3.a circle of radius 5 units passes through the points (- 3,3) and (3,1) .
i.how many circles can be drawn that meet the given criteria?
ii. what can be the centre of a circle(S)
b. the equation of any two diameters of a circle are given by the straight lines x-y-4=0 and 2x+ 3y + 7 =0.
find the equation of the circle if it passes through the point (2,4).
Answers
Answer:
See belowStep-by-step explanation:
Given:
Points (- 3,3) and (3,1) on a circler = 5i.
There are possible two points that can have a distance of 5 units from both of the given points, so possible two centers, hence two possible circles.
ii.
Let the points are A and B and the centers of circles are F and G.
The midpoint of AB, the point C is:
C = ((-3 + 3)/2, (3 + 1)/2) = (0, 2)The length of AB:
AB = [tex]\sqrt{(3 + 3)^2 + (1 - 3)^2} = \sqrt{6^2+2^2} = \sqrt{40} = 2\sqrt{10}[/tex]The distance AC = BC = 1/2AB = [tex]\sqrt{10}[/tex]
The distance FC or GC is:
FC = GC = [tex]\sqrt{5^2-10} = \sqrt{15}[/tex]Possible coordinates of center are (h, k).
We have radius:
(h + 3)² + (k - 3)² = 25(h - 3)² + (k - 1)² = 25Comparing the two we get:
(h + 3)² + (k - 3)² = (h - 3)² + (k - 1)²Simplifying to get:
k = 3h + 2We consider this in the distance FC or GC:
h² + (k - 2)² = 15h² + (3h + 2 - 2)² = 1510h² = 15h² = 1.5h = √1.5 orh = - √1.5Then k is:
k = 3√1.5 + 2 ork = -3√1.5 + 2So coordinates of centers:
(√1.5, 3√1.5 + 2) for G or(√1.5, 3√1.5 + 2) for F (or vice versa)-------------------------------------------------------------------------------------
b.
Diameters:
x - y - 4 = 02x + 3y + 7 = 0The intercession of the diameters is the center. We solve the system above and get. Not solving here as it is already a long answer:
x = 1, y = -3The point (2, 4) on he circle given.
Find the radius which is the distance between center and the given point:
r = [tex]\sqrt{(2 - 1)^2+(4+3)^2} = \sqrt{1^2+7^2} = \sqrt{50}[/tex]The equation of circle:
(x - 1)² + (y + 3)² = 50
Related Questions
Solve the following equation for x: 6( 4X +5) = 3( X +8) +3
Answers
Answer:
x= -1/7
Step-by-step explanation:
You weigh a random sample of adult golden retrievers and get the following results: 55, 64, 58, 61, 69, 64, 59, 69, 72, and 65. Which answer gives a 98% confidence interval for the mean of the population
Answers
Answer:
The 98% confidence interval for the mean of the population is (59, 68.2).
Step-by-step explanation:
Before building the confidence interval, we need to find the sample mean and the sample standard deviation.
Sample mean:
[tex]\overline{x} = \frac{55+64+58+61+69+64+59+69+72+65}{10} = 63.6[/tex]
Sample standard deviation:
[tex]s = \sqrt{\frac{(55-63.6)^2+(64-63.6)^2+(58-63.6)^2+(61-63.6)^2+(69-63.6)^2+(64-63.6)^2+(59-63.6)^2+(69-63.6)^2+(72-63.6)^2+(65-63.6)^2}{10}} = 5.142[/tex]
Confidence interval:
We have the standard deviation for the sample, and thus, we use the t-distribution.
The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So
df = 10 - 1 = 9
98% confidence interval
Now, we have to find a value of T, which is found looking at the t table, with 9 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.98}{2} = 0.99[/tex]. So we have T = 2.821
The margin of error is:
[tex]M = T\frac{s}{\sqrt{n}} = 2.821\frac{5.142}{\sqrt{10}} = 4.6[/tex]
In which s is the standard deviation of the sample and n is the size of the sample.
