Answers
In order to determine the zeros of this function, the steps are:
1. Assume f(x) = 0. Hence, the equation becomes:
[tex]0=x^2+2x-3[/tex]2. Factor the quadratic function by finding some factors of -3 that sums to the middle term 2.
a. -3 and 1 → -2
b. -1 and 3 → 2
So, the factors of -3 that sums to 2 are -1 and 3.
So, the quadratic equation can be factored into:
[tex]0=(x-1)(x+3)[/tex]3. Equate each factor to zero and solve for x.
[tex]\begin{gathered} x-1=0\Rightarrow x=1 \\ x+3=0\Rightarrow x=-3 \end{gathered}[/tex]Therefore, the zeroes of the function are at (-3, 0) and (1, 0). (Option C)
Related Questions
How many presents would Dracula wrap in 8 hours if he wrapped 3 presents every 20 minutes?
Answers
First, you can know how many minutes are 8 hours using the rule of three like this
[tex]\begin{gathered} 1\text{ hour}\rightarrow60\text{ minutes} \\ 8\text{ hours }\rightarrow\text{ x minutes} \end{gathered}[/tex][tex]\begin{gathered} x=\frac{8\text{ hours }\ast\text{ 60 minutes}}{1\text{ hour}} \\ x=480\text{ minutes} \end{gathered}[/tex]Now, using the rule of three again, you can find out how many gifts Dracula would wrap in 8 hours if she wrapped 3 gifts every 20 minutes
[tex]\begin{gathered} 20\text{ minutes}\rightarrow3\text{ presents} \\ 480\text{ minutes}\rightarrow x\text{presents} \end{gathered}[/tex][tex]\begin{gathered} x=\frac{480\text{ minutes}\ast3\text{ presents}}{20\text{ minutes}} \\ x=\frac{1440}{20}\text{ presents} \\ x=72\text{ presents} \end{gathered}[/tex]Therefore, Dracula would wrap 72 gifts in 8 hours if he wrapped 3 gifts in 20 minutes
Solve the equation on the interval 0<=theta<2pi2 sin^2 theta-V3 sin theta = 0
Answers
Given the equation
[tex]2\sin ^2\theta-\sqrt{3}\sin \theta=0[/tex]We can rewrite the given equation as:
[tex]2\sin ^{}\theta\sin ^{}\theta-\sqrt{3}\sin \theta=0[/tex]Factoring, we obtain:
[tex]\sin ^{}\theta(2\sin ^{}\theta-\sqrt{3})=0[/tex]Therefore, we can say:
[tex]\begin{gathered} \sin ^{}\theta=0\: \implies\theta=0 \\ \text{Similarly} \\ 2\sin ^{}\theta-\sqrt{3}=0 \\ \implies2\sin ^{}\theta=\sqrt{3} \\ \implies\sin ^{}\theta=\frac{\sqrt{3}}{2} \\ \implies\theta=\sin ^{-1}\frac{\sqrt{3}}{2} \\ \implies\theta=\frac{\pi}{3} \end{gathered}[/tex]Therefore, the solution set in the given interval is:
[tex]\left\lbrace 0,\frac{\pi}{3}\right\rbrace [/tex]Janice is going to go buy dinner but she wants to use all the change that she has collected in her purse. She has a total of $12.10 in quarters, nickels and dimes. She has double the amount of quarters compared to nickels. The number of dimes is 5 less than twice the number of nickels. q: quarters d: dimes n: nickels Choose the correct verbal expressions for problems into a system of equations or inequalities.
Answers
x=2y
z+5=2y
0.25x+0.05y+0.10z=12.10
Explanation
Step 1
Let
She has a total of $12.10 in quarters, nickels and dimes.=
[tex]\text{total = 1}2.10[/tex]a quarter =0.25 usd
a nickels=0.05 usd
a dime=0.10 usd
x= amount of quartes
y=amount of nickels
z=amount of dimes
total=0.25x+0.05y+0.10 z
Step 2
She has double the amount of quarters compared to nickels, in other words you have to multiply the amount of nickes by 2 to obtain the amount of quarters
[tex]x=2y[/tex]Also, The number of dimes is 5 less than twice the number of nickels, in other words, you have to add 5 to the number of dimes to obtain twice the number of nickels
[tex]z\text{ +5=2y}[/tex]Step 3
total
[tex]0.25x+0.05y+0.10z=12.10[/tex]and that's all, now you have a system of 3 equations and 3 variables(x,y,z)
The perimeter of a rectangular sports court is 122 feet. After a game, a player's coach estimates that the athlete has run a total of 423 feet, which is equivalent to 6 times the court's length plus 9 times its width. What are the dimensions of the sports court?
