Do the circles having the equations (x - 2)2 + y2 = 4 and (x + 2)2 + y2 = 4 intersect on the Cartesian plane? If so, where do they intersect?
Answers
Answer: (0,0)
Step-by-step explanation:
[tex]\displaystyle\\\left \{ {{(x-2)^2+y^2=4} \atop {(x+2)^2+y^2=4}} \right. \\Hence,\\(x-2)^2+y^2=(x+2)^2+y^2\\(x-2)^2=(x+2)^2\\x^2-2*x*2+2^2=x^2+2*x*2+2^2\\-4x=4x\\-4x+4x=4x+4x\\0=8x\\[/tex]
Divide both parts of the equation by 8:
[tex]0=x[/tex]
Hence,
[tex](0+2)^2+y^2=4\\2^2+y^2=4\\4+y^2=4\\y^2=0\\y=0\\Thus,\ (0,0)[/tex]
Answer:
The two circles intersect at one and only point A(0 , 0)
Step-by-step explanation:
Let ς₁ be the circle of equation :
ς₁ : (x - 2)² + y² = 4
and ς₂ be the circle of equation :
ς₂ : (x + 2)² + y² = 4
Consider the point M (x , y) ∈ ς₁∩ς₂
M ∈ ς₁ ⇔ (x - 2)² + y² = 4
M ∈ ς₂ ⇔ (x + 2)² + y² = 4
M (x , y) ∈ ς₁∩ς₂ ⇒ (x - 2)² + y² = (x + 2)² + y²
⇒ (x - 2)² = (x + 2)²
⇒ x² - 4x + 4 = x²+ 4x + 4
⇒ - 4x = 4x
⇒ 8x = 0
⇒ x = 0
Substitute x by 0 in the first equation:
(0 - 2)² + y² = 4
⇔ 4 + y² = 4
⇔ y² = 0
⇔ y = 0
Conclusion:
The two circles intersect at one and only point A(0 , 0).
Related Questions
Hugo grapes triangle PQR and (Rt*T<3,1>)(truabgle PQR), where the equation of the line t is y=2, made exactly one error. Explain Hugo’s error
Answers
The Hugo's error is that , he did the translation incorrectly. He should have translated triangle by 3 unit right and then 1 unit up.
What is a triangle?In geometry, a triangle is defined as the shape which has three sides and also has three angles. We can say that a triangle is a type of polygon with three sides and three vertex. Triangle follows angle sum theorem.
Triangle Angle-Sum TheoremAccording to triangle Angle Sum theorem, the measurement of the sum of all interior angles of a triangle is always equals to 180°. That means, For a given triangle say ΔABC if ∠A, ∠B and ∠C are the interior angles then their sum i.e. ∠A + ∠B + ∠C = 180°.
Some important formula of triangles:
Area of triangle = 1/2 . base .heightPerimeter of triangle = sum of side lengthsNumber of vertices = 3Number of edges = 3In the question given,
the equation of line is y=2
The Hugo's error is that , he did the translation incorrectly. He should have translated triangle by 3 unit right and then 1 unit up.
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The complete question is :
Hugo grapes triangle PQR and (Rt*T<3,1>)(Δ PQR), where the equation of the line t is y=2, made exactly one error. Explain Hugo’s error.
use the given conditions to write an equation for the line. passing through (−9,2) and parallel to the line whose equation is
Answers
The given conditions to write an equation for the line passing through (−9,2) and parallel to the line whose equation is y = −3x+ 2.
What is an equation?There are many different methods to define an equation. The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign. Mathematical algebraic equations typically include one or more variables.
More than one variable may be present in a linear equation. An equation is said to be linear if the maximum power of the variable is consistently 1. Another name for it is a one-degree equation.
[tex]$$We have the equation of a parallel line and a point which it passes through. To write the equation of the line in point-slope form, we will use the following formula:y−y1=m(x−x1)We know that the slope of parallel lines are same and we are given the equation for parallel line, y=−3x+2$$[/tex]
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Describe in words where cube root of 70 would be plotted on a number line.
A Between 3 and 4, but closer to 3
B Between 3 and 4, but closer to 4
C Between 4 and 5, but closer to 4
D Between 4 and 5, but closer to 5
Answers
Answer:
C Between 4 and 5, but closer to 4
Step-by-step explanation:
cube root of 70 is 4.1212
a charity benefit is attended by 25 people and three gift certificates are given away as door prizes: one gift certificate is in the amount of $100, the second is worth $25 and the third is worth $10. assuming that no person receives more than one prize, how many different ways can the three gift certificates be awarded?
