Answer:
Center: (3,-1)
Radius: 3
Step-by-step explanation:
Given:
[tex]\displaystyle \large{x^2+y^2-6x+2y+1=0}[/tex]
First, we have to convert the following standard circle equation to this:
[tex]\displaystyle \large{(x-h)^2+(y-k)^2=r^2}[/tex]
where h is horizontal shift, k is vertical shift and r is radius.
That means we have to complete the square for both x-term and y-term.
Rearrange the equation:
[tex]\displaystyle \large{x^2-6x+y^2+2y+1=0}\\\displaystyle \large{(x^2-6x)+(y^2+2y+1)=0}[/tex]
For [tex]\displaystyle \large{y^2+2y+1}[/tex], can be converted to perfect square as [tex]\displaystyle \large{(y+1)^2}[/tex]. Hence:
[tex]\displaystyle \large{(x^2-6x)+(y+1)^2=0}[/tex]
For the x-terms, we have to find another value that can complete the square. We know that [tex]\displaystyle \large{(a\pm b)^2 = a^2 \pm 2ab + b^2}[/tex].
For [tex]\displaystyle \large{x^2-6x}[/tex] can be [tex]\displaystyle \large{x^2-2(x)(3)+3^2 \to x^2-6x+9}[/tex]. So our another value is 9.
[tex]\displaystyle \large{(x^2-6x+9-9)+(y+1)^2=0}[/tex]
From above, we add -9 because the original expression isn’t actual perfect square.
Separate -9 out of [tex]\displaystyle \large{x^2-6x+9}[/tex]:
[tex]\displaystyle \large{(x^2-6x+9)-9+(y+1)^2=0}[/tex]
Transport -9 to add another side:
[tex]\displaystyle \large{(x^2-6x+9)+(y+1)^2=9}[/tex]
Complete the square:
[tex]\displaystyle \large{(x-3)^2+(y+1)^2=9}[/tex]
Finally, we have our needed equation to find radius and center. The coordinate of center is defined as the point (h,k) from [tex]\displaystyle \large{(x-h)^2+(y-k)^2=r^2}[/tex] and the radius is defined as r.
Hence, from the equation:
The coordinate of center is (3,-1) with radius equal to 3.
hellllp meeeee need help, 100 points
Answer:
Step-by-step explanation:
View the attached graph for what your image should look like.
I hope this helps or gives you a picture of what it should look like, because it's quite a long process.
Hope this helps!
29
= 30
31
An amount of $32,000 is borrowed for 6 years at 6.25% interest, compounded annually. If the loan is paid in full at the end of that period, how much must
paid back
[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$32000\\ r=rate\to 6.25\%\to \frac{6.25}{100}\dotfill &0.0625\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{annually, thus once} \end{array}\dotfill &1\\ t=years\dotfill &6 \end{cases} \\\\\\ A=32000\left(1+\frac{0.0625}{1}\right)^{1\cdot 6}\implies A=32000(1.0625)^6\implies A\approx 46038.78[/tex]
A container holds 4 gallons of lemonade. How much is this in pints
Answer:
i think I'd be / the answer is 46
Drag each figure to show if it is similar to the figure shown or why it is not similar.
1st one - not similar diff ratio2nd- similar3rd- not similar diff shape4- not similar diff ratio5- similar6- not so sure but i would go w either not similar diff shape or similar
Guys please help! i will mark brainliest to the right answers
Note: in order for me to mark a brainliest 2 people need to answer
Answer:
look at the picture i have attached and tell me what you think???
Step-by-step explanation:
parallel is two lines that go like this \\ or like this =
perpendicular is two lines that go like this +
which is it?
Answer:
they are parallel as gradient is the same because in first equation coefficient of x is -2 and in second equation after rearranging equation in form of y= mx + c, m is -2
An ellipse has a vertex at (0, −7), a co-vertex at (4, 0), and a center at the origin. Which is the equation of the ellipse in standard form?
Answer:
As Per Provided Information
An ellipse has a vertex at (0, −7), a co-vertex at (4, 0), and a center at the origin (0,0) .
We have been asked to find the equation of the ellipse in standard form .
