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?
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).
Part of the proceeds from a garage sale was $330 worth of $5 and 520 bills. If there were 6 more $5 bills than $20 bills, find the number of each denomination.
The number of bills worth $20 is found to be 18 and the number of bills worth $5 is 12.
What is defined as the linear equation in two variables?A linear equation in two variables is one that is written in the form;
ax + by + c=0, where a, b, and c are real numbers and also the coefficients of x and y, i.e. a and b, are not equal to zero.
Now, as per the given question;
Let 'X' be the number of bills worth $20.
Let 'Y' be the number of bills worth $5.
Then, the total cost of the bills $330 is written as;
330 = 20X + 5Y
Now, if 6 more $5 bills is added to than $20 bills.
Y = X + 6, as there are 6 more $5 bills than $20 bills.
Substitute the value of Y in original equation.
330 = 20X + 5(X+6)
330 = 20X + 5X + 30
Further solving the equation.
300 = 25X
X = 300/25
X = 12 (number of bills worth $20)
Substitute the value in Y to find the number of bills worth $5.
Since, there are 6 more $5 bills than $20 bills, Y = 12+6 = 18
Thus, there are 18 number of bills worth $20.
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What is 9.4 divide. By 4 equal
Answer:2.35
Step-by-step explanation:
The value of the expression is 2.35.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
9.4 ÷ 4
= 9.4/4
= 94/(10 x 4)
= 94/40
= 2.35
Thus,
The value of the expression is 2.35.
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4(-15).
Which problem would give the same result? Select two options.
15 + 15 + 15 + 15
4 + 4 + 4 + 4
(–1)(15 + 15 + 15 + 15)
(–15) + (–15) + (–15) + (–15)
Answer:
the last two because it needs to be negative
Answer:
The last 2 options
Step-by-step explanation:
4(-15) = -60.
(–1)(15 + 15 + 15 + 15) = -60.
(–15) + (–15) + (–15) + (–15) = -60.
You walk down a hill for 45 meters. You accomplish this in 9 seconds. What is your velocity?______m/s.
Don't forget to include a negative sign if the answer is negative!
Ex: 10 m/s or -10 m/s. DO NOT USE DECIMALS.
Velocity is 5m/s.
In the given statement is :
You walk down a hill for 45 meters. You accomplish this in 9 seconds. What is your velocity? ______m/s.
Firstly, Let's know the:
What is Velocity?
Velocity refers to the rate of change in displacement with respect to time.
Furthermore, distance and displacement are the key points of the velocity.
Now, Calculate the velocity, by using formula of Velocity
Velocity = Displacement/ time
And, Velocity = 45/9 = 5m/s.
Therefore Velocity is 5m/s
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HELP ASAP
Find the coordinates of B
Answer:
the answer is B
Step-by-step explanation:
PLEASE HELP ME!
A research group surveyed 150 students. The students were asked how often they go to the movies and whether they prefer action movies or comedies. Their responses are summarized in the following table.
Answer:
72% go twice a month
60% prefer comedies
Step-by-step explanation:
45+63=108
108/150=0.72 ---> 72%
63+27=90
90/150=0.6 ---> 60%
Point is located at coordinates (-4, 3). What are the coordinates of each point?
The images of points are
Point B after the transformation of the point A is (4,- 3)Point C after the transformation of the point A is (2, -3)Point D after the transformation of the point A is (6,3)How to determine the image of point B after the transformation of the point A?From the question, we have the coordinate of point A to be
A = (-4, 3)
The sequence of transformations is given as:
180 degrees rotation around the origin
The rule of the above transformation is
(x, y)= (-x, -y)
So, we have
A' = (4, -3)
This means that
B = (4, -3)
Hence, the image of point B after the transformation of the point A is (4,- 3)
How to determine the image of point C after the transformation of the point A?From the question, we have the coordinate of point A to be
A = (-4, 3)
The sequence of transformations is given as:
Translation two units to the rightReflection across the x-axisThe rules of the above transformations are
Translation two units to the right
(x, y)= (x + 2 , y)
So, we have
A' = (-2, 3)
Reflection across the x-axis
(x, y)= (x, -y)
So, we have
A'' = (2, -3)
This means that
C = (2, -3)
Hence, the image of point C after the transformation of the point A is (2, -3)
How to determine the image of point D after the transformation of the point A?From the question, we have the coordinate of point A to be
A = (-4, 3)
The sequence of transformations is given as:
Reflection across the y-axisTranslation two units to the rightThe rules of the above transformations are
Reflection across the y-axis
(x, y)= (-x, y)
So, we have
A' = (4, 3)
Translation two units to the right
(x, y)= (x + 2 , y)
So, we have
A'' = (6, 3)
This means that
D = (6,3)
Hence, the image of point D after the transformation of the point A is (6,3)
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Help I will AWard Brainlist !!! its Math problem Please Help find the length of b.
thank you means alot.
