The cost of the total bill for the friends is $154.665.
What is a tax?This implies a levy that's paid to the government by individuals and firms.
From the information, the.group of friends’ dinner bill before tax is $122.75, sales tax rate is 8% and they want to leave an 18% tip after tax.
The total bill will be:
= Cost of food + Tax + Tip
= $122.75 + (8% × $122.75) + (18% × $122.75)
= $122.75 + $9.82 + $22.095
= $154.665
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Which statement about the location of √ 7 on a number line is true?
The location of √ 7 on a number line between 2 and 3.
What is a number line?A number line is a picture of a graduated straight line that serves as a visual representation of real numbers in primary mathematics. Every number line point is considered to correspond to a real number and every real number to a number line point.
A number line is a long straight line with numbers marked at equal intervals. On a number line, we can argue that as we move to the right, the value of numbers increases. This signifies that the numbers on the right are more than those on the left.
A number line shows how numbers are related. It's a line with check marks next to each number. The numerals get smaller as you move left on the number line. The numbers grow larger as you move closer to the number line.
In this case, ✓7 is 2.65. This number can be found between 2 and 3. This should be the true statement since the options aren't given.
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a control chart for nonconformities is maintained on a process producing desk calculators. the inspection unit is defined as two calculators. the average number of nonconformities per machine when the process is in control is estimated to be two. (a) find the appropriate three-sigma control limits for this size inspection unit. (b) what is the probability of type i error for this control chart?
The three sigma control limits range from 0 to 8.20 for this size inspection limit and The probability of a type I error is 0.0038.
The inspection unit calculator in this case is 2
1.5 non-conformities on average per machine
Consequently, we would typically discover 2 * 1.5 = 3 non-conformities.
Here, C equals 3.
Lower Limit = C - 3 * c, which equals 3 - 3 * sqrt (3), which results in -2.19 (impossible), therefore 0
Reduced Limit = 0
Upper Limit: 8.20 when C + 3 * с + 3 + 3 * sqrt(3)
In this case, the three sigma control limits range from 0 to 8.20 for this size inspection limit.
(b) Type I errors happen when non confirmations go above the acceptable range.
This is a POISSON (3)
P(c > 8.20) = -1 POISSON (8, 3, true)
=1 - 0.9962
= 0.0038
In this case, the probability of a type I error is 0.0038.
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during a recent campaign for office, a candidate made a tour of a country that we assume lies in a plane. on the first day of the tour she went east, on the second day she went north, on the third day west, on the fourth day south, on the fifth day east, and so on. if the candidate went $n^2/2$ miles on the $n^{\text{th}}$ day of her tour, how many miles was she from her starting point at the end of the 40th day?
580 miles.
On the first day of the tour, she went = east
On the second day she went = north
On the third day = west
On the fourth day she went = south
On the fifth day she went = east
Miles was she from her starting point at the end of the 40th day =?
She was 580 miles from her starting point at the end of the 40th day.
Solution is given in the attached picture.
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4. Your test scores for the semester are 87, 84, and 85. Can you raise your test average to 90with your next test?DefineEquation:Answer:can i have help on 4, 5 and 6?
5.
The sum of three consecutive integers is 228. You can write this situation, in an algebraic way, as follow:
x + (x + 1) + (x + 2) = 228
where the lower number is x, and the largest number is (x + 2).
You solve the previous equation for x:
x + (x + 1) + (x + 2) = 228 eliminate prenthesis
x + x + 1 + x + 2 = 228 sum similar terms
3x + 3 = 228 rest 3 both sides
3x = 228 - 3
3x = 225 divide by 3
x = 225/3
x = 75
Then, the lower number is 75, and the largest one is (75+2) = 77
what percentage grade should a road have if the angle of elevation of the road is 44 degrees? (the percentage grade is defined as the change in the altitude of the road over a 100100 -foot horizontal distance. for example a 5%5% grade means that the road rises 55 feet for every 100100 feet of horizontal distance.)
For a 44° elevation angle, the grade will be 96%.
