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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Find the center of the circle whose equation is x² + y² = 4.
Answer:
The center of circle is [tex](0,0)[/tex]
Step-by-step explanation:
We need to find the center of the circle of the equation [tex]x^{2}+y^{2}=4[/tex]
Since, the general equation of circle is [tex](x-h)^{2}+(y-k)^{2} = r^{2}[/tex]
Where (h,k) is center of circle and r is radius.
Re-write the circle equation is [tex]x^{2}+y^{2}=4[/tex] as,
[tex]x^{2}+y^{2}=2^{2}[/tex]
Compare [tex]x^{2}+y^{2}=2^{2}[/tex] with [tex](x-h)^{2}+(y-k)^{2} = r^{2}[/tex]
so, [tex](x-0)^{2}+(y-0)^{2} = 2^{2}[/tex]
Hence, the center of circle is [tex](0,0)[/tex]
A company produces plates with area A=πr^2, where r is the radius of the plate. Find the inverse by solving for r without switching the variables.
The inverse is r=____
Explain your reasoning.
Final answer:
The inverse of the formula A = πr^2 is found by dividing the area A by π and then taking the square root of the resulting quotient, which gives r = √(A/π). The accuracy of this inverse is limited by the number of significant figures in the original measurement of the radius.
Explanation:
To find the inverse of the formula A = πr^2 for the area of a circle, we want to solve for the radius r in terms of A. We follow these steps:
Starting with A = πr^2, divide both sides of the equation by π to isolate r^2: A/π = r^2.
Take the square root of both sides of the equation to solve for r: r = √(A/π).
The inverse is therefore r = √(A/π).
When using a calculator, it is important to remember that the number of significant figures in a given measurement limits the accuracy of the calculations. As shown in the example, if the radius has two significant figures, the calculated area has to be limited to two significant figures as well, thus A=4.5 m².
whats the value of x??im really confused i thought it was 7 but that doesnt make sense can someone please help me!!!
A small toy car costs $3 . A large toy car costs 5 times as much as the small one . Aaron wants to buy one of each . Which equation can he use to find the cost (a) of the two cars ?
(A) 5x a = $3 +. $3
(B) 5x ($3 + $3 ) = a
(C) $3 +(5 x $3 ) =a
(D) (5 x $3 ) \ 3 = a
(/) division
Answer: the answer is B
Step-by-step explanation:
The equation used to find the cost (a) of the two cars will be $3 +(5 x $3 ) =a. The correct option is C.
What is an expression?Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.
Given that a small toy car costs $3. A large toy car costs 5 times as much as the small one.
The equation can be written as:-
a = $3 + ( 5 x $3 )
Therefore, the equation used to find the cost (a) of the two cars will be $3 +(5 x $3 ) =a. The correct option is C.
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Calculate the maximum volume of a box that has no top and that is to be manufactured from a 30 inch by 20 inch piece of cardboard
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Which of the following is equal to the expression below?
(160 * 243)^1/5
A. [tex] 6 \sqrt[5]{5} [/tex]
B.96
C.80
D.5[tex] 5 \sqrt[5]{5}
[/tex]
(160 * 243)^1/5
To simplify the above expression first step is to factor the numbers. Therefore,
[tex] (160*243)^{\frac{1}{5}} = ((2*2*2*2*2*5)*)(3*3*3*3*3)^{\frac{1}{5}} [/tex]
=[tex] (2^5*5*3^5)^{\frac{1}{5}} [/tex]
= [tex] (2^5)^{\frac{1}{5}} *(5)^{\frac{1}{5}} *(3^5)^{\frac{1}{5}} [/tex]
=[tex] 2 * (5)^{\frac{1}{5}} *3 [/tex]
= [tex] 6*(5)^{\frac{1}{5}} [/tex]
= [tex] 6\sqrt[5]{5} [/tex]
So, correct choice is A.
The product of x and 8 is less than or equal to 19
I need help remembering the steps to solve a polynomial equation
I'm confused on what this is asking me to do. Can someone explain to me, please?
