The number that goes in the box is 4, since 4 + (-2) = 2, which is the coefficient of x^2 in the equation. The third step is to add the same number to both sides of the equation, so the box needs to contain 4.
To complete the third step in solving a quadratic equation using the completing the square method, the number that goes in the box is 4. This is because the goal is to make the coefficient of x^2 on the left side of the equation equal to the coefficient of x^2 on the right side. The equation is x^2 - 8x + 2 = 0, so the coefficient of x^2 on the left side is 1, and the coefficient of x^2 on the right side is 2. Therefore, the number that needs to be added to the left side is 1, and the number that needs to be added to the right side is also 1. This means that 4 needs to be added to both sides of the equation, so 4 is the number that goes in the box.
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Can someone help? I’m stuck on these. I’ll give brainliest!!
The system of equations is y = - x - 5 and y = - x - 9.
y = - 4/3 x - 1/3 and y = - 5/4x + 1/4.
what is meant by equations?
The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions.For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.The point-slope form, standard form, and slope-intercept form are the three main types of linear equations.a formula that expresses the connection between two expressions on each side of a sign.Typically, it has a single variable and an equal sign. Like this: 2x - 4 Equals 2.Any equation's general form includes the degree of variables in descending order. A linear equation has the general form an x + b = 0.To learn more about equations refer to
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Use a right triangle to write the following expression as an algebraic expression. Assume that x is positive and that the given inverse trigonometric function is defined for the expression in X. cos (sin - 15x) Identify the right triangle that can be used to simplify the given expression. Choose the correct answer below.
The expression cos (sin - 15x) is a composition of two trigonometric functions, cosine and sine. To simplify this expression, we can use the identity cos (a - b) = cos a cos b + sin a sin b.
To use this identity, we need to identify a right triangle that relates the two trigonometric functions in the expression. One such triangle is the one that relates the sine and cosine functions, known as the "sine-cosine triangle".
This triangle relates the sine and cosine functions through the following identities:
sin a = y/r
cos a = x/r
Where a is the angle opposite to the side of length y, x is the side opposite to angle a and r is the hypotenuse of the triangle.
We can use these identities to write the given expression as:
cos (sin - 15x) = cos (y/r - 15x) = cos y/r cos(-15x) - sin y/r sin(-15x)
This is by using the identity cos (a-b) = cos a cos b - sin a sin b
The expression cos (sin - 15x) can be written as cos y/r cos(-15x) - sin y/r sin(-15x)
It's important to note that this simplified expression is still not in its final form as we have no information about the value of y and r, this is only possible if we have a specific angle or triangle that we are working with.
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List all the vertices, edges, and faces in the figure below.
The vertices are A, B, C, D, E, F. The edges are AB, BC, CA, ED, DF, FE, BD, CF, and AE and the faces are DBCF, DEAB, EFCA, EDF, and ABC.
What are vertices, edges, and faces?The three-dimensional shape's vertices are the points at which the edges converge. Edges are the lines where two faces converge, while faces are flat surfaces.
Vertices are the locations where the sides of a polyhedron constructed of line segments connect.
According to the definition given above, the vertices are A, B, C, D, E, and F.
Line segments from which the formation of a polyhedron takes place are known as edges.
Hence in the given figure, AB, BC, CA, ED, DF, FE, BD, CF, and AE are the edges.
Two-dimensional surfaces in a three-dimensional figure are known as faces.
In the given prism, DBCF, DEAB, EFCA, EDF, and ABC are the faces of the prism.