Given that,
if the angle of elevation of the road is 44 degrees,
The difference in the road's altitude over a horizontal distance of 100 feet is what is referred to as the percentage grade. For instance, a road with a 5% slope will rise 5 feet for every horizontal 100-foot distance.)
A tangent ?
One of the six basic trigonometric functions is tangent, denoted as tan().
The ratio of the opposite side length to the adjacent side length is the definition of the tangent value of the one sharp angle,, in a right triangle.
[tex]tan \alpha = sin\alpha /cos \alpha[/tex]
The tangent of the angle is the ratio of rise to run.
tan(angle) = grade
tan(44°) ≈ 0.96 = 96%
Therefore, The grade will be 96% for an angle of elevation of 44°.
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At 10:00 a.m., Han and Tyler both started running toward each other from opposite ends of a 10-mile path along a river. Han runs at a pace of 12 minutes per mile. Tyler runs at a pace of 15 minutes per mile.
Do Han and Tyler meet on the path within 1 hour?
If Han and Tyler both started running toward each other from opposite ends of a 10-mile path along a river. Han and Tyler will not meet on the path within 1 hour
Calculations to show if Han and Tyler meet on the path within 1 hourThe following information is gotten from the question
Han and Tyler both started running toward each other from opposite ends of a 10-mile path
Han runs at a pace of 12 minutes per mile
Tyler runs at a pace of 15 minutes per mile
Distance covered by Han in 1 hour
12 minutes = 1 mile
60 minutes = ? miles
cross multiplying gives
? = 60 / 12
? = 5 miles
Distance covered by Tyler in 1 hour
15 minutes = 1 mile
60 minutes = ? miles
cross multiplying gives
? = 60 / 15
? = 4 miles
This means that Han covers 5 miles in and Tyler covers 4 miles, in a 10 mile distance.
In one hour the distance covered
= 5 miles + 4 miles
= 9 miles
9 miles is less than 10 miles hence they will not meet in the path within one hour
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a 2.0 kg box is at rest on a table, The static friction coefficient μs between the box and table is 0.40, and the kinetic friction coefficient μk is 0.2
Then, a 25N horizontal force is applied to the box.
What is the best estimate of the magnitude of the box's acceleration?
The best estimate of the magnitude of the box's acceleration is equal to: B. 11 m/s².
How to determine the box's acceleration?In order to determine the magnitude of the acceleration of this box, we would first of all calculate the magnitude of the kinetic frictional force.
Mathematically, the kinetic frictional force that is acting on a physical body can be calculated by using this equation:
F = μkN = μk(mg)
Where:
μk is the coefficient of kinetic frictional force.N is the normal force.m is the mass.g is the acceleration due to gravity.Substituting the given parameters into the formula, we have;
F = 0.20 × 2.0 × 9.81
F = 3.924 Newton.
By applying Newton's second law of motion, the net force is given by:
∑Fx = Applied force - kinetic frictional force = ma
Acceleration, a = [Applied force - kinetic frictional force]/m
Acceleration, a = [25 - 3.924]/2
Acceleration, a = 21.076/2
Acceleration, a = 10.538 ≈ 11 m/s²
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what is the distance between the two points in simplest radical form
(−2,−7) and (5,0)
The distance between the two points in simplest radical form(−2,−7) and (5,0) is 9.8995
What is the distance?Distance can be described as the differences that exist between two points and this can be expressed i different form such as the radical form.
We can calculate the distance between the two points by firstly expressed them as :
(−2) - (5) = -7
(-7) - 0 = -7
Then the distance between them can be found as :
Distance = (-7)^2 + (-7)^2 = 49 +49 = 98
Then we will find the square root of the the figure as
= [tex]\sqrt{98}[/tex] = 9.8995
The formula can as well be used to find this by substituting the values of x and y into the formula as :
x1=-2
y1=-7
x2=5
y2=0
[tex]d = \sqrt{ ( x_{2} - x_{1} )^{2} + ( y_{2} - y_{1} )^{2}}[/tex]
then [tex]d = \sqrt{ ( 5 - (-2 )^{2} + ( 0 - (-7) )^{2}}[/tex]
= [tex]\sqrt{ 49^{2} + 49^{2} }[/tex]
= [tex]\sqrt{98}[/tex]
=9.8995
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[tex]a(a-9)=0[/tex] yyyyyyyyyyyyyyy
Answer:
a = 0 , a = 9
Step-by-step explanation:
a(a - 9) = 0
equate each factor to zero and solve for a
a = 0
a - 9 = 0 ⇒ a = 9
14. A function is defined by the
equation y = x² + 3x + 1. Which
statements are true? Select all
that apply.
