Therefore, the center of the circle is located at (0, 6), and the length of the radius is approximately equal to 7.43.
To determine the coordinates of the center and length of the radius of the circle, we need to rewrite the given equation in standard form, which is\((x - h)^2 + (y - k)^2 = r^2\), where (h, k) represents the center coordinates and r represents the radius.
Given equation: \(x^2 + y^2 - 12y - 20.25 = 0\)
To complete the square, we need to add and subtract the appropriate terms on the left side of the equation:
\(x^2 + y^2 - 12y - 20.25 + 36 = 36\)
\(x^2 + (y^2 - 12y + 36) - 20.25 + 36 = 36\)
Simplifying further:
\(x^2 + (y - 6)^2 = 55.25\)
Comparing this equation with the standard form, we can identify the following values:
Center coordinates: (h, k) = (0, 6)
Radius length:\(r^2\) = 55.25, so the radius length is √55.25.
Therefore, the center of the circle is located at (0, 6), and the length of the radius is approximately equal to 7.43.
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Help me on this pleaseee
53. A right triangle has a hypotenuse measuring 15 inches and one leg measuring 9 inches What is the length, in inches, of the other leg of the triangle?
A. 3
B.6
C. 10
D. 12
Answer:
D
Step-by-step explanation:
Pythagorean
\(x^{2} + 9^{2} = 15^{2}\) (x>0)
=> \(x=\sqrt{15^{2}-9^{2} }\) \(=12\)
Multiplying and Dividing Expressions with Radicals
Exercises 1–5
Simplify as much as possible.
1. √17 =
2. √510 =
3. √4x
1. Using Radicals the number √17 has a value of 4.123.
2. √510 =260100.
3. √4x = 2√x.
Simply multiply or divide the numbers at each point where it makes sense to multiply or divide a function. If the functions are specified by formulas, you can simply multiply or divide the formulas (inserting numbers before or after is irrelevant).
When multiplying or dividing, it is standard practise for the final result to contain the same number of significant figures as the number with the fewest significant figures. The division of two numbers can be calculated using the following formula: Dividend Divisor = Quotient + Remainder. The number that is being divided in this case is known as the dividend.
The number that divides the number (dividend) into equal parts is known as the divisor.
1. \(\sqrt{17}\\\) = 4.123 (The values of the number √17 is 4.123.)
2. √510
= 510^2
=(500+10)^2
=500^2+10^2+2×500×10
=250000+100+10000
=260100.
3. √4x = 2√x.
because 4 = 2*2
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Find the measure of angle x in the figure below:
Answer:
70 degrees
Step-by-step explanation:
The angle opposite x and x itself are vertical angles, meaning that they have the same angle measure. Since the sum of the interior angles of a triangle is 180 degrees:
x+55+55=180
x+110=180
x=180-110=70
Hope this helps!
The base of a triangular pyramid is an equilateral triangle. Each side of the base measures 12 in. The area of the base is 62.4 in². The slant height of the pyramid is 6 in.
What is the surface area of the pyramid?
Enter your answer in the box.
The surface area of the pyramid is given by the equation A = 170.4 inches²
What is the surface area of the pyramid?The total surface area is the summation of the areas of the base and the three other sides. A = B + ( 1/2 ) ( P x h ), where B is the area of the base of the pyramid, P is the perimeter of the base, and h is the slant height of the pyramid
Surface Area of Pyramid = B + ( 1/2 ) ( P x h )
Given data ,
Let the surface area of the pyramid be represented as A
Now , the equation will be
The slant height of the pyramid h = 6 inches
The side of the equilateral triangle = 12 inches
So , the perimeter of the triangle = 3 x side length
Substituting the values in the equation , we get
The perimeter of the triangle = 36 inches
The area of the base = 62.4 inches²
So , Surface Area of Pyramid = B + ( 1/2 ) ( P x h )
Substituting the values in the equation , we get
Surface Area of Pyramid = 62.4 + ( 1/2 ) ( 36 x 6 )
On simplifying the equation , we get
Surface Area of Pyramid = 62.4 + ( 108 )
Surface Area of Pyramid = 170.4 inches²
Hence , the surface area of pyramid is 170.4 inches²
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In the diagram, the dashed figure is the image of the solid figure.
