the output such that it undoes the function's effect.
The function that indicates the percentage of children taking that take antidepressants from from the year 2004 to the year 2009 is presented as follows;
f(x) = -0.086·x + 2.92
x = The number of years after the year 2000
The inverse of the function can be obtained by making x the subject of the function formula as follows;
f(x) = -0.086·x + 2.92
f(x) - 2.92 = -0.086·x
x = (f(x) - 2.92)/(-0.086) ≈ -11.63·f(x) + 33.95
x ≈ -11.63·f(x) + 33.95
Which through plugging in f⁻¹(x) = x, and f(x) = x,
Indicates;
f⁻¹(x) = -11.63·x + 33.95
In the inverse function, the argument is the percentage, while the output is the number of years, f⁻¹(x)
When x = 2.3,
f⁻¹(2.3) = -11.63×2.3 + 33.95 ≈ 7.2
The inverse when the percentage is 2.3% is 7.2 years
a. The inverse function is f⁻¹(x) = -11.63·x + 33.95
The output of the inverse function represents the number of years since 2000 when the percentage of the children taking antidepressants is x. The correct option is option B
b. The year in which the number of children taking antidepressant equals 2.3% is 2,000 + 7 = 2007
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150 pupils in a sports centre are surveyed.
The pupils can only use the swimming pool, the gym and the tennis courts.
30 pupils use the swimming pool, the gym and the tennis courts.
43 pupils use the swimming pool and the gym.
40 pupils use the gym and the tennis courts.
49 pupils use the tennis courts and the swimming pool.
71 pupils use the swimming pool.
78 pupils use the gym.
92 pupils use the tennis courts.
Find the probability to select a pupil that uses the tennis courts only.
The probability that a pupil selected uses the tennis courts only is the fraction 11/50 or 0.22
What is probabilityThe probability of an event occurring is the ratio of the number of required outcome divided by the total number of possible outcomes.
From the question,
The pupils that uses only tennis courts = 92 - (30+19+10) { where 30 is the number of pupils that uses all three, 19 is the number of pupils that uses only swimming pool and 10 is the number of pupils that uses only gym and tennis court}
The pupils that uses only Tennis courts = 92 - 59
The pupils that uses only Tennis courts = 33
The probability of selecting a pupil who uses only the tennis court = 33/150
Therefore by simplification, the probability that only a pupil selected uses only the tennis court is the fraction 11/50
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Yuson spends $584 on equipment to start his own landscaping company. He charges $26 per hour. Write a linear equation in slope-intercept form to represent his profits, y, after working x hours.
The equation for profit in slope-intercept form is written as y = 26x - 584
Linear EquationA linear equation is an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation. The standard form of a linear equation is given as y = mx + c
m = slopec = y-interceptIn this problem, the constant or fixed value is the amount he spent on the equipment and the slope is the amount he charges per hour.
The equation of profit can be represented as y = 26x - 584
Where x = number of hours he worked.
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A rectangle is 2 feet 11 inches wide and 1 yard 2 feet 1 inch long. What is the perimeter of the
rectangle in feet?
A 8 feet
B 24 feet
C 16 feet
D 18 feet
The perimeter of the rectangle is 16 feet.
The correct answer is an option (C)
In this question, the length of the rectangle is,
l = 1 yard 2 feet 1 inch
l = 3 feet + 2 feet + 0.0833 feet
l = 5.0833 feet
And the width of the rectangle is,
w = 2 feet 11 inches
w = 2 feet + 0.9167 feet
w = 2.9167 feet
So, the perimeter of the rectangle would be,
P = 2(l + w)
P = 2 * (5.0833 + 2.9167)
P = 16 feet
Therefore, the perimeter of the rectangle is 16 feet.
The correct answer is an option (C)
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someone help fast!! what is the slope of this graph!
Step-by-step explanation:
for every x change by +1, y changes by -3.
so, the slope is
-3/1 = -3
Answer:
-3
Step-by-step explanation:
I hope it helps :]
Yesterday, the temperature dropped
27°F in h hours. The temperature
dropped the same number of degrees
each hour. Write an expression that can
be used to find the change in
temperature each hour.
The expression that can be used to find the change in temperature each hour would be 27 h.
How to find the change in temperature each hour?It is given that the temperature dropped 27°F in h hours. The temperature dropped the same number of degrees each hour.
We have to find the change in temperature each hour.
We can express this mathematically:
27 h
Then the equation would be 27 h.
Therefore, The temperature dropped the same number of degrees each hour would be 27 h.