O The equation in vertex form is y =
5
(x + ²³2) ²
I
A LOT
4
O The equation in vertex form is y = (x + ²)² − ³/
-
O The graph of the function has a minimum of y =
O The domain of the function is all real numbers
-² at x = -²
The correct statements regarding the quadratic function y = x² + 3x + 1 are given as follows:
A. The equation written in vertex-form is: (x + 3/2)² - 5/4.C. The graph of the function has a minimum of y = -5/4 at x = -3/2.D. The domain of the function is all real values.How to analyze the quadratic function?The quadratic function in this problem is defined as follows:
y = x² + 3x + 1.
Hence the coefficients are given as follows:
a = 1, b = 3, c = 1.
The x-coordinate of the vertex is given as follows:
x = -b/2a = -3/2.
The y-coordinate of the vertex is then given as follows:
y = (-3/2)² + 3(-3/2) + 1
y = 9/4 - 9/2 + 1
y = 9/4 - 18/4 + 4/4
y = -5/4.
Hence the vertex-form definition of the quadratic equation is given as follows:
y = (x + 3/2)² - 5/4.
Due to the positive leading coefficient, the vertex means that the function has a minimum of y = -5/4 at x = -3/2.
The domain of the function is all real values, as the quadratic function has no constraints such as a fraction or an even root.
Missing InformationThe complete problem is given by the image shown at the end of the answer.
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A savings account increases from 250$ to 265$. What is the percent increase of the savings account?
a lake is stuck with 1,550 young carp. the number of the original fish alive after t years is given by the function P (t)= 1550e^-0.4t, when will there be 440 of the original fish left from to the nearest tenth
so the time needed is 3.1 years
solve the system by graphing; y= -5/3x + 3 y= 1/3x - 3
Answer:
The solution to the given system is:
x = 3
y = -3
Explanation:
Given the following system of equation:
[tex]\begin{gathered} y=-\frac{5}{3}x+3 \\ \\ y=\frac{1}{3}x-3 \end{gathered}[/tex]The solution to these is the point where the lines intersect.
The graph is shown below:
The solution is x = 3, y = -3
Is the following relation a function? {(0.3, 0.6), (0.4, 0.8), (0.3, 0.7), (0.5, 0.5)}
25 points
No, the given relation is not a function. An association between items of two sets—the domain and the codomain—is known as a binary relation.
What is a function ?A function in mathematics from a set X to a set Y allocates exactly one element of Y to each element of X. The sets X and Y are collectively referred to as the function's domain and codomain, respectively.
A binary connection in mathematics links elements of one set, referred to as the domain, with elements of another set, referred to as the codomain. A new set of ordered pairs made up of elements from sets X and Y and x in X is known as a binary relation across these sets.
Al-Biruni and Sharaf al-Din al-Tusi, two Persian mathematicians, are responsible for the earliest documented treatment of the concept of function. Initially, functions represented the idealised relationship between two changing quantities.
Consider the given relation
{(0.3, 0.6), (0.4, 0.8), (0.3, 0.7), (0.5, 0.5)}
We need to check whether the given relation is function or not.
A relation is a function if there exist a unique value of y for each value of x.
In the given relation, for x=0.3 there exist more than one value of y.
y=0.6 at x=0.3
y=0.7 at x=0.3
For one input there exist more than one output. Therefore, the given relation is not a function.
