Consider a circle whose equation is x2 + y2 – 2x – 8 = 0. Which statements are true? Select three options.
The radius of the circle is 3 units.
The center of the circle lies on the x-axis.
The center of the circle lies on the y-axis.
The standard form of the equation is (x – 1)² + y² = 3.
The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.
Answers
The x-axis is where the circle centre is located. Three units make up the circle's radius. This circle's radius coincides with the radius of the circle whose equation is x² + y² = 9.
What is the circle's equation when its centre is on the x-axis?The y coordinate of a circle's centre will be 0 if the circle's centre is on the x-axis. The circle's equation will therefore have the generic form x2 + y2 + 2gx + c = 0, where g and c are constants.
Circle's standard equation is written as:
x²+y²+2gx+2fy+C=0
Centre is (-g, -f)
radius = √g²+f²-C
Given a circle whose equation is : x²+y²-2x-8=0
Get the centre of the circle
2gx = -2x
2g = -2
g = -1
Similarly, 2fy = 0
f = 0
Centre = (-(-1), 0) = (1, 0)
This demonstrates circle's centre is on the x-axis.
r = radius = √g²+f²-C
radius = √1²+0²-(-8)
radius =√9 = 3 units
The circle has a radius of three units.
For the circle x²+y²=9, radius is expressed as:
r² = 9
r = 3 units
As a result, this circle's radius matches that of the circle whose equation is x² + y² = 9.
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Related Questions
10n + 7 > n -3(5-3n)
What’s The Value Of n?
Answers
9514 1404 393
Answer:
n may have any value
Step-by-step explanation:
Eliminate parentheses, subtract the right side from both sides.
10n +7 > n -15 +9n
(10n +7) -(10n -15) > 0
22 > 0 . . . . . . true for all values of n
n may have any value.
The diameter of a circle 18cm
Answers
Answer:
\(\text{Circumference}~ = 2 \pi r = 2 \pi \cdot \dfrac{18} 2 = 18 \pi =18 \times 3.14=56.52~ cm\)
Step-by-step explanation:
find the volume please thanks
Answers
answer:
volume= lwh
= 20*12*8
= 1920 cm³
PLEASE HELP!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Brandon invests $5800 in two different accounts. The first account paid 3 %, the second account paid 8 % in interest. At the end of the first year he had earned $229 in interest. How much was in each account?
$ ___ at 3 %
$ ____ at 8 %
Answers
Interest is a fee charged by a lender to a borrower for the use of money or credit, usually expressed as a percentage of the amount borrowed or invested over a period of time. Brandon invested $\(4700\) at 3% interest and $\(1100\) at \(8\)% interest. The total interest earned after one year is $229
How much was in each account?
Let x be the amount invested in the first account that pays 3% interest, and let y be the amount invested in the second account that pays 8% interest. Since the total amount invested is $5800, we have:
\(x + y = 5800\)
The amount of interest earned on the first account is 0.03x, and the amount of interest earned on the second account is 0.08y. Since the total interest earned after one year is $229, we have:
\(0.03x + 0.08y = 229\)
We now have two equations with two unknowns:
\(x + y = 5800\)
\(0.03x + 0.08y = 229\)
We can solve for x and y by using elimination or substitution method. Here, we will use the substitution method.
Solve the first equation for x:
\(x = 5800 - y\)
Substitute this expression for x into the second equation and solve for y:
\(0.03(5800 - y) + 0.08y = 229\)
\(174 - 0.03y + 0.08y = 229\)
\(0.05y = 55\)
\(y = 1100\)
Now substitute this value of y into either equation to solve for x:
\(x + 1100 = 5800\)
\(x = 4700\)
Therefore, Brandon invested $\(4700\) at 3% interest and $\(1100\) at \(8\)% interest.
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What is the answer of this triangle congruence question.
Answers
The value of x in the triangles are 9.
