To solve the quadratic equation, factor the expression and then clear x from each of the factors obtained.
[tex]\begin{gathered} x^2+6x+5=0 \\ (x+5)(x+1)=0 \\ x+5=0 \\ x=-5 \\ x+1=0 \\ x=-1 \end{gathered}[/tex]This equation has 2 solutions which are -5 and -1.
how do you simplify this expression to become x ^3 -8
we have the expression
[tex]\begin{gathered} (x^3-4)-4 \\ remove\text{ the parenthesis} \\ x^3-4-4 \\ combine\text{ like terms} \\ x^3-8 \end{gathered}[/tex]When the polynomial mx^3 - 3x^2 +nx +2 is divided by x+3, the remainder is -4. When it is divided by x-2, the remainder is -4. Determine the value of m and n.
Answer:
[tex]\begin{gathered} m\text{ =-2} \\ n\text{ =11} \end{gathered}[/tex]Explanation:
Here, we want to find the value of m and n
If we substituted a supposed root into the parent polynomial, the value after evaluation is the remainder. If the remainder is zero, then the value substituted is a root.
for x+ 3
x + 3 = 0
x = -3
Substitute this into the first equation as follows:
[tex]\begin{gathered} m(-3)^3-3(-3)^2-3(n)+\text{ 2 = -4} \\ -27m\text{ -27-3n+ 2 = -4} \\ -27m\text{ -3n = -4}+27-2 \\ -27m-3n\text{ = 21} \\ -9m\text{ - n = 7} \end{gathered}[/tex]We do this for the second value as follows:
x-2 = 0
x = 2
Substitute this value into the polynomial:
[tex]\begin{gathered} m(2)^3-3(2)^2+2(n)\text{ + 2 = -4} \\ 8m\text{ - 12 +2n + 2 = -4} \\ 8m\text{ + 2n = -4-2+12} \\ 8m\text{ + 2n = 6} \\ 4m\text{ + n = 3} \end{gathered}[/tex]Now, we have two equations so solve simultaneously:
[tex]\begin{gathered} -9m-n\text{ = 7} \\ 4m\text{ + n = 3} \end{gathered}[/tex]Add both equations:
[tex]\begin{gathered} -5m\text{ = 10} \\ m\text{ =-}\frac{10}{5} \\ m\text{ = -2} \end{gathered}[/tex]To get the value of n, we simply susbstitute the value of m into any of the two equations. Let us use the second one:
[tex]\begin{gathered} 4m\text{ +n = 3} \\ 4(-2)\text{ + n = 3} \\ -8\text{ + n = 3} \\ n\text{ = 8 + 3} \\ n\text{ = 11} \end{gathered}[/tex]I want to know how to determine whether the x or r in cos A = -2/5 is negative so when im using cos A's values in the x^2+y^2=r^2 equation I dont use the wrong number
INFORMATION:
STEP BY STEP EXPLANATION:
ANSWER:
2x2 + 5 = 6x Solve using the quadratic formula with the answer as a+bi form
Let's begin by listing out the information given to us:
[tex]\begin{gathered} 2x^2+5=6x \\ 2x^2-6x+5=0 \\ a=2,b=-6,c=5 \end{gathered}[/tex]We proceed to use the quadratic formula, we have:
[tex]\begin{gathered} x=\frac{-b\pm\sqrt{b^2-4ac}}{2a} \\ a=2,b=-6,c=5 \\ x=\frac{-(-6)\pm\sqrt[]{-6^2-4(2\cdot5)}}{2(2)} \\ x=\frac{6\pm\sqrt[]{36-40}}{4}=x=\frac{6\pm\sqrt[]{-4}}{4} \\ \sqrt[]{-4}=2i \\ x=\frac{6\pm\sqrt[]{-4}}{4}\Rightarrow\frac{6\pm2i}{4} \\ x=\frac{6}{4}+\frac{2i}{4},\frac{6}{4}-\frac{2i}{4} \\ x_1=1.5+0.5i \\ x_2=1.5-0.5i \end{gathered}[/tex]A circle is sliced into 16 pieces and rearranged into a shape that looks like aparallelogram. The dashed line indicates the base of the shape. The base isapproximately equal to which part of the circle?