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Which of the following statements are not true regarding functions?Check all that apply.A. A function is a relation in which each value of the input variable ispaired with at least one value of the output variable.I B. The vertical line test may be used to determine whether afunction is one-to-one.O C. A sequence is a function whose domain is the set of naturalnumbers.D D. The horizontal line test may be used to determine whether afunction is one-to-one.
Only B is not true, because the vertical line test is to know if a graph is from a function.
I dont know pls help me
In Close Encounters of a Bear Kind, the statement that represents the author's primary attitude towards John's work is that C. John's work is dangerous.
How to illustrate the information?According to the author, he stated that people don't usually realize that bears
can be very dangerous.
He further stated that they will reap people apart of they e the chance. The narrator gave an example about how he walked out at night and had to run back home for his dear life. This was why he stated that the job of John whom was a photographer was a dangerous one.
In conclusion, the correct option is C.
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Charmaine the trainer has two solo workout plans that she offers her clients: Plan A and Plan B. Each client does either one or the other (not both). On Friday there were 6 clients who did Plan A ands who did Plan
B. On Saturday there were 2 clients who did Plan A and 3 who did Plan B
Charmaine trained her Friday clients for a total of 7 hours and her Saturday clients for a total of 3 hours. How long does each of the workout plans last?
The number of hour (time) for which workout plan A would last is 0.75 hour. Also, the number of hour (time) for which workout plan B would last is 0.5 hour.
How to calculate the number of hours (time)?In order to solve this word problem, we would assign variables to the number of hours (time) each plan and then translate the word problem into algebraic equation as follows:
Let x be the number of hours (time) for workout plan A.Let y be the number of hours (time) for workout plan B.Translating the word problem into an algebraic equation, we have;
On Friday ⇒ 6x + 5y = 7 ....equation 1.
On Saturday ⇒ 2x + 3y = 3 ....equation 2.
Next, we would solve the simultaneous equation by using elimination method:
3 × (2x + 3y = 3) = 6x + 9y = 9 ........equation 3.
Subtracting equation 1 from equation 3, we have:
6x + 9y = 9
6x + 5y = 7
4y = 2
y = 2/4
y = 1/2
y = 0.5 hour.
For the value of x, we have:
6x + 5y = 7
6x + 5(0.5) = 7
6x + 2.5 = 7
6x = 7 - 2.5
6x = 4.5
x = 4.5/6
x = 0.75 hour.
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Complete Question:
Charmaine the trainer has two solo workout plans that she offers her clients: Plan A and Plan B. Each client does either one or the other (not both). On Friday there were 6 clients who did Plan A and 5 clients who did Plan B. On Saturday there were 2 clients who did Plan A and 3 who did Plan B Charmaine trained her Friday clients for a total of 7 hours and her Saturday clients for a total of 3 hours. How long does each of the workout plans last?
Use point-slope form to write the equation of a line that passes through the point (-12,15) with slope −1.
Answer: y = -1x + 3
Step-by-step explanation:
Point-Slope form: y - y1 = m(x-x1)
Replace the form with the values provided:
y - 15 = -1(x+12)
Once you get this, you need to get y by itself in order to get it in slope intercept form.