What is a quadratic equation?For variable x : ax² + bx + c = 0, where a≠0 is a standard quadratic equation, which is a second-order polynomial equation in a single variable. It has at least one solution since it is a second-order polynomial equation, which is guaranteed by the algebraic basic theorem.
Given:
The triangles are congruent.
That means, their corresponding angles are also congruent.
In ΔJKL,
the sum of all the angles of the triangle is 180°.
So,
x²-2x + x + 29 + 3x + 52 = 180
x² + 2x - 99 = 0
Solving the quadratic equation,
x² +11x - 9x - 99 = 0.
x (x + 11) -9 (x + 11) = 0
x = 9 and x = -11
Here, we take x = 9.
Therefore, the value of x is 9.
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observe that {b}->{a} appears to hold with respect to the given instance. does {a}->{b} holds with respect to the instance? g
Answers
false, {b}->{a} appears to hold with respect to the given instance.
what is instance?A variable created in a class that has a unique copy, or instance, for each instantiated object of the class is known as an instance variable in class-based, object-oriented programming. Although not static, an instance variable resembles a class variable.
A variable specified within a class but outside of constructors, methods, or blocks is known as an instance variable. All the constructors, methods, and blocks in the class have access to instance variables, which are created when an object is instantiated. To the instance variable, access modifiers can be applied.
false, {b}->{a} appears to hold with respect to the given instance.
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PLS HELP NO LINKS
A cardboard box has the dimensions 2 ft, 1.5 ft, and 1.2 ft. What is the volume of the box?
A. 3.2 ft
B. 3.6 ft
C. 4.7 ft
D. 14.4ft
Answers
Answer:
3.6 cubic feet
Step-by-step explanation:
The volume of the box is simply the product of the 3 sides. so \(2ft \times 1.5ft \times 1.2 ft = 3.6 ft^3\)
26. My little brother has a 4-digit bike lock with the digits 0 to 9 on each part of the lock as shown. He started on the correct combination and turned each part the same amount in the same direction and now the lock shows the combination 6348. Which of the following CAN- NOT be the correct combination of my brother's lock? (A) 8560 (B) 3015 (C) 4906 (D) 1893 (E) 6348 0782 Activate Windows
Answers
Answer:
A
Step-by-step explanation:
The answer is option (A) 8560. This combination cannot be the correct combination for your brother's lock because it contains the digit '6' in the same position as the correct combination (6348), but the other digits do not match.
Suppose you can spend no more than 15 hours a week at your two jobs. Mowing lawns pays $3 an hour and babysitting pays $5 an hour. You need to earn at least $60 a week.
-Write up a system of linear inequalities to represent the situation.
I really need help, I don't really understand this even after looking back at notes.
Answers
9514 1404 393
Answer:
m + b ≤ 153m + 5b ≥ 60Step-by-step explanation:
There are two requirements:
the need to limit timethe need for a certain incomeEach of these gives rise to an inequality.
The variables in the problem are the numbers of hours spent at each activity. If we let m represent hours mowing, and b represent hours babysitting, then we have ...
m + b ≤ 15 . . . . . . . . total hours can be no more than 15
The amount of money earned mowing is 3m. The amount of money earned babysitting is 5b. We want the total earned to be at least $60, so the other constraint can be expressed as ...
3m +5b ≥ 60 . . . . . . earnings must be at least $60
__
Then the system of inequalities is ...
m + b ≤ 153m + 5b ≥ 60Instructions: Find the surface area of each figure Round your answers to the nearest tenth, if necessary n 4 cm. 1 cm. Surface Area: 1cm²
Answers
Answer:
37.7cm²
Explanation:
The surface area of a cylinder is calculated using the formula below:
\(SA=2\pi r(r+h)\)From the given figure:
• The height of the cylinder = 1cm
,• The radius of the cylinder = 4/2 = 2cm
Therefore:
\(\begin{gathered} SA=2\times\pi\times2(2+1) \\ =4\times3\times\pi \\ =12\times\frac{22}{7} \\ =37.7\operatorname{cm}^2 \end{gathered}\)The surface area is 37.7cm² (to the nearest tenth).
tell how the communative and associative properties of adddition can help you evsaluate the expression using mental math? 8+(-8-5)
Answers
Using commutative and associative properties of addition, the solution for given expression is -5.