The lower end of the interval is the sample mean subtracted by M. So it is 63.6 - 4.6 = 59
The upper end of the interval is the sample mean added to M. So it is 63.6 + 4.6 = 68.2.
The 98% confidence interval for the mean of the population is (59, 68.2).
Find the quotient of these complex numbers (6-I) divided by (4+3i)=
Answers
Answer:
[tex]\frac{21}{25} -\frac{22}{25} i[/tex]
Step-by-step explanation:
We can start by writing the division as a fraction:
[tex]\frac{6-i}{4+3i}[/tex]
In order to rationalize the denominator, we need to multiply by the conjugate:
[tex]\frac{6-i}{4+3i} *\frac{4-3i}{4-3i}\\\\\frac{(6-i)(4-3i)}{4^2-(3i)^2}\\\\\frac{24-18i-4i+3i^2}{16+9}\\\\\frac{24-22i-3}{25}\\\\\frac{21-22i}{25} \\\\\frac{21}{25} -\frac{22}{25} i[/tex]
Which equation is written in factor form?
Answers
what is the value of b?
Answers
Answer:
24
Step-by-step explanation:
2b = b+24
2b-b = 24
b = 24
please help I'll give brilliantist:)
Answers
What is the name of a polygon that has three sides and three equal angles
Answers
Answer:
equilateral triangle
Step-by-step explanation:
equilateral triangle
A triangle: An equilateral triangle is a regular polygon with three equal side lengths and three equal angles.
What’s the answer and how do you figure these out?
Answers
Find the area of this isosceles trapezoid. A) 85.5 units2 B) 171 units2 C) 342 units? 345 units?
Answers
9514 1404 393
Answer:
B) 171 units^2
Step-by-step explanation:
The area is given by the formula ...
A = 1/2(b1 +b2)h
Filling in the given base and height values, we find the area to be ...
A = 1/2(23 +15)(9) = (19)(9) = 171 . . . square units
_____
Additional comment
You can select the correct answer choice simply on the basis of "reasonableness." If this were a 9×15 rectangle, its area would be 9×15 = 135 square units, more than 85.5. You know its area is less than a 9×23 rectangle, so is less than 9×23 = 207 square units. Only one answer choice is a value between 135 and 207.
__
Multiplication by 9 is not so hard. It is multiplication by 10-1:
15×9 = 15×(10 -1) = 150 -15 = 135
A and B are independent events. P(A) = 0.50 and P(B) = 0.30. What is
PA and B)?
Answers
Answer:
0.15
Step-by-step explanation:
Help pleaseeeee thanks
Answers
Answer:
We know that 3 l 3 = 3.3, so the values of the stem and leaf plot would be;
4 l 8, 9
5 l 1, 6, 8, 8, 9
6 l 8, 9, 9, 9, 9
7 l 0, 2, 2, 2, 5, 5
8 l 0, 9
Hope this helps!
Area of triangle with sides a=8, b= 10, c=7
Answers
Answer:
d equal 10 this is the answer
If you sleep 6 hours a day every day for a year you are sleeping of every year. If there are 365 days in a year, how
many days per year would you sleep? Simplify your answer and write it as a mixed number.
days
Answers
Answer:
Step-by-step explanation:
365 x 24 = 8,760
365 x 6 = 2,190
8,760 - 2,190 = 6,570
6,570 / 24 = 273 3/4
The person sleeps 91 (1/4) days per year.
What is multiplication?Multiplication is the process of adding a number up to a given number.
Given that, the person sleeps 6 hours a day.
The total hours of sleeping over a year are:
365 × 6
= 2190 hours per year
Since there are 24 hours in a day, divide 2190 by 24 to get the answer in days per hour:
2190/24
= 91 (1/4)
Hence, the person sleeps 91 (1/4) days per year.