All of the base of the slice corresponds to the circumference of the circle, but since half of it just accounts for the base of the parllelogram therefore, the base is approximately equal to only half of the circumference.
12. Consider the figure shown.11CDBWhat does ACB represent?A. a rayB an oroc. an angloDa lino sogmont
Take into account that ACB is an angle, because you can measure the vertex ACB just as an angle.
Then, the answer is:
ACB
Suzy has $2000 to invest and needs $2400 in 12 years. What annualrate of return will she need to get in order to accomplish her goal, if theinterest is compounded continuously? (Round your answer to twodecimal places) A = Pert
Given data:
Principal Amount=$2000.
Final Amount=$2400
Time period(t)=12 years
Let the rate of return be r.
As per formula of continous compunding:
[tex]\begin{gathered} \text{Final amount=Principal}(e^{rt}) \\ 2400=2000(e^{12r}) \\ e^{12r}=\frac{2400}{2000} \\ e^{12r}=1.2 \\ 12r=\ln (1.2) \\ 12r=0.1823 \\ r=0.01519 \end{gathered}[/tex]Thus, the rate of interest required is 1.519%.
Graph the inequality
y<= -(2/3)|x-3|+4
Please show how
We have the following inequality
[tex]y\leq-\frac{2}{3}\lvert x+3\rvert+4[/tex]We must graph this inequality, In order to understand this I will explain term by term
But first, we must remember that in mathematics, the absolute value or modulus of a real number x, denoted by |x|, is the non-negative value of x regardless of the sign, positive or negative. This must be taken into account for the |x+3| term.
That is to say that the value will always be assumed by its magnitude and we will tend to have the same behavior on both the negative and positive x-axis.
Taking this into account and that the slope is -2/3 the graph would look like this:
Now, we must remember two rules of function translation, these are as follows:
y = f(x) original funtion
y = f(x+c) it is moved horizontally "c" units to the left
y = f(x)+c it moves vertically "c" units upwards
So taking into account these rules our graph is shifted 3 units to the left and 4 units upwards.
In conclusion, this graph looks like this:
Let p be "x+4=13" and q be "x=9." Which of the following statements is a biconditional?Select the correct answer below:x+4=13 and x=9.If x+4=13, then x=9.x+4=13 if and only if x=9.x+4=13 only if x=9.
For two given simple statements P and Q, if they are connected with the logical connectivity 'if and only if', then the compund statement is called biconditional statement.
Now,
P: x+4=13
q: x=9
Then, their biconditional statement is x+4=13 if an donly if x=9
Hence the correct answer is (c)
I have attached the question
The following are the primary factors that the Cvp analysis employs to determine if the sales price per unit and variable costs per unit are impacted
Describe CVP Analysis?This is the term used to describe the cost-volume-profit analysis, which is used to determine how changes in cost and volume might directly affect operating costs.With this in mind, it is clear that the primary component that businesses utilize in their CVP analyses to ensure that their operational costs don't fluctuate arbitrary is cost changes. Profit = revenue - costs is the fundamental CVP formula. Naturally, you must understand how to calculate your revenue in order to use this formula:(Retail price * Units Sold)Additionally, you must understand how to calculate your costs: fixed costs plus (unit variable cost x number of units). Y = a + bx is the cost volume formula. Y = Total expense = Total fixed expense (that is, a cost that does not vary in proportion to activity)B is the variable cost per unit of activity; this cost does vary in relation to activity. Contribution/Sales is the P/V ratio. It is employed to gauge the company's profitability. The surplus of sales over variable costs is known as contribution. In essence, the P/V ratio is utilized to assess the level of contribution provided at various sales volumes.To learn more about Cpv analysis refer
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Which of the following are a qualitative catecorical variables
A qualitative variable, also called a categorical variable, is a variable that isn’t numerical. It describes data that fits into categories.
From the given options below, the arrival status of a train ( early, on time, late, canceled) and a person's blood type are the only qualitative variables.