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The wind chill Index W is the perceived temperature when the actual temperature is T and the wind speed is v, so we can write W = f(T, v)
Estimating : Ft( -15,40 ) = ( 1.2 + 1.4 ) / 2 = 1.30⁰c
when the actual temperature is -15⁰c and the wind speed is 40 km/h the apparent temperatures increase by 1.3⁰c that the actual temperature rises
estimating: Fv ( -15,40 ) = (-0.2 + -0.1 ) / 2 = -0.15⁰c
when the actual temperature -15⁰c and the wind speed is 40 km/h the apparent temperature decreases by 0.15⁰c for every km/h that the wind speed
A) Estimating the values of Ft(−15, 40) and fv(−15, 40)
To estimate the value of Ft( -15,40 ) we have to take an average value hence Ft ( -15,40 ) = ( 1.2 + 1.4 ) / 2 = 1.30
and this means that when the actual temperature is -15⁰c and the wind speed is 40 km/h the apparent temperatures increase by 1.3⁰c that the actual temperature rises
To estimate the value of Fv(-15,40 ) we have to take an average value
hence Fv ( -15,40 ) = (-0.2 + -0.1 ) / 2 = -0.15
and this means that when the actual temperature -15⁰c and the wind speed is 40 km/h the apparent temperature decreases by about 0.15⁰c for every km/h that the wind speed.
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The complete question is :
The wind-chill index W is the perceived temperature when the actual temperature is T and the wind speed is v, so we can write W = f(T, v). (a) Estimate the values of fT(−15, 40) and fv(−15, 40). (Round your answers to two decimal places.) fT(−15, 40) ≈ fv(−15, 40) ≈ What are the practical interpretations of these values? When the actual temperature is −15°C and the wind speed is 40 km/h, the apparent temperature ---Select--- by about °C for every degree that the actual temperature rises. When the actual temperature is −15°C and the wind speed is 40 km/h, the apparent temperature.
Find the area of the figure.
Answer:
A = 30 yd²
Step-by-step explanation:
the figure is a trapezium whose area (A) is calculated as
A = [tex]\frac{1}{2}[/tex] h (b₁ + b₂)
where h is the perpendicular height between bases b₁ and b₂
here h = 5 , b₁ = 8 , b₂ = 4 , then
A = [tex]\frac{1}{2}[/tex] × 5 × (8 + 4) = 2.5 × 12 = 30 yd²
At a college, 51% of the students are woken, 25% are business majors…
15. What is the probability that a randomly selected student will either be a woman or a business major?
The probability that a randomly selected student will either be a woman or a business major will be 76%.
How to calculate the probability?Probability simply means the chance that a particular thing or event will happen. It is the occurence of likely events. It is simply the area of mathematics that deals with the numerical estimates of the chance that an event will occur or that a particular statement is true.
In this case, at the college, 51% of the students are women, 25% are business major, the probability that a randomly selected student will either be a woman or a business major will be:
= 25% + 51%
= 76%
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Popcorn at a concession stand comes in two different-sized containers. The dimensions of the small container with a diameter of 4 in. are shown below.
A popcorn container shaped like a cylinder is shown. A dashed line across the top of the container is labeled four inches. The height of the container is labeled four and five tenths inches.
The large container of popcorn has the same height as the small container, but its diameter is 1.5 times greater. How do the volumes of the two containers of popcorn compare? Use 3.14 for π.
Select the answers from the drop-down lists to correctly complete each sentence.
The volume of the large container of popcorn is _______ in.^3
OPTIONS FOR BLANK :
A) 56.52
B) 84.78
C)127.17
D) 169.56
This is ______ times the volume of the small container.
OPTIONS FOR THIS BLANK :
A) 2.88
B) 2.25
C) 1.8
D) 1.5
The volume of the large container of popcorn is 56.52 in³
This is 2.25 times the volume of the small container.
How to determine how the volumes of the two containers of popcorn compare?The volume of a cylinder is given by the formula:
V = πr²h
where r and h represent the radius and height respectively
Volume of small container = 3.14 × 2² × 4.5 = 56.52 in³
For large container:
diameter = 1.5 × 4 = 6 in and radius = 3 in
Volume of large container = 3.14 × 3² × 4.5 = 127.17 in³
Volume of large container/Volume of small container = 127.17/56.52 = 2.25
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Heather , deon and trey sent a total of 109 text messages over their cell phones during the weekend. Trey sent 3 times as many messages as deon. Deon sent 9 fewer messages than heather . How many messages did they each send
Answer:
Deon sent 20 messages
Trey sent 60 messages
Heather sent 29 messages
Step-by-step explanation:
Explanation above
what percent of 125 is 250?
what percent of 45 is 9?
what percent of 250 is 100?
what percent of300 is 75?
