Find an equation for the circle that has center (−1, 4) and passes through the point (3, −5).
The correct answer for the equation of the circle with center (-1,4) and passes through point (3,-5) is [tex](x+1)^2 + (y-4)^2 = 97[/tex].
Given Co-ordinates:
Centre:
(-1,4)
Point of intersection:
(3,-5)
The standard equation of circle with center (h, k) is:
[tex](x-h)^2 + (y-k)^2 = r^2[/tex]
(h, k) are co-ordinates of center
Given in question:
h= -1
k = 4
Find radius of the circle:
distance between the center(-1,4) and the given point (3, -5).
[tex]r = [\sqrt{(x_{2}- x_{1})^2 + (y_{2}- y_{1})^2 }[/tex]
[tex]r = [\sqrt{((3- (-1))^2 + (-5-4)^2 }[/tex]
[tex]= \sqrt{(4)^2 + (-9)^2 }[/tex]
[tex]= \sqrt{16 + 81}[/tex]
[tex]= \sqrt{97}[/tex]
Now, Equation of circle:
[tex](x-(-1))^2 + (y-4)^2 = (\sqrt{97})^2[/tex]
[tex](x+1)^2 + (y-4)^2 = 97[/tex]
The equation of circle is [tex](x+1)^2 + (y-4)^2 = 97[/tex].
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The equation of the circle with center (-1, 4) and passing through the point (3, -5) is (x + 1)² + (y - 4)² = 97.
Explanation:The subject of this question is geometry, specifically about the equations of circles. We start by noting that the general equation of a circle is (x-h)² + (y-k)² = r², where (h, k) are the coordinates of the circle's center and r is the radius of the circle.
Here, the center of the circle is at (-1, 4). We don't know the radius yet, but we know that the circle passes through the point (3, -5). The radius is the distance from the center of the circle to any point on the circle. We can find this using the distance formula which is d = sqrt[(x₂ - x₁)² + (y₂ - y₁)²].
Substituting the given points into the distance formula, we get: r = sqrt[(3 - (-1))² + (-5 - 4)²] which simplifies to r = sqrt[(4)² + (-9)²] = sqrt[16 + 81] = sqrt[97].
Now we can write the equation of the circle, substituting the center and radius values into the equation. This gives us: (x - (-1))² + (y - 4)² = sqrt[97]² which simplifies to (x + 1)² + (y - 4)² = 97.
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Which of the following data sets represents a positive correlation?
A
B
C
A quadrilateral has angles that measure 71°, 74°, 113°, and x°. What is the measure of x?
(2)
For this problem I did 2.5/8 = 1.5/4.8, then I cross multiplied and got 12=12 so I would assume that the polygons are infact similar? It must be B or C based on this, but I am pretty confused about the whole ratio part.
Angle 2 and angle 3 are vertical angles. true or false
Answer: If you don't know the answer don't put one down but i do believe the answer is false.
Step-by-step explanation:
The statement 'Angle 2 and Angle 3 are vertical angles' can be true depending on their position, as vertical angles are those directly opposite from each other at the intersection of two lines.
Explanation:The question is asking about vertical angles. Vertical angles are pairs of non-adjacent angles formed when two lines intersect. This means they are the angles that are directly opposite from each other where the two lines intersect. So if Angle 2 and Angle 3 are directly opposite each other at the point where two lines cross, then they are indeed vertical angles. So, the statement 'Angle 2 and Angle 3 are vertical angles' can be true depending on their placed positions.
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The sum of 4 interior angles of a pentagon is 402. Find the measure of the fifth interior angle.
108
62
138
42
Three couples go to the movies and sit in six consecutive seats. if the couples must sit together, in how many ways can they be seated
A cruise ship travels 1900 miles per trip. There are a total of 4 stops the ship makes, and the distance to the first stop is 460 miles. If the variable d stands for the distance left to travel after the first stop, which of the following units could apply to this variable?
A. ships
B. days
C. stops
D. miles
Find the area of the shaded region?
What is the following quotient? sqrt 120 / sqrt 30
Answer:
[tex]2[/tex]
Step-by-step explanation:
we have
[tex]\frac{\sqrt{120}}{\sqrt{30}}[/tex]
we know that
[tex]\frac{\sqrt{120}}{\sqrt{30}}=\sqrt{\frac{120}{30}}=\sqrt{4} =2[/tex]
I need help on how to convert the radian into degrees for 7pi/10 !!
Which of the following statements is always true?
A: All rational numbers are whole numbers.
B: All real numbers are rational numbers.
C: All irrational numbers are real numbers.
D: All square roots are irrational numbers.
Answer:
b
Step-by-step explanation:
took the test got it right
Moving a figure around a fixed point in the plane is called making a ___.
Answer:
Rotation.
Step-by-step explanation:
There are three rigid motions (which do not change the shape and size of the figures): rotation, translation and reflection.
You make a rotation of a figure when you turn it about a fixed point (which can be inside, on an edge or outside the figure) and it is measured in degrees. The rotation can be clockwise or counterclockwise.
Answer:
The answer is Reflection
HELP!!!!!!!!!!!!!
To solve the equation 3x−2=4x−1 , Veronica graphs the functions f(x)=3x−2 and g(x)=4x−1
on the same set of coordinate axes.
Which statement describes the solution of the equation 3x−2=4x−1?
(A) The solution of the equation is the x-coordinate of the ordered pair where the graphs of the two functions intersect.
(B) The solution of the equation cannot be found graphically. Veronica should solve the equation algebraically.
(C) The solution of the equation is the y-coordinate of the ordered pair where the graphs of the two functions intersect.