[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]
Let's solve ~
Using Trigonometric ratios :
[tex]\qquad \sf \dashrightarrow \: \cos(45 \degree) = \dfrac{b}{ 4 } [/tex]
[tex]\qquad \sf \dashrightarrow \: \dfrac{1}{ \sqrt{2} } = \dfrac{b}{4} [/tex]
[tex]\qquad \sf \dashrightarrow \: b = \dfrac{4}{ \sqrt{2} } [/tex]
[tex]\qquad \sf \dashrightarrow \: b = 2 \sqrt{2} [/tex]
Mikey spent 20.25 on coffe tagt coat 4.50 per pound how many pounds did mikey buy
Answer:
4.5 lb of coffee
Step-by-step explanation:
4.5/20.25
a baker is building a rectangular solid box from cardboard to be able to safely deliver a birthday cake. the baker wants the volume of the delivery box to be 540 cubic inches. if the width of the delivery box is 3 inches longer than the length and the height is 4 inches longer than the length, what must the length of the delivery box be?
The length of the rectangular solid delivery box is 6 inches.
Volume of a rectangular solid, multiply its 3 dimensions: length x width x height. The volume is expressed in cubic units
It is given that, the volume of the delivery box is 540 cubic inches, the width of the delivery box is 3 inches longer than the length and the height is 4 inch longer than the length.
Width of the rectangular solid delivery box = (length + 3) inches
Height of the rectangular solid delivery box = (length + 4) inches
Now,
let us assume that the length of the rectangular solid delivery box is X.
So, Width = (X+3) inches and Height = (X+4) inches.
Volume of rectangular solid delivery box = Length × Width × Height
=> Length × Width × Height = 540 cubic inches.
After putting all the values in the above equation,
=> X × (X+3) × (X+4) = 540
=> X=6 inches
Therefore, the length of the rectangular solid delivery box is 6 inches.
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HELP ASAP DU TODAY...... WILL GIVE BRAINILIS.
Short Answer
Note: Your teacher will grade your responses to questions 6–7 to ensure that you receive proper credit for your answers.
1. Explain why (4, 1) is not a solution to the equation y = 3x +
2. Pizza costs $1.50 per slice. Use a table and an equation to represent the relationship between the number of slices of pizza bought and the total cost.
Answer: y = 3x+1
Step-by-step explanation: If (4,1) is a solution of y = 3x+1, that means if we plugin the respective values of (4,1), we should have an EQUALITY:
1 = 3(4) + 1
1 = 13 , which is wrong, then the point (4,1) is NOT a solution of y = 3x+1.
Evaluate the expression shown below and write your answer as a fraction in
simplest form.
3/4 - 3/10
corporation uses trucks to transport bottles from the warehouse to different retail outlets. gasoline costs are per mile driven. insurance costs are per year. calculate the total costs and the cost per mile for gasoline and insurance if the truck is driven (a) miles per year or (b) miles per year. (round the cost per mile to the nearest cent, $x.xx.)
The total cost = $5000 (Option A) and $9400 (Option B)
Cost per mile = $0.33 (option A) and $0.25 (Option B)
What is unitary method?A single unit's value can be determined from the values of multiple units, and multiple units' values can be determined from the values of single units using the unitary method.
Given:
Cost of gasoline for each mile driven = $0.20Cost of insurance for each year = $2000To find: Total costs and cost per mile, when the truck is driven (A) 15000 miles per year (B) 37000 miles per year.
Finding:
(A) By unitary method,
When the truck is driven 1 mile, cost of gasoline = $0.20
When the truck is driven 15000 miles, cost of gasoline = $ 0.20(15000) = $3000 in an year
Cost of insurance in an year = $2000
Thus, total cost = $ 3000 + $2000 = $5000
Now, for per mile cost:
Cost of gasoline = $0.20
Cost of insurance = $0.13
Thus, Cost per mile = $0.20 + $0.13 = $0.33
(B) Again, by unitary method,
When the truck is driven 1 mile, cost of gasoline = $0.20
When the truck is driven 37000 miles, cost of gasoline = $ 0.20(37000) = $7400 in an year
Cost of insurance in an year = $2000
Thus, total cost = $ 7400 + $2000 = $9400
Now, for per mile cost:
Cost of gasoline = $0.20
Cost of insurance = $0.5
Thus, Cost per mile = $0.20 + $0.5 = $0.25
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Find the coordinates of the other endpoint of the segment, given its midpoint and one endpoint. (Hint: Let (×,y) be the unknown endpoint. Apply the midpoint formula, and solve the
two equations for x and y.)
midpoint (=4,5), endpoint (0, - 4)
Answer:
See below
Step-by-step explanation:
For x : from end point to midpoint 0====> 4 is 4 units ...add 4 more to get x = 8 for other endpoint
For y 5====> -4 is - 9 add -9 more to midpoint to get y = -13
Using the following image, list four coplanar points in plane U.
