The value of P(F or G) using the general addition rule be 8/12.
What is meant by probability?Mathematical explanations of the likelihood that an event will occur or that a statement is true are referred to as probabilities. A number between 0 and 1 represents the likelihood of an event, with 0 generally denoting impossibility and 1 denoting certainty.
Probability is a synonym for potential. It is a field of mathematics that examines how random events happen. From zero to one, the value is stated. To forecast the likelihood of events, probability has been introduced in mathematics.
We have that
F∪G = {5, 6, 7, 8, 9, 10, 11, 12}
P(FG) = 0.667
P(F or G) = 5/12 + 4/12 - (1/12)
P(F or G) = 5/12 + 1/4
From the question we are told
S = {3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14},
F = [5, 6, 7, 8, 9]
G = {9, 10, 11, 12}
Generally
The P(F or G) by counting the number of outcomes in F or G exists
[tex]$F \& G=\{5,6,7,8,9,10,11,12\}$$[/tex]
P(F or G) using the general addition rule
[tex]$& P(F G)=\frac{N_f}{N_g} \\[/tex]
substitute the values in the above equation, we get
[tex]$& P(F G)=\frac{8}{12} \\[/tex]
simplifying the equation, we get
P(F G) = 0.667
Using addition Rue to attain P(F or G) we get
P(F or G) = PF + PG - P(F + G)
substitute the values in the above equation, we get
[tex]$& P(\text { For } G)=5 / 12+4 / 12-(1 / 12) \\[/tex]
simplifying the equation, we get
[tex]$ P({For} G)=5 / 12+1 / 4 \\[/tex]
[tex]$& P(\text { For } G)=\frac{8}{12}[/tex]
Therefore, the value of P(F or G) using the general addition rule be 8/12.
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How do you do the square root of 48 over the square root of 42 this is Algebra 1?
Answer:
Step-by-step explanation:
Simplify the following:
(sqrt(48))/(sqrt(42))
Rationalize the denominator. (sqrt(48))/(sqrt(42)) = (sqrt(48))/(sqrt(42))×(42^(1 - 1/2))/(42^(1 - 1/2)) = (sqrt(48)×42^(1 - 1/2))/42:
(sqrt(48)×42^(1 - 1/2))/42
Combine powers. (sqrt(48)×42^(1 - 1/2))/42 = sqrt(48)×42^((1 - 1/2) - 1):
sqrt(48)×42^((1 - 1/2) - 1)
Put 1 - 1/2 over the common denominator 2. 1 - 1/2 = 2/2 - 1/2:
sqrt(48)×42^((2/2 - 1/2) - 1)
2/2 - 1/2 = (2 - 1)/2:
sqrt(48)×42^(((2 - 1)/2) - 1)
2 - 1 = 1:
sqrt(48)×42^(1/2 - 1)
Put 1/2 - 1 over the common denominator 2. 1/2 - 1 = 1/2 - 2/2:
sqrt(48)×42^(1/2 - 2/2)
1/2 - 2/2 = (1 - 2)/2:
sqrt(48)×42^((1 - 2)/2)
1 - 2 = -1:
sqrt(48)×42^((-1)/2)
sqrt(48) = sqrt(2^4×3) = 2^2 sqrt(3):
2^2 sqrt(3) 1/sqrt(42)
2^2 = 4:
4 sqrt(3) 1/sqrt(42)
Rationalize the denominator. (4 sqrt(3))/(sqrt(42)) = (4 sqrt(3))/(sqrt(42))×(sqrt(42))/(sqrt(42)) = (4 sqrt(3) sqrt(42))/42:
(4 sqrt(3) sqrt(42))/42
The gcd of 4 and 42 is 2, so (4 sqrt(3) sqrt(42))/42 = ((2×2) sqrt(3) sqrt(42))/(2×21) = 2/2×(2 sqrt(3) sqrt(42))/21 = (2 sqrt(3) sqrt(42))/21:
(2 sqrt(3) sqrt(42))/21
sqrt(3) sqrt(42) = sqrt(3×42):
2/21 sqrt(3×42)
3×42 = 126:
(2 sqrt(126))/21
sqrt(126) = sqrt(3^2×14) = 3 sqrt(14):
2/21 3 sqrt(14)
3/21 = 3/(3×7) = 1/7:
Answer: (2 sqrt(14))/7
What is a set of all X values *?.