(D) The solution of the equation is the y-intercept of the linear equations.
we have that
f(x)=3x-2
g(x)=4x-1
3x-2=4x-1-------------> 4x-3x=-2+1--- > x=-1
find the value of f(x) or g(x) for x=-1
f(x)=3x-2 -------> f(-1)=3*(-1)-2 ------> f(-1)=-5
the solution is the point (-1,-5)
using a graph tool
see the attached figure
the answer is
case (A) The solution of the equation is the x-coordinate of the ordered pair where the graphs of the two functions intersect.The simplest form of square root of eighty can be written as a times square root of b, where a
A sample has a mean of m = 90. if each score in the sample is multiplied by 5, then what is the mean for the new distribution?
Final answer:
When each score in a sample is multiplied by a constant, the mean of the new distribution will also be multiplied by that constant, resulting in a new mean value of 450.
Explanation:
The mean of a sample is a measure of the average value of the data points in that sample.
When each score in a sample is multiplied by a constant, like 5 in this case, the resulting mean of the new distribution will also be multiplied by that constant.
In this scenario, since each score is multiplied by 5, the mean of the new distribution will be 5 times the original mean, giving a new mean of 450.
What is the question
Thomas is saving pennies in a jar. The first day he saves 3 pennies, the second day 12 pennies, the third day 48 pennies, and so on. How many pennies does Thomas have on the eighth day?
Given f(x)=5x^2−2x and g(x)=3x ^2+x−4 .
The addition of the two functions f(x) and g(x) is 8x² − x − 4. Then the correct option is C.
What is a function?The function is an expression, rule, or law that defines the relationship between one variable to another variable. Functions are ubiquitous in mathematics and are essential for formulating physical relationships.
The functions are given below.
[tex]\rm f(x)=5x^2-2x \\\\g(x)=3x ^2+x-4[/tex]
The addition of the functions is given as
f(x) + g(x) = 5x² − 2x + 3x² + x − 4
f(x) + g(x) = 8x² − x − 4
More about the function link is given below.
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please help!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Use the number line to find the ratio BG/AD Simplify the ratio.
The home that you are interested in purchasing is listed at $135,000. In order to get financing, you have to place a 15% down payment. From the given information, determine the amount of the down payment. a. $2,025 c. $114,750 b. $135,000 d. $20,250
Answer:
its D
Step-by-step explanation:
what is the product (7x^3y^3)(3x^5y^8)
a)10x^5y^15
b)10x^10y^24
c)21x^7y^11
d)21x^10y^24
You have studied polynomials consisting of constants and/or variables combined by addition or subtraction. The variables may include exponents. The examples so far have been limited to expressions such as 5x4 + 3x3 – 6x2 + 2x containing one variable, but polynomials can also contain multiple variables. An example of a polynomial with two variables is 4x2y – 2xy2 + x – 7.
Many formulas are polynomials with more than one variable, such as the formula for the surface area of a rectangular prism: 2ab + 2bc + 2ac, where a, b, and c are the lengths of the three sides. By substituting in the values of the lengths, you can determine the value of the surface area. By applying the same principles for polynomials with one variable, you can evaluate or combine like terms in polynomials with more than one variable.
The product of (7x²y³) and (3x⁵y⁸) is obtained by multiplying the coefficients and adding the exponents of like terms, resulting in c) 21x⁷y¹¹.
To find the product of the two algebraic expressions (7x²y³) and (3x⁵y⁸), we simply multiply the coefficients and add the exponents of corresponding variables:
Multiply the coefficients: 7 * 3 = 21
Add the exponents of x: x² * x⁵ = x²⁺⁵ = x⁷
Add the exponents of y: y³ * y⁸ = y³⁺⁸ = y¹¹
Therefore, the product is 21x⁷y¹¹, which corresponds to option (c).
The explicit rule for a sequence is
an=17−5n .
What is the recursive rule for the sequence?
can you explain also
Mrs. Smith and her daughter Laura want to learn ballet. The cost of beginning ballet classes for kids is $3,200 per year, and it increases by 2% every year. The cost of beginning ballet classes for adults is $4,800 per year, and it increases by 2.7% per year. Which function can Mrs. Smith use to determine the total cost of their ballet classes, T(x), after x years?
What is the greatest common factor of the polynomial's terms? 14a3b4−7ab7+21a2b
The Answer is 7(ab).
I did the quiz.
Answer: 7ab
Step-by-step explanation:
The given polynomial : [tex]14a^3b^4-7ab^7+21a^2b[/tex]
The terms of the above polynomial can be written as :
[tex]14a^3b^4=(7\times2)a^{2+1}b^{3+1}=(7\times2)a^2(a)b^3b\\\\-7ab^7=-7ab^{6+1}=-7ab^6(b)\\\\21a^2b=(7\times3)a^{1+1}b=(7\times3)a(a)b[/tex]
Now, we can see that the greatest common factor of the polynomial's terms= [tex]7ab[/tex]
What is the probability that the card is either a face card or a spade?
Randy bought a zero coupon bond and a TIPS 5 years ago for $2,500 each. Both had 10 years to maturity. The TIPS's coupon was 2% while the zero coupon bond will be redeemed for $3,000. What should the maximum real value of his bonds be if he tries to sell them today? Select the best answer from the choices provided. $250 $750 $5,250 $5,750
A 45° sector in a circle has an area of 13.75π cm².
What is the area of the circle?
Use 3.14 for pi.
Enter your answer as a decimal in the box.
Answer:
345.4
Step-by-step explanation:
I took the test
How to estimate the square root of a number that is not a perfect square?