What is commutative and associative property?
The associative and commutative characteristics are universal principles that apply to addition and multiplication. The associative property states that rearranging the numbers will get the same result, while the commutative property states that rearranging the numbers will yield the same result.
These properties tell that one can add in any order, the result will always be the same.
We are given an expression as 8+(-8-5).
So, in this instead of adding from left to right, we can see that the 8 + (-8) will be zero and only -5 will be left as an answer.
Hence, the solution for given expression is -5.
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An item that cost $220 has been marked up by 15% since last year. However, a person can buy the item for a 25%
employee discount. How much will the employee pay?
Answers
Answer:189.75
Step-by-step explanation: 220 * 0.15 = 33
220 + 33 = 253
253 * 0.25 = 63.25
253 - 63.25 = 189.75
No links please! Which expression has the same value as
Look below
Answers
Answer:
-5 1/3 - 3 1/3
Step-by-step explanation
both expressions equal -8 2/3
An employee at an organic food store is
assembling gift baskets for a display. Using
wicker baskets, the employee assembled 10
small baskets and 6 large baskets, using a
total of 148 pieces of fruit. Using wire
baskets, the employee assembled 10 small
baskets and 7 large baskets, using a total of
161 pieces of fruit. Assuming that each small
basket includes the same amount of fruit, as
does every large basket, how many pieces
are in each?
The small baskets each include
pieces and the large ones each include
pieces.
Answers
Solving a system of equations we can see that there are 13 pieces of fruit ina large basket and 7 on a smaller one.
How many pieces of fruit are in each basket?Let's define the variables:
x = number of pieces in a small basket.
y = number of pieces in a large basket.
With the given information we can write a system of equations:
10x + 6y = 148
10x + 7y = 161
If we take the difference between the two equations we get:
(10x + 7y) - (10x + 6y) = 161 - 148
y = 13
So there are 13 pieces of fruit on a large basket, and we can find the value of x by evaluatin one of the equations in y = 13.
10x + 6*13 = 148
10x = 148 - 6*13
10x = 70
x = 70/10 = 7
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There are 3,785 milliliters in 1 gallon, and there are 4 quarts in 1 gallon.
How many milliliters are in 3 gallons?
Answers
Answer:11,356
Step-by-step explanation: that is the answer! I’m sure
Answer:11.355
Step-by-step explanation:
A. 5x – 2 + 2 = 2 - 4
B.
5x +2 = 2-4
1) How can we get Equation B from Equation A?
Choose 1 answer:
А
Add/subtract a quantity to/from only one side
B
Add/subtract the same quantity to/from both sides
Rewrite one side (or both) using the distributive property
Answers
Answer:a
Step-by-step explanation:
A group of friends wants to go to the amusement park. They have no more than $160
to spend on parking and admission. Parking is $8, and tickets cost $38 per person,
including tax. Write and solve an inequality which can be used to determine p, the
number of people who can go to the amusement park.
Answers
Answer:
I tried figuring out this problem but it is a tad confusing. sorry :/
Step-by-step explanation:
Please help I am struggling bad with this question thank you all
Answers
b = speed of the boat in still water
c = speed of the current
when going Upstream, the boat is not really going "b" fast, is really going slower, is going "b - c", because the current is subtracting speed from it, likewise, when going Downstream the boat is not going "b" fast, is really going faster, is going "b + c", because the current is adding its speed to it.
Now, the boat goes Upstream 48 miles, so Downstream must be travelling the same 48 miles back.