1) 250÷125=2×100=200%
2) 9÷45= 0.2×100= 20%
3) 100÷250=0.4×100=40%
4) 75÷300=0.214×100=21.4%
Determine whether the quantitative variable is discrete or continuous. the low temperature in degrees Fahrenheit on January 1st in Cheyenne, Wyoming discrete continuous
Whether a discrete or continuous quantity is used. the lowest temperature recorded on January 1st in Cheyenne, Wyoming, in degrees Fahrenheit
What is meant by Fahrenheit temperature?The Fahrenheit temperature scale divides the distance between the freezing point of water, 32°, and the boiling point of water, 212°, into 180 equal parts. Add 32 and multiply by.5556 (or 5/9) to convert temperatures from degrees Fahrenheit to degrees Celsius. Add 32 and multiply by 1.8 (or 9/5) to convert temperatures from degrees Celsius to Fahrenheit.The temperature is measured in Fahrenheit (°F) in the US. 30 degrees Fahrenheit is extremely cold, whereas 100 degrees is extremely hot. A really cold day is indicated by the left thermometer.What makes America utilise Fahrenheit. Fahrenheit had made significant progress in the 18 years it had been as the only temperature scale.To learn more about Fahrenheit, refer to:
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Solve and graph. --6x < 21
[tex]-6x < 21[/tex]
Divide both sides by -6:
[tex]\dfrac{-6x}{-6} < \dfrac{21}{-6}[/tex]
[tex]x > -\dfrac{7}{2}[/tex], [tex]x > -3.5[/tex]
: find the point on a directed line segment between two given points that partitions the segment in a given ratio.
The point that partitions the line in the ratio of 1:3 is (1.333, 3.333).
Given two points P1(x1,y1) and P2(x2,y2), the point that partitions the directed line between these two points in a given ratio r can be calculated using the following formula:
P(x,y) = (x1 + r(x2-x1), y1 + r(y2-y1))
For example, if we have P1(1,2) and P2(4,6) and we want to partition the line in a ratio of 1:3, the point P(x,y) can be calculated as follows:
P(x,y) = (1 + 1/3(4-1), 2 + 1/3(6-2)) = (1.333,3.333)
Therefore, the point that partitions the line in the ratio of 1:3 is (1.333, 3.333).
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The perimeter of the shape is 51.42 cm
Calculate the value of the diameter d.
Take to be 3.142
TU
Answer:
The perimeter of a circle is equal 2 * pi * radius. So, if we let "d" be the diameter of the circle, we can use the following to solve for the radius:
Perimeter = 2 *p * radius = 51.42 cm
we can then use the relationship between the diameter and the radius to solve for the diameter:
d = 2 * radius
substitute the value of the perimeter equation into the diameter equation:
d= 2 * (51.42 cm / 2 * 3.142)
d= 33.49 cm
therefore, the diameter d is 33.49 cm
There were seven serving lines at the
annual pancake breakfast. The total
number of people served at each of
the seven lines were 126, 118, 127, 134,
98, 132, and 121. What was the median
number of people served?
Please help!! :)
In the figure, GH = HI = IJ. Find each length.
It takes Johnny 42 minutes to get to the zoo.After 18 minutes he stopped to get gas for his car .Write an equation to express how many more minutes he had to travel after getting gas
The equation to express how many more minutes he had to travel after getting gas is 42 - 18 = x.
What are the relation between time, distance, and speed?
The formula for speed is speed = distance ÷ time. To work out what the units are for speed, you need to know the units for distance and time. In this example, distance is in meters (m) and time is in seconds (s), so the units will be in meters per second (m/s).
The equation to express how many more minutes Johnny had to travel after getting gas is:
42 - 18 = x
Johnny's total travel time to the zoo is 42 minutes
He stopped for 18 minutes to get gas for his car
To find out how many more minutes he had to travel after getting gas, we need to subtract the 18 minutes he spent getting gas from his total travel time.
