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
What is the common ratio between successive terms in the sequence?
2, 4, 8, -16, 32, -64,
Ο Ο Ο Ο
2
Answers
Step-by-step explanation:
[tex]r = \frac{4}{2} \\ r = 2[/tex]
Answer:
-2
Step-by-step explanation:
The "common ratio" is the number you multiply a term by to get the next term.
-4 = 2 x -2
8 = -4 x -2
-16 = 8 x -2
Which one is the least value?
Answers
Answer:
6/20
Step-by-step explanation:
trust
Determine the area of the triangle.
Answers
Answer:
no triangle given try to use a = 1/2(b x h) for the area
Step-by-step explanation:
Use a net to find the surface area of the prism.
27 cm
6.5 cm
15 cm
The surface area of the prism is
(Simplify your answer.)
Cm2
Answers
Answer:
Step-by-step explanation:
fx= ab*2÷t*2, make t the subhect of the formulae
[tex]fx = ab { }^{2} \div t {?}^{2} [/tex]
Answers
Answer:
t = √ab²/fx
Step-by-step explanation:
fx= ab*2÷t*2, make t the subject of the formulae
Given the function
fx = ab²/t²
We are to make t the subject of the formula
fxt² = ab²
t² = ab²/fx
Take the square root of both sides
√t² = √ab²/fx
t = √ab²/fx
Hence the required value of t is √ab²/fx
The base length of a triangle is 4 feet and the height is 2 feet. What is the area of the triangle? (5 points) a 2 square feet b 4 square feet c 6 square feet d 8 square feet
Answers
Answer:
B. 4 square feet
Step-by-step explanation:
The formula for area of a triangle is length x height / 2 so 4 x 2 is 8 then divided by 2 is 4.
Answer: 4
Base 4
hight 2
4x2=8 ÷ 2 or 1/2 Equals 4
Formula L x W ÷ 2 or 1/2
a rectangle has a base of 10 and height of 12 what is its area
Answers
Answer:
120 units squared
Step-by-step explanation:
What is the length of BD?
Answers
Answer:
From -6 to positive 1 the length is 7
Step-by-step explanation:
you still add'em.
Answer:
length of BD is 18
just count on the number line and ×2 because it is counting on by 2
A government agency estimates the number of young adults (ages 18 to 24) in a particular country to be 31,000 (in thousands) in 2010 and changing at the rate of −x2 + 90x − 200 thousand per year, where x is the number of years since 2010. Find a formula for the size of this population at any time x. [Hint: Keep all calculations in units of thousands.]
Answers
Answer:
[tex]\mathbf{L(x)= ( - \dfrac{1}{3})x^3 + 45x^2 -200x +31000}[/tex]
Step-by-step explanation:
From the given information:
Let assume the population is denoted by L
The rate of change of the young adults per year given can be represented as;
[tex]\dfrac{dL}{dx}= -x^2 +90x - 200[/tex]
where;
x = 0 since 2010
[tex]dL = -x^2 +90x -200 dx[/tex]
[tex]L = \int( -x^2 +90x -200 ) \ dx[/tex]
[tex]L = - \dfrac{1}{3}x^3 + 45x^2 -200x +C[/tex]
here;
L(0) = 31000
∴
[tex]- \dfrac{1}{3}(0)^3 + 45(0)^2 -200(0)+C= 31000[/tex]
C = 31000
[tex]\mathbf{L(x)= ( - \dfrac{1}{3})x^3 + 45x^2 -200x +31000}[/tex]
find the outlier of 22,26,31,37,3126,35,28,24
Answers
Answer:
3126
Step-by-step explanation:
Because it is so much bigger than the other numbers.
Can someone please help, ty!
Will mark brainliest!
Answers
Answer:
I and II
Step-by-step explanation:
I used a graphing calculator to find the answers.
Which of the following functions has a vertical asymptote at x=3?
Answers
Answer:
the last one: f(x) = 1/(x-3)
Step-by-step explanation:
Vertical asymptote at x=3 means dividing by zero for x=3. If you examine all denominators with x=3, you find that the last one divides by zero (3-3).
Select the values that make the inequality h < 2 true.
(Numbers written in order from least to greatest going across.)
Answers
Given:
The inequality is:
[tex]h\leq 2[/tex]
To find:
The values that make the given inequality true.
Solution:
We have,
[tex]h\leq 2[/tex]
It means the value of h must be less than or equal to 2.
In the given options, the list of numbers which are less than or equal to 2 is
-6, -3, -1, 1, 1.9, 1.99, 1.999, 2
The list of numbers which are greater than 2 is
2.001, 2.01, 2.1, 3, 5, 7, 10
Therefore, the first 8 options are correct and the required values are -6, -3, -1, 1, 1.9, 1.99, 1.999, 2.