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the radius of a right circular cone is increasing at a rate of 2 inches per second and its height is decreasing at a rate of 5 inches per second. at what rate is the volume of the cone changing when the radius is 40 inches and the height is 40 inches?
Using the concepts of Application of derivative, we got that 1657.92inches³/sec rate of the volume of the cone changing when the radius is 40 inches and the height is 40 inches for a right circular cone.
We know that volume of right circular cone is given by =(1/3πr²h)
We are given rate of change of radius(dr/dt) and rate of change of the height(dh/dt)
Therefore ,differentiating the volume with respect to time and applying the chain rule.
dV/dt = [(1/3)πr²×(dh/dt)+ (1/3)π·2·r·(dr/dt)·h]
=>dV/dt=[(1/3)× π×r × [(r×dh/dt)+2h×(dr/dt)]]
We are given that dr/dt=2inc/sec and dh/dt= -5inc/sec
So, on putting the values, we get
=>dV/dt=[ ( (1/3)×3.14×40)×[40×(-5)+2×40×2]]
=>dV/dt=[0.33×3.14×40×[-200+160]
=>dV/dt=[0.33×3.14×40×(-40)]
=>dV/dt= -1657.92inches³/sec(negative sign denote volume is decreasing)
Hence, if the radius of a right circular cone is increasing at the rate of 2 inches per second and its height is decreasing at the rate of 5 inches per second. the rate of the volume of the cone changing when the radius is 40 inches and the height is 40 inches is 1657.92inches³/sec.
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Are these 4 problems SSS SAS ASA AAS HL
1. The first figure posses the SSS property.
2. The second figure posses the ASA property.
3. The third figure posses the hypotenuse length property.
4. The fourth figure posses the SAS property.
Given:
1. The first figure shows the SSS property.
Side-Side-Side criterion is referred to as the SSS criterion. According to this standard, two triangles are congruent if their respective triangles' three sides are equal to one another.
hence the two triangles are congruent.
2. The second figure posses the ASA property.
Angle-Side-Angle criterion is also known as ASA criterion. According to the ASA criterion, two triangles are congruent if any two of their included sides and related angles are equivalent in size to those of the other triangle.
hence the two triangles are congruent.
3. The third figure posses the hypotenuse length properety.
RHS criterion stands for right angle-hypotenuse-side congruence criterion. Under this criterion, two triangles are congruent, if the hypotenuse and side of one right-angled triangle are equal to the hypotenuse and the corresponding side of another right-angled triangle.
hence the two triangles are congruent.
4. The fourth figure posses the SAS property.
Side-Angle-Side criterion is referred to as the SAS criterion. According to this standard, two triangles are said to be congruent if their matching sides and included angles are the same on each side of each other.
hence the two triangles are congruent.
Hence we get the required answer.
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if florist B increases the cost per roses to $5.20 for what number of roses is it less expensive to order from florist a? from florist b ?
Answer: florist a is cheaper than florist b
Step-by-step explanation: the price of florist B's flowers are 5.20$ more than florist A's
PLEASE HELP ME WILL GIVE BRAINLIEST!!!!!!!!!!!!!!
Solve this system of equations using the LINEAR COMBINATION method, then answer the questions below. 2x - y = - 46x + 5y = 4What did you get for the (x, y) solution to this system? (2.5 points)Explain what you did to create a pair of opposites so that you could combine the equations. (2.5 points)
Answer:x=5, y=-4
Step-by-step explanation:2x+9y = -26
-3x-7y = 13
Multiply the first equation by 3
3(2x+9y = -26)
6x +27y = -78
Multiply the second equation by 2
2(-3x-7y = 13)
-6x -14y = 26
Add these two equations together
6x +27y = -78
-6x -14y = 26
---------------------
13y = -52
Divide by 13
13y/13 = -52/13
y = -4
Now we need to find x
2x+9y = -26
2x+9(-4) = -26
2x-36=-26
Add 36 to each side
2x-36+36 = -26+36
2x=10
Divide by 2
2x/2 =10/2
x=5
helpl i have cookies
Answer:30
Step-by-step explanation:6 times 4 is24 and to the nearest 100 it will be 30
a car uses 6 gallons of gas every 246 miles it drives. How many miles does it travel on 1 gallon
Answer: 41 miles per gallon
Step-by-step explanation: Divide 256 by 6 and you get 41
A population of beetles grows by 25% every month. If the beetle population starts with 1,600 beetles, which equation represents the population, P, after t months?
The equation which represents the population, P after t months is:
y = 1600(1+ 0.25)^t.