Distribute:
y -15 = -1x - 12
Add -15 to the right side:
y = -1x + 3
for anyone that knows how to do this i only need help with these two questions
-4x-1=-y
solve for y
-4y+20+3x=0
solve for y
[tex]-4x-1=-y\\y[/tex]
Flip the equation:
[tex]-y=-4x-1[/tex]
Divide both sides by -1:
[tex]\frac{-y}{-1} =\frac{-4x-1}{-1}[/tex]
[tex]y=4x+1[/tex]
__________________________________________________________
[tex]-4y+20+3x=0\\y[/tex]
Add -3x to both sides of the equation:
[tex]3x-4y+20+-3x=0+-3x\\-4y+20=-3x[/tex]
Add -20 to both sides of the equation:
[tex]-4y+20+-20=-3x+-20\\-4y=-3x-20[/tex]
Divide both sides by -4:
[tex]\frac{-4y}{-4} =\frac{-3x-20}{-4}[/tex]
[tex]y=\frac{3}{4} x+5[/tex]
Find the other endpoint of the line segment with the given endpoint and midpoint. Endpoint: (9,1) Midpoint: (-4,-6)
Answer:
(-13, - 6)
Step-by-step explanation:
Midpoint =(x₁ + x₂)/2, (y₁ + y₂)/2
(-4,-6) = (9+x)/2, (1+y)/2
9+x= - 4
X= - 13
1+y= - 6
Y= - 7
Ans=
(-13, - 6)
Solve the equation. (Enter your answers as a comma-separated list.)x210x − 6x10x = 27(10x)x =
Answer:
x = -3, 9
Explanation:
First, let us divide both sides of the equation by 10^x; this gives,
[tex]\frac{x^210^x-6x\times10^x}{10^x}=\frac{27\times10^x}{10^x}[/tex][tex]\Rightarrow x^2-6x=27[/tex]subtracting 27 from both sides gives
[tex]x^2-6x-27=0[/tex]The left-hand side can be factored as
[tex](x-9)(x+3)=0[/tex]which gives us two further equations
[tex]\begin{gathered} x-9=0 \\ \boxed{x=9.} \end{gathered}[/tex][tex]\begin{gathered} x+3=0 \\ \Rightarrow\boxed{x=-3.} \end{gathered}[/tex]Hence, the two solutions we get are x = 9 and x = -3.
hemoglobin determinations were made on sixteen animals exposed to ionizing radiation. the following observations were recorded: 15.6, 14.4, 14.8, 13.8, 16.6, 14.0, 17.4, 17.3, 18.6, 16.2, 15.7, 14.7, 16.4, 13.9, 14.8, 17.5. construct a 95 percent confidence interval for population standard deviation?
The required values for a 95 percent confidence interval for population standard deviation are CI₈² = [1.1894, 5.221]
CI₈ = [1.0906, 2.2849]
n = 16, Standard Deviation = 1.4764, Var = 2.1796
X²₀.₀₂₅,₁₅ = 6.26, X²₀.₉₇₅,₁₅ = 27.49
CI₈² = [(15ₓ2.1796/27.48),(15ₓ2.1796/6.26)] = [1.1894, 5.221]
CI₈ = [[tex]\sqrt{15*2.1796/27.48} , \sqrt{15*2.1796/6.26}[/tex]] = [1.0906, 2.2849]
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39+(20.4) can u help me with this answer I don't know how to do it
You have the following expression:
39 + (-20.4)
In order to simplify the previous expression, you first eliminate the parenthesis. To do that, you take into account that the sign before the parenthesis must multiply the sign inisde. In this case, you have a positive sign + before the parenthesis, and inside you have a minus -. When the parenthesis is eliminated, these signs are multiplied (here you use the multiplication rule for signs). Thus, you have that - x + = - (positive multiplied by negative is equal to negative). And the expression becomes:
39 + (-20.4)
= 39 - 20.4
= 18.6
Hence, the simplified expression is 18.6
What is the midpoint of line segment (-6,-10) ,(-2,-8)
The mid-point of two coordinates is the average of the x and y coordinates thus the midpoint of the line segment with endpoints (-6,-10),(-2,-8) is (-4,-9).
What is a line segment?A line section that can connect two places is referred to as a segment.
A line segment is just part of a big line that is straight and going unlimited in both directions.
The line is here! It extends endlessly in both directions and has no beginning or conclusion.
The midpoint associated with two points (x₁, y₁) and (x₂, y₂) is given by
x = (x₁ + x₂)/2 , y = (y₁ + y₂)/2
x = (-6 - 2)/2 = -4 , y = (-10 - 8)/2 = -9
So, the coordinate will be (-4,-9).
Hence "The mid-point of two coordinates is the average of the x and y coordinates thus the midpoint of the line segment with endpoints (-6,-10),(-2,-8) is (-4,-9)".
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Jayden had $8 last week. He now has $11. what is the percent of change?
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data
initial money = $8
final money = $11
percent of change = ?
Step 02:
percent of change
percent of change = ( final money - initial money ) / initial money * 100
= ( 11 - 8 ) / 8 * 100
= 3/8 * 100
= 0.375 * 100 = 37.5 %
The answer is:
The percent of change is 37.5 %
"Northside Christian Academy has 528 students enrolled this year. That is an in- crease of 10% over last year's enrollment. How many students were enrolled last year?" Please help meee
Northside Christian Academy has 528 students enrolled this year. That is an in- crease of 10% over last year's enrollment. How many students were enrolled last year?
Let
x ------> students enrolled last year
we have that
100%+10%=110%=110/100=1.10
so
528=1.10x
solve for x
x=528/1.10
x=480
answer is 480 studentsshelly wants to tile a rectangular floor that measures 132 feet by 150 feet using square tiles that are all of the same size, with no overlap and no squares hanging over the edge. what is the measurement of the largest square tiles she can use?
The measurement of the largest square tiles she can use is 6 feet.
Finding all common factors between two numbers and choosing the biggest one yields the highest common factor (HCF). For instance, the numbers 8 and 12 share the elements 1, 2, and 4. Four is the greatest common factor.
Steps for calculating HCF:
Step 1: Write each integer as the sum of its prime factors in step one.
Step 2: List the shared factors between the two numbers.
Step 3: The HCF is the sum of all the common prime factors ( use the lower power of each common factor)
Given,
Measurement of the rectangular floor:
length = 150 feet
breadth = 132 feet
The measurement of the largest square can be calculated by finding the HCF of 132 and 150.
132 = 2*2*3*11
150 = 2*3*5*5
So, HCF (132, 150) = 2*3 = 6.
Hence, the measurement of the largest square tiles she can use is 6 feet.
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-3/2 = -2/3w - 4/5 solve for w and simplify your answer as much as possible
The result of the equation -3/2 = (-2/3)w - 4/5 is w = 21/20
The equation is
(-2/3)w - 4/5 = -3/2
Here we have to rearrange the terms and combine the like terms.
Mover 4/5 to the right hand side of the equation
(-2/3)w = -3/2 + 4/5
(-2/3)w = -7/10
Move the number (-2/3) to the right hand side of the equation
x = -7/10 ÷ (-2/3)
To make it multiplication, take the reciprocal of the the second number
x = -7/10 × (-3/2)
Multiply the numbers
x = 21/20
Hence, the result of the equation -3/2 = (-2/3)w - 4/5 is w = 21/20
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hi I circled the answer but I just need to figure out how to do it
Let's begin by listing out the information given to us:
216^(-2n) = (1/6)^(3n+2)
6 is a factor of 216: 216 = 6³
1/6 = 6^(-1)
⇒ 6^(-2*3n) = 6^[(-1*(3n+2)]
⇒ 6^(-6n) = 6^(-3n-2)
Since both sides are in the same base, we equate the exponents. We have:
-6n = -3n - 2
Add "6n" from both sides, we have:
-6n + 6n = -3n + 6n - 2 ⇒ 0 = 3n - 2
⇒ 3n = 2
A quadratic function y=f(x)y=f(x) is plotted on a graph and the vertex of the resulting parabola is (5, 3)(5,3). What is the vertex of the function defined as g(x)=f(x+2)+2g(x)=f(x+2)+2?
The function; g(x)=f(x+ 2)+2, it follows that the vertex of the function is;
(5, 3+2) +2 = (5, 5) + 2
Given,
A quadratic function y=f(x)y=f(x) is plotted on a graph and the vertex of the resulting parabola is (5, 3)(5,3).
To find the what is the vertex of the function defined as g(x)=f(x+2)+2g(x)=f(x+2)+2
Now,
What is the equation of the parabola?
Let the point (h, k) be the vertex of the parabola and a be the leading coefficient.
Then the equation of the parabola will be given as,
y = a(x - h)² + k
A quadratic function y = f(x) is plotted on a graph and the vertex of the resulting parabola is (5, 3).
Hence, if the function; g(x)=f(x+ 2)+2, it follows that the vertex of the function is; (5, 3+2) +2 = (5, 5) + 2.
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