What is the image of
A
B
C
D
Answer:
the answer is A because it is ap
a product sells for $210 per unit, and its variable costs per unit are $138. the fixed costs are $422,000. if the firm wants to earn $47,440 pretax income, how many units must be sold?
6,520 units must be sold.
How to find sold units?
Let x be the number of units sold.
The total revenue (TR) generated by selling x units is:
TR = 210x
The total variable costs (TVC) incurred in producing x units is:
TVC = 138x
The total cost (TC) of producing x units is the sum of the fixed costs (FC) and the total variable costs (TVC):
TC = FC + TVC
= 422,000 + 138x
The pretax income (PI) is the difference between the total revenue (TR) and the total cost (TC):
PI = TR - TC
= 210x - (422,000 + 138x)
= 72x - 422,000
To find the number of units x that must be sold to earn a pretax income of $47,440, we set PI equal to $47,440 and solve for x:
72x - 422,000 = 47,440
72x = 469,440
x = 6,520
Therefore, the firm must sell 6,520 units to earn a pretax income of $47,440.
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The stem-and-leaf plot shows test scores for students in Math 7. How many students earned more than a 65 on their test? Key 4|5 = 45 A) 58 students B) 28 students C) 60 students D) 65 students
Answer:
68 studentsStep-by-step explanation:
Count the number of scores greater than 65
60's ⇒ 8 (2 of 66, 4 of 68, 2 of 69)70's ⇒ 18 (4 of 72, 2 of 74, 2 of 75, 2 of 76, 2 of 78, 6 of 79)80's ⇒ 10 (2 of 81, 2 of 85, 2 of 86, 2 of 87, 2 of 88)90's ⇒ 22 (6 of 90, 2 of 92, 2 of 93, 2 of 94, 6 of 95, 2 of 98, 2 of 99)Total number is
8 + 18 + 10 + 10 + 22 = 68Note: none of answer choices reflect this
Answer:
68 student hope that helps
The explicit formula for a sequence an = 5 – 7n . What is the value of a12?
Answer: its just 12 because a is just a variable
Step-by-step explanation: so like 5 - 7n its just 5 - 7 which in 2 so 12a is just 12
Answer:
-79
Step-by-step explanation:
an=5-7n This is the given equation
Now, we substitute 12 for n and do the equation
a(12)=5-7(12)
a(12)=5-84
a(12)=-79 This is our answer, negative 79
4. In a class of students, the following data table
summarizes how many students have a cat or a dog. What
is the probability that a student chosen randomly from the
class has a dog?
Has a dog
Does not have a dog
Has a cat Does not have a cat
16
4
6
3
The probability that a student who had a dog also had a cat would be = 7/25.
How to calculate the possible outcome of the given event?To calculate the possible outcome of the given event, the formula for probability should be used and it's given below as follows. That is;
Probability = possible outcome/sample space
possible outcome = 7
sample space = 7+2+3+13 = 25
Probability = 7/25
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Charlie bought a pair of shorts at the store when they were having a 45 percent of sale.If the regular price of the shorts was 24 dollars how much did charlie pay
Answer:
Your answer would be 13 dollars and 20 cents
The cone is formed from 3,200 ft3 of gravel. If the height of the cone is 24 feet, what is the radius, in feet, of the base of the cone? Use the π button on your calculator to determine the answer. Round your answer to the nearest tenth of afoot. The radius of the base of the cone is approximately ____ feet
The radius of the base of the cone is approximately 12.65 feet if The cone is formed from 3,200 ft of gravel.
Height of cone = 24 feet
The volume of the cone = \(3,200 ft^3\)
To find the volume of the cone, the formula used here is:
V =π* \(r^2h\)
Here, the values of V and H are known terms. we need to calculate the radius r of the cone.
π = 3.14 constant value
Substituting the values in the above equation, we get:
\(3,200 = (1/3)^2*(24)*\) π
\(r^2\)= 3,200 / (8π)
\(r^2\) = 400 / π
r = 12.65
Therefore, we can conclude that the radius of the base of the cone is 12.65 feet.