\({\Large \begin{array}{llll} \underset{distance}{d}=\underset{rate}{r} \stackrel{time}{t} \end{array}} \\\\[-0.35em] ~\dotfill\\\\ \begin{array}{lcccl} &\stackrel{miles}{distance}&\stackrel{mph}{rate}&\stackrel{hours}{time}\\ \cline{2-4}&\\ Upstream&48&b-c&3\\ Downstream&48&b+c&2 \end{array}\hspace{5em} \begin{cases} 48=(b-c)(3)\\\\ 48=(b+c)(2) \end{cases} \\\\[-0.35em] ~\dotfill\)
\(\stackrel{\textit{using the 1st equation}}{48=(b-c)3}\implies \cfrac{48}{3}=b-c\implies 16=b-c\implies \boxed{16+c=b} \\\\\\ \stackrel{\textit{using the 2nd equation}}{48=(b+c)2}\implies \cfrac{48}{2}=b+c\implies 24=b+c\implies \stackrel{\textit{substituting}}{24=(16+c)+c} \\\\\\ 24=16+2c\implies 8=2c\implies \cfrac{8}{4}=c\implies \boxed{2=c}~\hfill~\stackrel{ 16~~ + ~~2 }{\boxed{b=18}}\)
Which expression is equivalent to the given expression
Answers
Answer:
i think the answer is A. 2x^3y^2
the age of some kids that partecipate to a race are
13 13 17 16 15 15 18 14 18 17 16 17 15 15 15 14 15 14 16 15
a) put from least to biggest, create a table and calcolate the absolute frequency, relative and percentual.
b) Reppresent graphically with a histogram the absolute frequency.
c) calcolate mode mean median
Calcolate the probability of having
d) 13 years old
e) 14 or 16 years old
f) doesn't have 15 years
I WILL GIVE BRAINLY IF YOU GIVE ME THE RIGHT ANSWERS
Answers
c) Mode: 15 (appears 6 times)
Mean: 15.25
Median: 15
d) Probability of being 13 years old: 2/20 = 0.1 or 10%
e) Probability of being 14 or 16 years old: 6/20 = 0.3 or 30%
f) Probability of not having 15 years old: 1 - (6/20) = 14/20 = 0.7 or 70%
a) To create a table and calculate the absolute frequency, relative frequency, and percentual frequency, we organize the given ages in ascending order:
13 13 14 14 15 15 15 15 15 16 16 17 17 17 18 18
Age Absolute Frequency Relative Frequency Percentual Frequency
13 2 2/16 12.5%
14 2 2/16 12.5%
15 5 5/16 31.25%
16 2 2/16 12.5%
17 3 3/16 18.75%
18 2 2/16 12.5%
b) To represent the data graphically with a histogram, we plot the ages on the x-axis and the absolute frequency on the y-axis:
c) To calculate the mode, mean, and median:
Mode: The mode is the most frequently occurring age in the dataset. In this case, the mode is 15, as it appears 5 times.
Mean: The mean is the average of all the ages. To calculate it, we sum up all the ages and divide by the total number of ages:
(13 + 13 + 14 + 14 + 15 + 15 + 15 + 15 + 15 + 16 + 16 + 17 + 17 + 17 + 18 + 18) / 20 = 306 / 20 = 15.3
Median: The median is the middle value in the dataset when arranged in ascending order. In this case, the median is 15 since it falls in the middle.
d) To calculate the probability of having 13 years old, we divide the absolute frequency of 13 (2) by the total number of ages (20):
Probability of 13 years old = 2/20 = 0.1 or 10%
e) To calculate the probability of having 14 or 16 years old, we add the absolute frequencies of 14 and 16 (2 + 2 = 4) and divide by the total number of ages (20):
Probability of 14 or 16 years old = 4/20 = 0.2 or 20%
f) To calculate the probability of not having 15 years old, we subtract the absolute frequency of 15 (5) from the total number of ages (20):
Probability of not having 15 years old = (20 - 5)/20 = 0.75 or 75%
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Find the value of Y helpppp
Answers
Answer:
y = 4
Step-by-step explanation:
Both the triangles are congruent by SSS postulate.