Answers
The dimensions of the sports court is
Width = 19 feet
Length = 42 feet
What is perimeter of rectangle ?A rectangle's perimeter (P) is the sum of the lengths of its four sides. A rectangle has two equal lengths and two equal widths since its opposite sides are equal. The following is the formula for calculating a rectangle's perimeter: The formula for perimeter is length + length + width + width. P = l + l + w + w.
Given: Perimeter of rectangular sports court = 122 feet
Assume;
Length = l
Width = b
So,
6l + 9b = 423 feet.......Eq1
Perimeter of rectangular sports court = 122 feet
2l + 2b = 122
l + b = 61
l = 61- b
From Eq 1
6l + 9b = 423
6[61 - b] + 9b =423
366 - 6b + 9b = 423
b = 19
Width = 19feet
l + b = 61
l + 19 = 61
l = 42
Length = 42feet
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sketch the graph of the function3.) [tex]y = \sqrt{x} [/tex]I got (0,0) as my answer but I want to see if I got it correct!!
Answers
You have to graph the following function
[tex]y=x[/tex]This is a linear function with slope m=1, this means that each time x increases one unit, y also increases one unit.
To sketch this function you have to choose at least two values of x and determine the corresponding value of y.
Then plot the points and draw the line.
I will make a table with 5 points of the line:
Now what's left is to plot all points and link them with a line:
(Score for Question 1: of 10 points)1. Consider the quadratic function.(d) Graph the function on the coordinate plane. Include the axis of symme(b) What is the equation of the axis of symmetry?(c) What are the coordinates of the vertex?(a) What are the x-intercepts and y-intercept?Answer:f(x) = - (x + 4) * (x - 1)
Answers
Given:
[tex]f(x)=-(x+4)(x-1)[/tex]Explanation:
a) To draw: The Graph
Let us find the intercepts.
When x = 0, we get
[tex]\begin{gathered} y=-(4)(-1) \\ y=4 \end{gathered}[/tex]Therefore, the y-intercept is (0, 4).
The x-intercepts are,
[tex](-4,0),(1,0)[/tex]Let us find the vertex.
The given function can be written as,
[tex]\begin{gathered} f(x)=-(x+4)(x-1) \\ =-(x^2+3x-4) \\ =-(x^2+3x+(\frac{3}{2})^2-(\frac{3}{2})^2-4) \\ =-[(x+\frac{3}{2})^2-\frac{9}{4}-4] \\ =-[(x+\frac{3}{2})^2-\frac{25}{4}] \\ f(x)=(x+\frac{3}{2})^2+\frac{25}{4} \end{gathered}[/tex]So, the vertex is,
[tex]\begin{gathered} (h,k)=(-\frac{3}{2},\frac{25}{4}) \\ (or) \\ (h,k)=(-1.5,6.25) \end{gathered}[/tex]The graph becomes,
b) The equation of symmetry is,
[tex]x=-\frac{3}{2}[/tex]This line divides the parabola into two equal parts.
c) The coordinates of the vertex is,
[tex](h,k)=(-1.5,6.25)[/tex]d) Intercepts:
The x-intercepts are,
[tex](-4,0),(1,0)[/tex]The y-intercept is (0, 4).
A farmers land is separated in sections of size 2 1/7 acres. Suppose there are 4 3/8 such sections. How many acres of land does the farmer own? Write your answer as a mixed number in simplest form.