Hence, Option 3 and Option 5 are the correct answers.
which equation represents a line having a slope of 5/2 and a y intercept of (0,-4)
First you must know the standard equation of a line and this is expressed as:
[tex]y\text{ = mx+c}[/tex]where:
m is the slope of the line
c is the intercept
Given
Slope m = 5/2
Next is to get the intercept c:
To do that, you will substitute m = 5/2 and the coordinate (0, -4) into the equation above as shown:
[tex]\begin{gathered} -4\text{ = 5/2(0)+c} \\ -4\text{ = 0+c} \\ c\text{ = -4} \end{gathered}[/tex]Next is to get the required equation by substituting m = 5/2 and c = -4 into the equation above as shown:
[tex]\begin{gathered} y\text{ = mx + c} \\ y\text{ = }\frac{5}{2}x\text{ +(-4)} \\ y\text{ = }\frac{5}{2}x\text{ - 4} \end{gathered}[/tex]Hence the required equation is espressed as:
[tex]y\text{ = }\frac{5}{2}x-4[/tex]I need help with a math question. Ilinked it below
EXPLANATION:
We are given a dot plot as shown which indicates the ages of members of an intermediate swim class.
The dot plot indicates a cluster to the right for the values;
[tex]11yrs-14yrs[/tex]This indicates that a reasonable amount of the members are within that age range.
For this reason, it is not likely that Mira will be able to convince her mother.
This is because Mira's age (13 years old) is within the area where the data are clustered.
Therefore;
ANSWER:
(1) The data are clustered between 11 and 14 years old
(2) It is not likely that she will be able to convince her mother
(3) Mira's age is within the area where the data are clustered.
you are standing 200 feet from a tall building . The angle from your feet to the top of the building is 51°.
the sum of angles in a triangle is 180
missing angle + 90 + 51 = 180
missing angle = 180 - 141
missing angle = 39 degrees.
in the triangle,
[tex]\frac{x}{200}=\tan 51[/tex]x = 200 tan51
x = 200 * 1.234
x = 246.97 ft apporx 247 ft
'so the length x = 247 ft
that is greater than 200
so the answer is
x > 200 ft
O EQUATIONS AND INEQUALITIESSolving a decimal word problem using a linear equation with th.
Given:
[tex]PlanA=0.16\text{ for each minutes of calls}[/tex][tex]PlanB=25\text{ monthly fee plus 0.12 for each minute of calls}[/tex]To Determine: The numbers of calls for the which the two plans are equal
Solution
Let x be the number of minutes of calls for which the two plans are equal
The cost of plan A is
[tex]C_{ost\text{ of plan A}}=0.16x[/tex]The cost of plan B
[tex]C_{ost\text{ of plan B}}=25+0.12x[/tex]If the cost for the two plans are equal, then
[tex]0.16x=25+0.12x[/tex]Solve for x
[tex]\begin{gathered} 0.16x-0.12x=25 \\ 0.04x=25 \\ x=\frac{25}{0.04} \\ x=625 \end{gathered}[/tex]Hence, the number of minutes of calls for which two plans are equal is 625 minutes
Which of the following are solutions to the inequality below? Select all that apply.
The first step to solving this problem is to put the variable on one side. Thus, you must move 7 to the right side to make [tex]\frac{f}{25} \leq -3[/tex]
Next, you must multiply the 25 to the right side to isolate the variable
You get [tex]f \leq -75[/tex]
With this explained, the answer would be the second option (f=-75)
Hope this helped :)
I need help with this quadratic function… I thought I knew the answer, but obviously I don’t
Let us start with the following quadratic function:
[tex]f(x)=x^2-x-12[/tex]the X-intercepts are the collection of values to X which makes f(x) = 0, and it can be calculated by the Bhaskara formula:
[tex]x_{1,2}=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]where the values a, b, and c are given by:
[tex]f(x)=ax^2+bx+c[/tex]Substituting the values from the proposed equation, we have:
[tex]\begin{gathered} x_{1,2}=\frac{1\pm\sqrt{1^2-4*1*(-12)}}{2*1} \\ x_{1,2}=\frac{1\pm\sqrt{1+48}}{2}=\frac{1\pm\sqrt{49}}{2} \\ x_{1,2}=\frac{1\pm7}{2} \\ \\ x_1=\frac{1+7}{2}=\frac{8}{2}=4 \\ x_2=\frac{1-7}{2}=-\frac{6}{2}=-3 \end{gathered}[/tex]From the above-developed solution, we are able to conclude that the solution for the first box is:
(-3,0) ,(4,0)Now, the y-intercept, is just the value of y when x = 0, which can be calculated as follows:
[tex]\begin{gathered} f(0)=0^2-0-12=-12 \\ f(0)=-12 \end{gathered}[/tex]From this, we are able to conclude that the solution for the second box is:
(0, -12)Now, the vertex is the value of minimum, or maximum, in the quadratic equation, and use to be calculated as follows:
[tex]\begin{gathered} Vertex \\ x=-\frac{b}{2a} \\ y=\frac{4ac-b^2}{2a} \end{gathered}[/tex]substituting the values, we have:
[tex]\begin{gathered} x=-\frac{-1}{2*1}=\frac{1}{2} \\ y=\frac{4*1*(-12)-(-1)^2}{4*1}=\frac{-48-1}{4}=\frac{-49}{4} \end{gathered}[/tex]which means that the solution for the thirst box is:
(1/2, -49/4) (just as in the photo)Now, the line of symmetry equation of a quadratic function is a vertical line that passes through the vertex, which was calculated to be in the point: (1/2, -49,4).
Because this is a vertical line, it is represented as follows:
[tex]x=\frac{1}{2}[/tex]Instructions: Find the value of that completes the square and creates a perfect square trinomial.
Solution:
Given the expression;
[tex]x^2+18x+c[/tex]c is the half of square of coefficient of x. That is;
[tex]\begin{gathered} x^2+18x+c=x^2+18x+(\frac{1}{2}(18))^2 \\ \\ x^2+18x+c=x^2+18x+9^2 \\ \\ x^2+18x+c=x^2+18x+81 \\ \\ x^2+18x+81=(x+9)(x+9) \end{gathered}[/tex]Hence, the value of c is;
[tex]c=81[/tex]Select the correct answer.Consider this equation,tan(6)If 8 is an angle in quadrant II, what is the value of cos(8),OA.B._vOD.
Remember the definition of the tangent function:
[tex]\tan \theta=\frac{\sin \theta}{\cos \theta}[/tex]Then, we notice that:
[tex]\tan (\theta)=-\sqrt[]{\frac{19}{17}=}-\sqrt[]{\frac{\frac{19}{6}}{\frac{6}{17}}}=\frac{\sin \theta}{\cos \theta}[/tex]Then, we can conclude that:
[tex]\frac{\sin \theta}{\cos \theta}=-\frac{\sqrt[]{\frac{19}{6}}}{\sqrt[]{\frac{6}{17}}}[/tex]Something important to remember is that, in quadrant II, the value of sin(x) is positive, whereas the value of cos(x) is negative
So,
[tex]\begin{gathered} \sin (\theta)=\sqrt[]{\frac{19}{6}} \\ \Rightarrow\frac{1}{\cos \theta}=-\frac{1}{\sqrt[]{\frac{6}{17}}} \\ \Rightarrow\cos \theta=-\sqrt[]{\frac{17}{6}} \end{gathered}[/tex]Therefore, the answer to the question is option A
1. Beyonce went to the mall and saw a massage chair that she would have to take a loan out for $6,500 to purchase. The bank said that she could get a simple interest rate of 8% for 5 years. What is the TOTAL amount that Beyonce will pay for the chair? * O $2,600 $910 O $9,100 O $260
The simple interest formula is:
[tex]i=\text{Prt}[/tex]Where
i is the interest earned
P is the initial (loan) amount
r is the rate of interest
t is the time
Given,
P = 6500
r = 8%, or, 8/100 = 0.08
t = 5
Substituting, we get:
[tex]\begin{gathered} i=\text{Prt} \\ i=6500\times0.08\times5 \\ i=2600 \end{gathered}[/tex]This is only the interest. Beyonce would need to pay the original (6500) plus this interest (2600) in total. Thus, she will have to pay:
[tex]6500+2600=9100[/tex]Question 10
Answer:
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A tyre made of rubber (density 1.2 g/cm³) has a mass of 3.6 kg.
Find its volume.
(Use ^sign from the computer's keyboard to express the power of the units for the volume
Question 11
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What percentage of the grid is shaded?
