A circle is centered at the point (-3,2) and passes through the point (1,5). What's the radius
radius = square root (( x2-x1)^2 +(y2-y1)^2)
= sqrt(1-(-3)^2+(5-2)^2
= sqrt(16+9)
=sqrt(25)
= 5
radius is 5
The radius of the circle is [tex]\boxed{5{\text{ units}}}.[/tex]
Further explanation:
The standard equationof the circle with center [tex]\left( {h,k}\right)[/tex] and radius r can be expressed as,
[tex]{\left( {x - h}\right)^2} + {\left({y - k} \right)^2}= {r^2}.[/tex]
Given:
A circle with center at [tex]\left({ - 3,2} \right).[/tex]
The passing through point is [tex]\left( {1,5} \right).[/tex]
Explanation:
The center is at [tex]\left( { - 3,2} \right).[/tex]
The passing through point is [tex]\left( {1,5} \right)[/tex]. Therefore, the point satisfies the equation of circle.
Substitute 1 for x, 5 for y, -3 for h and 2 for k in general equation of the circle to obtain the radius of circle.
[tex]\begin{aligned}{\left( {x - h}\right)^2}+{\left({y - k}\right)^2}&={r^2}\\{\left( {1 + 3} \right)^2} + {\left( {5 - 2}\right)^2}&= {r^2}\\16 + 9&= {r^2}\\\sqrt{25}&= r\\5&= r\\\end{aligned}[/tex]
The radius of the circle is [tex]\boxed{5{\text{ units}}}.[/tex]
The radius of the circle is [tex]\boxed{5{\text{ units}}}.[/tex]
Learn more:
1. Learn more about equation of circle brainly.com/question/1506955.
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3. Learn more about coplanar https://brainly.com/question/4165000.
Answer details:
Grade: Middle School
Subject: Mathematics
Chapter: Circle
Keywords: Circle, centered point, (-3,2), passes point (1,5), standard form of the circle, equation of the circle, center, diameter of circle, radius of the circle,center-radius form, general equation of circle, tangent, area of circle.
The value of 7 in 503,497 is what times the value of 7 in 26,475?
plz help and thank you!
The answer to your question is the third option:
1/2(n+4) = 5/n - 3
you can buy 3 apples at quick market for $1.17, you can buy 5 of the same apples at Stop and Save for $2.40.
a.Which store is the better buy?
b. How much will you save per apple if you purchase it from the cheaper store?
Sergei says that 10%
of a number will always be less than 20%
of any other number.
Complete one inequality to support Sergei's claim and one to show that he is incorrect.
10% of 100 < 20% of 200.
10% of 1000 > 20% of 100.
What are the numbers that make the claims correct?Percentage is the fraction out of an amount that is usually expressed as a number out of hundred. Percentages are a measure of frequency. The sign used to represent percentages is %.
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PLease ANSWER
You get 30 points
On your math quiz, you earn 5 points for each question that you answer correctly. In the table below, x represents the number of questions that you answer correctly on your math quiz, and y represents the total number of points that you score on your quiz. The relationship between these two variables can be expressed by the following equation: y=5x. Suppose you answer 40 questions correctly on your math quiz.
There is 16 pink stripes and green stripes. Find the ratio o pink stripes to green stripes
The next even integer that is larger than 2n, if 2n is an even integer.
Lucas has five buttons in a container. Each button is a different shape. There is a star, an oval, a hexagon, a circle, and a heart. He picks one button, replaces it, and then picks another button. The sample size for this compound event is__ . Suppose one square-shaped button is added to the container. If Lucas repeats the same picking process, then the sample size would be__ .
Answer:
25,35
Step-by-step explanation:
Part A: There are five buttons in all in all in the given item. The item above can be answered through the fundamental principles of counting.
There are 5 items to choose from during the first pick. Because the shape can be returned and picked again, there are also 5 items to choose from in the second pick. Multiplying them,
n = 5 x 5 = 25
Therefore, the sample size for the compound event is equal to 25.
Part B: The same concept can be used in this part of the item; however, instead of 5 there are 6 buttons to choose from.
n = 6 x 6 = 36
Hence, the sample size of this picking process is 36.
Why is the polynomial, 4x^2y + 5xy classified as a 3rd degree binomial?
900 is 1/10 of what
an equilateral triangle has an altitude of 2√3in. and a perimeter of 12 in. what is the area of the triangle?
How many intersections are there of the graphs of the equations below? 1/2x + 5y = 6 3x + 30y = 36 none one two infinitely many
Answer:
D infinitely many
Step-by-step explanation:
They lines never cross
If 30% of John's photographs were perfect, but 210 photographs were not perfect, then how many photographs were there in all?
To find the total number of photographs, we use the fact that 30% were perfect, meaning 70% were not perfect. By setting up the equation 0.70x = 210, we can solve for x, finding that there were 300 photographs in total.
If 30% of John's photographs were perfect and 210 were not perfect, determining the total number of photographs involves understanding percentages and basic algebra. Here's the step-by-step breakdown of solving the problem:
Let's call the total number of photographs 'x'.Since 70% of the photographs are not perfect (as 30% are perfect), we know that 0.70x equals the number of not perfect photographs.We can set up the equation: 0.70x = 210.To find 'x', divide both sides of the equation by 0.70: x = 210 / 0.70.This gives us the total number of photographs, x = 300.Therefore, there were 300 photographs in total.
The total number of photographs is 300.
If 30% of John's photographs were perfect, it means that 70% were not perfect. Since 210 photographs were not perfect, we can set up an equation to find the total number of photographs. Let x represent the total number of photographs. We know that 70% of x equals 210:
[tex]\[ 0.70x = 210 \][/tex]
Solving this equation, we find that
[tex]\( x = \frac{210}{0.70} = 300 \)[/tex]
Therefore, there were 300 photographs in total. This calculation assumes that all photographs are either perfect or imperfect, with no other categories.
A phane takes off at an angle of elevation of 15 ° and travels in a straight line for 3,000 meters. What is the height of plane above the ground at this instant ?
Final answer:
The height of the plane above the ground after traveling 3,000 meters at a 15° angle of elevation is approximately 776.4 meters. This is calculated using the sine function: height = 3,000 m × sin(15°).
Explanation:
To find the height of the plane above the ground after taking off at an angle of elevation of 15° and traveling for 3,000 meters, we can use trigonometric functions. Specifically, the sine function relates the opposite side of a right-angled triangle (in this case, the height above ground) to the hypotenuse (the distance traveled by the plane).
The sine of an angle in a right triangle is equal to the length of the opposite side divided by the length of the hypotenuse. The formula is:
height = hypotenuse × sin(angle)
Here, the hypotenuse is the distance traveled by the plane (3,000 m), and the angle is 15°. Thus, the calculation would be:
height = 3,000 m × sin(15°)
We can calculate the sine of 15° using a calculator.
height = 3,000 m × 0.2588 (approximately)
height = 776.4 m (approximately)
Therefore, the plane is approximately 776.4 meters above the ground.
Does it matter which way you subtract the values when finding distance explain?
No, as long as you remember that distance is awlays zero or positive.
Consider 8x2 - 48x = -104. Write the equation so that a = 1
Answer:
x² + (-6x) = -13
ALSO the second answer,
x² + (-6x) __ = -13 + __
Both blanks are 9
Third answer, factor the trinomial and simplify:
(x + -3 )²= -4
Use the square root property of equality to solve
(x – 3)2 = –4.
The solutions are
The correct option is C. 3 ± 2i.
:D
The equation 8x² - 48x = -104 can be rewritten with 'a' = 1 by dividing all terms by 8 and rearranging to the form ax² + bx + c = 0, yielding x² - 6x + 13 = 0.
Explanation:To rewrite the equation so that 'a' = 1, it would be useful to adjust the coefficients in your equation first. Starting with the given equation: 8x² - 48x = -104. We can divide all terms by 8 to normalize the 'a' coefficient.
Doing that gives us: x² - 6x = -13. Now, to write the equation in the form ax² + bx + c = 0, we can add 13 to both sides which results in: x² - 6x + 13 = 0. Now your equation is in the standard quadratic form with 'a' = 1.
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Find the quotient of 9 divided by 5/8 .
9 / 5/8 =
9/1 / 5/8 =
9/1 * 8/5 = 72/5 = 14 2/5
Rachel wants to paint her cupboard. The length of the cupboard is 2.5 meters, its width is 1 meter, and its height is 2 meters. How much area will she need to paint if she paints both the bases and all the lateral faces?
Answer:
the answer is 10 m2
Step-by-step explanation:
Which number line represents all of the values of x for the equation x2 = 16? A number line is shown from negative 10 to 0 to positive 10. There are increments of 2 on the number line, and all these are increments are labeled. A dot is shown on positive 4 and is labeled as p. A number line is shown from negative 10 to 0 to positive 10. There are increments of 2 on the number line, and all these are increments are labeled. A dot is shown on positive 8 and is labeled as p. A number line is shown from negative 10 to 0 to positive 10. There are increments of 2 on the number line, and all these are increments are labeled. A dot is shown on positive 4, another dot is shown on negative 4, and are labeled as p and q, respectively. A number line is shown from negative 10 to 0 to positive 10. There are increments of 2 on the number line, and all these are increments are labeled. A dot is shown on positive 8, another dot is shown on negative 8, and are labeled as p and q, respectively.
Answer: Its the 3rd choice.
Help! I've been struggled on this for a loooong time!!
Algebraic expression that best describes the sequence 2,4,8,16,32,...?
Answer:
Algebraic expression that best describes the sequence is:
[tex]2^{n}[/tex]
Step-by-step explanation:
We have the sequence 2, 4, 8, 16, 32,...?
With the Algebraic expression:
[tex]2^{n}[/tex] (1)
n is the number into the sequence that you want to find, we can prove it if we replace in the equation (1)
For example in the first term, n=1
[tex]2^{1}=2[/tex]
in the second term, n=2, and so on
[tex]2^{2}=4\\2^{3}=8\\2^{4}=16\\2^{5}=32\\2^{6}=64\\[/tex]
A thief can travel 260 miles total with on tank of gas. Using only one tank of gas, what is the farthest city that the thief can reach? (4.5 cm = 150miles)
0.55555555555 As a fraction
Answer:
11/20
Step-by-step explanation:
After a devastating winter, when thousands of fish died, an environmental scientist has replenished the trout stock in a fishing pond. He started with 5,000 baby trout and has finished a count to find that, in 4 years, the population is estimated to be 8,500. Assuming an exponential growth pattern, what is the annual growth rate (rounded to the nearest tenth of a percent) of the new trout population?
The annual growth rate of the new trout population is approximately 12.0%.
Explanation:To find the annual growth rate of the trout population, we can use the exponential growth formula:
P = P0ert
where P is the final population, P0 is the initial population, r is the annual growth rate, and t is the number of years.
In this case, we have P = 8,500, P0 = 5,000, and t = 4. Plugging these values into the formula, we can solve for r:
8,500 = 5,000e4r
Divide both sides by 5,000:
1.7 = e4r
Take the natural logarithm of both sides:
ln(1.7) = 4r
Divide both sides by 4:
r ≈ ln(1.7)/4 ≈ 0.120
Final answer:
The annual growth rate of the trout population is calculated using the formula for exponential growth. By substituting the given values into the formula, the growth rate is determined to be approximately 13.41% per year. After rounding, the annual growth rate is 13.4%.
Explanation:
To calculate the annual growth rate of the trout population, we can use the formula for exponential growth, which is P = P0e(rt), where:
P is the final population size,
P0 is the initial population size,
r is the annual growth rate,
t is the time in years.
We know that P0 = 5,000 (initial population), P = 8,500 (final population), and t = 4 years. To find r, we rearrange the formula to solve for r:
r = (ln(P/P0)) / t
Plugging in the values gives us:
r = (ln(8500/5000)) / 4 = ln(1.7) / 4 ≈ 0.1341 or 13.41% per year
Rounding to the nearest tenth of a percent, the annual growth rate is 13.4%.
a jar of 25 lollipops in a clinic has 7 that are grape, 10 cherry, and 8 orange. If a nurse selects 4 lollipops randomly, what is the probability that they will all be grape?
Frankie purchases a 3 1/2 pound bag of chicken.he uses 1 1/3 of chicken for fajitas how many pounds of chicken are left?
how do you find the sum of all integers between square root of 12 + square root of 40?
how to factorise x squared minus 16
The diameter of the moon is 2155 miles. Find volume of the moon. Round answers to the nearest whole number and leave pi in the answer
Answer: [tex]1667978979\pi[/tex] cubic miles
Step-by-step explanation:
We know that the shape of moon is sphere.
The volume of sphere is given by :-
[tex]\text{V}=\dfrac{4}{3}\pi r^3[/tex], where r is the radius of sphere.
Given : The diameter of moon = 2155 miles
Then the radius of moon=[tex]\dfrac{2155}{2}[/tex]
Then , the volume of moon is given by :-
[tex]\text{V}=\dfrac{4}{3}\pi (\dfrac{2155}{2})^3=1667978979.2\pi\approx1667978979\pi \text{ cubic miles}[/tex]