Given,
A population of beetles grows by 25% every month.
the beetle population starts with 1,600 beetles,
we are asked to determine the equation which represents the population, P after t months.
The equation for the population is:
Pf = Pi(1-r)^t
where pf = final value
pi = initial value
r = growth factor
t = time in years.
substitute the values in the equations.
let y represent the final population after t years.
r = 25%
convert percentage to decimal.
r = 0.25
y = 1600(1+ 0.25)^t
Hence we get the required answer.
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J.D. opened a savings account with $425. After
2 years, the total interest he earned was $10.20.
What was the annual interest rate?
The annual interest rate is 1.2%
The principal amount = $425
The total interest her earned = $10.20
The final amount = 425 + 10.20
= $435.2
Time period = 2 years
The simple interest
A = P(1 + rt)
Where A is the final amount
P is principal amount
r is the interest rate
t is the time period
Substitute the values in the equation
435.2 = 425(1 + r×2)
1 + 2r = 435.2 / 425
Divide the terms
1 + 2r = 1.024
2r = 1.024 - 1
2r = 0.024
r = 0.024/2
Divide the terms
r = 0.012
Then the percentage will be
r = 1.2%
Hence, the annual interest rate is 1.2%
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a student wanted to know if the bags of potato chips they were buying contained the correct weight of chips compared to the listed weight on the bag of 42.5 grams. the student collected a sample of 30 bags of chips and weighed each bag. the average weight of the bags they collected was 41 grams with a standard deviation of 1.6 grams. assume a 95% level of confidence.
According to the given standard deviation, the bag that the student brought has more than 1 gram of potato chip than the average chip bag.
Standard deviation:
Standard deviation refers the measure of how scattered the data is in relation to the mean.
Given,
The student wanted to know if the bags of potato chips they were buying contained the correct weight of chips compared to the listed weight on the bag of 42.5 grams.
And the student collected a sample of 30 bags of chips and weighed each bag. Here the average weight of the bags they collected was 41 grams with a standard deviation of 1.6 grams. assume a 95% level of confidence.
Now, we have to find the confidence interval for this situation.
From, the given details, we have obtained the following things,
Bag weight = 42.5 gram
Number of samples = 30
Average weight = 41 grams
Standard deviation = 1.6 grams
Confidence level = 95%
So, according to the formula of confidence interval,
The value of it is calculated as,
=> CI = x ± Z × s / √n
When we apply the values on the formula, then we get,
=> CI = 41 ± 1.9600 × 1.6 / √30
=> CI = 41 ± 0.573
Therefore, Confidence Interval 41 ±0.573 (±1.4%) [40.427 – 41.573].
While we compare this one with the given bag weight we get the difference of,
=> 42.5 - 41.5
=> 1
Therefore, the bag that the student brought has more than 1 gram of potato chip than the average chip bag.
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Exercises 5-22, a parametrization si given for a curve.
(a) Graph the curve. What are the initial and terminal
any? Indicate thedirection ni which the curvesi traced.
(b) Find a Cartesian equation for a curve that contains the parametrized curve. What portionofthe graph of the Cartesian equation istraced by het parametrized curve?
5.x=31, y=917, 0-<1<00 6. x= -Vi, y= 1, 120
7.x= ,1 y= Vi. 120
8 . x = ( s e c ? t ) - , 1 y = t a n t , - ” / 2 < 1 くm / 2
9.x=cost, y=sint, 0515 a
10. x= sin (2nt), y= cos (2mt), 0 ≤ 1≤ ,1
11. x= cos( T- t), y = sin( m- 0). 0 S i s T
12.x=4cost,y=2sint. 0≤1≤27 13. x= 4sint, y= 2cost, 0515 n
parameter interval that traces the c u r v e exactly 1. x= 3sin (21), y= 1.5 cos t
2. x= sni? ,1 y= cos',
3. x= 7sin /- sin (71),
4.x=21sint-3sin(61),
a()
once.
points, fi
)c(
5.12
(a) Va? = a (c) V4a? = a|2|
(b)Va?= at
'y= 7 cos
a) Refer to the attachment for graph:
The ellipse in counter clockwise direction starting from the point (1,0)
b) Cartesian equation for a curve that contains the parametrized curve is
x²+ y/4=1
What are trigonometric expressions?
Trigonometric identities are, by definition, reciprocal. These formulas show the connections between the sine/cosine functions and tangents.
a) Given: x= cost , y= 2 sin t, 0<t≤2π
y= 2 sin t,
sin t= y/2
we know that,
cos²t + sin²t=1
x²+ y/4=1
b) The point (x,y) moves on the ellipse x²+ y/4=1
t increases from 0 to 2π. The point (x,y) moves around the ellipse around the ellipse in counter clockwise direction starting from the point (1,0)
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a delivery driver has an average daily gasoline expense of $55.00. the standard deviation is $10.00. the owner takes a sample of 54 bills. what is the probability the mean of his sample will be between $45.00 and $65.00? enter all answers to the nearest tenth.
The probability the mean of his sample will be between $45.00 and $65.00 is 0.6826.
Given:
A delivery driver has an average daily gasoline expense of $55.00. the standard deviation is $10.00. the owner takes a sample of 54 bills.
n = 54
standard error = 10/[tex]\sqrt{54}[/tex]
= 2.205
when x = 45,
z score = 45 - 55 / 10
= -10/10
= -1
probability at z = -1 is 0.3413
z score for x = 65
z = 65 - 55 / 10
= 10/10
= 1
probability at z = 1 is 0.3413
Total probability = 0.3413+0.3413
= 0.6826
Therefore the probability the mean of his sample will be between $45.00 and $65.00 is 0.6826.
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Write an equation for the table. Then find the value of y when x = 18
Distance
24
36
42
48
54
traveled, x
Time, y
1
7
10
13
16
Answer: maybe
12
Step-by-step explanation:
the answer is 12
I WILL GIVE 30 POINTS TO THOSE WHO ANSWER THIS QUESTION RIGHT NOOOO SCAMS
Answer:
Step-by-step explanation:
Its the last two and the first one
PLEASEEE ANSWER ASAP!
Question
Evaluate the expression.
2−[(2+10(−1)÷2)+1]
What is the value of the expression?
Enter your answer in the box.
The value of the expression will be;
⇒ 4
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 expression is,
⇒ 2 - [(2 + 10(−1) ÷ 2) + 1]
Now,
Solve the expression by using BODMAS rule as;
The expression is,
⇒ 2 - [(2 + 10(−1) ÷ 2) + 1]
⇒ 2 - [ (2 - 10 ÷ 2) + 1 ]
⇒ 2 - [(2 - 5) + 1 ]
⇒ 2 - [ - 3 + 1 ]
⇒ 2 - { - 2 ]
⇒ 2 + 2
⇒ 4
Thus, The value of the expression will be;
⇒ 4
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A farmer wants to construct a fence around an area of 2400 square feet in a rectangular field and then divide it in half with a fence parallel to one of the sides of the rectangle. What dimension should the fenced area have in order to minimize the length of fencing used?
Step-by-step explanation:
The lengths of the sides of the rectangular field should be 40 ft (smaller value) and 60 ft (larger value) respectively.
Let L = length of rectangle area and W = width of rectangle area.
Let the length of the side that divides the area be parallel to the width of the area.
The total length of fencing F = 2L + 2W + W
F = 2L + 3W
Since the area is a rectangle, its area is A = LW
Since the area = 2400 square feet,
LW = 2400 ft²
So, L = 2400/W
Substituting L into F, we have
F = 2L + 3W
F = 2(2400/W) + 3W
F = 4800/W + 3W
To find the value at which F is minimum, we differentiate F with respect to W.
So, dF/dW = d(4800/W + 3W)/dW
dF/dW = -4800/W² + 3
Equating dF/dW to zero, we have
-4800/W² + 3 = 0
-4800/W² = - 3
W² = -4800/-3
W² = 1600
W = √1600
W = 40 ft
To determine if this is a value that gives minimum F, we differentiate F twice to get
d²F/dW² = d(-4800/W² + 3)/dW
d²F/dW² = 14400/W³ + 0
d²F/dW² = 14400/W³
substituting W = 40 into the equation, we have
d²F/dW² = 14400/(40)³
d²F/dW² = 14400/64000
d²F/dW² = 0.225
Since d²F/dW² = 0.225 > 0, W = 40 is a minimum point for F
Since L = 2400/W
So, L = 2400/40
L = 60 ft
So, the lengths of the sides of the rectangular field should be 40 ft (smaller value) and 60 ft (larger value) respectively.
What is m Please help!
Answer:
Step-by-step explanation:
m just means measure. So the question is asking you what is the MEASURE of the ANGLE AEB.
Since angles AEB and CED are vertical angles, you can set the two expressions equal to each other and solve for X.
1) 3x + 54 = 7x - 30
2) 54 = 4x - 30
3) 84 = 4x
4) x = 21
Now that you know x, plug x into the expression for AEB, which is 3x + 54
3(21) + 54 = 117
m∠AEB = 117°
Joe is playing a game with a regular die. If the number that turns up is
even, he will gain 5 times the number that comes up. If it is odd, he will
lose 10 times the number that comes
up. He tosses a 3. Express the
results as an integer.
The required solution will be -30 which is expressed as an integer.
To represent this in a general context, we may utilize functions that are referred to in terms of the number tossed.
We know that if the number he gets is an even number, he will get 5 times the number.
As a result, the function for when the integer x is even is f(x) = 5x.
If the number is an odd number, he will lose 10 times the number.
As a result, the function for when the integer x is odd is f(x)=-10x.
Finally, Joe tosses a 3, which is an odd integer, hence the function we will represent is f(x) = - 10x.
⇒ f(3) = -10(3) = -30
Thus, the required solution will be -30 which is expressed as an integer.
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Raja manages a perfume store. She makes 0,4-ounce samples from a 2.8- ounce bottle of perfume. How many perfume samples cán Raja make?
Raja can make 7 perfume samples from a 2.8 ounce bottle of perfume.
According to the question,
We have the following information:
Raja manages a perfume store. She makes 0.4-ounce samples from a 2.8- ounce bottle of perfume.
So, we have the following expressions:
1 bottle of perfume sample = 0.4 ounce
Total ounces of perfume in the bottle = 2.8 ounce
Now, we can easily find the number of perfume samples that can be made from this perfume by dividing the total ounces of perfume in bottle by the ounces of perfume sample.
Number of perfume samples = 2.8/0.4
Number of perfume samples = 7
Hence, Raja can make 7 perfume samples from a 2.8 ounce bottle of perfume.
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To rent a certain meeting room, a college charges a reservation fee of $37 and an additional fee of $6.40 per hour. The chemistry club wants to spend at most $88.20 on renting the meeting room. What are the possible amounts of time for which they could rent the meeting room? Use t for the number of hours the meeting room is rented, and solve your inequality for t .
If the chemistry club wants to spend at most $88.20 on renting the meeting room. The possible amounts of time for which they could rent the meeting room is 8.
How to find the possible amounts of time?Let t represent the number of hours the meeting room is rented
Formulate an inequality and use the inequality to find the time
37 + 6.40t < 88.20
Combine like terms
6.40t < 88.20 - 37
6.40t < 51.20
Divide both side by 6.40t
t = 51.20 /6.40
t < 8
Therefore the time is 8.
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HELP!!
If the product of two numbers is positive, which of the following expressions must be true?
1. The factors had different signs.
2. One of the factors was negative.
3. One of the factors was positive.
4. The factors had the same sign.
Answer:
4: The factors had the same sign
Step-by-step explanation:
They are both positive (i think)
Which of the following is equivalent to 17g - 2g?
The equivalent expression to 17g-2g will be (17-2)g.
According to the question,
We have the following expression:
17g-2g
Now, we can simplify this expression easily to find the equivalent expression.
So, our first step will be to take g as a common factor from both the terms. Now, we have the following expression:
(Note that the common factor means that the variable or the number taken as a common factor should be able to divide the terms given in the expression.)
(17-2)g
Now, this can be solved further because 2 can be subtracted from 17 because they both are integers without any variable.
Hence, the correct option is C.
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What's the value of the expression below?
40÷[20−4⋅(7−4)]
Answer:
5
Step-by-step explanation:
Answer:
The answer for the question is five!
Please solve with explanation (High Points)
The equation of the transformed function is f(x)= -1/3[tex]\sqrt{2(x-6)}[/tex] -3.
Given that,
The f(x) = square root of X base function is transformed by a reflection in the x-axis, a vertical stretch by a factor of 3, a horizontal compression by a factor of 1/2, a vertical translation by a factor of 3, a vertical translation by a factor of 3 down, and then a horizontal translation by a factor of 6 right.
We have to verify the changed function's equation.
Take the function
f(x)=√x
The function reflection in the x-axis,
f(x)=-√x
The function is vertical stretch by a factor of 3.
f(x)= -1/3√x
The function is horizontal compression by a factor of 1/2.
f(x)= -1/3[tex]\sqrt{2x}[/tex]
The function is vertical translation by a factor of 3 down,
f(x)= -1/3[tex]\sqrt{2x}[/tex] -3
The function is horizontal translation by a factor of 6 right.
f(x)= -1/3[tex]\sqrt{2(x-6)}[/tex] -3
Therefore, The equation of the transformed function is f(x)= -1/3[tex]\sqrt{2(x-6)}[/tex] -3.
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