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Serenity filled up her car with gas before embarking on a road trip across the country. Let � G represent the number of gallons of gas remaining in her gas tank after driving for � t hours. A graph of � G is shown below. Write an equation for � G then state the � y-intercept of the graph and determine its interpretation in the context of the problem.
The equation is: G = -⁵/₄t + 15
The slope of the function represents that ⁵/₄ gallons of gas is consumed to drive the car for one hour.
How to find the linear equation of the graph?The formula for the equation of a line in slope intercept form is:
y = mx + c
where:
m is slope
c is y-intercept
From the graph, we see that:
y-intercept = 15 gallons
Now, the slope is gotten from the formula:
Slope = (y₂ - y₁)/(x₂ - x₁)
Slope = (10 - 5)/(4 - 8)
Slope = -⁵/₄
Thus, equation is:
G = -⁵/₄t + 15
The slope of the function represents that ⁵/₄ gallons of gas is consumed to drive the car for one hour.
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D.1 Give an estimate for the total volume of food and water you've ingested in the last day, in milliliters. D.2 How many times larger is the amount of blood your heart has pumped in the last day than the amount of food and drink you took in? D.3 How much error do you expect in your answer to 4 b ? You should give an quantitative response to this, but not one generated by a formula. Instead, estimate the error by examining how closely you think you know the values you estimated for food intake and blood flow. You don't need to use advanced error propagation; an approximate response is fine. D.4 What is the relevance of this calculation to the theory that all the blood that flows through your veins is generated in the liver?
An estimate for the total volume of food and water you've ingested in the last day is 3000-5000 milliliters. On average, the heart pumps about 5 liters of blood per minute. 10-20% or more error I'm expecting. Calculating heart blood volume compared to food and drink consumption is crucial for understanding circulation and liver function.
D.1 Estimating the amount of food and water consumed in a day can be difficult without specific measurements, but a rough estimate can be made based on typical intake amounts. On average, a person may consume 2-3 liters of water and 1000-2000 calories per day, resulting in an estimated total volume of 3000-5000 milliliters.
D.2 The amount of blood pumped by the heart varies from person to person and depends on factors such as heart rate and overall health. On average, the heart pumps about 5 liters of blood per minute, which is much larger than the estimated volume of food and water intake.
D.3 Estimating food and water intake and blood flow is prone to error due to variability and uncertainties in personal measurements. Individuals' habits, health, and physical activity levels can affect these estimates, potentially resulting in a significant error of 10-20% or more.
D.4 The calculation of the heart's blood volume compared to food and drink consumption is crucial for understanding the circulation system and liver role.
The liver processes nutrients, detoxifies, and produces blood components, while the heart is responsible for circulating blood throughout the body. The vast difference in volume between the two is emphasized, emphasizing the heart's crucial role in maintaining circulation.
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How might this number be shown on a calculator? 6.2x1015 6.2011
Answer:
This is the answer to your question
Bill and Ted plan to buy a ps4 for $299.00. Games for the system cost $60 each. They plan to buy one console to share. If bill and Ted buy 1 console and 3 games, how much will they spend total?
Answer:
$459
Step-by-step explanation:
60x3=180
$299+180=$459
f(x)=2x^2-5x-3 g(x)=2x^2+5x+2 find (f/g)(x)
If f(x)=2x²-5x-3 g(x)=2x²+5x+2 then (f/g)(x) = (x - 3) / (x + 2).
What is function?
In mathematics, a function is a relationship between two sets of elements, called the domain and the range, such that each element in the domain is associated with a unique element in the range.
To find (f/g)(x), we need to divide f(x) by g(x) as follows:
f(x) = 2x² - 5x - 3
g(x) = 2x² + 5x + 2
f(x) / g(x) = (2x² - 5x - 3) / (2x² + 5x + 2)
To simplify this expression, we can factor the numerator and denominator:
f(x) / g(x) = [(2x + 1)(x - 3)] / [(2x + 1)(x + 2)]
Now, we can cancel out the common factor of (2x + 1) from both the numerator and denominator:
f(x) / g(x) = (x - 3) / (x + 2)
Therefore, (f/g)(x) = (x - 3) / (x + 2).