The domain is actually the set of all "x" values, whereas the range is the set of all "y" values in an ordered pair.
Given,
What is the definition of the word "domain"?
Remember which of the following symbols corresponds to which ordered pair: (x, y).
When analyzing a set of ordered pairs, first list all the x values from the relation to establish the domain.To find the range, list each of the y values from the ordered pairs first.It is sufficient to list repeated values once as long as they fit within the domain or range.A relation cannot be a function unless each x value has a different value for the y value.If an x value has more than one y value connected with it, such as in the relation (4, 1), (4, 2), where the x value of 4 has y values of 1 and 2, a collection of ordered pairs is not a function.
Thus, the connection is referred to as a function if there is only one y value for every x value.
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How do you find product of mixed number and a fraction?.
1: Convert the mixed number into an improper fraction.
2: Rewrite the whole number as a fraction with the denominator 1.
3: Multiply two fractions by multiplying the numerators and denominators separately.
4: Convert it into simplified form if required.
Now, According to the question:
A mixed number is a whole number and a proper fraction represented together. It generally represents a number between any two whole numbers.
To multiply a mixed number with a fraction, first, convert the mixed number to a fraction and then multiply the two fractions. Two fractions can be multiplied by multiplying the numerators and denominators separately to get a fraction as an answer. The fraction can be written in its simplest form by removing any common factors between the numerator and denominator.
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If 6/7=A/49, then the value of a is
Answer:
A = 42
Step-by-step explanation:
If 6 / 7 = A / 49, then:
(multiply both sides of the equation by 49)
A = 49 * 6 / 7
A = 42
You can also solve by the rule of proportions (see picture):
7 * A = 6 * 49
A = 6 * 49 / 7
A = 6 * 7 = 42
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K As a town gets smaller, the population of its high school decreases by 4% each year. The senior class has 250 students now. In how m students? Write an equation. Then solve the equation. Write an equation to represent this situation. Let n be the number of years before the class will have 100 students. 0 (Type an equation using n as the variable. Use integers or decimals for any numbers in the equation.) Solve the equation. In n = years the senior class will have about 100 students. (Type an integer or decimal rounded to the nearest hundredth as needed.)
Answer:
y = 250(0.96^n)
Step-by-step explanation:
You want an equation for the number of students in the senior class after n years, when it has 250 students now and decreases at 4% per year. You also want to know the number of years until the class is 100 students.
Exponential equationThe exponential equation will have the form ...
y = a·b^x
where 'a' is the initial value, 'b' is the growth factor, and x is the independent variable.
ApplicationYou have an initial value of 250, a growth factor of (1+(-4%)) = 0.96, and an independent variable of 'n', representing the number of years the population has been declining. The equation is ...
y = 250(0.96^n)
100 studentsThe population will reach 100 students when n has the value that satisfies ...
100 = 250·0.96^n
0.4 = 0.96^n . . . . . . . . . divide by 250
log(0.4) = n·log(0.96) . . . . . take logarithms
n = log(0.4)/log(0.96) ≈ 22.45
The senior class will have about 100 students in 22.45 years.
__
Additional comment
The growth factor used in these exponential equations is (1 + growth rate), where the growth rate is the fractional change in the period of interest. The independent variable (x or n) is the number of such periods. Here, the fractional change is given as -4%, a 4% per year decrease. This tells us a period is 1 year. Of course -4% is the decimal fraction -0.04.
Mr. Blair and Ms. Stevenson are teaching their classes how to write in cursive. Mr. Blair has already taught his class 4 letters. The students in Ms. Stevenson's class, who started the unit later, currently know how to write 2 letters. Mr. Blair plans to teach his class 1 new letter per week, and Ms. Stevenson intends to cover 2. new letters per week. Eventually, the students in both classes will know how to write the same number of letters. How long will that take?