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1.volume = mass*density
v = 1.2 * 3.6 = 4.32 cm3
The density of a substance quantifies how tightly its molecules are packed, which affects how heavy or light it is.
Density is calculated as follows: density=mass/volume. Most often, mass is measured in grams or kilograms. Most often, volume is measured in cubic centimeters (cm3), cubic meters (m3), or millileters (mL).
How can you find mass from density?
multiply the volume by the density.
Mass per unit volume is the definition of density.
ρ = m V
This can be rearranged to yield the mass expression.
m = ρ × V
Example:
What mass of the liquid is present if 500 mL of it has a density of 1.11 g/mL
m = ρ × V = 500 mL × 1.11 g
1 mL = 555 g
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The Terrell Middle School wants to plant a community garden. They plan togrow and harvest vegetables, which will then be sold to raise funds for futuregardening.1. The science teacher, Ms. Maeda, wants the school to start composting.She borrows $392 from a school fund for supplies to make thecompost bins.Part AStudents plan to pay back half the debt now through fundraising,and the rest after the harvest. Write and solve an equation to representthe debt they will repay through fundraising. Use a negative integer toshow debt.
Total money $392
half of $392 is 196
one half would be paid through fundraising
The debt would be the other half
[tex]\begin{gathered} The\text{ debt} \\ x=\frac{-1}{2}(392) \\ x=-196\text{ dollars} \end{gathered}[/tex]THE FINAL ANSWER
x=-196 dollars
fredrico has earned scores of 7.2, 8.4, and 8.4 on his first 3 dives he has one dive left what score must he get on his last dive to have an average of at least 7.4 on all four dives
For Fredrico to make an average of at least 7.4 on all four dives, he must get at least 5.6 in his last dive.
What is the average?The average is the mean of the total scores that Fredrico scored in his dives.
The average can be computed by dividing the total scores by the number of dives.
The average is the quotient of the division operation of the total scores and the number of dives.
The total score based on an average of 7.4 = 29.6
The total scores obtained = 24 (7.2 + 8.4 + 8.4)
The remaining score to obtain to get the average of 7.4 = 5.6 (29.6 - 24)
Thus, Fredrico needs an additional 5.6 score in the last dive to make the average.
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Fredrico needs to score at least 5.6 on his final dive in order to achieve an average of at least 7.4 on all four dives.
Let's assume the required score would be x on his final dive
Mean = ∑x/n
The average represents the mean of all of Fredrico's dive-related scores.
Here, n = 4
Sum of Observations (∑x) = 7.2 + 8.4 + 8.4 + x
∑x = x + 24
Mean = ∑x/n
Substitute the values in the above formula,
⇒ 7.4 = (x + 24) / 4
Apply the cross-multiplication operation in the above equation,
⇒ 7.4 × 4= (x + 24)
⇒ 29.6 = x + 24
⇒ x = 29.6 - 24
Apply the subtraction operation to get
⇒ x = 5.4
Therefore, Fredrico needs to score at least 5.6 on his final dive
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An old blackboard needs to be covered with cork. The picture shows the size of the blackboard. 40 in. 60 in. What is the area to be covered? A 100 in? B 200 in? C 1200 in 2 D2,400 in2
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data
area = ?
Step 02:
The difference of 4R and 108
The expression of the mathematical statement given as the difference of 4R and 108 is |4R - 108|
How to rewrite the mathematical statement as an expression?From the question, the mathematical statement is given as
The difference of 4R and 108
In mathematics, the difference of numbers or expressions implies that we subtract one of the numbers from the other number or expression
This in other words means that difference means subtraction
So, we have the following representation
The difference of 4R and 108 ⇒ 4R - 108
However, we do not know the bigger number.
So, the expression can be rewritten as
The difference of 4R and 108 ⇒ 108 - 4R
So, we have two options
4R - 108 and 108 - 4R
When both expressions are combined, we introduce the absolute value symbol i.e. |.....|
|4R - 108|
Hence, the expression represented by the statement is |4R - 108|
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help meeeeeeeeee pleaseee !!!!!
The composition of functions g(x) and f(x) evaluated in x = 5 is:
(g o f)(5) = 6
How to evaluate the composition?