Answers
We were told that the farmer's land is separated in sections of size 2 1/7 acres. Converting 2 1/7 to improper fraction, we multiply 2 by 7 and add 1. The denominator remains 7. it becomes 15/2
There are 4 3/8 such sections. Converting 4 3/8 to improper fraction, it becomes 35/8
Therefore, the number of acres of land that the farmer owns is
15/2 * 35/8 = 525/16
Converting to improper fraction, it becomes
32 13/16 acres
Answer:
32 13/16 acres
Step-by-step explanation:
Kurt is flying his airplane over a campground. he spots a small fire below at an angle of depression of 32°. If the horizontal d9stance from Kurt's plane to the fire is 3600 feet, find the approximate altitude of his plane.
Answers
ANSWER:
A. 2,250 feet
STEP-BY-STEP EXPLANATION:
We can calculate the value of the height thanks to the tangent trigonometric function, which relates the opposite leg (altitude) and the adjacent leg (horizontal), as follows:
[tex]\begin{gathered} \tan \theta=\frac{\text{opposite}}{\text{adjacent}} \\ \theta=32\text{\degree} \\ \text{opposite = x} \\ \text{adjacent = 3600} \end{gathered}[/tex]Replacing and solving for x:
[tex]\begin{gathered} \tan 32=\frac{x}{3600} \\ x=3600\cdot\tan 32 \\ x=2249.53\cong2250 \end{gathered}[/tex]The altitude value is 2250 feet
(a)A child has a box full of colored building blocks. She will choose one block without looking. The odds against choosing a blue block are 5/12 . What is the probability of choosing a blue block?
Ivanna is playing a role-playing game with her friends. She will roll dice to determine if her character unlocks a treasure chest. The probability of her character unlocking the treasure chest is 9/20 . Find the odds in favor of her character unlocking the treasure chest
Answers
(a) 12/17 is the probability of choosing a blue block.
b )The odds in favor of her character unlocking the treasure chest are 9/11
What is probability?
probability has to do with the chance of a particular thing happening.
a)
We need the probability of choosing a blue block,
Odds:
The odds of an event is the ratio of the probability of an event to the probability of its complement. In other words, it is the ratio of favorable outcomes to unfavorable outcomes.
The odds against choosing a blue block are 5/12 means. In 12 chances, 5 events will happen in which blue block will not be chosen and 12 events will happen in which blue blocks will be chosen.
So, the probability of not choosing the blue block is 12/17.
Probability of choosing blue block: complement of 5/12 which is equal to 12/17.
(b)
The probability of Ivanna character unlocking the treasure chest is 9/20
It means, in 20 total chances, 9 times an event will happen where Amanda's character unlocks the treasure chest while the rest 11 times, her character would not open treasure chest.
Favorable events: 9
Unfavorable events: 11
Hence, the odds in favor of her character unlocking the treasure chest are 9/11
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If Jason eats 3/6 of a birthday cake and Mike eats 2/6 of the same cake, how much of the birthday cake was eaten?
a.5/6
b.5/12
If a pizza is divided into 8 equal slices and Lily eats 3/8 of the pizza, how much of the pizza is left?
a.3/6
b.5/8
There are 10 t-shirts. 7/10 of the tee-shirts are blue. The rest are green. How many t-shirts are green?
a.7
b.3
Answers
1. The quantity of the birthday cake eaten by Jason and Mike is a. 5/6 or 83.3%.
2. The quantity of the pizza left after Lily has eaten 3/8 is b. 5/8.
3. The number of green t-shirts is b. 3.
How are the numbers determined?The various numbers are determined using the mathematical operations of subtraction, addition, multiplication, and division.
These basic mathematical operations result in the difference, sum, product, and quotient, respectively.
a) Birthday Cake:The quantity of the birthday cake = 1 or 6/6
The amount consumed by Jason = 3/6
The amount consumed by Mike = 2/6
The total quantity consumed by Jason and Mike = 5/6 (3/6 + 2/6)
b) Pizza:The quantity of the pizza = 1 or 8/8
The amount consumed by Lily = 3/8
The amount left unconsumed = 5/8 (1 - 3/8)
c) T-shirts:The total number of t-shirts = 10
The fractional size of blue t-shirts = 7/10
Since the rest are green, the fractional size of the green t-shirts = 3/10 (1 - 7/10)
3/10 of 10 = 3
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On a sheet of paper using the number line below, represent the set of data in a dot plot. Determine the median. 1. Length of summer camps in days: 7, 7, 12, 10, 5, 10, 5, 7, 10, 9, 7, 9, 6, 10, 5, 8, 7, and 8
Answers
Graphing the set of data in a dot plot, we have:
Since this set has 18 elements, the median is the average between the 9th and 10th elements using the set in the crescent order.