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Which is 1,250,000,000 written in scientific notation?
A 12.5 1010
B 12.5 x 10
© 1.25 * 109
D 1.25 x 108
answer is c
Step-by-step explanation:
u can use calculator to check the answer
answer is c
Step-by-step explanation:
u can use calculator to check the answer
Find the volume of this prism.
Please help.
Answer:
840cm³is a required answer.
8th grade easy math help
A. Find the parametric form for the plane containing the points
(1, -2, 1), (0, 5, 3) and (2, 4, 7)
B. Find the normal form ax + by + cz = d for the plane
containing the points (1,-2,1), (0, 5, 3) and
If the points are (1, −2, 1), (0, 5, 3) and (2, 4, 7), then the parametric form for the plane is -40x-8y+43z=-11 and the normal form ax+by+cd=d for the plane is -40x-8y+43z=65.
a) To find the parametric form of the plane, follow these steps:
We use any two points to find the direction vectors and then the cross product of the direction vectors will give us the normal vector of the plane.To get two vectors, we take two points (1, −2, 1) and (0, 5, 3) on the plane, the direction vector is \(\vec{v1}=\begin{pmatrix}0-1\\5-(-2)\\3-1\end{pmatrix}=\begin{pmatrix}-1\\7\\2\end{pmatrix}\)Similarly, we take two points (1, −2, 1) and (2, 4, 7), the direction vector is \(\vec{v2}=\begin{pmatrix}2-1\\4-(-2)\\7-1\end{pmatrix}=\begin{pmatrix}1\\6\\6\end{pmatrix}\)The normal vector of the plane is the cross product of v1 and v2, that is \(\vec{n}=\vec{v1} \times \vec{v2}=\begin{pmatrix}-1\\7\\2\end{pmatrix} \times \begin{pmatrix}1\\6\\6\end{pmatrix}\). By calculating this cross product we get,\(\vec{n}=\begin{pmatrix}-40\\-8\\43\end{pmatrix}\). Now, we can write the equation of the plane as \(\vec {r}.\vec{n}= d\) where d is the distance of the plane from the origin. To find d, we substitute the coordinates of any one point, say (1, −2, 1), we get, \(\begin{pmatrix}1\\-2\\1\end{pmatrix} . \begin{pmatrix}-40\\-8\\43\end{pmatrix}=d \Rightarrow -40+16+43=d \Rightarrow d=-11\). Hence the equation of the plane in vector form is, \(\begin{pmatrix}x\\y\\z\end{pmatrix}.\begin{pmatrix}-40\\-8\\43\end{pmatrix}=-11 \Rightarrow -40x-8y+43z=-11\)b) To find the normal form, follow these steps:
The normal form is ax+by+cz=d. Substituting the coordinates of any one point (1, −2, 1), we get the value of d as, -40(1)-8(-2)+43(1)=65. The equation of the plane in the normal form is, -40x-8y+43z=65. Hence, the normal form is -40x-8y+43z=65.Learn more about parametric form:
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An airplane 40,000 feet above the ground begins descending at a rate of 1,500 feet per minute. Write an equation to model the situtation.
Answer:
h(t) = 40,000 - 1,500t
Step-by-step explanation:
Let h(t) be the height of the airplane after t minutes.
h(t) = 40,000 - 1,500t
What is the value of x?
HELP! Please
Answer:
a. 68
Step-by-step explanation:
You just have to subtract these two numbers from 180 because adding all the angles of a triangle the resulta is 180. Subtracting those numbers from 180 will give you the result.
the teacher workroom has a small room used for the meetings that it shaped like a square . if one wall measures 8 feet what is the area of the floor of that meeting room
The area of the teacher workroom is 64 feet squared
What is the correlation coefficient of these six data points? express your answer as a decimal, fraction, or simple mathematical expression. your fraction does not need to be reduced. x y 0 8 1 11 3 10 4 13 7 10 10 6
The correlation coefficient is -0.29.