To learn more about multiplication, click here:
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If there are 8 people, and each person has 4 coins, there are ____ times as many coins as people.
Answers
Answer:
2 times
Step-by-step explanation:
Answer:
4 times
Step-by-step explanation:
8 x 4 = 32 total coins
32÷8 = 4
Therefore, there are 4 times as many coins as people.
Hope this helps! :)
A two-sample t-test for a difference in means will be conducted to investigate whether the average amount of money spent per customer at Department Store M is different from that at Department Store V. From a random sample of 35 customers at Store M, the average amount spent was $300 with standard deviation $40. From a random sample of 40 customers at Store V, the average amount spent was $290 with standard deviation $35. Assuming a null hypothesis of no difference in population means, what is the test statistic for the appropriate test to investigate whether there is a difference in population means?
Answers
The test statistic is 1.145 for the appropriate test to investigate whether there is a difference in population means.
A test statistic is a numerical value calculated from sample data in hypothesis testing.
Given that
Sample 1: Store M
Sample size, [tex]n_1[/tex] = 35,
Sample mean, [tex]\bar{X_1}[/tex] = 300,
Standard deviation, [tex]s_1[/tex] = 40.
Sample 2: Store V
Sample size, [tex]n_2[/tex] = 40,
Sample mean, [tex]\bar{X_2}[/tex] = 290,
Standard deviation, [tex]s_2[/tex] = 35.
The null hypothesis, [tex]H_o[/tex] : there is no difference in population means, i.e.,
[tex]\mu_1 =\mu_2[/tex].
The alternate hypothesis, [tex]H_1[/tex] : there is a significant difference in population means, i.e.,
[tex]\mu_1 \neq\mu_2[/tex].
Under the null hypothesis, the test statistic is
[tex]t = \dfrac{\bar{X_1}-\bar{X_2}}{\sqrt{\frac{s_1^2}{n_1}+\frac{s_2^2}{n_2} }}[/tex]
[tex]= \dfrac{300-290}{\sqrt{\frac{40^2}{35}+\frac{35^2}{40} }}\\=\dfrac{10}{\sqrt{\frac{1600}{35}+\frac{1225}{40} }} \\=\dfrac{10}{\sqrt{45.714+30.625 }} \\=\dfrac{10}{\sqrt{76.339 }}\\=\dfrac{10}{8.737}\\=1.145[/tex]
Hence the test statistic is 1.145.
Learn more about test statistics here:
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Click on the area of the square?
Answers
Answer:
The answer for this question is 64 square centimeters
Step-by-step explanation:
To find the area of square , the formula is :
side × side , so in this question we should do 8×8 , since one of the side is 8 cm .
8×8 = 64
Thus the answer of your question is 64
—————————————————
[tex]\mathrm{A = s²}[/tex]
[tex]\mathrm{A = (8 \: cm)²}[/tex]
[tex]\mathrm{A = (8 \: cm)(8 \: cm)}[/tex]
[tex]{\boxed{\mathrm\green{A = 64 \: cm²}}}[/tex]
༆ANSWER:—————————————————
[tex]\purple{\boxed{\boxed{\tt\pink{64 \: square \: centimeters}}}}[/tex]
Hence, the area of the square that has a side of 8 cm, is 64 cm².Remember!To find the area of a square, just use the formula "A = s²".A regression was run to determine if there is a relationship between hours of tv watched per day (x) and the number of situps a person can do (y).The results of the regression were:y=ax+ba=−1.077b=30.98r2=0.744769r=−0.863Use this to predict the number of situps a person who watches 13.5 hours of TV can do.