Answer:
Step-by-step explanation:
plz plz plz plz help me
Answers
Answer:
240 plantsStep-by-step explanation:
Find the area of the garden:
A = 1/2bhA = 1/2(8)(15) = 60 m²Number of plants:
60*4 = 240 plantsAnswer:
Solution given:
perpendicular [P]=15m
base[B]=8m
hypotenuse [H]=17m
rate :4 plants per square metre
no of plants=?
we have
Area of triangular garden: ½(P*B)=½(15*8)=60m²
Now
Total no of plants =rate ×Area =4×60=240
Michael needs 240 plants in the garden.
If Sofia randomly picks a number from 1 to 25, what is the probability that the number will have “1” as one of the digits?
Answers
Make an equation that is equal to 2/3
Answers
Answer:
Replace the 4 with a 3 to make the equation true
brainliestt
for righto
Answers
Answer:
Hello! answer: 13/16
Hope that helps!
Given that ABCD is an inscribed quadrilateral and m(∠DAB)=78°. What is m (DAB)
Answers
Answer:
Step-by-step explanation:
I'm going to go out on a limb here and guess that you are looking for the answer to the measure of arc DAB, since we already know that angle DAB is 78. Angle DAB is an inscribed angle. That inscribed angle intercepts arc DCB, and the theorem for that is that an inscribed angle is half the measure of the arc it intercepts. That means that arc DCB measures twice 78, so arc DCB measures 156 degrees. Since the measure around the outside of any circle is 360 degrees, arc DAB is 360 - 156 which is 204 degrees. If this is not what you are looking for, sorry and be more specific next time.
Write the equation of the line in slope-intercept form.
Answers
Answer:
y = 50x+40
Step-by-step explanation:
Slope intercept form is
y = mx+b where m is the slope and b is the y intercept
First find two points on the line
(0,40) and (2 ,140)
The slope is
m= (y2-y1)/(x2-x1)
= (140-40)/(2-0) = 100/2= 50
The y intercept is where it crosses the y axis which is 40
y = 50x+40
A farmer sells 8.2kg of apples and pears at the farmers market. 4/5 of this weight is apples and the rest is pears. How many kg of pears did she sell at the market?
Answers
9514 1404 393
Answer:
1.64 kg of pears
Step-by-step explanation:
If 4/5 of the weight is apples, the remaining 1/5 is pears.
(1/5)(8.2 kg) = 1.64 kg
She sold 1.64 kg of pears.
Answer:
Solution :-Weight of pears = 1 - Weight of apple
=> 1 - 4/5
=> 5 - 4/5
=> 1/5
Now
Weight of pears = ⅕ × 8.2
Weight of pears = 1.64 kg
[tex] \\ [/tex]
20% of the patron's order the chef's special. The probability that 2 out of the next ten customers will order the chef's special is
Answers
Answer:
[tex]P(x =2) = 0.3020[/tex]
Step-by-step explanation:
Given
[tex]p =20\% = 0.20[/tex]
[tex]n = 10[/tex]
Required
[tex]P(x = 2)[/tex]
This question is an illustration of binomial distribution where:
[tex]P(X = x) = ^nC_x * p^x * (1 - p)^{n-x[/tex]
So, we have:
[tex]P(x =2) = ^{10}C_2 * 0.20^2 * (1 - 0.20)^{10-2}[/tex]
[tex]P(x =2) = ^{10}C_2 * 0.20^2 * 0.80^8[/tex]
This gives
[tex]P(x =2) = \frac{10!}{(10 - 2)!2!} * 0.20^2 * 0.80^8[/tex]
[tex]P(x =2) = \frac{10!}{8!2!} * 0.20^2 * 0.80^8[/tex]
Expand
[tex]P(x =2) = \frac{10*9*8!}{8!2*1} * 0.20^2 * 0.80^8[/tex]
[tex]P(x =2) = \frac{10*9}{2} * 0.20^2 * 0.80^8[/tex]
[tex]P(x =2) = 45 * 0.20^2 * 0.80^8[/tex]
[tex]P(x =2) = 0.3020[/tex]
The probability that 2 out of the next ten customers will order the chef special is 0.3020. and this can be determined by using the binomial distribution.
Given :
20% of the patron's order the chef's special. Sample size, n = 10To determine the probability formula of the binomial distribution is used, that is:
[tex]\rm P(x = r) = \; ^nC_r \times p^r \times (1 - p)^{n-r}[/tex]
Now, at n = 10 and r = 2, the probability is given by:
[tex]\rm P(x = 2) = \; ^{10}C_2 \times (0.2)^2 \times (1 - 0.2)^{10-2}[/tex]
[tex]\rm P(x = 2) = \; ^{10}C_2 \times (0.2)^2 \times (0.8)^{10-2}[/tex]
[tex]\rm P(x = 2) = \; \dfrac{10!}{(10-2)!\times 2!} \times (0.2)^2 \times (0.8)^{8}[/tex]
[tex]\rm P(x = 2) = \; 45 \times (0.2)^2 \times (0.8)^{8}[/tex]
P(x = 2) = 0.3020
The probability that 2 out of the next ten customers will order the chef special is 0.3020.
