The solution to the cube root equation ^3√(x + 1) - 2 = 0 is x = 7.
To solve the cube root equation ^3√(x + 1) - 2 = 0, you can follow these steps:
Isolate the cube root term: Add 2 to both sides of the equation, resulting in ^3√(x + 1) = 2.
Remove the cube root by raising both sides to the power of 3: Cubing both sides gives (^3√(x + 1))^3 = 2^3. This simplifies to x + 1 = 8.
Isolate the variable x: Subtract 1 from both sides of the equation, resulting in x = 8 - 1, which simplifies to x = 7.
In summary, to solve a cube root equation, you need to isolate the cube root term by performing inverse operations on the equation. In this case, adding 2 to both sides isolated the cube root term.
Then, you remove the cube root by raising both sides to the power of 3, which simplifies the equation to x + 1 = 8. Finally, by isolating the variable x, you subtract 1 from both sides to obtain the solution x = 7.
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Four points partition the directed line segment from A to B.
• Point P partitions the directed line segment from A to B into a 3:4 ratio.
• Point Q partitions the directed line segment from A to B into a 4:3 ratio.
• Point R partitions the directed line segment from A to B into a 2:5 ratio.
• Point S partitions the directed line segment from A to B into a 5:2 ratio.
A number line has points A and B. A line is drawn from point A to point B.
Which distance measures 5 units?
A number line going from negative 8 to positive 8. A closed circle appears at negative 8 and is labeled W. A closed circle appears at negative 3 and is labeled X. A closed circle appears at positive 1 and is labeled Y. A closed circle appears at positive 5 and is labeled Z. An orange arrow line extends the length of the number line and contains all points.
the distance between points W and X
the distance between points X and Y
the distance between points X and Z
the distance between points Y and Z
The correct option is (iii) the distance between points X and Z. Distance between points Y and Z: 2 units
We can find the distance between points on the line segment by finding the difference between their coordinates.
The correct option is the distance between points X and Z, which is equal to 6.
There are four points that partition the directed line segment from A to B.
The partition ratio at each point is as follows:
Point P partitions the directed line segment from A to B into a 3:4 ratio.
Point Q partitions the directed line segment from A to B into a 4:3 ratio.Point R partitions the directed line segment from A to B into a 2:5 ratio.
Distance between points Y and Z:
Again, the number line does not provide the exact coordinates of the points Y and Z. However, the line segment from A to B is split 5:2 at point S, so the distance can be concluded as: Between Y and Z is 2 units.
So the distance between the given points is:
Distance between points W and X: 5 units
Distance between points X and Y: 4 units
Distance between points X and Z: 5 units
Distance between points Y and Z: 2 units
Point S partitions the directed line segment from A to B into a 5:2 ratio.
Here, we have to measure the distance of each of the following:
(i) The distance between points W and X
(ii) The distance between points X and Y
(iii) The distance between points X and Z
(iv) The distance between points Y and ZThe distance between points X and Z is 6 units.
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The distances are described as follows:
The distance between points W and X is 5 units.
The distance between points X and Y is 4 units.
The distance between points X and Z is 8 units.
The distance between points Y and Z is 4 units.
How do we calculate?The distance between points W and X is gotten:
We subtract the coordinates of point W from the coordinates of point X to get the distance
Distance = X - W = (-3) - (-8) = 5 units.
The distance between points X and Y shown as :
we will also subtract the coordinates of point X from the coordinates of point Y.
Distance = Y - X = 1 - (-3) = 4 units.
The distance between points X and Z is :
We also subtract the coordinates of point X from the coordinates of point Z.
Distance = Z - X = 5 - (-3) = 8 units.
The distance between points Y and Z:
Finally, we subtract the coordinates of point Y from the coordinates of point Z.
Distance = Z - Y = 5 - 1 = 4 units.
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14
Type the correct answer in the box. Round off your answer to the nearest integer.
Two planes, A and B, start from the same place and move in different directions, making an angle of 50° between them. The speed of plane A is
200 miles per hour, and the speed of plane B is 300 miles per hour.
The two planes are
miles apart after one hour.
The two planes are approximately 200 miles apart, rounded off to the nearest integer.
Using the Law of Cosines formula,
The distance between the two planes can be determined.
The formula for the Law of Cosines is as follows: c^2 = a^2 + b^2 - 2ab*cos(C), where c is the side opposite the angle C and a and b are the other two sides.