As we know the standard equation of an ellipse with centre at the origin (0,0). Since its vertex is on y-axis
[tex] \underline\purple{\boxed{\bf \: \dfrac{ {y}^{2} }{ {a}^{2} } \: + \: \dfrac{ {x}^{2} }{ {b}^{2} } = \: 1}}[/tex]
where,
a = -7 b = 4Substituting these values in the above equation and let's solve it
[tex] \qquad\sf \longrightarrow \: \dfrac{ {y}^{2} }{ {( - 7)}^{2} } \: + \dfrac{ {x}^{2} }{ {(4)}^{2} } = 1 \\ \\ \\ \qquad\sf \longrightarrow \: \dfrac{ {y}^{2} }{49} \: + \frac{ {x}^{2} }{16} = 1 \\ \\ \\ \qquad\sf \longrightarrow \: \: \dfrac{ {x}^{2} }{16} \: + \dfrac{ {y}^{2} }{49} = 1[/tex]
Therefore,
Required standard equation is x²/16 + y²/16 = 1So, your answer is 2nd Picture.
To visit the top of the Empire State Building, a ticket cost $ 4.00 in 1999. In 2009, the price rose to $ 20.00. What was the percent charge
Answer:
500%
Step-by-step explanation:
500% is 500/100 which is just 5*4=20
Plsss help mee I’m not sure what the answer is
Answer:
D. would be the correct answer
A manufacturing company has two plants at different locations producing three different items equally within each plant. Based on the number of workers and the demand for the items in their respective locations, the number of items manufactured per day by each plant is listed in the table. Plant A Plant B Item 1 22 15 Item 2 8 12 Item 3 14 25 Select the observed and expected frequencies for Item 2 produced by Plant B.
Answer:
the answer would be 12-19+23=18 so you need a new calculator
Step-by-step explanation:
yes
CAN SOMEONE PLS ANSWER THIS QUESTION FAST
I WILL MARK BRAINLIEST
Answer:
20%
Step-by-step explanation:
add up all the values, then do 9 (alex's score) and divide it by 45 (total that was added up)
Answer:
A. 9
Step-by-step explanation:
Add all basketball shots then divide by 5
7.4 Practice
A medicine is effective on 70% of patients.
The table shows 30 randomly generated
numbers from to 999. Use the table to
estimate the probability of the event.
1. The modicine is effective on at least two
of the next three patients.
028837 618 205 984
724 301249 946 925
042 | 113 | 696 985 632
312085 | 997 198 | 398
117 240 853:373 597
606 077 016 012
695
2. The medicine is effective on none
of the next three patients.
Design and use a simulation to find the experimental probability.
3. A bowler hats the headpin 90% of the time that all ten pins are standing.
What is the experimental probability that the bowler hits the headpin
exactly four of the next five times that all ten pins are standing?
The simulation of the medicine and the bowler hat are illustrations of probability
The probability that the medicine is effective on at least two is 0.767The probability that the medicine is effective on none is 0The probability that the bowler hits a headpin 4 out of 5 times is 0.3281The probability that the medicine is effective on at least twoFrom the question,
Numbers 1 to 7 represents the medicine being effective0, 8 and 9 represents the medicine not being effectiveFrom the simulation, 23 of the 30 randomly generated numbers show that the medicine is effective on at least two
So, the probability is:
p = 23/30
p = 0.767
Hence, the probability that the medicine is effective on at least two is 0.767
The probability that the medicine is effective on noneFrom the simulation, 0 of the 30 randomly generated numbers show that the medicine is effective on none
So, the probability is:
p = 0/30
p = 0
Hence, the probability that the medicine is effective on none is 0
The probability a bowler hits a headpinThe probability of hitting a headpin is:
p = 90%
The probability a bowler hits a headpin 4 out of 5 times is:
P(x) = nCx * p^x * (1 - p)^(n - x)
So, we have:
P(4) = 5C4 * (90%)^4 * (1 - 90%)^1
P(4) = 0.3281
Hence, the probability that the bowler hits a headpin 4 out of 5 times is 0.3281
Read more about probabilities at:
https://brainly.com/question/25870256
Please help!!!
What is the value of y?
60
45
2V2
Enter your answer, as an exact value in the box
y =
Answer:
Step-by-step explanation:
Ratio of sides of 45-45-90 triangle = x : x : x√2
x√2 is the side opposite to angle 90
So, from the picture,
x√2 = 2√2
x = [tex]\frac{2\sqrt{2}}{\sqrt{2}}[/tex]
x = 2
Ratio of sides of 30-60-90 tirangle = a : 2a : a√3
Short side that is oppoiste to 30° = a
Side opposite to 60° = a√3
Hypotenuse (oppoiste to 90°) = 2a
a = 2
y =a√3
y = 2√3
Tom and Blair live the same
distance from their school.
Marcia lives 2 blocks from the
school, but 7 blocks from Blair.