Looking at the dot plot, the 9th element is 7 and the 10th element is 8, so the median is (7 + 8)/2, that is, the median is 7.5.
√98-√18
how would I get the answer to this
SURDS
Answers
The value of √98-√18 in surds will be 4✓2.
Whet is surds?A surd simply means an expression that include the square root, the cube root or other root symbols.
In this case, the value given is illustrated as:
√98-√18
= ✓(2 × 49) - ✓(2 × 9)
= 7✓2 - 3✓2
= 4✓2
The value is 4✓2.
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Complete these sentences to describe the rules of dividing signed numbers.
The quotient of two integers with same sign is always
The quotient of two integers with different signs is always
Answers
Answer:
1) Positive, 2) NegativeStep-by-step explanation:
The quotient of two integers with same sign is always positive, because:
Positive / positive = positive andNegative / negative = positiveThe quotient of two integers with different signs is always negative, because:
Positive / negative = negative andNegative / positive = negativeAnswer:
1) Positive (+)
2) Negative (-)
Step-by-step explanation:
1) Positive
→ (+) ÷ (+) = (+)
→ (-) ÷ (-) = (+)
Hence, it is proved.
2) Negative
→ (+) ÷ (-) = (-)
→ (-) ÷ (+) = (-)
Hence, it is proved.
I find 4heb diagram.
Answers
We are asked to find the volume of the given pyramid.
Recall that the volume of a pyramid is given by
[tex]V=\frac{1}{3}\cdot B\cdot h[/tex]Where B is the area of the base and h is the height of the pyramid.
As you can see from the figure, the base of the pyramid is rectangular
The length is 23 yd and the width is 14 yd of the rectangular base.
So, the area of the rectangular base is
[tex]\begin{gathered} B=l\cdot w \\ B=23\cdot14 \\ B=322\: yd^2 \end{gathered}[/tex]The height of the pyramid is 25 yd
So, the volume of the pyramid is
[tex]\begin{gathered} V=\frac{1}{3}\cdot B\cdot h \\ V=\frac{1}{3}\cdot322\cdot25 \\ V=2683.3\: yd^3 \end{gathered}[/tex]Therefore, the volume of the rectangular pyramid is 2683.3 cubic yards.
The type of pyramid is the rectangular pyramid.
The triangles shown below are similar.Similar Help30Sole for
Answers
Here, we want to find the value of x
From the question, we have that the two triangles are similar
When two triangles are similar, the the ratio of their corresponding sides are equal
Thus, we have it that;
[tex]\begin{gathered} \frac{24}{30}\text{ = }\frac{8}{x} \\ \\ 24\text{ }\times\text{ x = 30}\times8 \\ x\text{ =}\frac{30\times8}{24} \\ x\text{ = 10} \end{gathered}[/tex]selecting from milligram, gram, kilogram, and tonne, determine the best unit of measure to express a butterfly weight
Answers
Solution
For this case we can conclude that the best answer for this case is:
gram
Since a butterfly can weight about 0.04-1 grams
Find the greatest common factor of the following monomials50a^5b^2 6a^3b^4 12a^4b^4
Answers
From the question;
We are to find the greatest common factor of the following monomials
[tex]\begin{gathered} 50a^5b^2 \\ 6a^{3^{}}b^4 \\ 12a^4b^4 \end{gathered}[/tex]solution
By prime factorisation
[tex]\begin{gathered} 50a^5b^2\text{ = 2 }\times5\times5\times a\times a\times a\times a\times a\times b\times b \\ 6a^3b^4\text{ = 2}\times3\times a\times a\times a\times b\times b\times b\times b \\ 12a^4b^4\text{ = 2 }\times2\times3\times a\times a\times a\times a\times b\times b\times b\times b \end{gathered}[/tex]From the above factorisation
The Greatest common factor is
[tex]\begin{gathered} G\mathrm{}C\mathrm{}F\text{ = 2}\times a\times a\times a\times b\times b \\ G\mathrm{}C\mathrm{}F=2a^3b^2 \end{gathered}[/tex]Therefore the greatest common factor is
[tex]2a^3b^2[/tex]A law firm is going to designate associates and partners to a big new case. The daily rate charged to the client for each associate is $700 and the daily rate for each partner is $1300. The law firm assigned a total of 19 lawyers to the case and was able to charge the client $19300 per day for these lawyers' services. Write a system of equations that could be used to determine the number of associates assigned to the case and the number of partners assigned to the case. Define the variables that you use to write the system.