Answers
Number of ways that the three gift certificates can be awarded = 13800 ways
There are a total of 25 people attended the charity benefit. There are three gift certificates: one gift certificate is in the amount of $100, the second is worth $25 and the third is worth $10.
Assume that no person receives more than one prize.
One of the 25 people can get gift certificate of $100.
⇒ 25 ways for $100 gift certificate.
Then remaining 24 people are considered for further counting.
One of the 24 people can get gift certificate of $25.
⇒ 24 ways for $25 gift certificate.
Now there are 23 people remained.
One of the 23 people can get the $10 gift certificate.
⇒ 23 ways for $10 gift certificate.
Therefore, Number of ways that the three gift certificates can be awarded = 25 x 24 x 23 = 13800 ways.
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the scores on a statistics test had a mean of 81 and a standard deviation of 9. one student was absent on the test day, and his score wasn’t included in the calculation. if his score of 84 was added to the distribution of scores, what would happen to the mean and standard deviation?
Answers
Considering the concepts of the mean and the standard deviation, we have that:
The mean would increase.The standard deviation would remain constant.What are the mean and the standard deviation of a data-set?The mean of a data-set is given by the sum of all values in the data-set, divided by the number of values.The standard deviation of a data-set is given by the square root of the sum of the differences squared between each observation and the mean, divided by the number of values.When the measure of 84 is added, we have that:
A measure greater than the mean is added, hence the mean would increase.The difference squared between 84 and the mean of 81 is of 9, which is the same as the standard deviation, which would remain constant.More can be learned about the mean and the standard deviation of a data-set at https://brainly.com/question/26941429
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An angle measures 84.2° less than the measure of its supplementary angle. What is the measure of each angle?
Answers
The measure of the supplementary angles are 48° and 132°.
Let the measure angle be x.
Its supplementary angle will be x + 84
We know that the sum of supplementary angles is 180°.
So, we get the equation as:
x + x + 84 = 180
Combining the like terms, we get that:
2 x + 84 = 180
Subtract 84 from both sides, we get that:
2 x = 180 - 84
2 x = 96
Divide both sides by 2, we get that:
x = 96 / 2
x = 48°
x + 84 = 48+ 84 = 132°
Therefore, we get that, the measure of the supplementary angles are 48° and 132°.
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π x 910(10)
PLEAS ENEMOPOEJDHE HELP
Answers
Answer:
The correct is the 9100πx
which type of transformation preserves the symmetry of an even function f(x) but does not preserve the symmetry of an odd function g(x)?vertical translationhorizontal translationreflection over the x-axisreflection over the y-axis
Answers
The type of transformation that preserves the symmetry is Vertical translation.
For instance, a parabola is still symmetric about the y-axis if you move it up. It loses its symmetry if you move it to the left or right. Reflection keeps both even and odd functions symmetrical.
What is the difference between even and odd function ?The symmetry of a function is described using the terms even and odd. On a graph, an even function is symmetric about the y-axis. An odd function has symmetric behavior around a graph's origin [tex](0, 0)[/tex]. This means that if you rotate an odd function 180 degrees around the origin, the function you started with will still exist.
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an equilateral triangle has three congruent sides that measure 1.5 inches on each side. what is the perimeter of the triangle?
Answers
The perimeter of the triangle is 4.5inches.
Equilateral Triangle : can be defined as a triangle having all three sides equal.
Perimeter of triangle is defined as the sum of the lengths of the three side.
Perimeter of triangle is denoted by 3x(side).
Given that the side of the triangle is 1.5 inches
Perimeter = 3x(1.5)
Perimeter=4.5 inches
Therefore , The Perimeter of the triangle is 4.5 inches .
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How can u determine whether a relation represented as an equation is a function
Answers
It can be determined that a relation represented as an equation is a function if and only if for each value on x-axis, there is a corresponding value on Y-axis.
which also signifies that for each value of x , there is a value of y which exists and is real.
A function is a mapping from one set to another such that nothing in the first set is mapped to more than one thing in the second set.
Or in simple words if there is no corresponding value of y for any x, then that is not a function.
For example,
[tex]x^{2} +y^{2}[/tex]=1
when the value of x is 0 , then value of y is 1 or -1, Thus, it will not be a function.