Answer:
2 weeks
Step-by-step explanation:
The next week Mr Blair’s class will have written 5 letters because his class wrote one more letter, while Ms Stevenson’s class will have written 4 letters because her class wrote 2 more letters. This next week Mr Blair’s class will write another letter leaving them at 6 letters, and Ms Stevenson’s class will write 2 more letters leaving them at 6 letters also. So all in all, in 2 weeks, the two classes will be at equal amounts and caught up to each other.
What is the slope of the line that passes through the points (4, 8) and (8, 6)? Write
your answer in simplest form.
PSSPY
Answer:
The slope is simply the gradient of the two points . use the gradient equation (Y2-Y1/X2-X1) to find the answer ;)
Graphing on a Number Line
18. Describe how to graph -6 and 5 on a number line.
Count 6 point from zero to the left side from zero for negative (-6) and for 5 count 5 points right from the zero on the number line.
What is number line?A number line in mathematics is a horizontal straight line with numbers spaced equally apart along that line. Some will have a defined beginning and end. We refer to these as closed number lines. Number lines may also be left empty or blank. A number ladder is almost a vertical number line.
Number lines are frequently used in elementary and middle school to help students develop skills like counting, adding, and subtracting numbers. They are typically introduced in kindergarten.
Additionally, it is very easy to read number lines. The values provided enable kids to compare and visualise the relationships between the numbers shown on the line, despite the fact that it isn't a ruler and the space between the numbers isn't fixed. In turn, this promotes the growth of number sense.
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What function is f/x )= Logbx?.
The logarithmic function
[tex] f(x) = log_{b}(x) [/tex] is represent the inverse of an exponential function f(x)= bˣ.
A logarithmic function involves logarithms. Its basic form is
[tex]f(x) = log_{a}(x) ,[/tex] , where a > 0. It is Log functions include natural logarithm (ln) or common logarithm (log). For example f(x) = ln(x). An exponential function is defined as a mathematical function in the form f(x) = aˣ , where “x” represent a variable and “a” is a constant number which is known as the base of the function and it's value always be greater than zero. Transcendental number e is mostly used as a base of exponential function base is f. We have, the logarithmic function
[tex]f(x) = log_{b}(x) [/tex] , is the inverse of an exponential function f(x) =bˣ, and which means that
[tex]y = log_{b}(x) [/tex], is bʸ = x. The expression bʸ = x is said to be the “exponential form” for the logarithm
[tex]y = log_{b}(x) [/tex].
Here, b is called the base (of the logarithm) and it should be positive constant.
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Complete question:
What function is
[tex]f(x)= log_{b}(x) ?[/tex]
2h²g∧4h∧5g-7hg²h∧6g³-4g²h³h∧4g³
simplify
every variable/coefficient is one individual thing
also ^means raised to the power of
The simplified exponential expression for this problem is given as follows:
-9h^7g^5.
How to simplify the exponential expression?The exponential expression for this problem is defined as follows:
2h²g^4h^5g - 7hg²h^6g³ - 4g²h³h^4g³.
When two terms with the same base and different exponents are multiplied, the bases are kept while the exponents are added.
Hence the terms are simplified as follows:
2h²g^4h^5g = 2h^(2 + 5)g^(4 + 1) = 2h^7g^5.7hg²h^6g³ = 7h^(1 + 6)g^(2 + 3) = 7h^7g^5.4g²h³h^4g³ = 4h^(3 + 4)g^(2 + 3) = 4h^7g^5.Hence the simplified expression is given as follows:
2h^7g^5 - 7h^7g^5 - 4h^7g^5.
(2 - 7 - 4)h^7g^5.
-9h^7g^5.
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Select the correct answer.
What is this expression in simplest form?
see picture
Answer:
1.
-x² + 2x
Step-by-step explanation:
x² + x - 2.
=x³ - x² + 2x - 2.