She lives 1 block closer to the
school than she does to Tom.
They all live on the same street
as the school. How far apart do
Tom and Blair live?
Answer:
Step-by-step explanation:
We can think of this problem like a triangle that Tom, Blair, and Marcia live in.
This triangle is a right triangle.
the opposite is 3, the hypotenuse is 7, and the adjacent side is unknown.
Solving for the adjacent side will give us the distance that Tom and Blair live from each other
a^2 +b^2 = c^2
3^2 + b^2= 7^2
Now we solve for B
7^2 =49
3^3=9
9+b^2=49
Now we subtract
49-9=40
9+40=49
The square root of 40 is 6.3246
Now we check our work
3^2 +6.32^2=7^2
9+ 40 =49
The answer is, tom and Blair live approximately 6.3246 blocks from each other
Hope this helps!
Without dividing,
how can you tell if the quotient for
5,873 = 8 is greater than 700? Explain
whether the quotient is less than 800.
Answer:
The quotient is between 700 and 800Step-by-step explanation:
Prove by multiplication
700*8 = 5600 < 5873Similarly
800*8 = 6400 > 5873So the expression is 5873/8
Now
We can prove the given statement to multiplication
Multiply with 8
700×85600And
800×86400Yes
We see 5873 lies between 5600 and 6400 hence the quotient is greater than 700 but less than 800
If yesterday's day after tomorrow is Sunday, what day is tomorrow's day before
yesterday?
Answer:
friday
Step-by-step explanation:
A Ferris wheel is 20 meters in diameter and completes 1 full revolution in 8 minutes.
A round Ferris wheel
A Ferris wheel is 20 meters in diameter and boarded from a platform that is 1 meter above the ground. The six o’clock position on the Ferris wheel is level with the loading platform. The wheel completes 1 full revolution in 8 minutes. The function h(t) gives a person’s height in meters above the ground t minutes after the wheel begins to turn.
a. Find the amplitude, midline, and period of h(t).
Enter the exact answers.
Amplitude: A= meters
Midline: h= meters
Period: P= minutes
b. Assume that a person has just boarded the Ferris wheel from the platform and that the Ferris wheel starts spinning at time t=0. Find a formula for the height function h(t).
Hints:
What is the value of h(0)?
Is this the maximum value of h(t), the minimum value of h(t), or a value between the two?
The function sin(t) has a value between its maximum and minimum at t=0 , so can h(t) be a straight sine function?
The function cos(t) has its maximum at t=0, so can h(t) be a straight cosine function?
c. If the Ferris wheel continues to turn, how high off the ground is a person after 30 minutes?
Given that the Ferris diameter is 20 meters, with a rate of rotation of 1 turn in 8 minutes, we have;
a. Amplitude: A = 10 meters
Midline: h = 11 meters
Period, P = 8 minutes
b. h(t) = 10•cos((π/4)•t + π) + 11
c. 11 meters
How can the Ferris wheel be evaluated?The amplitude is the same as the radius of the Ferris wheel,
The radius of the Ferris wheel = 20 ÷ 2 = 10
Therefore;
Amplitude: A = 10 meters[tex]the \: midline \: = \frac{max \: height \: + min \: height}{2} [/tex]
Therefore;
[tex]midline \: = \frac{10 + 10 + 1 + 1}{2} = 11[/tex]
Midline: h = 11 metersThe period is the time to complete one rotation, therefore;
Period, P = 8 minutesb. h(t) = A•cos(B•t + C) + h
Where;
B = 2•π/P
When t = 0, h(t) = 1
Which gives;
h(0) = 1 = 10 × cos(B×0 + C) + 11
-10/10 = -1 = cos(C)
C = arcos(-1) = π
Therefore;
h(t) = 10•cos((π/4)•t + π) + 11h(0) = 1
h(0) is the minimum value of h(t)
h(t) cannot be a straight sine function because of the vertical shifth(t) cannot be a straight cosine function because at t = 0, is the minimum pointc. After 30 minutes, we have;
h(30) = 10•cos((π/4)×30 + π) + 11 = 11
The height of a person after 30 minutes is 11 metersLearn more about the Ferris wheel here:
https://brainly.com/question/86214
Is the table a linear or exponential function?
The table represents linear because the x represent the exponential functions
Marco has two number cubes. The faces of each number cube are numbered from 1 to 6. Marco rolled the number cubes and recorded the number showing on the top face of each number cube. The results are shown in the table.