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The cost of one pound of grapes, g, is 15 cents more than one pound of apples, a. The cost of one pound of
bananas, b, is twice as much as one pound of grapes. Write an equation that represents the cost of one pound of bananas in terms of the cost of one pound of apples
Answers
An equation that represents the cost of one pound of bananas in terms of the cost of one pound of apples is,
⇒ b = 2a + 30
What is Multiplication?
To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.
Given that;
Cost of one pound of grapes = g
Cost of one pound of apples = a
Cost of one pound of banana = b
Since, The cost of one pound of grapes is 15 cents more than one pound of apples.
It can be written as;
g = a + 15 .... (i)
And, The cost of one pound of bananas is twice as much as one pound of grapes.
It can be written as;
b = 2g ..... (ii)
To find an equation that represents the cost of one pound of bananas in terms of the cost of one pound of apples as,
Put the value of g from (i) in (ii) we get,
b = 2 ( a + 15 )
b = 2a + 30
Hence, An equation that represents the cost of one pound of bananas in terms of the cost of one pound of apples is,
⇒ b = 2a + 30
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A skin on skin 63 photos in a minute if it’s skins photos at a consistent rate it can scan bring photos in 21 minutes
Answers
When it skins photos at a consistent rate, the number of photos in 21 minutes will be 1323 photos.
How to calculate the value?From the information, it should be noted that the skin on skin 63 photos in a minute.
Therefore, the number of photos that can be skinned at a particular minutes will be illustrated as:
p = 63m
where p = number of photos
m = number of minutes
Therefore, it should be noted that using p = 63m. The appropriate number of photos will be:
p = 63m
p = 63 × 21
p = 1323 photos
Therefore, when it skins photos at a consistent rate, the number of photos in 21 minutes will be 1323 photos.
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Mariana is younger than yaritza. their ages are consecutive odd integers. find mariana's age if the sum of mariana's age and 5 times yaritza's age is 100.
Answers
Translating the given word problem into a set of linear equations, Mariana's age is 15 years old.
Translate the given word problem into algebraic equations.
Let x be Mariana's age
Let y be Yaritza's age
Mariana is younger than Yaritza, their ages are consecutive odd integers.
Since the difference of consecutive odd integers is 2, then:
y = x + 2 ....... (1)
Sum of Mariana's age and 5 times Yaritza's age is 100.
x + 5y = 100 ..... (2)
Substitute equation (1) to equation (2)
x + 5y = 100
x + 5(x+2) = 100
6x + 10 = 100
6x = 90
x = 15
Thus, Mariana's age is 15 years old.
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Answer:
15
Step-by-step explanation:
i just got it right on delta
50 points mathamatics please help
Answers
Answer:
Option B: 6342
Step-by-step explanation:
Answer: 6342
Step-by-step explanation:
906 x 7 = 6342
Solve for the value of x in the diagram below.
Answers
Step by step
It appears they are showing two pairs of congruent adjacent angles. One set is showing each at 40 degrees.
2 x 40 = 80.
We know the supplemental angle is 180 degrees. 180 - 80 = 100 for the second set that we are looking for.
Since x and it’s adjacent angle are congruent, or equal, we divide 100 by 2 equal parts = 50 degrees each. So x = 50 degrees.
$600 son repartidos entre 3 amigos en la razón (2w + 3) : (w + 2) : (3w + 4), en donde w es un número positivo.
a) Si la menor parte es $125, forma una ecuación en términos de w y resuélvelo.
b) Luego, expresa la razón en la forma más simple.
c) Los 3 amigos deciden donar $50 cada uno a una caridad. Determina la razón de sus partes luego de la donación
Answers
The equation will be (2w ,+ 3) + (w + 2) + (3w + 4) = 600
The ratio in lowest term will be 2:1:3
When they donate $50, the ratio will be 1:4.
How to calculate the value?a. The equation based on the information will be:
(2w + 3) + (w + 2) + (3w + 4) = 600
6w + 9 = 600
6w = 600 - 9
6w = 591
Divide
w = 591/6
w = 98.5
b. Therefore, (2w + 3) = 2×98.5 + 3 = 200
(w + 2) = 98.5 + 2 = 100.5
(3w + 4) = 3(98.5) + 4 = 299.5
The ratio in lowest term will be 2:1:3.
c. When they donate $50, the ratio will be:
= (50 × 3)/600
= 150/600
= 1:4
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Error Analysis A worker in a silver mine descends 78 feet. Use an integer to represent the change in the worker's position.
Answers
An integer to represent the change in the worker position is -78
If the worker is descending, he is going down.The change in his position could be marked on a graph by translating the original point down by 60 units. Integers are a set of numbers that include the positive whole numbers (1,2,3,4,5,....), their opposites (-1,-2,-3,-4,-5,...) are zero. This number line shows the integers from -5 to 5 .You can use integers to help represent many real - world situations, such as:Increase and decreases in temperature.Profits and losses of moneyLocations above and below sea level.Hence, An integer to represent the change in the worker position is -78
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Im doing geometry, I forgot how to do this.
Answers
Answer:
12
Step-by-step explanation:
You have a right triangle, so use the Pythagorean theorem.
a² + b² = c²
5² + b² = 13²
25 + b² = 169
b² = 144
b = 12
researchers are investigating whether taking aspirin regularly reduces the risk of heart attacks. four hundred men participate in the study. the men are divided randomly into two groups: one group takes aspirin pills, and the other group takes placebo pills (a pill with no aspirin in it). the men each take one pill a day, and they do not know which group they are in. at the end of the study, researchers will count the number of men in each group who have had heart attacks. identify the explanatory and response variables in this situation.
Answers
Explanatory variable: The type of pill the men took each day.
Response variable: Whether a subject had a heart attack.
We have been given that :
Participated candidates are 400
Men are divided randomly so we find out explanatory and response variable.
The explanatory variable is the variable that is manipulated by the researcher. Explanatory Variable also known as the independent or predictor variable, it explains variations in the response variable; in an experimental study, it is manipulated by the researcher.
Response variable: Response Variable is the result of the experiment where the explanatory variable is manipulated. It is a factor whose variation is explained by the other factors. Response Variable is often referred to as the Dependent Variable or the Outcome Variable.
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-20=4x-6x
solve equation
Answers
Answer:
X=10
Step-by-step explanation:
-20=4x-6x
4x-6x=-20
[tex]\frac{-2x}{-2} =\frac{-20}{-2}[/tex]
X=10
Answer:
x = 10
Step-by-step explanation:
STEPS FOR SOLVING LINEAR EQUATION
−20=4x−6x
Combine 4x and −6x to get −2x.
−20=−2x
Swap sides so that all variable terms are on the left hand side.
−2x=−20
Divide both sides by −2.
x=
−2
−20
Divide −20 by −2 to get 10.
x=10
If segment RS has endpoint R(5,1) and midpoint M(1,4), what will be point S?
Answers
Answer:
S(-3,7)
Step-by-step explanation:
Rise/Run
M(1,4) R(5,1)
1+run=5 4+rise=1
run=4 rise= -3
1-4= -3 4+3=7
work out the surface area of the prism
Answers
The surface area of the prism is 200 cm².
The surface area of the prism is given by the formula:
Surface area (S) = 2 B + p h
where B is the area of base of prism
p = perimeter of base
h = height of the prism.
Perimeter = 2(5 + 3) cm
p = 16 cm
B = 5 cm × 4 cm = 20 cm²
h = 10 cm
Substituting it in the formula, we get that:
S = 2 B + p h
S = 2 (20) + (16) (10)
S = 40 + 160
S = 200 cm²
Therefore, we get that, the surface area of the prism is 200 cm².
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The altitude a (in feet) of a plain t minutes after liftoff is given by a= 3400t + 600. How many minutes after liftoff is the plane at an altitude of 21,000 feet?
Answers
The number of minutes after liftoff of the plane at an altitude of 21,000 feet is 6 minutes
What is a function?A function can be defined as an expression or law that shows the relationship between a dependent and independent variable.
Given the function;
a= 3400 t + 600
Where;
a is the altitude in feett is the time in minutesIf the altitude is 21000 feet, let's determine the time
Substitute the value into the function
21000 = 3400t + 600
collect like terms
21000 - 600 = 3400t
20400 = 3400t
Make 't' the subject
t = 20400/ 3400
t = 6 minutes
Thus, the number of minutes after liftoff of the plane at an altitude of 21,000 feet is 6 minutes
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Hello I will AWard Brainlist !!! Help its A Math Question Please Help I will AWard Brainlist thanls so much !!!
Answers
The lengths 9, 9 / 2 and 9√3 are not part of a 30 - 60 - 90 right triangles. (Correct choice: A)
What set of measures are associated with a 30 - 60 - 90 right triangles?