For more information, refer to the link given below:
https://brainly.com/question/1957976
Yesterday, there were 60 problems assigned for math homework. Albert did 30% of them correctly. How many problems did Albert get right?
Answers
1. María expandió el siguiente cuadrado de la manera que sigue: (x+3)2 = x² + 9,
¿Está correcta la forma que usó María?
Answers
Answer:
La expansión de María[tex](x + 3) {}^{2} = x {}^{2} + 9[/tex]
Correcta expansión[tex](x + 3) {}^{2} \\ = {x}^{2} + 2 \times x \times 3 + 3 {}^{2} \\ = x {}^{2} + 6x + 9[/tex]
Note - (a + b)² = a² + 2ab + b²
✐ La expansión de Mary está mal. Correcta expansión ⇻ x² + 6x + 9
ʰᵒᵖᵉ ⁱᵗ ʰᵉˡᵖˢ
# ꧁❣ RainbowSalt2²2² ࿐
Tyrone is building a skateboard ramp with a piece of plywood that is 33 feet long.He wants the height of the ramp to be 22 feet.To make a strong ramp, the base must form a right angle with the back of the ramp.What will be the length of the base rounded to the nearest tenth of a foot?
please hurry and and please show your work!!
Answers
Answer:
24.6 ft
Step-by-step explanation:
Use the Pythagorean theorem.
a^2 + b^2 = c^2
a^2 + (22 ft)^2 = (33 ft)^2
a^2 + 484 ft^2 = 1089 ft^2
a^2 = 605 ft^2
a = 24.6 ft
Answer: 24.6 ft
Find each quotient.
494 ÷ 95 =
136.8 ÷ 24 =
96.9 ÷ 19 =
43.2 ÷ 8 =
Answers
Answer:
1. 5.2
2. 5.7
3. 5.1
4. 5.425 or 5.4
Step-by-step explanation:
hope this helps :)
Answer:
1. 5.2
2. 5.7
3. 5.1
4. 5.4
Step-by-step explanation:
you can use the app photo math, you just take a picture of the problem and it will give you the answer and explain the steps.
A garden table and a bench cost $672 combined. The garden table costs $78 less than the bench. What is the cost of the bench?
Answers
Answer:
b = $375
Step-by-step explanation:
b = cost of the bench
t = cost of the table
t = b - 78
b + b - 78 = 672
2b = 750
b = $375
Matt can plant 27 trees in 3 hours. At that
rate, how many trees can Matt plant in an
8 hour day?
Answers
Answer:
72 trees.
Step-by-step explanation:
27 divided by 3 equals 9. so that means Matt can plant 9 trees in one hour so 9 is our unit rate ( what we multiply by) so now you multiply 9 by 8 and your answer is 72
girlcome 5324611502
p:1234
Answers
Answer:
ok then
Step-by-step explanation:
Answer:
Subscribe to my animations Y0UTUBE channel! Channel name: Let Me Explain Studios. Have a nice day!
Step-by-step explanation:
Given f (x) = StartLayout Enlarged left-brace first row x squared minus one-third x, for x not-equals negative 1 second row negative 1, for x = negative 1 EndLayout. What is Limit of f (x) as x approaches negative 1?
Negative five-thirds
Negative four-thirds
Four-thirds
Five-thirds
Answers
Answer:
It's C, 4/3! Just did the question and got it right
Step-by-step explanation:
The limit of f(x) as x approaches negative 1 is four thirds.
What is Limits?Limits are defined as the value of a function as the input approaches a certain number. Limits are the concepts used essentially in calculus to define continuity, integrals and derivatives.
Given function is,
[tex]f(x) =\left \{ {{x^{2} -\frac{1}{3}x, x\neq -1 } \atop {-1, x=-1}} \right.[/tex]
We have to find the value of the limit as x approaches to negative 1.
This is not the same value as the value of the function at negative 1. Limit of the function as x approaches some value is the value of the function which is closest to the exact value of the function at the input.
We have,
f(x) = x² - [tex]\frac{1}{3}[/tex] x when x ≠ -1
Substitute x = -1 in the above equation
x² - [tex]\frac{1}{3}[/tex] x = (-1)² - (1 / 3) (-1)
= 1 + [tex]\frac{1}{3}[/tex]
= [tex]\frac{4}{3}[/tex]
[tex]\lim_{x \to -1} x^{2} -\frac{x}{3}[/tex] = [tex]\frac{4}{3}[/tex]
Hence the limit of f(x) = x² - [tex]\frac{1}{3}[/tex] x when x tends to -1 is 4/3.
To learn more about Limits, click on the link given below :
https://brainly.com/question/12207539
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Find the area and the circumference of a circle with diameter 10 m.
Write your answers in terms of pi, and be sure to include the correct units in your answers.
Answers
Step-by-step explanation:
area of a circle= πr²
and r= half diameter
therefore we have r=10/2=5
area= 5² x π
area= 25π
circumference=2πr
circumference= 2xπx5
circumference=10π