4, 2 5, 2 3, 1 3, 4 2, 6
1, 1 4, 2 2, 3 3, 3 5, 1
1, 5 5, 2 1, 5 1, 2 1, 5
2, 4 4, 2 2, 4 5, 3 2, 4
Based on these results, what is the experimental probability that the next time the number cubes are rolled, they will land with a 2 showing on the top face of one number cube and a 4 showing on the top face of the other number cube?
A.
3
10
B.
9
20
C.
11
20
D.
1
36
Using it's concept, it is found that the probability that the next trial will result in a 2 and 4 is given by:
A. [tex]\frac{3}{10}[/tex].
What is a probability?A probability is given by the number of desired outcomes divided by the number of total outcomes.
In an experimental probability, the number of outcomes are taken from previous trials.
In this problem, the table states that of 20 trials, 6 resulted in either (2,4) or (4,2), hence the probability is given by:
p = 6/20 = 3/10.
Which means that option A is correct.
More can be learned about probabilities at https://brainly.com/question/14398287
solve the system by substitution
Find the product. (6y - 2)2
A. 36y2 - 24y + 4
B. 36y2 + 24y = 4
C. 36y2 + 4
D. 12y2 - 16y + 4
Answer:
A. 36y² - 24y + 4Step-by-step explanation:
Use identity
(a ± b)² = a² ± 2ab + b²Here we have a = 6y, b = 2
(6y - 2)² = (6y)² - 2(6y)(2) + 2² = 36y² - 24y + 4Correct choice is A
Although the numbers are not included on either axis, it is possible to determine from shape and location that the equation y = -1.2x+4 corresponds to graph
It looks like your question is incomplete. I believe you also have options to pick which graph is correct. However, I can still give you the information you are looking for.
The slope of the line is -1.2
The Y-intersect is (0, 4)
I have also attached an image of what the graph would look like.
Hope this helps.
The first three terms of a sequence are given. Round to the nearest thousandth (if
necessary).
9, 15, 25, ...
Find the 10th term
Answer:
Step-by-step explanation:
This is a Geometric Sequence with common ratio 15/9 = 5/3
25/15 is also = 5/3
So the 10th term = ar^(n-1)
= 9*(5/3)^9
= 893.061 to nearest thousandth.
La medida de cada ángulo interno de un polígono regular es 162º. Hallar el número de lados.
Número de lados=
Answer:
n = 20
Step-by-step explanation:
[ 180° ( n - 2 ) ] / n = 162°
180 ( n - 2 ) = 162 n
180n - 360 = 162n
18n = 360
n = 20
5
Solve for x. Round all answers to the nearest tenth.
X
32
14
O 11
O 11.7
O 10.2
O 11.9
Answer:
11.9
Step-by-step explanation:
Making sure your calculator is in degree mode, we have:
[tex] \cos(32) = \frac{x}{14} [/tex]
[tex]x = 14 \cos(32) = 11.9[/tex]
expand the following
1. ( m+n)(10m-4n)
2.(6x+y)
hope it helps....!!!!!
Frank is surveying shoppers about their use of the new food court in a mall. Which question in his survey is a statistical question?
How many hours do you spend at the food court each month?
Where is the food court located in the mall?
How many restaurants are there in the food court?
Who is the manager of the food court?
Answer:
A How many hours do you spend at the food court each month? is a statistical question
Step-by-step explanation:
Because that can have many answers unlike where is the food court in the mall? that question is not statistical because there can only be one answer and so are all the other ones.
Answer:
How many hours do you spend at the food court each month?
Step-by-step explanation:
I just took test got 100% this answer is correct
How many hours do you spend at the food court each month?
a man buys a vehicle at a cost prize of R60 000 from Cape Town. He transported the vehicle from cape town to Gauteng province, where he stays, at a cost prize of R4 500. at what prize must he sell the car to make an overall profit of 25% ?
Answer:
R80625
Step-by-step explanation:
Total Cost : 60000 + 4500 = 64500
To make 25% profit: 64500 X 1.25 = 80625
Is x + 2 a factor of p(x) = x°- 3x² – 7x + 6 ? Explain your answer.
Answer:
True
Determine whether x+2 is a factor of x³-3x²-7x+6:
↓
[tex]True[/tex]
I hope this helps you
:)
Please help and I'll mark brainliest
Answer:
the answer is 60
Step-by-step explanation:
brainliest please
Answer:
B.) I'm not 100% sure
Step-by-step explanation:
Hope this helped
I need help with this question!
Answer:
B
Step-by-step explanation: