Answers
A system of inequalities to represent the constraints of this problem are x ≥ 0 and y ≥ 0.
A graph of the system of inequalities is shown on the coordinate plane below.
How to write the required system of linear inequalities?In order to write a system of linear inequalities to describe this situation, we would assign variables to the number of HD Big View television produced in one day and number of Mega Tele box television produced in one day respectively, and then translate the word problem into algebraic equation as follows:
Let the variable x represent the number of HD Big View television produced in one day.Let the variable y represent the number of Mega Tele box television produced in one day.Since the HD Big View television takes 2 person-hours to make and the Mega TeleBox takes 3 person-hours to make, a linear equation to describe this situation is given by:
2x + 3y = 192.
Additionally, TVs4U’s total manufacturing capacity is 72 televisions per day;
x + y = 72
For the constraints, we have the following system of linear inequalities:
x ≥ 0.
y ≥ 0.
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Related Questions
Find a basis of the subspace ofR4defined by the equation3x1−9x2+2x3−3x4=0
Answers
The basis of the subspace of R4 defined by the equation3x1−9x2+2x3−3x4=0 is {(3, 1, 0, 0), (-2/3, 0, 1, 0), (1, 0, 0, 1)}
A basis of the subspace of R4 defined by the equation 3x1−9x2+2x3−3x4=0 can be found by solving the equation for one of the variables in terms of the others and then writing the general solution as a linear combination of vectors.
First, solve the equation for x1 in terms of the other variables:
3x1 = 9x2 - 2x3 + 3x4
x1 = 3x2 - (2/3)x3 + x4
Next, write the general solution as a linear combination of vectors:
(x1, x2, x3, x4) = (3x2 - (2/3)x3 + x4, x2, x3, x4)
= x2(3, 1, 0, 0) + x3(-2/3, 0, 1, 0) + x4(1, 0, 0, 1)
Finally, the basis of the subspace is the set of vectors that make up the linear combination:
{(3, 1, 0, 0), (-2/3, 0, 1, 0), (1, 0, 0, 1)}
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6. A hiker looks down into a valley with binoculars. The angle of depression to the farthest edge of the river is 61. The angle to the closest edge of the river below is 63. If the valley is 1250
feet deep, how wide is the river? Round the answer to the nearest foot.
Answers
Answer:
w ≈ 640 feet
Step-by-step explanation:
Let's call the distance from the hiker's position to the closest edge of the river "x", and the width of the river "w". We can use trigonometry to set up two equations involving these values:
In the first triangle, the angle of depression is 63 degrees, and the opposite side is x + w. Therefore, we can use the tangent function:
tan(63) = (x + w) / 1250
In the second triangle, the angle of depression is 61 degrees, and the opposite side is x. Therefore, we can use the tangent function again:
tan(61) = x / 1250
Now we can solve these equations for "w" and "x", respectively:
w = 1250 * tan(63) - x
x = 1250 * tan(61)
Substituting the second equation into the first:
w = 1250 * tan(63) - 1250 * tan(61)
Plugging this into a calculator, we get:
w ≈ 640 feet
Therefore, the width of the river is approximately 640 feet rounded to the nearest foot.
What is one number that rounds to 213,000 when rounded to the nearest thousands
Answers
Answer:
212,500
Step-by-step explanation:
One number that rounds to 213,000 when rounded to the nearest thousands is 212,500.
A small publishing company is planning to publish a new book. The production costs will include one-time fixed costs (such as editing) and variable costs (such as printing). There are two production methods it could use. With one method, the one-time fixed costs will total $82,363, and the variable costs will be $9. 25 per book. With the other method, the one-time fixed costs will total $21,162 , and the variable costs will be $21. 50 per book. For how many books produced will the costs from the two methods be the same?
Answers
In the first production method, the company produces approximately 4,996 books.
Let's represent the number of books produced as x.
Total cost of method 1 = One-time fixed cost + Variable cost * Number of books produced
= $82,363 + $9.25x
Total cost of method 2 = One-time fixed cost + Variable cost * Number of books produced
= $21,162 + $21.50x
Setting the two equations equal to each other, we get:
$82,363 + $9.25x = $21,162 + $21.50x
Simplifying this equation, we get:
$61,201 = $12.25x
Dividing both sides by $12.25, we get:
x = 4,995.92
This means that the costs from the two methods will be the same when the company produces approximately 4,996 books.