Suppose you’re making a triangle where you know the measures of two angles and the length of the side between those two angles. Write two angle measures and the length of the side between them for your triangle. You can use any measurements you want as long as they could really be used to form a triangle.
Solve.
0 = x² + 8x + 15
Enter your answers in the boxes.
The solutions are _____
and _____.
For this case we have the following polynomial:
[tex] 0 = x ^ 2 + 8x + 15
[/tex]
We can rewrite the polynomial by factoring the expression.
We have then:
[tex] (x + 3) (x + 5) = 0
[/tex]
From here, we look for the solutions of the polynomial.
We have then:
Solution 1:
[tex] x + 3 = 0
x = -3
[/tex]
Solution 2:
[tex] x + 5 = 0
x = -5
[/tex]
Answer:
The solutions of the polynomial are given by:
[tex] x = -3
x = -5 [/tex]
The graph of f ′ (x), the derivative of f of x, is continuous for all x and consists of five line segments as shown below. Given f (–3) = 6, find the absolute maximum value of f (x) over the interval [–3, 0].
Graph of line segments increasing from x equals negative 4 to x equals negative 3, decreasing from x equals negative 3 to x equals 0, increasing from x equals 0 to x equals 3, constant from x equals 2 to x equals 4 and decreases from x equals 4 to x equals 5. x intercepts at x equals negative 4, x equals 0, x equals 5.
3
4.5
6
10.5
Answer
10.5
Step-by-step explanation:
The other answer is correct until solving for C. f(-3) = 6, not -6. So C = 21/2. This makes f(0) = 10.5. Local Max should occur at x intercepts on the f'(x) graph.
Answer: 10.5
Step-by-step explanation: The other answer is correct until solving for C. f(-3) = 6, not -6. So C = 21/2. This makes f(0) = 10.5. Local Max should occur at x intercepts on the f'(x) graph. A fraction is a number that shows how many equal parts there are. When we write fractions, we show one number with a line above (or a slash next to) another number. For example, 14, 1⁄4 and 1/4.are different ways of writing the same fraction (in this case a quarter). The top number tells us how many parts there are, and the bottom number tells us the total number of parts. The top part of the fraction is called a numerator. The bottom part of the fraction is called a denominator. For example, for the fraction 14 the 1 is the numerator, and the 4 is the denominator.
Which property is illustrated by this problem?
(3+4) + 5 = 3 + (4+5)
A. Associate property of addition
B. Additive identity
C. Commutative property of addition
Use the diagram of g | | h, with transversal f, to answer the questions.
A pair of corresponding angles is
a. angle 1 and angle 3
b. angle 4 and 2
c.angle 4 and angle 8
Angle 2 is blank angle 8.
a. greater than
b. less than
c. congruent to
A pair of same-side interior angles is......
a. angle 2 and angle 5
b. angle 4 and angle 7
c. angle 5 and angle 7
Answer:
1) Angle 4 and angle 8.
2) c. Congruent to.
3) a. Angle 2 and angle 5.
Step-by-step explanation:
1) When a transversal cuts the shown parallel lines, the angles that are in the same relative position are call correponding angles.
2) Angle 2 and 8 are Alternal internal angles, therefore they are congruent.
3) Angle 2 and angle 5 are on one side of the transversal, therefore, they are same-side interior angles.
Find the value of y when x equals -14 -2x-3y=49
So i need help (picture included)
Kenya has 2 hours to work a 100 problem math test. At what rate must she work in order to finish in 2 hours?
A) 0.83 problems per minute
B) 1.23 problems per minute
C) 1.35 problems per minute
D) 1.41
problems per minute
What does this quote tell us about the media’s influence during the Nixon investigation?