1
=-x² + 2x.
note: x³ cancel x² and x, and -2 cancel -2.
pleaz pleaz help i'll give 100 points pleazz help
Answer:
D. y = 5x
Step-by-step explanation:
This graph shows a linear relationship between the number of sandwiches bought (x) and their cost (y). In this question, we are asked to define the relationship between x and y using an equation. Since this relationship is linear and thus has a constant of proportionality, we can represent it in the form: y = mx, where m is the ratio of the cost of sandwiches to the number of sandwiches. We can solve for m with the formula:
m = rise / run
So, the value m of the given line is:
m = 10 / 2
m = 5
Hence, the equation that displays the proportional relationship between the number of sandwiches bought (x) and their cost (y) is D. y = 5x.
Factor the expression completely. 14 x 4 − 35 x
2
1 point
A motorcyclist is travelling at a constant speed of 40 miles an hour. How far will he travel in two and a half hours?
Type your answer...
I
OI
Answer: 183sr3, 370sr3
Step-by-step explanation:
What is the multiplicative inverse of − 6?.
The multiplicative inverse of 'a' is stipulate by a-1 or 1/a. on other side, the multiplicative inverse of a number is expounded as 1 divided by the number.
The multiplication inverse of 6 is 1/6.
hence, the multiplicative inverse of -6 is -1/6.
The multiplicative inverse is defined as the reciprocal of a given number. It is used to define mathematical expressions.
The word 'inverse' concludes something opposite/contrary in effect, order, position. or direction. A number when multiplied by its multiplicative inverse results in 1.
The multiplicative inverse formula is called that the multiply of a number and its reciprocal is 1.
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Point M is online to LN given LN equals 10 and LM equals 8 determine the length of mn
Answer:
2 ...
Step-by-step explanation:
since LM = 8
and LN = 10
therefore MN = LN - LM .
MN = 10 - 8 .
MN = 2
MARK ME AS BRAINLIEST ...The source or origin of a word is called its
Answer:
Etymology
Step-by-step explanation:
How to proof quadrilaterals? in geometry
Different quadrilaterals have different properties to get proven.
what are quadrilaterals?
A quadrilateral is a polygon with four sides, four vertices, and four angles.
It is formed by joining four non-collinear points. The sum of the interior angles of quadrilaterals is always equal to 360 degrees. The word quadrilateral is derived from the Latin words ‘Quadra’ which means four and ‘Latus’ means ‘sides’. Not all the four sides of a quadrilateral need to be equal in length. Hence, we can have different types of quadrilaterals based on sides and angles.
Now,
Five special quadrilaterals are shown below in the image, along with their definitions and pictures, and points for them to get proven.
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In the diagram below of triangle MNOP, P is the midpoint of MO and Q is the midpoint of NO. If PQ=5x+62 and MN=6x-4, what is the measure of PQ
The measure of length PQ will be 22 units.
What is the mid-point theorem?A triangle's third side is stated to be parallel to the line segment uniting its two midpoints, and it is also half as long as the third side.
Given:
PQ = 5x + 62, and MN = 6x-4
Now, using Mid- Point Theorem
PQ= 1/2 MN
-5x+ 62 = 1/2( 6x - 4)
-5x+ 62 = 3x - 2
-5x- 3x = -2 - 62
-8x = -64
x= 8
PQ= 5x+ 62 = -5(8) + 62 = -40 + 62 = 22
Hence, the measure of PQ is 22 units.
The missing image is attached below.
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How to calculate std deviation in R?.
To calculate std deviation in R you can create a list of values or import a CSV file to find the standard deviation.
It is simple to compute an average and standard deviation in R. The mean() and sd() functions compute the average and standard deviation, respectively.
The positive square root of the variance is the standard deviation. One of the fundamental techniques used in statistical analysis is standard deviation. Standard deviation, also known as SD or indicated by the symbol "," indicates how far a value deviates from the mean value.
A low standard deviation indicates that the values are often within a few standard deviations of the mean, whereas a large standard deviation indicates that the values are much outside of the mean. Learn how to determine a random variable's standard deviation as well as the standard deviation of data that has been grouped and ungrouped.