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You are 14ft away from a flagpole and are looking up at if from an angle of 74.4 How is the flagpole ?
Answers
Answer:
23.4 ft tall
Step-by-step explanation:
Answer:
Step-by-step explanation:
Given: Distance from the flagpole = 14 ft
Angle of elevation θ = 74.4°
To find: Length of the flagpole
Answer:
tan(74.4°) = [tex]\frac{L}{14}[/tex]
L = 14 tan(74.4°) = 50.142 ft
So the length of the pole is 50.142 ft.
1.Let f be a linear function. Given f(2) = - 7 and f(6) = - 17, find f(x).
2.FInd the slope of the line passing through the points A( 6, 3 ) and B( 15, - 3)
3. Find the equation of the line that contains point A(5,-3) and has slope m=3/5
4.Find the equation of the line that contains the point A ( 4 , - 8 ) and is parallel to the graph of the function :f(x)=1/4x+3
5. find the zero of the function f(x)=4x-2
Answers
By using the slope-intercept form it can be concluded that:
the equation of the line is f(x) = -2.5x - 2the slope of the line is -2/3the equation of the line is y = (3/5)x - 6the equation of the line is y = (1/4)x - 9the zero of the function is x = 1/2.The slope-intercept form of an equation is represented as follows:
y = mx + c or y - y₁ = m(x - x₁) , where
m = slope
c = y-intercept
(x₁, y₁) = point on the line
The slope of the line when given two points can be calculated as follows:
m = (y₂ - y₁) / (x₂ - x₁)
1. Given f(2) = - 7 and f(6) = - 17. To find f(x), we need to use the slope-intercept form of a linear function: f(x) = mx + b. First, we need to find the slope of the line by using the two given points:
m = (y₂ - y₁) / (x₂ - x₁)
= (f(x₂) - f(x₁)) / (x₂ - x₁)
= (-17 - (-7)) / (6 - 2)
= (-10) / (4)
= -2.5
Now, we can plug in one of the points to find the y-intercept:
f(x) = mx + b
f(2) = (-2.5)(2) + b
-7 = -5 + b
b = -2
Therefore, the equation of the line is f(x) = -2.5x - 2.
2. To find the slope of the line passing through points A(6,3) and B(15,-3), we use the formula:
m = (y₂ - y₁) / (x₂ - x₁)
= (-3 - 3) / (15 - 6)
= (-6) / (9)
= -2/3
Therefore, the slope of the line is -2/3.
3. To find the equation of the line that contains point A(5,-3) and has slope m=3/5, we use the point-slope form of a linear function:
y - y₁ = m(x - x₁)
y - (-3) = (3/5)(x - 5)
y + 3 = (3/5)x - 3
y = (3/5)x - 6
Therefore, the equation of the line is y = (3/5)x - 6.
4. To find the equation of the line that contains the point A(4,-8) and is parallel to the graph of the function f(x)=1/4x+3, we know that the slope of the new line will be the same as the slope of the given function, which is 1/4. We can use the point-slope form of a linear function to find the equation of the new line:
y - y₁ = m(x - x₁)
y - (-8) = (1/4)(x - 4)
y + 8 = (1/4)x - 1
y = (1/4)x - 9
Therefore, the equation of the line is y = (1/4)x - 9.
5. To find the zero of the function f(x) = 4x - 2, we need to set the function equal to zero and solve for x:
f(x) = 0
4x - 2 = 0
4x = 2
x = 2/4
= 1/2
Therefore, the zero of the function is x = 1/2.
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NEED HELP DUE FRIDAY!!!!
Here is another triangle similar to DEF found in the lesson section labeled “Shrinking Triangles”.
• Label the triangle D”E”F”.
• What is the scale factor from triangle DEF to triangle D”E”F”?
• What are the coordinates of F”? Explain how you know.
• What are cos(D”), sin(D”), and tan(D”)?