Here we have two functions f(x) and g(x), and we want to find the composition evaluated in x = 5, this is:
(g o f)(5) = g( f(5) )
So first we need to evaluate f(x) in x = 5, and then g(x) in f(5).
f(5) = 5² - 6*5 + 2 = 25 - 30 + 2 = -3
Then we have:
(g o f)(5) = g( f(5) ) = g(-3)
Evaluating g(x) in x = -3 gives:
g(-3) = -2*(-3) = 6
Then the composition is:
(g o f)(5) = 6
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Personal Math Trainer Lesson 15.2 - Homework - Homework 112131415 5 16 17 8 Margo can purchase tile at a store for $0.69 per tile and rent a tile saw for $56. At another store she can borrow the tile saw for free if she buys tiles there for $1.39 per tile. How many tiles must she buy for the cost to be the same at both stores? Margo must buy tiles for the cost to be the same at both stores.
Let Margo buy x number of tiles, So total cost of tiles and tile saw at first store is,
[tex]y=0.69x+56[/tex]The total cost equation for tile and tile saw for second store (which provide tile saw for free).
[tex]\begin{gathered} y=1.39x+0 \\ =1.39x \end{gathered}[/tex]Determine the number of tiles for total cost of tiles and tile saw to be equal from both store is,
[tex]\begin{gathered} 1.39x+0.69x+56 \\ 1.39x-0.69x=56 \\ 0.70x=56 \\ x=\frac{56}{0.70} \\ =80 \end{gathered}[/tex]So Margo purchase 80 tiles, such that total cost is equal from both the stores.
I dont want you to answer question for me, i have already answered it as shown in the picture. I want you to let me know if i have provided an answer worth full marks and if not tell me how i could improve it
Answer:
[tex]\begin{equation} \sqrt{3}-1,2 \sqrt{10} \div 5, \sqrt{14}, 3 \sqrt{2}, \sqrt{19}+1,6 \end{equation}[/tex]Explanation:
Given the irrational numbers:
[tex]$3 \sqrt{2}, \sqrt{3}-1, \sqrt{19}+1,6$, $2 \sqrt{10} \div 5,\sqrt{14}$[/tex]In order to arrange the numbers from the least to the greatest, we convert each number into its decimal equivalent.
[tex]\begin{gathered} 3\sqrt{2}=3\times1.414\approx4.242 \\ \sqrt{3}-1\approx1.732-1=0.732 \\ \sqrt{19}+1\approx4.3589+1=5.3589 \\ 6=6 \\ 2\sqrt{10}\div5=2(3.1623)\div5=1.2649 \\ \sqrt{14}=3.7147 \end{gathered}[/tex]Finally, sort these numbers in ascending order..
[tex]\begin{gathered} \sqrt{3}-1\approx1.732-1=0.732 \\ 2\sqrt{10}\div5=2(3.1623)\div5=1.2649 \\ \sqrt{14}=3.7147 \\ 3\sqrt{2}=3\times1.414\approx4.242 \\ \sqrt{19}+1\approx4.3589+1=5.3589 \\ 6=6 \end{gathered}[/tex]The given numbers in ascending order is:
[tex]\begin{equation} \sqrt{3}-1,2 \sqrt{10} \div 5, \sqrt{14}, 3 \sqrt{2}, \sqrt{19}+1,6 \end{equation}[/tex]Note: In your solution, you can make the conversion of each irrational begin on a new line.
Evaluate( - 4) ^ 3/2
Answer: 8i
On a circle of radius 9 feet, what angle would subtend an arc of length 7 feet?
_____ degrees
The angle subtend an arc length of 7 feet is 44.56°
Given,
Radius of a circle = 9 feet
Arc length of a circle = 7 feet
Arc length :
The distance between two places along a segment of a curve is known as the arc length.
Formula for arc length:
AL = 2πr (C/360)
Where,
r is the radius of the circle
C is the central angle in degrees
Now,
AL = 2πr (C/360)
7 = 2 × π × 9 (C/360)
7 = 18 π (C/360)
7/18π = C/360
C = (7 × 360) / (18 × π)
C = (7 × 20) / π
C = 140 / π
C = 44.56°
That is,
The angle subtend an arc length of 7 feet is 44.56°
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