Using the formula, the distance between the two planes after one hour can be calculated as follows:
[tex]c^2[/tex] = [tex]200^2[/tex] + [tex]300^2[/tex] - 2(200)(300)cos(50°)[tex]c^2[/tex]
= 40,000 + 90,000 - 120,000cos(50°)[tex]c^2[/tex]
= 130,000 - 89,873.86c
= sqrt(40,126.14)c
= 200.315 miles
Therefore, after one hour, the two planes are approximately 200 miles apart, rounded off to the nearest integer.
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Considering only the domain shown on the graph, over which interval is the value of the exponential function greater than
the value of the quadratic function?
O-2.5≤x≤-0.75
0 1
O-05≤x<1
01
The range for which the graph of the exponential is greater than the quadratic function is the required range which is -0.5≤x<1
The parabolic curve drawn on the graph represents the quadratic function while the other curved line represents the exponential function.
The required range is where the exponential curve is above the quadratic curve. At this range the value of the exponential function would be greater than that of the quadratic function.
Hence, the required interval is -0.5≤x<1
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Here is a data set summarized as a stem-and-leaf plot:
5
00012333478
6
01112445778888
7
03579
8
667
How many data values are in this data set? n =
The number of values in the data-set in this problem is given as follows:
n = 33.
What is a stem-and-leaf plot?The stem-and-leaf plot lists all the measures in a data-set, with the first number as the key, for example:
4|5 = 45.
The number of values in the data-set is given by the number of leafs of the plot.
Hence the number of values in the data-set in this problem is obtained as follows:
11 + 14 + 5 + 3 = 33.
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The total of 50 leaves in the given stem-and-leaf plot. There are 50 data values in this dataset.
A stem-and-leaf plot is a method for displaying data.
It is commonly used to depict the distribution of a dataset.
Determining the number of data values in a given dataset requires counting the individual data points represented by the stem-leaf diagram.
In a stem-and-leaf plot, each data value is split into a stem and a leaf, which is then arranged in order.
In the given stem-and-leaf plot, the data values are:
5 0 0, 0 1, 2 3 3 3, 4 7 8, 6 0 1 1 1 2, 4 4 5 7 7 8 8 8, 7 0 3 5 7 9, 8 6 6 7
There are different methods to determine the number of data values in a dataset.
Looking at the stem-and-leaf graph, we can see that each digit represents a data point.
Counting the digits in each stem gives:
stem 5: 1 digit
stem 6: 5 digits
stem 7: 4 digits
stem 8: 3 digits
Summing the digits of each stem gives:
1 + 5 + 4 + 3 = 13
So there are 13 data values in this dataset.
The simplest method is to count the number of data values by looking at the stem-and-leaf plot.
By counting the number of leaves in the plot, we can determine the number of data values in the dataset.
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Central High School plays Eastern High School in a basketball game. Eastern had double the score of Central before Central scored a three-pointer as the game ended.
The variable, c, represents Central's score before the three-pointer. Express the total points scored in the game as a variable expression. Check all that apply.
2c + c
3c + 3
2c + 3
2c + c – 3
2c – c + 3
2c + c + 3
750$ were deposited intoan account with 7% interest rate compounded monthly how many years was it in the bank if the current amount is 1405$?
Answer:
Step-by-step explanation:
Compound interest is interest on interest.
To calculate the time for compound interest,
we can use the formula - A = P (1 + r/n)^(nt) ,
where A ⇒ future value of the investment,
P ⇒ the principal amount,
r ⇒ the annual interest rate,
n ⇒ is the number of times interest is compounded per year and
t ⇒ the number of years.
Given that,
P = 750$,
A = 1405$,
r = 7% and
n = 12 (since interest is compounded monthly).
We can solve for t by plugging in these values into the formula and solving for t :
1405 = 750(1 + 0.07/12)^(12t)
⇒ t ≈ 6.5 years
Therefore, the money was in the bank for approximately 6.5 years.
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Explain *step by step*
(I have no idea how to do this so a *very detailed* explanation would be very much appreciated)
Extra points given for that effort
2x+7
Step-by-step explanation:
When finding (x) not relating to a y=mx+b equation, start by setting your equation up to equal zero.
2x+7=0
Next you want to "isolate" the variable (get it by itself) as best as possible. Start by removing your extra number from the side of the equation where x resides. You may do this by opposing its symbol. ALWAYS MAKE SURE TO DO SOMETHING ON BOTH SIDES OF THE EQUAL SYMBOL!!
2x+7=0 -> subtract 7 from each side of the equal symbol so that the value still exists within the equation.
This would show:
(2x+7)-7=0-7
2x=-7
From here you want to continue isolating the variable.
Divide each side of the equal symbol by 2, so that we get rid of the coefficient, and arrive at what x truly equals by itself.
This would show:
2x/2=-7/2
x=[tex]\frac{-7}{2}[/tex]
In conclusion, the value of x is -7/2 (negative 7 halves)
does anyone have the keys for edmentum guided notes!!! please help
It is important to note that sharing or requesting specific keys or answers to educational materials, including guided notes, would be considered unethical and potentially a violation of academic integrity.
Guided notes are intended to assist students in actively engaging with course material and enhancing their learning experience. It is recommended that you approach your teacher or instructor for any clarification or additional resources you may need to fully understand the content.
They are in the best position to provide you with the necessary guidance and support.
Instead of seeking shortcuts or unauthorized access to answers, it is more beneficial to invest time and effort in studying, asking questions, and actively participating in your educational journey.
This approach will not only help you grasp the subject matter more effectively but also promote personal growth and knowledge development.
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For each value of w, determine whether it is a solution to -13=
W
9
27
[tex] - 13 = \frac{w}{9} - 6 \\ - 13 + 6 = \frac{w}{9} \\ - 7 = \frac{w}{9} \\ w = - 63[/tex]
so only -63 is the solution, the rest three are NOT solution for this equation.
how much water should be added to 16mL of 9% alcohol solution to reduce the concentration to 8%?
2mL of water must be added to 16mL of 9% alcohol solution to reduce the concentration to 8%.
To reduce the concentration of 16mL of 9% alcohol solution to 8%, we need to calculate the amount of water that must be added.
Here are the steps to follow:
The initial amount of alcohol in the solution
To calculate the initial amount of alcohol, we multiply the initial volume of the solution (16mL) by its initial concentration (9%):
Initial amount of alcohol = 16mL x 9%
= 1.44mL
Determine the final volume of the solutionWe can use the following formula to determine the final volume of the solution:
Initial amount of alcohol/ final concentration of alcohol = Final volume of solution
1.44mL / 8% = Final volume of solution
Final volume of solution = 18mL
The amount of water to addThe amount of water to add is the difference between the final volume of the solution and the initial volume of the solution:
Amount of water to add = Final volume of solution - Initial volume of solution
Amount of water to add = 18mL - 16mL
Amount of water to add = 2mL
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29.For n ≥ 3, a pattern can be made by overlapping n circles, each of circumference 1 unit, so that each circle passes through a central point and the resulting pattern has order-n rotational symmetry.
For instance, the diagram shows the pattern where n = 7.
If the total length of visible ares is 60 units, what is n?
The value of n can be determined by finding the number of visible arcs in the pattern, which is 30 in this case.
To determine the value of n, we need to find the relationship between the total length of visible areas and the number of circles (n).
In the given pattern, each circle contributes to the visible area twice: once as its circumference and once as the overlapping part with the adjacent circles. Since the circumference of each circle is 1 unit, the visible area contributed by each circle is 2 units.
Therefore, the total length of visible areas can be expressed as 2n. Given that the total length is 60 units, we can set up the equation:
2n = 60
Solving this equation, we find:
n = 60/2 = 30
Thus, the value of n is 30.
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Cakculate the Length of line x
The length of line x in the figure of the cube given is 19.
Calculate the length of the base of the cube, which is the diagonal of the lower sides :
base length = √10² + 6²
base length = √136
The length of x is the diagonal of the cube
x = √baselength² + 15²x = √(√136)² + 15²
x = √136 + 225
x = √361
x = 19
Therefore, the length of line x in the figure given is 19.
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The gasoline tax is a ______ tax
Answer:
Excise tax
Step-by-step explanation:
Correct me if I'm wrong <3
[14-(-6) + (-6)) : ( 17 + (-7) - (+3)] =
[4-(-1) + (-1)]: (23 + (−2) - (+2)) =
Answer:UNIT 1.7 - ALGEBRA 7 - SIMULTANEOUS LINEAR EQUATIONS. 1.7.1 Two ... 2. x−1(4x − x2) − 6(1 − 3x) ≡ 4 − x − 6 + 18x ≡ 17x − 2. ... (3)] we obtain.
Step-by-step explanation:
What is an example of "A one-to-one function of P onto Q is an isomorphism of P and Q "?
An example of a one-to-one function that is an isomorphism between sets P and Q is the function f: P -> Q defined as f(x) = 2x, where P and Q are the sets of integers.
How to Identify a One-to-One Function?An example of a one-to-one function that is an isomorphism between sets P and Q is the function f: P -> Q defined as f(x) = 2x, where P and Q are the sets of integers.
This function is one-to-one because for every element x in P, there is a unique element 2x in Q. It is onto because every element y in Q has a preimage x in P such that f(x) = y (e.g., y/2 = x).
Furthermore, this function preserves the group structure between P and Q, as it satisfies the properties of an isomorphism. In this case, the group structure is addition, and the function f preserves addition: f(x + y) = 2(x + y) = 2x + 2y = f(x) + f(y) for all x, y in P.
Therefore, the function f: P -> Q defined as f(x) = 2x is an example of a one-to-one function that is an isomorphism between sets P and Q.
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Finde the value of x in the proportion ( 5x+ 1 ):3 =(2x +2): 7(6 x) = (4x) :7
In the proportion (5x + 1):3 = (2x + 2):7, the value of x is -1/29.
In the proportion (6x):(4x) = 7, there is no value of x that satisfies the proportion.
To find the value of x in the given proportions, let's solve them one by one:
(5x + 1) : 3 = (2x + 2) : 7
To solve this proportion, we can cross-multiply:
7(5x + 1) = 3(2x + 2)
35x + 7 = 6x + 6
Subtracting 6x from both sides and subtracting 7 from both sides:
35x - 6x = 6 - 7
29x = -1
Dividing both sides by 29:
x = -1/29
Therefore, the value of x in the first proportion is -1/29.
(6x) : (4x) = 7
To solve this proportion, we can simplify the left side:
6x / 4x = 7
Dividing both sides by 2x:
3/2 = 7
This equation is not true, as 3/2 is not equal to 7.
Therefore, there is no value of x that satisfies the second proportion.
In summary, the value of x in the proportion (5x + 1) : 3 = (2x + 2) : 7 is -1/29, and there is no value of x that satisfies the proportion (6x) : (4x) = 7.
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Which of the following is a solution to the equation x^2=-81?
A. x=9
B. This equation has no real solution.
C. All real numbers.
D. x=-9
The answer is:
B. This equation has no real solution
Work/explanation:
To solve this equation, we square-root both sides:
[tex]\sf{x^2=-81}[/tex]
[tex]\sf{\sqrt{x^2} =\sqrt{-81}}[/tex]
And here things begin to happen. We cannot take the square root of a negative number.
So this leads us to the conclusion that this equation doesn't have a solution in the "Real Numbers" set.
However, we do have a solution in the "Complex Numbers" set.
Hence, B is the answer.Jameson Middle School gives bottles of water to teachers and students who are going
on a field trip. The school orders 25 bottles of water. The teachers get 6 bottles of water
altogether. Each student needs 2 bottles of water. At most, how many students could be
going on the field trip? Show your work.
At most, 9 students could be going on the field trip.
Let's denote the number of students going on the field trip as "x". We know that the total number of bottles of water ordered is 25.
The teachers receive 6 bottles of water altogether. Therefore, the number of bottles allocated to the students is 25 - 6 = 19.
Since each student needs 2 bottles of water, we can set up the equation:
2x = 19
To find the maximum number of students, we divide 19 by 2:
x = 19/2
The result is x = 9.5, which indicates that the maximum number of students going on the field trip can be 9 students. Since we can't have a fractional number of students, we round down to the nearest whole number. Therefore, at most, 9 students could be going on the field trip.
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sin(x) = 5/7 and x is in quadrant 2, determine the exact value of each of the following. Use fractions and radicals only, no decimals. You do not need to rationalize the denominator. sin(x/2) = COS = tan(x/2) =
Using the given information sin(x) = 5/7 and x in quadrant 2, the exact values are:
sin(x/2) = √[(1 - √24/7)/2],
cos(x/2) = -√[(1 + √24/7)/2],
tan(x/2) = (√[(1 - √24/7)/2]) / (-√[(1 + √24/7)/2]).
To determine the exact values of sin(x/2), cos(x/2), and tan(x/2) when sin(x) = 5/7 and x is in quadrant 2, we can utilize the half-angle formulas. These formulas allow us to express the trigonometric functions of an angle in terms of the trigonometric functions of half that angle.
Given sin(x) = 5/7, we can find cos(x) using the Pythagorean identity:
cos(x) = √(1 - sin^2(x)) = √(1 - (5/7)^2) = √(1 - 25/49) = √(24/49) = √24/7.
To find sin(x/2), we use the half-angle formula for sine:
sin(x/2) = ±√[(1 - cos(x))/2] = ±√[(1 - √24/7)/2].
Since x is in quadrant 2, sin(x) is positive. Therefore, sin(x/2) is also positive. Thus, we have:
sin(x/2) = √[(1 - √24/7)/2].
Similarly, we can find cos(x/2) using the half-angle formula for cosine:
cos(x/2) = ±√[(1 + cos(x))/2] = ±√[(1 + √24/7)/2].
Since x is in quadrant 2, cos(x) is negative. Therefore, cos(x/2) is also negative. Thus, we have:
cos(x/2) = -√[(1 + √24/7)/2].
Lastly, we can find tan(x/2) using the half-angle formula for tangent:
tan(x/2) = sin(x/2) / cos(x/2) = (√[(1 - √24/7)/2]) / (-√[(1 + √24/7)/2]).
Combining these results, the exact values for sin(x/2), cos(x/2), and tan(x/2) when sin(x) = 5/7 and x is in quadrant 2 are:
sin(x/2) = √[(1 - √24/7)/2],
cos(x/2) = -√[(1 + √24/7)/2],
tan(x/2) = (√[(1 - √24/7)/2]) / (-√[(1 + √24/7)/2]).
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PLEASE HELP!! I need to answer this photos
Answer: [m and n], and [o and p]
Step-by-step explanation:
The parallel groups of lines are m and n, and the group o and p.
Instructions: Create a table of values for the function graphed below using the
plotted points. Remember, table of values are written with the x-values in order
from least to greatest (read the graph from left to right). Then, state the domain
and range of the function.
-10
x
5
?
The graph is bounded and does not extend to infinity, the range is the subset of real numbers within that constraint.
To create a table of values for the given function graph, we will identify the x-values and their corresponding y-values.
Reading the graph from left to right, the x-values in order from least to greatest are: -10, -5, 0, 5.
By looking at the graph, we can determine the corresponding y-values for each x-value.
Let's say the y-values are y1, y2, y3, and y4 respectively.
Now, we can create the table of values:
x | y
-10 | y1
-5 | y2
0 | y3
5 | y4
To state the domain and range of the function, we need to consider the set of all possible x-values and the set of all possible y-values.
In this case, the domain of the function is the set of x-values, which is {-10, -5, 0, 5}.
The range of the function is the set of y-values, which corresponds to {y1, y2, y3, y4}.
It is important to note that without specific values for y1, y2, y3, and y4, we cannot provide the exact range of the function.
The domain of the function is {-10, -5, 0, 5}, which is the set of all possible x-values.
Regarding the scope of the function, since you said that the y values correspond to {y1, y2, y3, y4}, it i not possible to determine the exact scope of the function since there are no specific values. y4 function for y1, y2, y3.
However, based on the chart and the information given, we can say that the range will be a series of real numbers, depending on how the chart behaves.
If the graph extends infinitely in both the positive y-direction and the negative y-direction, the range consists entirely of real numbers.
However, we can say that the range will be a set of real numbers depending on the behavior of the graph.
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Question 13 of 40
Use the graph to write the factorization of x2 - x - 6
Answer:
The graph is not shown.
x² - x - 6 = (x - 3)(x + 2)
What is (f−g)(x)? f(x)=3x5+6x2−5 g(x)=2x4+7x2−x+16
Answer: We have f(x)=3x⁵+6x²-5 and g(x)= 2x⁴+7x²-x+16
(f-g)(x)= 3x⁵-2x⁴-x²+x-21
Step-by-step explanation:
Here we have,
Given : f(x)=3x⁵+6x²-5 and g(x)= 2x⁴+7x²-x+16
We know,
(f-g)(x)= f(x)-g(x)
= (3x⁵+6x²-5 ) - ( 2x⁴+7x²-x+16)
On subtracting g(x) from f(x) we get,
(f-g)(x)= (3x⁵+6x²-5 - 2x⁴-7x²+x-16)
On simplify,
(f-g)(x) =3x⁵-2x⁴-x²+x-21
Hence,
(f-g)(x) = f(x) - g(x) = 3x⁵-2x⁴-x²+x-21
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which solution is extraneous
The extraneous solution for the rational expression 2 · x² - 2 = (x - 1) · (x - 2) is equal to x = 1.
Is there any solution extraneous to a rational expression?
In this problem we must determine whether an extraneous solution exist to a given rational expression. The procedure is now summarized. First, use algebra properties to eliminate denominators:
1 / (x - 1) = (x - 2) / (2 · x² - 2)
2 · x² - 2 = (x - 1) · (x - 2)
Second, expand and simplify the expression until a polynomial in standard form is found:
2 · x² - 2 = x² - 3 · x + 2
x² + 3 · x - 4 = 0
Third, factor the quadratic equation:
(x + 4) · (x - 1) = 0
x = - 4 or x = 1
Fifth, check in initial expression:
1 / (- 4 - 1) = (- 4 - 2) / [2 · (- 4)² - 2]
- 1 / 5 = - 6 / 30
- 1 / 5 = - 1 / 5
1 / (1 - 1) = (1 - 2) / (2 · 1² - 2)
1 / 0 = - 1 / 0 (EXTRANEOUS)
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Which expression demonstrates the use of the commutative property of addition in the first step of simplifying the expression (–3 + i) + (18 + 5i)?
Answer: [tex](-3+18)+(i+5i)[/tex]
Step-by-step explanation:
The commutative property of addition states that the order in which numbers are added does not change the sum. In the context of complex numbers, this means that you can rearrange the real and imaginary parts separately.
So, the expression that demonstrates the use of the commutative property of addition in the first step of simplifying the expression [tex](-3+i)+(18+5i)[/tex]
would be:
[tex](-3+18)+(i+5i)[/tex]
In the similar triangles below , what is the measure of D
45
22.5
63
90
sum angel measure of angles in triangle is 180° according to this rule
(n-2)180 , n is the no. of sides
so E+D+F=180
72+D+63=180
135+D=180
D=180-135
D=45°
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Question #10
Find the value of x
9
16
4
Answer: 9
Step-by-step explanation:
How many solutions does this system have? no solutions one unique solution O O two solutions O or an infinite number of solutions
Answer:
no solutions
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
equation of blue line is y = x + 2 , in slope- intercept form
with slope m = 1
equation of red line is y = x - 3 , in slope- intercept form
with slope m = 1
• Parallel lines have equal slopes
then the blue and red lines are parallel.
the solution to the system is at the point of intersection of the 2 lines
since the lines are parallel then they do not intersect each other.
thus the system shown has no solution.
Question #8
Solve for x
04
01
03
2
9
7x
8
10x
Answer:
x = 1
Step-by-step explanation:
given 2 secants to a circle from an external point , then
the product of the measures of one secant's external part and that entire secant is equal to the product of the measures of the other secant's external part and that entire secant, that is
8(8 + 10x) = 9(9 + 7x) ← distribute parenthesis
64 + 80x = 81 + 63x ( subtract 63x from both sides )
64 + 17x = 81 ( subtract 64 from both sides )
17x = 17 ( divide both sides by 17 )
x = 1
The diameter of Jacob's circular tabletop is 6 feet. What is the area, in square feet, of Jacob's tabletop?
Answer:
approximately 28.26 square feet
Step-by-step explanation:
The formula for the area of a circle is A = pi(r)^2. So, the radius is half of the diameter, meaning it's 3 feet. Then we square it to get 9, and multiply by pi, or 3.14. This leads us to the approximated answer of 28.26 square feet.
The area is:
28.27 square feet
Work/explanation:
Since the tabletop is circular, we use the formula for a circle's area, which is: [tex]\bf{A=\pi r^2}[/tex].
We have the diameter, and to find the radius, we divide the diameter by 2, which gives us 6 ÷ 2 = 3 feet, so the radius of the tabletop is 3 feet.
Now, here's a diagram for you;
[tex]\setlength{\unitlength}{1cm}\begin{picture}(0,0)\thicklines\qbezier(2.3,0)(2.121,2.121)(0,2.3)\qbezier(-2.3,0)(-2.121,2.121)(0,2.3)\qbezier(-2.3,0)(-2.121,-2.121)(0,-2.3)\qbezier(2.3,0)(2.121,-2.121)(-0,-2.3)\put(0,0){\line(1,0){2.3}}\put(0.5,0.3){\bf\large 3\ ft}\end{picture}[/tex]
Plug in the data:
[tex]\sf{A=\pi\times3^2}[/tex]
[tex]\sf{A=\pi\times9}[/tex]
[tex]\sf{A=28.27\:ft^2}[/tex]
Hence, the area is 28.27 square feet.