Therefore,
\(4y + 8 = 24 \\ (corresponding \: sides \: of \: \\ congruent \: \triangle s) \\ 4y = 24 - 8 \\ \\ 4y = 16 \\ \\ y = \frac{16}{4} \\ \\ y = 4\)
Please help !!!!!! 20 points
Answers
The value of x in the polygon will be 13.25 degrees.
The value of x is 10.
We can find the value of x by plugging in the number of sides of the regular polygon into the formula x = (n-2)*15° - 1.
How to calculate the valueThe sum of the interior angles of a regular polygon with n sides is (n-2) x 180 degrees.
Sum of angles = (24-2) x 180 = 22 x 180 = 3960 degrees
Since all the angles in a regular polygon are congruent, we can divide the sum of the angles by the number of angles to find the measure of one angle:
Measure of one angle = 3960/24 = 165 degrees
165 = 12x + 6
159 = 12x
x = 13.25
Therefore, the value of x is 13.25 degrees.
Each of the triangles in our decomposition has one angle equal to (17x+2)°, so the sum of all the angles in the triangles is 43 × (17x+2)° = 731x+86°.
Therefore, we have:
731x+86° = 7380°
Solving for x, we get:
731x = 7294°
x = 10
Therefore, the value of x is 10.
The equation that can be used to find the value of x is:
(9x+48)° + (15x-24)° = (n-2)*180°
24x + 24 = (n-2)*180°
Dividing both sides by 24, we get:
x + 1 = (n-2)*15°
Subtracting 1 from both sides, we get:
x = (n-2)*15° - 1
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What is the relative change from Ohio to Indiana if Indiana has 6546 new mathematics teachers and Ohio has 4392 new mathematics teachers?
Answers
The relative change from Ohio to Indiana in terms of new mathematics teachers is approximately 49.08%. This indicates that Indiana has experienced a significant increase compared to Ohio in the number of new mathematics teachers.
To calculate the relative change from Ohio to Indiana in terms of new mathematics teachers, we need to determine the percentage increase or decrease in the number of teachers between the two states.
The relative change can be calculated using the formula:
Relative Change = (New Value - Old Value) / Old Value * 100
Let's apply this formula to the given data:
Ohio: Old Value = 4392
Indiana: New Value = 6546
Relative Change = (6546 - 4392) / 4392 * 100
Simplifying the equation:
Relative Change = 2154 / 4392 * 100
Relative Change ≈ 0.4908 * 100
Relative Change ≈ 49.08%
The relative change from Ohio to Indiana in terms of new mathematics teachers is approximately 49.08%. This indicates that Indiana has experienced a significant increase compared to Ohio in the number of new mathematics teachers.
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This may be hard to put together, but I need help with an angle equation. I'm looking for example equations and how to do these types of equations. *please note that this equation is completely random and probably ends with an ugly number. it's just an example of a type of problem*
Answers
Example: (2x - 4) x=7 so (2x (x=7) - 4) =18
A newborn turtle has a shell with a 1-inch diameter. The shell keeps a similar shape as the turtle grows. After a year, the shell is 3 inches in diameter. Note: you do not need to know the shape of the shell to complete this question.
1. How many times greater is the volume of the turtle's shell after a year than it was when it was born?
2. How many times greater is the surface area of the turtle's shell after a year than it was when it was born?
Answers
Answer:
I think the volume would be 9 times greater, and the surface area would be 3 times greater
Step-by-step explanation:
Answer:
the volume would be 9 times greater
the surface area would be 3 times greater
Step-by-step explanation:
Because if the shell grows from 1 inch diameter to 3 inch diameter, the surface area will increase 3x more. And the volume I assume is 3x greater because of the height is presumably 3 inches as well.