The coplanar points in plane U are
Point P
Point W
Point S
Point L
Coplanar and Collinear pointsCoplanar points are three or more points which all lie in the same plane
Collinear points are the points that lie on the same straight line or in a single line.
In the image attached, points A, B, C, and D are coplanar points. This is because they all lie on the same plane.
Now,
In the given image, points P, W, and S all lie on the same straight line. Thus, they are collinear.
and
Points P, W, S, and L all lie on plane U. This means the points are coplanar.
Hence, the coplanar points in plane U are
Point P
Point W
Point S
Point L
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What is the value of the function when x = 8?
Enter your answer in the box.
Coordinate grid with a line graphed.
Answer:-4 is your answer
Step-by-step explanation: When x = 8 your y = –4 (which is the function)
The figure shows three quadrilaterals on a coordinate grid: A coordinate plane is shown. Figure Q is a quadrilateral with sides measuring 5 and 2. Figure S is a quadrilateral with sides measuring 5 and 2. Figure W is a quadrilateral with sides measuring 10 and 4. Which of the following statements is true about the three quadrilaterals? (4 points) a Q and W are similar but not congruent. b W and S are similar and congruent. c W and Q are similar and congruent. d Q and S are similar but not congruent.
Using the concepts of similarity and congruence, the correct statement is given by:
a. Q and W are similar but not congruent.
What are similar figures and what are congruent figures?Similar figures are figures that have the same angles and the same format, for example, all quadrilaterals are similar.Congruent figures are similar and also have equal side lengths.For this problem, we have that:
All the figures are quadrilaterals, hence all the figures are similar.Figures Q and S have the same side lengths, while Figure W has different side lengths. Hence Q and S are congruent, while Q and W and W and S are not.Hence the correct statement is given as follows:
a. Q and W are similar but not congruent.
From the two bullet points, we justify we the other statements are not correct.
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what is the value of 64 ⅔ ?
Answer:16
explanation:
=64⅔
=(4)3×⅔(there is 3 and 3 will be cancel)
=(4)²(4²=4×4)
=16 Ans
Clara knows she is 450 yards from the local swimming pool on the map on her phone the pool is 2/3 inch from her current location if her current locations is 4 inches from home on the same map how far is she from home
Clara is 2700 yards far from the home.
How to Calculate Yard and inches?In mathematics, yard and inches are two different units of length. we can say that yard is the one of the measurement of length. Conversion of yard in various quantities is as below:
In inches :1 yard = 36 inches
In feet :1 yard = 3 feet
In meters :1 yard = 0.914 meters
How to solve statement based questions ?For the statement based question first of all try to find out that what is given in the statement and what we have to find out. Now, try to form the statements in the mathematical notation and then solve the equations by performing certain mathematical and algebra operations according to need.
Now, for the given question :
as, Clara is 450 yards from the local swimming pool on the map on her phone and the pool is 2/3 inch from her current location.
Therefore, the pool distance is 450 / (2/3) = 675 yards
Now, distance of current location = 4 inches
Thus, Distance from the home = 675 × 4 = 2700 yards
Hence, Clara is 2700 yards far from the home.
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Can someone please help mee (20 points
brainliest!!!)
Answers:
16.50 for the first box
10 for the second box
======================================
Explanation:
Part (a)
Plug in x = 20 and solve for p.
0.2x+4p = 70
0.2*20+4p = 70
4 + 4p = 70
4p = 70-4
4p = 66
p = 66/4
p = 16.50
They should charge $16.50 per gallon if the demand is 20 million gallons.
------------------------
Part (b)
Let's say the price is initially $10 per gallon. The starting price could be anything you want.
Plug p = 10 into the equation and solve for x.
0.2x+4p = 70
0.2x+4*10 = 70
0.2x + 40 = 70
0.2x = 70-40
0.2x = 30
x = 30/(0.2)
x = 150
The demand is 150 million gallons if the price were $10 per gallon.
Now let's increase the price by $0.50 to get to p = 10.50
Let's solve for x based on this larger value of p.
0.2x+4p = 70
0.2x+4*10.50 = 70
0.2x+42 = 70
0.2x = 70-42
0.2x = 28
x = 28/(0.2)
x = 140
The demand is now 140 million gallons if the price were $10.50 per gallon.
The demand has gone down by 10 million gallons (since 150-140 = 10).
Maggie owes the clerk $85 dollars. Each of 5 friends will help pay the debt. How much will each friend pay? Find the solution and what it means in the context of the problem.
The equation 7(v-5)=-21 is solved in several steps below. For each step, choose the reason that best justifies it.
The solution to the equation is, v = 2.
See the steps explained below.
How to Solve an Equation?Given an equation, 7(v - 5) = -21, the following steps would be taken as shown below:
7(v - 5) = -21 ---> Given
7v - 35 = -21 ----> distribution property
7v - 35 + 35 = -21 + 35 -----> addition property of equality
7v = 14
Divide both sides by 7
7v/7 = 14/7 -----> division property of equality
v = 2
Thus, the solution to the equation as solved above is: v = 2.
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A: >
B: <
C: =
PLS HELP WILL MARK BRAINLIEST!!!!
Answer:
B: <
Step-by-step explanation:
2 1/4 is smaller than 3 1/4 because first of all, 2 is smaller than 3. Also, when you make both an improper fraction, than 2 1/4 will be 9/4 and 3 1/4 would be 13/4. 9/4 is smaller than 13/4.
Given the following piecewise defined functions, evaluate each of the problems below.
h(x) ={7, when x<0
{x+1, when 0 ≤x ≤4
{√x-1, when x>4
1.h(0)
2.h(10)
3.h(-3)
4.h(3)
The values of the functions are h(0) = 1, h(10) = 3, h(-3) = 7 and h(3) = 4
How to evaluate each of the function values from the piecewise function?The piecewise function is given as:
h(x) = {7, when x<0
{x+1, when 0 ≤x ≤4
{√x-1, when x>4
Next, we solve the function values
1. Function h(0)
This means that x = 0
To do this, we make use of h(x) = x + 1 because x= 0 is in its domain
So, we have
h(0) = 0 + 1
h(0) = 1
2. Function h(10)
This means that x = 10
To do this, we make use of h(x) = √x - 1 because x= 10 is in its domain
So, we have
h(10) = √10 - 1
h(10) = √9
h(10) = 3
3. Function h(-3)
This means that x = -3
To do this, we make use of h(x) = 7 because x= -3 is in its domain
So, we have
h(-3) = 7
4. Function h(3)
This means that x = 3
To do this, we make use of h(x) = x + 1 because x= 3 is in its domain
So, we have
h(3) = 3 + 1
h(3) = 4
Hence, the values of the functions are h(0) = 1, h(10) = 3, h(-3) = 7 and h(3) = 4
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Solve for x
-10x>=-100
Answer:
x>−10
Step-by-step explanation:
x = 100/9 ............
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What will be the location of the x value of R' after using the translation rule (x + 4, y - 7), if the pre-image R is located at ( 24, -13)
The location of the x value of R' after using the translation rule is 28
What will be the location of the y value of R' after using the translation rule?The translation rule is given as:
(x + 4, y - 7)
The pre-image of R is located at (24, -13)
Rewrite as
R = (24, -13)
When the translation rule is applied, we have:
R' = (24 + 4, -13 - 7)
Evaluate
R' = (28, -20)
Remove the y coordinate
R'x = 28
Hence, the location of the x value of R' after using the translation rule is 28
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Find the values of x and y.
(2x + 25)°
yº
(3x - 10)°
(They are angles btw)
Rewrite x^4y^2 − 2x^3y^3 using a common factor.
x^2y(xy − 2xy^2)
x^2y^2(x^2 − 2xy)
2xy^2(x^2 − x^2y)
2xy(x^3y − x^2y)
Answer:
x^2y^2(x^2 − 2xy) ..............
The rewritten polynomial of x⁴y² - 2x³y³ is x²y²(x²-2xy).
What is the greatest common factor?The greatest number that can divide the numbers in equal parts.
It is called as greatest common factor.
We have a polynomial,
x⁴y² - 2x³y³.
Factor out the common terms,
x⁴y² - 2x³y³,
= x²y²(x²-2xy)
Therefore, x²y²(x²-2xy) is the required expression.
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Chang wants to plant grass in his backyard. His backyard is in the shape of a rectangle. Its length is 32 feet and its width is 21 feet. Suppose each pack of seed covers 12 square feet. How many packs of seed will he need to cover the backyard?
Answer:
56 packs of seeds
Step-by-step explanation:
To find the area of Chang's backyard, we can use the formula for an area of a rectangle.
Area = length·width or A = lw
32·21 = 672 sq ft.
To find how many packets of seed he will need to cover the backyard, we can take the area of Chang's yard and divide it by how many square feet each pack of seed covers.
672/12 = 56
Chang will need 56 packs of seeds to cover the backyard.