This is represented by the equation 42 - 18 = x, where x represents the number of minutes he had left to travel after getting gas.
Hence, The equation to express how many more minutes he had to travel after getting gas is 42 - 18 = x.
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The lengths of the two sides of a right triangle containing the right angle differ by 2 cm. If the area of the triangle is 24cm 2
, find the perimeter of the triangle.
The perimeter of the triangle is 28 cm. The perimeter of the triangle containing the right angle with two sides that differ by 2 cm is 28 cm. This can be determined by using the Pythagorean Theorem to solve for the length of the sides.
Let the two sides of the right triangle be x and x+2
Apply the Pythagorean Theorem:
(x)^2 + (x + 2)^2 = 24
x^2 + x^2 + 4x + 4 = 24
2x^2 + 4x = 20
2x(x + 2) = 20
x(x + 2) = 10
x = 5 and x + 2 = 7
Therefore the perimeter of the triangle is 5 + 7 + 7 = 19 cm.
The perimeter of the triangle is 28 cm.
The perimeter of the triangle containing the right angle with two sides that differ by 2 cm is 28 cm. This can be determined by using the Pythagorean Theorem to solve for the b of the sides. The equation 2x(x + 2) = 20 can be used to solve for x, which is equal to 5. Therefore, the two sides of the triangle are 5 cm and 7 cm. Adding these lengths together, the perimeter of the triangle is 5 + 7 + 7 = 28 cm.
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Ivan must choose a number between 55 and 101 that is a multiple of 4, 10, and 20. Write all the numbers that he could choose. If there is more than one number, separate them with commas.
Using the LCM, the numbers that Ivan could choose between 55 and 101 which are multiples of 4, 10, and 20 are 60, 80, and 100.
What is a multiple of numbers?A multiple of numbers is the lowest common multiple (lcm) of two or more numbers.
The LCM shows the numbers into which the given numbers can divide without a remainder. The result is always an even integer.
Between 55 and 101, we know that 4, 10, and 20 can each divide 60, 80, and 100 without leaving a remainder.
For example, when 4 divides 60, 80, and 100, we have 15, 20, and 25.
When 10 divides 60, 80, and 100, we have 6, 8, and 10.
Lastly, when 20 divides 60, 80, and 100, we have 3, 4, and 5.
Thus, Ivan can choose 60, 80, and 100, which are between 55 and 101 as the multiples of 4, 10, and 20.
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Directions: Solve for x. Round to the nearest tenth.
Answer:
x = 73
Step-by-step explanation:
Since it's asking for the angle it's going to be inverse (sin-1,cos-1,tan-1)
It only gives you the opposite side and the hypotenuse
You can find the opposite side by going opposite from the missing angle like basically the side that is not being touched by x (The 4) This is the opposite angle
The hypotenuse is always going to be the long angle that is on the opposite side of the right angle (The 6) This is the hypotenuse
The adjacent side is the side not opposite to the x
Remember the acronym SOH CAH TOA
sin-opposite/hypotenuse
cos-adjacent/hypotenuse
tan-opposite/adjacent
The opposite and hypotenuse are the only sides that gave a number so it is sin and is inverse
[tex]sin^{-1} (\frac{4}{6} ) = .729[/tex]
hope this helps
A store sells oranges and apples. Oranges cost $1.00 each and apples cost $2.00 each. In the first sale of the day, 15 fruits were sold in total, and the price was $25. How many of each type of frust was sold?
A store sells 5 oranges and 10 apples.
What is the cost amount?
The cost of an asset to you often serves as its basis. The cost is the sum that you pay for it using money, debt, other goods, or services. Sales tax and other purchase-related costs are included in the price.
Here, we have
Given: A store sells oranges and apples. Oranges cost $1.00 each and apples cost $2.00 each. In the first sale of the day, 15 fruits were sold in total, and the price was $25.
We have to determine how many of each type of fruit were sold.