"We saw the public man in his first administration, and we were impressed. Now in about 300,000 words we have seen the private man, and we are appalled." – Clayton Kirkpatrick, editor of the Chicago Tribune, a newspaper that published the entire transcript of Nixon’s released communications
A. The media shared real evidence and their opinions on it, which probably influenced citizen opinion. B. The media disapproved of the president’s private actions but still supported and re-elected him. C.The media rallied behind the president because of his great record during his first term in office. D. The media could not publish or discuss real evidence related to the president or the investigation. please help me.
the answer for u is
2 hours=120 minutes
You simply just do 120/100=1.2
So the answer is B. 1.23 or 1.2 (rounded) per minute
A grid map marks the plot of Harold’s garden in meters. The coordinates of the quadrilateral-shaped property are G(–8, 3), A(4, 8), R(10, 0), and D(–2, –5). He wants to build a short fence around the garden. The perimeter of his garden is meters.
Answer:
46, i did the assignment on edge hope this helps! :)
Step-by-step explanation:
On a coordinate plane, quadrilateral D G A R is shown. Point G is at (negative 8, 3), point A is (4, 8), point R is at (10, 0), and point (negative 2, negative 5).
A grid map marks the plot of Harold’s garden in meters. The coordinates of the quadrilateral-shaped property are G(–8, 3), A(4, 8), R(10, 0), and D(–2, –5). He wants to build a short fence around the garden.
The perimeter of his garden is meters. 46
The Perimeter of garden as shown in the quadrilateral 46 units
Distance
The distance between two points is the amount of space between the points. From the quadrilateral:
[tex]AG=\sqrt{(8-3)^2+(4-(-8))^2}=13 \ units\\\\AR=\sqrt{(8-0)^2+(4-10)^2}=10 \ units\\\\GD=\sqrt{(-5-3)^2+(-2-(-8))^2}=10 \ units\\\\RD=\sqrt{(-5-0)^2+(-2-10)^2}=13 \ units\\[/tex]
Perimeter of garden = AG + AR + GD + RD = 13 + 10 + 13 + 10 = 46 units
The Perimeter of garden as shown in the quadrilateral 46 units
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The teacher bought new crayons for her class. She bought 7 packs of 9 crayons. She already has 17 crayons in her classroom. She wants to divide the crayons evenly between her 10 students. How many crayons will each student receive? Use c as the variable. Write an equation and solve the problem.
What is the range of the function f(x) = –2(6x) + 3?
A) (-oo,-2)
B) (-oo,3)
C) [-2,oo)
D) [3,oo
Answer:
The range of the function is (-∞,3)
B is correct.
Step-by-step explanation:
Given: [tex]f(x)=-2(6)^x+3[/tex]
It is an exponential function which coefficient is negative.
Exponential function: [tex]f(x)=ab^x+c[/tex]
If a>0 then range (c,∞)
If a<0 then range (-∞,c)
[tex]-2(6)^x+3\rightarrow ab^x+c[/tex]
[tex]a=-2[/tex]
[tex]c=3[/tex]
Range: (-∞,3)
Hence, The range of the function is (-∞,3)
if a circle has a diameter of 24 inches, which expression gives its area in square inches?
Show that all of the powers in the prime-power factorization of an integer n are even if and only if n is a perfect square
If you have 240 homies and the Crips rolls up on your block poppin 128 of yo homies, how many homies do ya got left?
Answer:
You'll have 112 blood homies left
240b-128b=112b
112
A certain species of tree grows an average of 3.1 cm per week. Write an equation for the sequence that represents the weekly height of this tree in centimeters if the measurements begin when the tree is 400 centimeters tall.
Answer:
h = 400 + 3.1(n - 1)
Step-by-step explanation:
this is an arithmetic sequence so instead the answer would be
h = 400 + 3.1(n - 1)
where h is the height of the tree after n weeks
what is 9^21 can somebody please help me
0.025 milliliters is the same as: cm3 and L
0.025 milliliters is equal to 0.025 cubic centimeters and 0.000025 liters. The conversion is based on the fact that 1 milliliter is equivalent to 1 cubic centimeter, and there are 1000 milliliters in 1 liter.
To convert 0.025 milliliters to cubic centimeters (cm³) and liters (L), we need to understand the relationships between these units.
Cubic Centimeters (cm³):
Since 1 milliliter is equivalent to 1 cubic centimeter, 0.025 milliliters is equal to 0.025 cubic centimeters.