Herein we must find what set of lengths are part of a 30 - 60 - 90 right triangle. In accordance with the Euclidean geometry, there are the following relationships for the sides of the 30 - 60 - 90 right triangle:
The longest leg is √3 times the length of the shortest leg.The hypotenuse is 2 times the length of the shortest leg.The hypotenuse is 2√3 / 3 times the length of the longest leg.Now we proceed to check if each set of sides belongs to a 30 - 60 - 90 right triangle:
Case 1
The length of the shortest leg of the triangle is 9 / 2, then the lengths of the longest leg and the hypotenuse are 9√3 / 2 and 9, respectively. (False)
Case 2
The length of the shortest leg of the triangle is 4, then the lengths of the longest leg and the hypotenuse are 4√3 and 8, respectively. (True)
Case 3
The length of the shortest leg of the triangle is 7, then the lengths of the longest leg and the hypotenuse are 7√3 and 14, respectively. (True)
Case 4
The length of the shortest leg of the triangle is 5 / 3, then the lengths of the longest leg and the hypotenuse are 5√3 / 3 and 10 / 3, respectively. (True)
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At the end of 1994 Walters Was half as old as his grandmother. The sum of the years in which they were born in 3838. How old will Walter be at the end of 1999?
Answers
The age of Walter at the end of year 1999 will be equal to 55 years.
What is algebra ?
Algebra is a branch of mathematics that deals with various symbols and the arithmetic operations such as addition , subtraction , etc.
Let's assume respective age of Walter and Walter's grandmother is x and y years respectively.
In 1994 , age of Walter was :
x = y / 2
or y = 2x
It is also given that the sum of years they were born is 3838.
The year Walter was born = (1994 - x)
The year Walter's grandmother was born :
= (1994 - y)
= 1994 - 2x (∵ y = 2x)
So , we can write an equation to find out Walter's age which is :
1994 - x + 1994 - 2x = 3838
3988 - 3x = 3838
3x = 3988 - 3838
x = 150 / 3
x = 50 years
or the age of Walter in 1994 is 50 years.
At end of 1999 Walter's age will be:
= 50 + 5.
= 55 years
Therefore , the age of Walter at the end of year 1999 will be equal to 55 years.
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HELP PLEASE I DON'T UNDERSTAND :[
Answers
Answer: the first option i believe
Step-by-step explanation:
please help me with this Qestion
Answers
Answer: 5.5 inches
Step-by-step explanation:
Using the formula for the area of a square, we can plug the known values in and solve.
a = x²
30 = x²
[tex]\sqrt{30 } =\sqrt{x^2}[/tex]
[tex]\sqrt{30 }[/tex] = x
5.477 ≈ x
Now, we will round to the nearest tenth.
5.477 ≈ 5.5 inches
An electrician charges $24 per hour and $36 for each hour of overtime. For a job, the electrician works 8 regular hours and overtime hours. He also charges $202 for materials. The total amount of the bill for the job is $538. How many overtime hours did the electrician work?
Fill in the blanks to create an equation that represents the situation.
Blanks-
24( )+ x+202=538
Answers
Answer:
hindi kasi ka nag aaral hhahhaha
One of the main financial services that is provided by a bank involves offering accounts where people can safely store their money for a period of time, all the while earning interest and being protected by insurance. What is this common financial service called? A. payment services B. savings C. loans D. financial planning
Answers
Banks are known to carry out different functions. The common financial service called savings.
Financial services is known to be a very wide term that comprises of all of the activities such as banking, investing, and insurance.
Financial services by banks includes savings, investment, etc. Savings is thee process whereby bank helps to keep the money of its customers. It is known to be the most common services offered by banks.
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Which quadratic inequality does the graph below represent?
Oy≤2x²-8x+3
O y≥ 2x² +8x+3
Oy≤2x²-8x-3
2 3 4 5 6 x
Answers
Answer:
A. y≤2x²-8x+3
Step-by-step explanation:
If you graph the function y≤2x²-8x+3, you would see that these both match.
The inequality y ≤ 2x² - 8x + 3 represents the given graph.
What is Inequality?An inequality is a relation which makes a non-equal comparison between two numbers or other mathematical expressions. It is used most often to compare two numbers on the number line by their size.
Here, The y-intercept is 3, not -3, so answer C is eliminated
Choose a point that is clearly in the shaded area or one that is clearly in the unshaded region
Here, I choose the point (0, 0) and substituted these values in the equation and since 0 < 3,
Option A is the correct answer
Thus, the inequality y ≤ 2x² - 8x + 3 represents the given graph.
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