Answers
The scale factor of dilation is 0.075 and the coordinates of F" are (0.9, 0.375)
Label the triangle D”E”F”.The label of the triangle is added as an attachment
The scale factor of the dilationFrom the complete question, we have
DE = 12 units
Then, we have
D"E" = 0.9 units
Using the above as a guide, we have the following:
Scale factor = D"E"/DE
Scale factor = 0.9/12
Scale factor = 0.075
So, the scale factor of dilation is 0.075
The coordinates of F"This is calculated as
F = Scale factor * F
So, we have
F = 0.075 * (12, 5)
F = (0.9, 0.375)
The trigonometry ratiosThe sine, cosine and tangent are calculated as
sin(D") = EF/DF
cos(D") = DE/DF
tan(D") = EF/DE
So, we have
sin(D") = 0.375/1 = 0.375
cos(D") = 0.9/1 = 0.9
tan(D") = 0.375/0.9 = 0.416
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Missing information in the question
Triangle DEF has coordinates D(0,0) E(12,0) F(12,5) and pictured is triangle D”E”F”.
DE = 0.9, EF = 0.375 and DF = 0.9
How many roots does the polynomial equation have? 2x^(5)+6x^(4)-3x^(3)+x^(2)-9x-1=0
Answers
The polynomial equation 2x^(5)+6x^(4)-3x^(3)+x^(2)-9x-1=0 has 5 roots. This is because the degree of the equation is 5, and the number of roots of a polynomial equation is equal to its degree. Therefore, this equation has 5 roots. To find the roots of the equation, you can use the Rational Root Theorem, synthetic division, or other methods. However, finding the exact roots of a fifth-degree polynomial equation can be difficult and may require the use of a graphing calculator or computer software.
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The three angles of a quadrilateral are 60°,80° and 120° find the fourth angle?
Answers
Answer:
Step-by-step explanation:
Angles in a quadrilateral add to 360°. So
[tex]60+80+120+x=360[/tex] (where [tex]x[/tex] is the fourth angle)
[tex]260+x=360[/tex]
[tex]x=100[/tex]° (after subtracted 260 from both sides of equation)
Verifica que solo los numeros pares tienen cuadrados pares, Pista; ¿que forma tienen los numeros pares y que forma tienen los numeros impares?
Answers
Podemos concluir que solo los números pares tienen cuadrados pares, ya que cualquier número par elevado al cuadrado es divisible por 2 y, por lo tanto, es par.
Que son numeros pares?Los números pares tienen la forma 2n, donde n es un número entero. Si elevamos al cuadrado un número par, obtenemos:
(2n)² = 4n²
Y podemos ver que 4n² es un número par, ya que se puede escribir como 2 x 2n².
Por otro lado, los números impares tienen la forma 2n+1, donde n es un número entero. Si elevamos al cuadrado un número impar, obtenemos:
(2n+1)² = 4n² + 4n + 1
Y podemos ver que 4n² + 4n es un número par, ya que se puede escribir como 2 x (2n² + 2n), mientras que 4n² + 4n + 1 es un número impar.
Por lo tanto, podemos concluir que solo los números pares tienen cuadrados pares, mientras que los números impares tienen cuadrados impares.
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jenna borrows 8,000 for college at a yearly simple interest rate of 6 she takes 15 years
Answers
The amount of interest earned on Jenna's loan of $8000 for 15 years is $7200
How to determine the amount of interestThe given variables and their values from the question are listed as follows:
Principal = 8000
Rate = 6%
Time = 15 years
The general formula to calculate simple interest is:
Simple interest = Principal * Rate * Time
By replacing the given values into the equation mentioned above, we obtain the subsequent expression
Simple interest = 8000 * 6% * 15
Evaluate the products in the expression
Simple interest = 7200
Hence, the amount of interest is $7200
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Complete question
Jenna borrows 8,000 for college at a yearly simple interest rate of 6 she takes 15 years
Determine the amount of interest
HURRY I NEED THIS PLEASE WORTH 60 points
Triangle ABC has been reflected over the x-axis to create triangle A'B'C'. Which of the following statements is true?
Answers
Answer: choose Answer B
Step-by-step explanation:
because if you flip the triangle back to what it was previously A B lines up with answer B so it’s B
Label the tick marks on the two number lines in two different ways. In each case, your labeling should fit with the structure of the base-ten system and the fact that the tick marks at the ends of the number lines are longer than the other tick marks.
Answers
One way to label the tick marks on the number lines is to use whole numbers for the longer tick marks and decimals for the shorter tick marks.
For example, on the first number line, you could label the longer tick marks as 0, 1, 2, 3, 4, and 5, and the shorter tick marks as 0.1, 0.2, 0.3, etc.
This fits with the structure of the base-ten system because each whole number is ten times greater than the corresponding decimal.
Another way to label the tick marks is to use fractions for the shorter tick marks. For example, on the second number line, you could label the longer tick marks as 0, 1, 2, 3, 4, and 5, and the shorter tick marks as 1/10, 2/10, 3/10, etc.
This also fits with the structure of the base-ten system because each fraction is one-tenth of the corresponding whole number.
Both of these labeling methods are accurate and fit with the structure of the base-ten system, so either one would be an appropriate way to label the tick marks on the number lines.
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According to the map on the left, Central Park is about 50 blocks long by 9 blocks wide. What is the approximate area of the park? Show your work.
Answers
In the given map, the approximate area of the Central Park is 450 blocks
Calculating the approximate area of the parkFroom the question, we are to determine the approximate area of the central park.
The park is a rectangular park and the approximate area of the park can be calculated by using the formula for calculating the area of a rectangle.
If Central Park is about 50 blocks long by 9 blocks wide, we can find its approximate area by multiplying the length and width:
Area = Length x Width
Area = 50 x 9
Area = 450
Hence, the approximate area of Central Park is 450 blocks.
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Find the value of x.
3x +30 2x 4x
Answers
Answer:
9x+30
Step-by-step explanation:
because form rule of like and unlike term
10. A plane traveled 322 miles from El Paso in a direction 57° northeast as shown
below.
N
57°
322 miles
NE
E
El Paso
What is the height of the plane, to the nearest mile?
Answers
Answer:
To find the height of the plane, we need to use trigonometry. Let's call the height of the plane "h". We can use the given angle of 57° and the opposite side (height) to the angle to find the adjacent side (distance traveled east) using the tangent function:
tan(57°) = h / distance traveled east
We can rearrange this equation to solve for h:
h = distance traveled east x tan(57°)
To find the distance traveled east, we need to use the given distance of 322 miles and the direction traveled. Since the plane is traveling at a 57° angle northeast, we can split this into two right triangles, one facing northeast and the other facing southeast, as shown below:
N
|
|
|\ 57°
|
\
The distance traveled east is the adjacent side of the southeast-facing right triangle, which can be found using the cosine function:
cos(57°) = distance traveled east / 322
We can rearrange this equation to solve for the distance traveled east:
distance traveled east = 322 x cos(57°)
Now we can plug in this value for the distance traveled east into the equation for the height of the plane:
h = distance traveled east x tan(57°)
h = (322 x cos(57°)) x tan(57°)
Using a calculator, we can evaluate this expression to find:
h ≈ 389.4 miles
Therefore, the height of the plane to the nearest mile is 389 miles.
Helppppppppppppppppppppp;pppppppppp
Answers
Answer:
Step-by-step explanation:
Ok, I hate point-slope form but I can help!
I'm going to answer slope-intercept first, then point slope.
2. y = 1/4x - 1 ; y+2 = 1/4(x+4)
3. y = -3/2x + 1 ; y+2 = -3/2(x-2)
4. y = x - 2 ; y-1 = 1(x-3)
Hope this helps!
question in picture
WILL MARK BRAINLIEST
Answers
Answer:
A. y = 52x
Step-by-step explanation:
The equation is set up in slope-intercept form y = mx + b
m = the slope
b = y-intercept
Slope = rise/run or (y2 - y1) / (x2 - x1)
Pick 2 points (0,0) (4, 208)
We see the y increase by 208 and the x increase by 4, so the slope is
m = 208/4 = 52
Y-intercept is located at (0,0)
So, our equation is y = 52x
The answer is option A
What values are between 7 x 10 to the power of -6 and 6x10 to the power of-5?
Answers
The values between[tex]7 * 10^-6[/tex] and [tex]6 * 10^-5 = 5.3 * 10^-5[/tex]
What is the difference of values?The result of subtracting one number from another. How much one number differs from another.
Example: The difference between 8 and 3 is 5.Another example is the difference between 100 and 50= 100-50 = 50
The difference simply means subtracting a number from another
Similarly the difference between [tex]7 * 10^-6 and 6 * 10^-5 = 6 * 10^-5 - 7 * 10^-6[/tex]
changing [tex]7 *10^-6 0.7 * 10^-5[/tex]= [tex](6 * 10^-5) - (0.7 * 10^-5)= 5.3 * 10^-5[/tex]
Therefore the values between [tex]7 * 10^-6[/tex] and [tex]6 * 10^-5[/tex] is [tex]5.3 * 10^-5[/tex]
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Find the Area of the figure below, composed of a rectangle with a semicircle removed from it. Round to the nearest tenth place.
Answers
Answer:
Below
Step-by-step explanation:
Area of WHOLE rectangle = 9 x 6 = 54 units^2
now subtract the area of the semicircle with radius 3
whole circle is pi r^2 ( one-half of this is 1/2 pi r^2)
54 units^2 - 1/2 pi r^2
54 - 1/2 * pi * 3^2 = 39.9 units^2
Eight: Adding & Subtracting K Subtract and simplify your answer. (5x)/(x^(2)-49)-(6)/(x+7)
Answers
The simplified answer is (5x)/(x^(2)-49)-(6)/(x+7) = -(x - 42)/((x + 7)(x - 7)).
To subtract and simplify the given expression, we need to find a common denominator and combine the numerators. The common denominator in this case will be (x^2 - 49), which can be factored into (x + 7)(x - 7).
So, the expression becomes:
(5x)/((x + 7)(x - 7)) - (6)/(x + 7)
To get a common denominator, we need to multiply the second term by (x - 7)/(x - 7):
(5x)/((x + 7)(x - 7)) - (6(x - 7))/((x + 7)(x - 7))
Now we can combine the numerators:
(5x - 6(x - 7))/((x + 7)(x - 7))
Simplifying the numerator gives us:
(-x + 42)/((x + 7)(x - 7))
And finally, we can simplify the expression by factoring out a -1 from the numerator:
-1(x - 42)/((x + 7)(x - 7))
So the final answer is:
-(x - 42)/((x + 7)(x - 7))
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oey's friend asked him what his math test score was. Joey said, "I did better than 5 points more than the class average." The class average was 88.
Which of the following number sentences represents J, Joey's math test score?
A. 88 + 5 < J
B. 88 + J < 5
C. 88 - 5 > J
D. 88 + 5 > J
Answers
Answer: The class average is 88, and Joey did better than 5 points more than the class average. Therefore, Joey's math test score is greater than 88 + 5 = 93.
So, the number sentence that represents Joey's math test score is:
D. 88 + 5 > J
Step-by-step explanation:
Rewrite the fraction in the sentence below as a percentage.
At a certain wedding 11/20, of the guests were over 25 years old.
What is the Percent notation: %?
Answers
The percent notation is 55%.
What is the percent notation?Percentage is the fraction of an amount that is usually expressed as a number out of hundred. Percentage is a measure of frequency. The sign that is used to represent percentage is %. In order to convert a fraction to percentage notation, multiply by 100.
Percent notation = fraction that attended the wedding x 100
= 11/20 x 100 = 55%
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Kyra is making squares with toothpicks. She uses 4 toothpicks to make a square. Then she adds 3 more toothpicks to make two squares side by side. To build three squares in a line, she used a total of 10 toothpicks. If she continues this pattern, how many toothpicks will she use to make 90 squares in a straight line?
How many squares can Kyra make in this pattern if she has a box of 1,000 toothpicks?
Answers
The toothpicks she will use to make 90 squares in a straight line are 271. Squares can Kyra make if she has a box of 1,000 toothpicks are 333.
How many toothpicks are needed for making the first three squares?A total of 4 toothpicks are needed.
A total of 9 toothpicks are needed for further 3 squares.
So, the number of toothpicks needed to make 87 squares = [tex]\frac{87*9}{3}[/tex]
= 261
Hence, the number of toothpicks needed to make 90 squares = [tex]261+10[/tex]
= 271
The number of squares formed by 261 toothpicks = 87
So, the number of squares formed by 1000 toothpicks = [tex]\frac{996*87}{261} + 1[/tex]
= 333
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PLEASE SOMEONE HELP ME I DONT KNOW TRIGONOMETRY
Answers
Applying the right trigonometry ratio, each value of x is:
13. x ≈ 28.1°
14. x ≈ 13.5
15. x ≈ 219.9
16. x ≈ 59.0°
What are the Trigonometry Ratios?Trigonometry ratios are mathematical relationships between the angles and sides of a right triangle. The three primary trigonometry ratios are:
Sine (sin) ratio: The ratio of the length of the side opposite an angle to the length of the hypotenuse of a right triangle.Cosine (cos) ratio: The ratio of the length of the adjacent side to an angle to the length of the hypotenuse of a right triangle.Tangent (tan) ratio: The ratio of the length of the side opposite an angle to the length of the adjacent side of a right triangle.13. Apply the cosine ratio:
cos x = 15/17
x = cos^(-1)(15/17)
x ≈ 28.1°
14. Apply the sine ratio:
sin 75 = 13/x
x = 13/sin 75
x ≈ 13.5
15. Apply the tangent ratio:
tan 83 = x/27
x = 27 * tan 83
x ≈ 219.9
16. Apply the tangent ratio:
sin x = 12/14
x = sin^(-1)(12/14)
x ≈ 59.0°
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Use the properties of logarithms to rewrite and simplify the logarithmic expression.
Answers
After using the properties of logarithms to rewrite and simplify the logarithmic expression ln((e⁸)/7) simplifies to 1.
What are natural logarithms?
Natural logarithms are a type of logarithm that uses the number e as its base. The natural logarithm of a positive number x (written as ln(x)) is the exponent to which e must be raised to get x. In other words, ln(x) represents the power to which e must be raised to obtain x.
The number e is a mathematical constant that is approximately equal to 2.71828. It is a special number that appears in many areas of mathematics, science, and engineering. Natural logarithms have a variety of applications in fields such as calculus, probability theory, and statistics.
Some properties of natural logarithms include:
ln(1) = 0
ln(e) = 1
ln(xy) = ln(x) + ln(y) for any positive numbers x and y
ln(x/y) = ln(x) - ln(y) for any positive numbers x and y
ln(xᵃ) = a ln(x) for any positive number x and any real number a
Natural logarithms can be evaluated using a calculator or by using the properties of logarithms to simplify expressions. They are commonly used in mathematical and scientific calculations that involve exponential growth or decay.
We can use the property of logarithms that states: log(aᵇ) = b log(a) for any base a and any real number b.
Using this property, we can rewrite ln((e⁸)/7) as:
ln((e⁸)/(e⁷))
[tex]= ln(e^{(8-7)})[/tex]
= ln(e)
= 1
Therefore, ln((e⁸)/7) simplifies to 1.
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What is the total surface area of the rectangular prism shown?
Answers
Answer:
128 in^2
Step-by-step explanation:
L * W
16 * 8 = 128 in^2
If f(x)=-7x-13 what is the value of f(-4)
Answers
Answer:
f(-4) = 15
Step-by-step explanation:
A function is notated as f(x), because the x is the value you are putting in. For example. In f(x) = x + 5, the value you are putting in is x, and the output would be x + 5.
So in this case, we have f(x) = -7x-13. We are to figure out f(-4), so we can simply put in -4 as the x-value;
-7(-4) - 13
28 - 13
15
And so the value of f(-4) = 15
if you liked this answer please mark brainliest!
Answer:
9
Step-by-step explanation:
f times 9 = 7x - 13 = 9 pls make me brianlist
Judy bought 1 pound 6 ounces of almonds, 2 pounds 3 ounces of walnuts, and 8 ounces of cashews. What was the total weight of the nuts (in pounds and ounces)?
Answers
By answering the above question, we may state that This expression's equation evaluation results in: r = 8.5 ft
What is equation?A mathematical equation is a process that links two statements and indicates equality using the equals sign (=). A formal statement that proves the equality of two calculations is known as an equation in algebra. For instance, the equal sign separates the numbers 3x + 5 and 14 in the equation 3x + 5 = 14. A mathematical formula may be used to understand the link between the two phrases that are inscribed on opposite sides of a letter. Frequently, the logo and indeed the particular software are identical. like in 2x - 4 = 2, for example.
The following is the formula for a circle's circumference:
C = 2πr
where is a mathematical constant that is roughly equivalent to 3.14159, C is the circumference, r is the radius, and.
The circle's circumference is stated to be 17 feet. In order to find r, we may put this equal to the circumference formula as follows:
17π = 2πr
When we divide both sides by 2, we obtain:
r = 17π / (2π)
Units cancel out, leaving:
r = 17 / 2
This expression's evaluation results in:
r = 8.5 ft
As a result, the circle's radius is 8.5 feet.
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