A study was done to investigate the population of bald eagle breeding pairs over time. The correlating regression model is shown
below, wiere x represents the number of years after 1986, and y represents the number of bald eagle breeding pairs. Interpret the y-
intercept
y = 1,772 +334x
Answers
Answer:
There were approximately 1,772 eagle breeding pairs in 1986.
Step-by-step explanation:
There were approximately 1.772 eagle breeding pairs in 1986
It is required to choose the correct option.
What is linear regression?Linear regression analysis is used to predict the value of a variable based on the value of another variable. The variable you want to predict is called the dependent variable. It is used to model the relationship between two continuous variables.
Given:
The regression equation :
y = 1,772 +334x
We know that the general form of a linear regression equation :
y = mx + c
y = predicted variable ; x = predictor Variable ; c = intercept ; m = slope
x = number of years after 1986 ; y = number of bald eagle breeding pairs.
The intercept is a constant value at time t = 0
For x to be 0, on a graph, this the value on the y axis where the regression line crosses the y - axis.
That is in 1986; the number of y when in 1986 when x = 0 is 1,772.
Therefore, there were approximately 1.772 eagle breeding pairs in 1986.
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Option is missing
A. There were approximately 334 eagle breeding pairs in 1986.
B. There were approximately 1.772 eagle breeding pairs in 1986.
c. There were approximately 1.772 additional eagle breeding pairs each year after 1986.
D. There were approximately 334 additional eagle breeding pairs each year after 1986.
How much would you have to deposit today to accumulate the SAME AMOUNT OF MONEY that $75 monthly payments at a rate of 3.5% compounding monthly for 10 years in an annuity would earn?
Answers
Answer:
7606.62
Step-by-step explanation:
Start by finding how much you will have through the annuity. The question isn't that clear, so i will just assume it's an annuity due.
\(p(\frac{(1+i)^n-1}{i})*(1+i)\\i=.035/12= .0029166667\\n=10*12=120\\p=75 (given)\\75\frac{(1+.0029166667)^{120}-1}{.0029166667}*(1+.0029166667)= 10788.814149\\\)
Now just equate this to a time 0 payment at the same rate
\(10788.814149=(1+.0029166667)^{120}*x\\x= 7606.6228603=7606.62\)
As a quick note, if you were supposed to assume that your annuity was an annuity immediate the answer would be 7584.50.
PLEASE PLEASE HELP THIS IS DUE SOONNNN
Answers
Answer:
The height of the tabletop is 75.6 centimeters. Just take 6426 and divide it by 85 and you get 75.6.
Step-by-step explanation:
hope this helped.
35 is what percent of 120?
I got 29.16 as the answer but 2 other websites say the correct answer is 29.17.
I did
35x100/120 = 3500/120 = 29.16
I can’t wrap my head why they have it as 29.17? Can someone help me. Thank you.
Answers
Answer:
Below
Step-by-step explanation:
35/120 x 100% = 29.1666% = 29 .17 % rounded to nearest 100th
What
is an arithmetic sequence with a common difference of −2?
Answers
Answer:
An arithmetic sequence with a common difference of −2 is 20,18,16,14,12..
Step-by-step explanation:
An arithmetic sequence is a sequence of numbers in which the difference between consecutive terms is same. Here, the common difference is -2, which means that each term in the sequence is obtained by subtracting 2 from the previous term.
To find the arithmetic sequence with a common difference of -2, you can start with an first term and then subtract 2 successively to find the subsequent terms.
Let the initial term is 20. Subtracting 2 from 20, we get 18. Subtracting 2 from 18, we get 16. Continuing this pattern, we subtract 2 from each subsequent term to generate the sequence. The arithmetic sequence with a common difference of -2 starting from 20 is
20,18,16,14,12
In this sequence, each term is obtained by subtracting 2 from the previous term, resulting in a common difference of -2.