Answers
Answer:
The number of situps is: 16.4405
Step-by-step explanation:
Given
[tex]y = ax + b[/tex]
[tex]a =-1.077[/tex]
[tex]b=30.98[/tex]
[tex]r^2 = 0.74476[/tex]
Required
Predict y when [tex]x = 13.5[/tex]
In the result, we have:
[tex]y = ax + b[/tex]
[tex]a =-1.077[/tex]
[tex]b=30.98[/tex]
This implies that:
[tex]y = -1.077x + 30.98[/tex]
To make prediction when [tex]x = 13.5[/tex]
We have:
[tex]y = -1.077*13.5 + 30.98[/tex]
[tex]y = -14.5395 + 30.98[/tex]
[tex]y = 16.4405[/tex]
A study records the lengths of pregnancy (in days) of 500 women. The data is normally distributed with a mean of 266 days and a standard deviation of 16 days. How many women in the study had a pregnancy between 250 days and 282 days in length?
Answers
Answer:
371 women had their pregnancy between 250 days and 282 days in length.
di po ako sure sa answer ko, but it is based on what I remembered.
Step-by-step explanation:
z=532-266
16
√500
= 371.74 or 371
Which best describes the relationship between the successive terms in the sequence shown?
9, -1, -11, -21,
The common difference is -10,
The common difference is 10
The common ratio is -9)
The common ratio is 9.
Answers
Answer:
the common difference is 10
I NEED HELP ASAP PLEASE
Answers
Answer:
A and E
Step-by-step explanation:
B and D is unchangeable, species of bears and types of vegetables that existed in the world never changed.
C only consist of one data, temperature of Chicago at noon yesterday only.
Let f (x) = 10/x-4
What is the average rate of change of f (x) from 2 to 8 ?
Enter your response as a decimal.
Answers
Answer:
1.875
Step-by-step explanation:
The rate of change is the derivative of the function.
[tex]f(x) = \frac{10}{x-4}\\\\f'(x)=10\times \frac {d}{dx}\frac{1}{x-4}\\\\f'(x)=\frac{-10}{(x-4)^{2}}\\\\f'(2) = \frac{-10}{(2-4)^{2}} =-2.5\\\\f'(8)= \frac{-10}{(8-4)^{2}} =-0.625\\[/tex]
So, the rate of change is
f'(8) - f'(2) = - 0.625 + 2.5 = 1.875
If the equation y = |x| is graphed and then
moved up 3 units on the y-axis, what will be
the equation of the new graph?
Answers
Answer:
Step-by-step explanation:
The new equation will be
y = abs(x) + 3
I have made a graph to show you this.
The red graph is y = abs(x)
The blue graph is y = abs(x) + 3
You need only look at the point 0,0 to see what happened. On the red graph (0,0) is the lowest point. When you add 3 to get the lowest point, you should notice that the lowest point is now (0,3)
What is -4.5 need help pls help fast I will give u a brilliant and thank
Answers
Answer:
its -4.5??? what is the question you're asking
The average number of employees that call in sick for the day over the course of a year is 25. The number of employees that call in sick on 12 days are 25, 10, 16, 39, 27, 25, 32, 25, 25, 22, 28, and 14. Enter the sample mean and the population mean in the boxes
Answers
Answer:
sample mean (x with the bar on top) =24
Step-by-step explanation:
Take the mean of all the number of employees but divide by the number of days size: (25+10+16...)/12=25
population mean (mu) =11.52
The same goes for the other one but divide by the population which is 25
a street light is mounted at the top of a 15-foot pole. A 6-foot tall man walks away from the pole along a straight path. How long is his shadow when he is 40 feet from the pole
Answers
Answer:
[tex]x=26.67[/tex]
Step-by-step explanation:
From the question we are told that:
Height of Pole [tex]h_p=15 foot[/tex]
Height of Man [tex]h_m =6ft[/tex]
Distance from Pole [tex]d_p=40ft[/tex]
Generally the equation for similar Property is mathematically given by
[tex]\frac{h_p}{h_m}=\frac{d_p+x}{x}[/tex]
[tex]x=\frac{h_m*(d_p+x)}{h_p}[/tex]
[tex]x=\frac{6*(40+x)}{15}[/tex]
[tex]x=\frac{240+6x}{15}[/tex]
[tex]x=16+0.4x\\x-0.4x=16[/tex]
[tex]x=16\0.6[/tex]
[tex]x=26.67[/tex]
Can someone help with this problem please.