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The base of an isosceles triangle is equal to 1/3 of the lateral side. The height of the base together with the height is 9.2 cm. Calculate the perimeter of the triangle
The perimeter of the isosceles triangle is 128.8/(√35 +2) cm.
What is an isosceles triangle?
A triangle with two equal sides is said to be isosceles. Also equal are the two angles that face the two equal sides. In other terms, an isosceles triangle is a triangle with two sides that are the same length.
We are given that the base of an isosceles triangle is equal to 1/3 of the lateral side.
Also, the height of the base together with the height is 9.2 cm.
Let the lateral side be 'x' and the height be 'h'
So, the base is x/3
Since the height of the triangle, divides it into two right angled triangles, therefore,
x^2= h^2 + (x/6)^2
⇒h^2 = x^2 - (x/6)^2
⇒h^2 = √[x^2 - (x/6)^2]
We are given h+b=9.2 cm
So,
⇒√[x^2 - (x/6)^2] + x/3 = 9.2
⇒x√35/6 + x/3 = 9.2
⇒(x√35 +2x)/6 = 9.2
⇒x√35 +2x = 55.2
⇒x(√35 +2) = 55.2
⇒x = 55.2/(√35 +2)
So, the base is 1/3*55.2/(√35 +2) = 18.4/(√35 +2)
Perimeter = 2*55.2/(√35 +2) + 18.4/(√35 +2)
= (110.4 + 18.4)/(√35 +2)
= 128.8/(√35 +2) cm
Hence, the perimeter of the isosceles triangle is 128.8/(√35 +2) cm.
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5. Expresss 12,600 as a product of it's prime factors.
Answer:
Below in bold.
Step-by-step explanation:
To do this we keep dividing by successive primes, using the lowest prime that divides exactly.
2) 12600
2) 6300
2) 3150
3) 1575
3) 525
5) 175
5) 35
7 <---we end up with a prime number so tha's the end of the process
So, 12,600 = 2*2*2*3*3*5*5*7 or 2^3*3^2*5^2*7.
Do a majority of the seniors prefer the prom at the high school ar at a hall? Decide if this is census or sample. Justify your answer.
A)Sample. There are too many seniors at a high school.
B)Census. There are too many seniors at a high school.
C)Sample. It's pretty easy to survey all the students at a high school.
D)Census. It's pretty easy to survey all the students at a high school.
The true statement is D)Census. It's pretty easy to survey all the students at a high school.
What are Census and Sampling:Census:All units or participants in the target population under the survey are statistically compiled as part of the census method's process.
Population in this context refers to the total collection of observations associated with a specific study.
For instance, if university students are asked for input on the teaching staff, the latter group will be considered the study's population.
SamplingThe targeted population is used to choose the various sample entities. With this approach, a predetermined number of observations that come from a bigger pool of populations are statistically analyzed.
Different types of sample methodology can be used, including basic random sampling, systematic sampling, cluster sampling, stratified sampling, and more.
By the above observations, we can conclude that This given situation is a Census as we can survey it among a collection of people that is the batch of senior students and it is easy to survey as there will be a few members of seniors in a school.
Therefore,
The true statement is D)Census. It's pretty easy to survey all the students at a high school.
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Write the equation of a square root function that has been reflected across the y-axis, stretched vertically by a factor of 2, and shifted up 4 units.
A. y= 2[tex]\sqrt{-x}-4[/tex]
B. y= 2[tex]\sqrt{-x}+4[/tex]
C. y= -2[tex]\sqrt{x}-4[/tex]
D. y= [tex]\sqrt{2x}+4[/tex]
Step-by-step explanation:
DISCUSSION QUESTIONS (DQ's).
1. Is division always a negative in a religious faith? Why or why not?
What are the solution's to the quadratic equation 9x2 4 group of answer choices?.
The exact solutions of an quadratic equation, 9x² - 4 is equals to the values of x, i.e., x = 2/3, - 2/3.