Liters (L):
There are 1000 milliliters in 1 liter. Therefore, to convert milliliters to liters, we divide the volume in milliliters by 1000.
0.025 milliliters ÷ 1000 = 0.000025 liters.
In summary, 0.025 milliliters is equivalent to 0.025 cubic centimeters and 0.000025 liters.
The question probable may be:
What would be the value of 0.025 milliliters in cm^3 and also in L.
0.025 milliliters is equivalent to 0.025 cubic centimeters because 1 milliliter equals 1 cubic centimeter. Also, 0.025 milliliters is equal to 0.000025 liters as there are 1,000 milliliters in a liter.
Explanation:The student's question is: 0.025 milliliters is the same as how many cubic centimeters (cm3) and liters (L). This is a conversion problem involving units of volume. From the provided information, we understand that 1 milliliter (mL) is exactly equal to 1 cubic centimeter (cm3). Therefore, if the student has 0.025 mL, this is directly equivalent to 0.025 cm3 because the conversion factor between mL and cm3 is 1.
Furthermore, recalling that 1 liter is equal to 1,000 milliliters, and since we are given a volume in milliliters, we can convert this to liters by dividing by 1,000. Consequently, 0.025 mL is equal to 0.025 / 1,000 L, which simplifies to 0.000025 L.
Given this proportion, what ratio completes the equivilent proportion a/8?
[tex] \frac{a}{b}= \frac{8}{15} [/tex]
Please show your work so that I know how to do this.
suppose that w and t vary inversely and that t=1/5 when w=4. write a function that models the inverse variation and find t when w=9
A. t= 1/5w; 4/45
B. t= 1/5w; 1/5
C. t= 1/20w; 1/80
D. t= 4/5w;4/45
The answer is D. t=4/5w; 4/45
4x-7+7x=3x-1
Please help hurry for crutal test.
The solution to the equation is [tex]x = \frac{3}{4}[/tex] .
We start by rewriting the equation:
4x-7+7x=3x-1
Combine the x terms on the left side:
11x - 7 = 3x - 1
Isolate the x terms on one side of the equation. To do this, we’ll move the 3x term from the right side to the left side by subtracting 3x from both sides:
11x - 3x - 7 = -1
Simplify:
8x - 7 = -1
Add 7 to both sides to get rid of the constant term on the left side:
8x = 6
Divide both sides by 8 to find the value of x:
[tex]x = \frac{6}{8} = \frac{3}{4}[/tex]
Therefore, the solution to the equation is [tex]x = \frac{3}{4}[/tex] .
The ratio of the measures of the sides of a triangle is 9:15:5. If the perimeter of the triangle is 130 feet, find the measures of the sides.
∆ABC has side lengths of 10 units, 20 units, and 24 units. ∆XYZ is similar to ∆ABC, and the length of its longest side is 60 units. The perimeter of ∆XYZ is units. If the height of ∆ABC, with respect to its longest side being the base, is 8 units, the area of ∆XYZ is square units. NextReset
Final answer:
The perimeter of ΔXYZ is 25 units and the area of ΔXYZ is 40 square units.
Explanation:
In this problem, we are given that ΔABC has side lengths of 10 units, 20 units, and 24 units, and ΔXYZ is similar to ΔABC. We are also given the length of the longest side of ΔXYZ as 60 units. To find the perimeter of ΔXYZ, we need to add up the lengths of all its sides. Since the longest side of ΔABC is 24 units, and the longest side of ΔXYZ is 60 units, we can set up the following proportion:
24/10 = 60/x
Cross-multiplying gives us:
24x = 600
x = 600/24 = 25 units
Therefore, the perimeter of ΔXYZ is 25 units.
Now, to find the area of ΔXYZ, we can use the proportional relationship between the areas of similar triangles. Since the ratio of the longest sides is 60/24 = 5/2, the ratio of the areas will be (5/2)^2 = 25/4. Since the area of ΔABC is 1/2 times the base times the height, we can use the same formula for ΔXYZ with the corresponding measurements:
Area of ΔXYZ = (1/2) * 10 * 8 = 40 square units