Correlation refers to a process for establishing whether or not relationships exist between two given variables.
In statistics, correlation coefficients are used to quantify the strength of the association between two variables. Like Pearson's correlation, which is frequently employed in linear regression, there are other varieties of correlation coefficients. It is widely used in statistics and is highly well-liked.
X Y X² Y² XY
0 8 0 64 8
1 11 1 121 11
3 10 9 100 30
4 13 16 169 52
7 10 49 100 70
10 6 100 36 60
∑X = 25
∑Y = 58
∑X² = 175
∑Y²= 590
∑XY= 231
r = N×∑XY−(∑X∑Y) / √[N∑x2−(∑x)2][N∑y2−(∑y)2]
Putting all the values,
r = 6*231 - (25*58) / √(6*175-625)(6*590-3364)
r = 1368 - 1450 / √(425)(176)
r = -82/ √ 74800
r = -82/ 273.49
r= -0.29
Therefore, the correlation coefficient is -0.29.
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which answer choice correctly shows 0.3% as a decimal?
a.300
b.3
0c.0.03
d.0.003
d.0.003 choice correctly shows 0.3% as a decimal.
Here, we have,
given that,
the percent is: 0.3%
now, we know that,
percentage, a relative value indicating hundredth parts of any quantity. One percent (symbolized 1%) is a hundredth part; thus, 100 percent represents the entirety and 200 percent specifies twice the given quantity. percentage.
now, we get,
0.3%
=0.3 ÷ 100
=0.003
now, we know, 0.003 is a decimal.
so, we get,
d.0.003 choice correctly shows 0.3% as a decimal.
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Which number is rational and a real number, but not an integer?
A. √2
OB. -5
5
O c. 9/10
OD. There is no such number.
Option (c) is the correct option.
9/10 is rational and a real no. but not an integer.
What is a rational number?
A number with the form p/q, where p and q are integers and q is not equal to 0, is said to be rational.
What is an integer?
In the category of real numbers are irrational numbers, fractions, and rational numbers like positive and negative integers.
What is a real number?
Integers, which can be both negative and positive and include zero, are numbers without a decimal or fractional component.
Our objective is to find a number which is rational and a real number but not an integer.
√2 is not rational and not a real number.
-5 is rational and a real number but It is an integer.
9/10 is rational and a real number and also not an integer.
Hence, (c) is the correct option.
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Eloise bought 12 grapefruits. Each grapefruit weighed 0.52 pound.
How many pounds of grapefruits did Eloise buy?
Answer:
6.24 pounds
Step-by-step explanation:
12 x .52 = 6.24 pounds
Answer:
The answer would be 6.24lb
Step-by-step explanation:
I took the k12 test
Kurt company purchased $5000 of merchandise from Marilyn company with terms of 2/10 n/40. What amount will Kurt company pay to Marilyn company if Kurt company takes advantage of the purchase discount?
If Kurt company takes advantage of the purchase discount, they will pay $4900 to Marilyn company.
The terms of "2/10 n/40" indicate that Kurt company can take advantage of a 2% discount if they pay within 10 days. The full payment is due within 40 days.
To calculate the amount Kurt company will pay to Marilyn company if they take advantage of the purchase discount, we need to subtract the discount from the total amount.
The total amount of merchandise purchased is $5000.
To calculate the discount amount, we multiply the total amount by the discount percentage:
Discount amount = 2% of $5000 = 0.02 * $5000 = $100
Therefore, if Kurt company takes advantage of the purchase discount, they will pay $100 less than the total amount.
The amount Kurt company will pay to Marilyn company is:
Total amount - Discount amount = $5000 - $100 = $4900
Hence, if Kurt company takes advantage of the purchase discount, they will pay $4900 to Marilyn company.
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kings hotel had 160 rooms and 35% of the rooms did not have ocean view. Write an equation to find the total number of rooms that had an ocean view
Answer:
ok so we now now many do have 0.35 so now lets just find out how many do
1-0.35=0.65
65% do have a ocean room so lets just multiply
0.65*160=104
104 do have a ocean facing room
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