We, let the oranges be x.
let the apples be y.
x + y = 15...(1)
1x + 2y = 25...(2)
We subtract equation(2) from equation(1), we get
y = 10
Now we put the value of y in equation (1) and we get
x + 10 = 15
x= 5
Hence, a store sells 5 oranges and 10 apples.
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The function f is defined by the following rule
f(x)=2x+1
Complete the function table
Function Table:
x f(x)
0 1
1 3
2 5
3 7
4 9
5 11
6 13
7 15
8 17
9 19
And so on, f(x) will always be 2x + 1.
V
Let sets A and B be defined as follows.
A={c, d, e, f, g}
B is the set of integers greater than -5 and less than 4
(a) Find the cardinalities of A and B.
n(A) = 5
n(B) = [
Answer:
n(A) = 5
n(B) = 8
Step-by-step explanation:
Cardinality of a set is the number of elements in that set
A has 5 elements so n(A) = 5
The set of integers >- 5 but less than 4 is
B: {- 4, - 3, - 2, - 1, 0, 1, 2, 3}
There are 8 elements in set B so n(B) = 8
PLEASE THIS IS DUE SOON!!!!
QUESTION DOWN BELOW
The data are reported with a mean and standard deviation of 3 and 1.72, respectively.
What is the standard deviation?The term "standard deviation" (or "") refers to a measurement of the data's dispersion from the mean. A low standard deviation implies that the data are grouped around the mean, whereas a large standard deviation shows that the data are more dispersed.
Given a histogram and we need to find the values of the Mean and standard deviation.
For mean:
Step 1: Multiply the category (number) by the height of each bar in our histogram (how many of each number we have).
Step 2: To obtain the total of our data, add each of the goods determined in Step 1 together.
Step 3: To determine our mean, divide this amount by the total of the bars' heights.
Multiply each category by its respective height.
1* 60 = 60
2 * 30 = 60
3*10 = 30
4 * 30 = 120
5 * 60 = 300
Add the products from Step 1 together.
Adding these products together, we get: 60 + 60 + 30 + 120 + 300
Sum = 570
Divide this sum by the sum of the heights of the categories.
The sum of the heights of the categories will tell us how many individual pieces of data we have. In this case, this is:
60 + 30 + 10 + 30 +60
Sum of frequency = 190
So, we need to divide the sum of the products in Step 2 by the sum of the heights given above to get our mean.
Mean = 570 /190
Mean = 3
Therefore, the Mean and standard deviation of the given data are 3 and 1.72 respectively.
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For a nonnegative real number x > 0, let {x} denote its fractional part. For instance, {1.2345} = 0.2345, {n} = 0.14159..., {} = 0.4, and so on.
The domain and the range of an exponential parent function mean that the domain is all real numbers and the range signifies positive real numbers y > 0.
What is an exponential parent function?
The simplest parent function of an exponential function takes the form:
f(x)= p ^x , where p refers to the base.
So, if we have a number such that x = 3 and the base is 2
f(3) = 2³
f(3) = 6
Therefore, we can conclude that the domain of an exponential parent function is all real numbers, and the range is positive real numbers (y > 0).
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the principal of a large high school is concerned about the number of absences for students in his school to investigate friends list showing the numbers of absences during the last month of each of the 250
The shape of the sampling distribution of the sample mean is approximately normal because the sample size is greater than 3.
Why do we use sampling distribution?The sampling distribution is the probability distribution of a statistic obtained from a larger sample size drawn from a particular population. The sampling distribution of a certain population is the frequency distribution of a set of possible outcomes for a population statistic.The sampling distribution is the probability distribution of a statistic that is created by drawing several samples from a certain population. Researchers use sample distributions to simplify the statistical inference process.The sampling distribution of a proportion is obtained by repeating your survey or poll for each possible sample of the population. For instance, instead of asking 1,000 cat owners what cat food they like, you could conduct a number of surveys.Given data :
a ) Approximately normal because the sample size is greater than 3.
b ) b ) ux = 1.1 and Jx = = 0.198
c ) c ) P ( ux ∠ 1 ) = normal cdf ( lower : 1000, upper : 1, u : 1.1 , J : 0.198 ) = 0.3068
d ) The principal could pick 50 students may times and find the median and repeat several times until he has every possible sampling distribution.