Answers
The ball is 57 feet from the hole.
Explanation:
The distance from the tee to the hole is 181 yards.
Using the Pythagoras Theorem,
x^2 + 180^2 = 181^2
x^2 + 32400 = 32761
x^2 = 361
x = sqrt(361)
x = 19 yards
1 yard = 3 feet
x = 19 yards = 57 feet
Given that is directly proportional to (p-1)2 and p is always positive, find the
value of p when q = 80 , if 9= 30 when p = 7
A) 4
B) 6
Ch 10.82
Answers
Answer:
p = 10.8
Step-by-step explanation:
Given that p is directly proportional to (p-1)² and p is always positive, then;
q = k (p-1)²
If q = 30 and p = 7
30 = k(7-1)²
30 = 6²k
30 = 36k
5 = 6k
k = 5/6
To get p when q = 80
q =k (p-1)²
80 = 5/6((p-1)²
480 = 5(p-1)²
480/5 = (p-1)²
(p-1)² = 96
p-1 = √96
p-1 = 9.8
p = 9.8 + 1
p = 10.8
B) 6
Ch 10.82
3X + 2 = 17 how do I show my work for this?
Answers
Answer:
x = 5
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightEquality Properties
Multiplication Property of Equality Division Property of Equality Addition Property of Equality Subtraction Property of EqualityStep-by-step explanation:
Step 1: Define
Identify
3x + 2 = 17
Step 2: Solve for x
[Subtraction Property of Equality] Subtract 2 on both sides: 3x = 15[Division Property of Equality] Divide 3 on both sides: x = 5Answer:
you subtract two both side, then divide three both side, you'll get x = 5.
Step-by-step explanation:
3x + 2 = 17
(3x + 2) -2 = (17) -2. First, you subtract 2 for both sides
3x = 15
(3x)/2 = (15)/2. Second, you divide 3 both side
x = 5. Last, you get your answer
PLZ HELP WILL GIVE 50 POINTS - QUADRATIC APPLICATIONS
find how far away (ground distance) from the catapult will white bird be at its highest. (round to the nearest 2 decimal points)
h= -0.114x^2+2.29x+3.5
Answers
Answer:
The bird will be at a ground distance of 10.04 units away.
Step-by-step explanation:
Vertex of a quadratic function:
Suppose we have a quadratic function in the following format:
[tex]f(x) = ax^{2} + bx + c[/tex]
It's vertex is the point [tex](x_{v}, y_{v})[/tex]
In which
[tex]x_{v} = -\frac{b}{2a}[/tex]
[tex]y_{v} = -\frac{\Delta}{4a}[/tex]
Where
[tex]\Delta = b^2-4ac[/tex]
If a<0, the vertex is a maximum point, that is, the maximum value happens at [tex]x_{v}[/tex], and it's value is [tex]y_{v}[/tex].
Equation for the height:
The height of the bird after x seconds is given by:
[tex]h(x) = -0.114x^2 + 2.29x + 3.5[/tex]
Which is a quadratic equation with [tex]a = -0.114, b = 2.29, c = 3.5[/tex].
When the bird is at its highest?
Quadratic equation with [tex]a < 0[/tex], and thus, at the vertex. The ground distance is the x-value of the vertex. Thus
[tex]x_{v} = -\frac{b}{2a} = -\frac{2.29}{2(-0.114)} = 10.04[/tex]
The bird will be at a ground distance of 10.04 units away.
Puzzle- Please help me with this question
Answers
Answer:
Step-by-step explanation:
Multiply the two top numbers together. Then record the first digit of the answer.
5*4 =20 Record 2
9*8 = 81 Record 8
3*6 =18 Record 1
7*5 = 35 Record 3