Answers
The number of associates is 9 and the number of partners is 10.
Given, The daily rate charged to the client for each associate is $700 and the daily rate for each partner is $1300.
The law firm assigned a total of 19 lawyers to the case and was able to charge the client $19300 per day for these lawyers' services.
we need to determine the number of associates assigned to the case and the number of partners assigned to the case.
Suppose the number of associates is x and the number of partners be y.
Then the required equations are formed:
x+y=19 ..eq(1)
700x+1300y=19300 ...eq(2)
from eq(1) we get:
y=19-x .. eq(3)
Plug eq(3) into eq(2)
700x+1300(19-x)=19300
700x+24700-1300x=19300
700x-1300x=19300-24700
-600x=-5400
x=9
Thus, y=19-9
y=10
Thus the number of associates are 9 and the number of partners are 10.
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2x+y=-11 rewrite in slope intercept form
Answers
Answer:
In slope-intercept form:
[tex]y = - 2x - 11[/tex]
Triangle RST has vertices R(1, 2), S(4, -2), and T(2, -5). The triangle is rotated 90° counterclockwise about the origin. Which are the coordinates of the image of vertex T?
Answers
Answer:
(5, 2)
Explanation:
If point P with coordinates (x, y) is rotated 90 degrees counterclockwise about the origin, the image will have (-y, x) as coordinates of the image, P'.
So if triangle RST was rotated 90 degrees counterclockwise about the origin, we'll have the below as coordinates of the image of vertex T;
[tex]T(2,-5)\rightarrow T^{\prime}\lbrack(-(-5),2)\rbrack\rightarrow T^{\prime}(5,2)[/tex]What is the slope intercept equation for the following line.
Answers
to get the equation of any straight line, we simply need two points off of it, let's use those ones in the picture below
[tex](\stackrel{x_1}{-2}~,~\stackrel{y_1}{-2})\qquad (\stackrel{x_2}{2}~,~\stackrel{y_2}{-4}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-4}-\stackrel{y1}{(-2)}}}{\underset{run} {\underset{x_2}{2}-\underset{x_1}{(-2)}}} \implies \cfrac{-4 +2}{2 +2} \implies \cfrac{ -2 }{ 4 } \implies - \cfrac{ 1 }{ 2 }[/tex]
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-2)}=\stackrel{m}{- \cfrac{ 1 }{ 2 }}(x-\stackrel{x_1}{(-2)}) \implies y +2= -\cfrac{ 1 }{ 2 } (x +2) \\\\\\ y+2=-\cfrac{ 1 }{ 2 }x-1\implies {\Large \begin{array}{llll} y=-\cfrac{ 1 }{ 2 }x-3 \end{array}}[/tex]
Which is the correct simplified version ofthe expression -7(2x - 3)?a. - 14x + 21b. - 14x - 21c. -5x – 10d. -14% - 10
Answers
The given expression is - 7(2x - 3)
The first step is to open the bracket by multiplying each term inside the bracket by the term outside. Then we would add or subtract where necessary.
It becomes
- 7 * 2x + - 7 * - 3
Recall, - * - = +
The simplified expression would be
- 14x + 21
The correct option is A
The value of a stock decreases by an average of 10 dollars each week. Which of the following represents the total average decrease in the stock after 8 weeks?
O 1-101-181=2 dollars
O -8110) = 80 dollars
O 1-101-8=2 dollars
0 81-101 = 80 dollars
Answers
The following describes the total moderate decrease in the wares after 8 weeks is 8 | -10 |= 80 dollars.