In algebra, a quadratic equation is any equation that can be written in standard form as ax² + bx + c = 0, where x represents an unknown variable, and a, b, and c are known constants, where a ≠ 0. The solutions of a quadratic equation represent x values, where values stratified the equation . Quadratic formula is used to find the solution of standard equation and it can be written as, x = (- b ±√b² - 4ac)/2a .
We have, an quadratic equation,9x²- 4=0
Comparing it with standard equation ax² + bx + c = 0, we get, a = 9 , b = 0 , c = - 4
Using the quadratic formula to determine the solution of it , x = (- b ±√b² - 4ac)/2a
=> x = { -0 ±√0 - 4×9×(-4)}/2×9
=> x = ±(√144/18)
=> x = ± 12/18 = ± 2/3
Hence, the required solution are x = ± 2/3.
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What is the rule for ordered pairs?.
An ordered pair contains one point's coordinates. The name of a point in an ordered pair is (x, y).
The first number stands for the x-coordinate, and the second for the y-coordinate. To graph a point, a dot must be placed at the ordered pair's coordinates. The name of a point in an ordered pair is (x, y). The first number stands for the x-coordinate, and the second for the y-coordinate. To graph a point, a dot must be placed at the ordered pair's coordinates.
A set of ordered pairs is any pair of components that are wrapped in brackets and exist in a specific sequence. If there are two components, "a" and "b," the two distinct pairings are "(a, b)" (b, a). A and B are referred to as the first and second elements, respectively, in an ordered pair (a, b). The relationship between the input or domain and the output or range is described by the function rule. If and only if there is only one value in the range for each domain value, a relation is a function.
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What is a negative exponential function called?.
Answer:
Step-by-step explanation:
Y = e−x
Answer: A negative exponential function or y = e−x, is otherwise known as exponential decay
Step-by-step explanation: I hope this helps!
Is 0 a real value of x?.
Yes. Zero is a real value of x.
Given,
Real value of x;
The non-negative value of a real number x, regardless of its sign, is its absolute value (or modulus), | x |. For instance, 5 has an absolute value of 5, and 5 has a value of 5.
How do you discover the true worth?
The influence of price level changes is subtracted from the nominal value of a good, service, or time-series data to create real value, which provides a more accurate view of economic trends. A deflator is used to alter the nominal value of time-series data, such as GDP and incomes, in order to produce real values.
Here,
The real value of x includes 0.
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Gentiana i going to the movie to ee Wakanda Forever. Her mom gave her $40 to pend. Gentiana ue $10 for her entrance fee, 25% on a luhie, 20 % on popcorn and the remaining on a pizza pie. How much money did the pizza pie cot?
The pizza pie cost $16.50.
We have the following information. An equation is a mathematical statement that asserts the equality of two expressions. It is written in the form of "left-hand side = right-hand side," where both sides are expressions that are made up of numbers, variables, and mathematical operations.
Gentiana spent $10 on her entrance fee, so she has $40 - $10 = $30 left.
25% of $30 is $30 x 0.25 = $7.50.
She spent $7.50 on a Movie.
20% of $30 is $30 x 0.20 = $6.
She spent $6 on popcorn.
So, the total amount spent on Movie and popcorn is $7.50 + $6 = $13.50.
Therefore, the pizza pie cost $30 - $13.50 = $16.50
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25% of $30 is $30 x 0.25 = $7.50.
She spent $7.50 on a Movie.
20% of $30 is $30 x 0.20 = $6.
She spent $6 on popcorn.
So, the total amount spent on Movie and popcorn is $7.50 + $6 = $13.50.
Therefore, the pizza pie cost $30 - $13.50 = $16.50
What is the example of perfect square trinomial?.
Answer:
x^2 + 6x + 9 and x^2 + 8x + 16 are examples of perfect-square trinomial
Step-by-step explanation:
1. x2 + 6x + 9
(x + 3)^2
= (x + 3)(x + 3)
= x2 + 6x + 9
2. x^2 + 8x + 16
x^2 + 8x + 16
= x^2 + 2(x)(4) + 4^2
= (x + 4)^2