Completed question :
The principal of a large high school is concerned about the number of absences for students at his school. to investigate, he prints a list showing the number of absences during the last month for each of the 2500 students at the school. for this population of students, the distribution of absences last month is skewed to the right with a mean of 1.1 and a standard deviation of (1.4). suppose that a random sample of 50 students is selected from the list printed by the principal and the sample mean number of absences is calculated.
a.) What is the shape of the sampling distribution of the sample mean? Explain
b.) What are the mean and standard deviation of the sampling distribution of the sampling mean?
c.) What is the probability that the mean number of absences in a random sample of 50 students is less than 1?
d.) Because the population distribution is skewed, the principal is considering using the median number of absences last month instead of the mean number of absences to summarize the distribution. Describe how the principal could use a simulation to estimate the standard deviation of the sampling distribution of the sample median for random samples of size 50.
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Unit 3 Cumulative Assessment
What is the height, x, in the triangle below?
5
X
O A 2√5
OB. 5
O C. 5√2
OD. 10
10
The height, x, in the triangle is 0 units.
What to find perpendicular distance?
Perpendicular distance is a measure of the distance between a point and a line. It is the shortest distance between the point and the line, and it is always perpendicular to the line. The perpendicular distance is also known as the "altitude" or "height" in geometry.
In the triangle, the side OB is 5 units and the side OC is 5√2 units. The height, x, is the perpendicular distance from the vertex O to the line segment OB.
Using the Pythagorean theorem, we can find the value of x:
x^2 + (5)^2 = (5√2)^2
x^2 = (5√2)^2 - (5)^2
x^2 = 25 - 25
x^2 = 0
x = 0
Therefore, the height, x, in the triangle is 0 units.
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given a list of clothing items [a, b, c, ...] and a list of illegal outfits [[a, b], [a, c], ...], return the number of legal outfit combinations. a combination has to have at least 1 outfit and must not contain any illegal combination.
The objective of backtracking, an algorithmic methodology, is to find every possible solution to a problem by applying the "brute force" method.
What is backtracking used for?
Crosswords, verbal arithmetic, Sudoku, and many other puzzles that need constraint fulfilment may all be solved using backtracking. For parsing, the knapsack problem, and other combinatorial optimization issues, it is frequently the most practical method.
The objective of backtracking, an algorithmic methodology, is to find every possible solution to a problem by applying the "brute force" method. It entails gradually compiling a collection of each answer. A issue would have limits, so any solutions that don't meet them would be eliminated
.
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16w) 3 4 Write your answer in the form A or A B , where A and B are constants or variable expressions that have no variables in common. All exponents in your answer should be positive. Submit
The required expression is 4w4w² or Aw.Bw².
What is an expression?One mathematical expression makes up a term. It might be a single variable (a letter), a single number (positive or negative), or a number of variables multiplied but never added or subtracted. Variables in certain words have a number in front of them. A coefficient is the number used before a phrase.
Given:
An expression,
16w³.
To write an answer in the form A or AB, where A and B are constants or variable expressions that have no variables in common:
16w³,
= 4w 4w²
Where A = 4 and B = 4.
So, 16w³ = Aw.Bw².
Therefore, the expression is 4w4w² or Aw.Bw².
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Find the volume of a square based pyramid with a base length of 7 and a height of 12
Answer:
V=a2h3
Step-by-step explanation:
help me solve this pls
Answer:
30.25π mm^2
Step-by-step explanation:
The area of a circle is π · r^2. simply plug in the radius of 5.5 into "r" and then you square it. Squaring it would result in 30.25. Finally, you multiply it with π. Since you are multiplying two unlike terms, you put the coefficient first and then the variable. The measurements are in millimeters squared so you would have to add them after 30.25π otherwise it would be wrong.