What is meant by value?The value refers to the worth of each digit in relation to its position in the number. We compute it by multiplying the digit's place and face values. Place Value + Face Value = Value. As an example: If we look at the number 45. In this case, digit 4 is in the tens column. Values are benchmarks or ideals against which we judge actions, people, things, or situations. Many people support values such as beauty, honesty, justice, peace, and generosity. The actual population value obtained with perfect measuring instruments and without committing any type of error, both in collecting primary data and in performing mathematical operations.
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A chemist is using 326 milliliters of a solution of acid and water. If 18.3% of the solution is acid, how many milliliters of acid are there? Round your answer to the nearest tenth.
Answers
We have a 326 ml of a solution with 18.3% of acid.
We have to calculate the amount of acid there is.
We can find it as the volume of the solution, 326 ml, times the proportion of acid, 18.3/100 = 0.183:
[tex]326\cdot0.183=59.658\approx59.7[/tex]Answer: there are 59.7 ml of acid.
A car's rear windshield wiper rotates 130°. the total length of the wiper mechanism is 21 inches and the length of the wiper blade is 14 inches. find the area wiped by the wiper blade. (round your answer to one decimal place.)
Answers
We have that the formula for the area of the sector of a circle is:
[tex]A=\frac{\pi\cdot r^2\cdot\alpha}{360}[/tex]In this case, we have to find the area of the sector of a circle with radius r= 21 and then the area in the case of the r=21-14=7, and then find the difference.
Given the information, we have the following:
[tex]\begin{gathered} \alpha=130 \\ r_1=21 \\ r_2=7 \\ \Rightarrow A_1=\frac{(3.1416)(21)^2(130)}{360}=500.3 \\ \Rightarrow A_2=\frac{(3.1416)(7)^2(130)}{360}=55.6_{} \\ \Rightarrow A=A_1-A_2=500.3-55.6=444.7_{} \\ A=444.7 \end{gathered}[/tex]therefore, the area wiped by the wiper blade is 444.7in²1/2 minute how long does it take for jing to complete 10 questions
Answers
ANSWER
A. 300 seconds
EXPLANATION
Half a minute is 30 seconds. If Jing answers 1 question in 30 seconds, then he will answer 10 questions in:
[tex]10\times30=300[/tex]300 seconds.
Answer:
300
Step-by-step explanation:
30 (seconds) x 10 (minutes) = 300 (seconds) hope this helps!
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Choose the appropriate pattern and use it to find the product: (p4−q4)(p4+q4).
Answers
The expression can be solved by expanding the bracket and multiplying out the terms
[tex](p^4-q^4)(p^4+q^4)[/tex][tex]\begin{gathered} =p^4(p^4+q^4)-q^4(p^4+q^4) \\ =p^8+p^4q^4-p^4q^4-q^8 \\ =p^8-q^8 \end{gathered}[/tex]Therefore, the expression can be simplified as;
[tex]p^8-q^8[/tex]Alternatively, using the theorem of difference of two squares, which is
[tex]a^2-b^2=(a-b)(a+b)[/tex]Hence,
[tex]p^8-q^8=(p^4)^2-(q^4)^2[/tex]
Evaluate the expression 4x-2+m when x=3 and m=5
Answers
12-2+3
10+3
13
Question 2
I measure the length of a building 10 times, using a tape measure. Use the following observations to
determine the 50% Error of this sample.
26.583m
26.454m
26.858m
26.808m
26.819m
26.573m
26.466m
26.826m
26.872m
26.319m
O 0.1295
0.2024
0.3329
10 pts
0.1365
Answers
a blow up pool in your backyard has a diameter of 8 ft what is the circumference of the pool round to the nearest hundredth
Answers
A blow-up pool in your backyard has a diameter of 8 ft.
We are asked to find the circumference of the pool. (rounded to the nearest hundredth)
Recall that the circumference of a circular shape is given by
[tex]C=\pi\cdot D[/tex]Where π is a constant and D is the diameter.
Let us substitute the given values into the above formula
[tex]\begin{gathered} C=\pi\cdot D \\ C=\pi\cdot(8) \\ C=25.13\: ft \end{gathered}[/tex]Therefore, the circumference of the pool is 25.13 feet (rounded to the nearest hundredth)
