Answer:
(5,7)
x = 5
y = 7
solve each system of equations by elimination. 3x-4y=-14 and 3x+2y=-2
Answer: x=6, y=8
Using elimination means that we eliminate one of the variables in both equations which help find out the other variable, which we then substitute to find the whole equation.
3x-4y=-14
+ 3x+2y=-2
=>-4y=-14
+ 2y=-2
=>-2y=-16
=>y=8
So to find x,
3x-4(8)=-14
=3x=-14+32
=x=18/3 so x=6
PLEASE MARK BRAINLIEST IF THIS HELPED!
HELP LOL!
Given ∠ BAD ≅ ∠BED, what can you conclude?
Responses
A Δ ABC is isosceles
B BD is the perpendicular bisector of AC
C AE ≅ DE
D ∠ ABD ≅ ∠ BDE
E Δ ABE is isosceles
Answer:
E. ∆ABE is isosceles
Step-by-step explanation:
Given ∠BAD ≅ ∠BED in ∆ABE you want to know what can be concluded.
Isosceles triangleAn isosceles triangle has sides of equal measure opposite angles of equal measure. The base angles A and E in triangle ABE are given as congruent, so we can conclude ∆ABE is isosceles.
Do this photos plisssssssss
the first question answer is 15/17
Chapter 10 Test
11. Nate uses a cube shaped bead with side lengths
measuring 6mm. Each bead has a circular hole in
the middle. The diameter of the circular hole is 3mm.
[not drawn to scale]
Answer:
Step-by-step explanation:
I'm guessing you need the volume of the bead with the hole.
We need to get the volume of two objects; a cube and a cylinder. We need the cylinder for the hole.
V(square) = 6^3
V(square) = 216 mm^3
V(cylinder) = pi(r^2)(h)
pi(1.5^2)(6)
Radius is half the diameter, and 6 represents the height, since it's as long as the cube.
V(cylinder) = 42.41 or 13.5pi
We need to do V(s) - V(c) to find the volume of the bead.
216 - 13.5pi = 173.588 or 173.59 or 173.6
I hope this helps!
help a girl out ??? :)
We can conclude that -
General exponential growth equation is : [tex]$f(x)=a(1+r)^{x}[/tex]General exponential decay equation is : [tex]$\frac {dN}{dt}= -\lambda N[/tex]Option {A} and option {E} represent the exponential decay.Option {B}, {E} and {D} represent exponential growth.What is exponential function?The exponential function is of the form -
f(x) = eˣ
Given is to write the exponential growth and exponential decay equation.
{ 1 } -
The general exponential growth equation is -
[tex]$f(x)=a(1+r)^{x}[/tex]
{ 2 } -
The general exponential decay equation is -
[tex]$\frac {dN}{dt}= -\lambda N[/tex]
Option {A} and option {E} represent the exponential decay. Option {B}, {E} and {D} represent exponential growth.
Therefore, we can conclude that -
General exponential growth equation is : [tex]$f(x)=a(1+r)^{x}[/tex]General exponential decay equation is : [tex]$\frac {dN}{dt}= -\lambda N[/tex]Option {A} and option {E} represent the exponential decay.Option {B}, {E} and {D} represent exponential growth.To solve more questions on functions, visit the link-
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The manager of a coffee shop record the number of costumers who put vanilla creamer or chocolate creamer in their coffee during one hour and classified them by age the results are shown in the table what percentage of these customers put chocolate creamer in their coffee during this hour
Throughout the hour, 70 percentage of customers add chocolate creamer to their coffee.
How do you find the percentage?Find the proportion of consumers who selected chocolate creamer and add up all of the customers who visited throughout the hour to determine the appropriate percentage.
The number of clients who selected chocolate creamer is calculated by dividing the total number of customers by 100.
Here it is,
For one hour, the manager of a coffee shop counted the number of patrons who added vanilla or chocolate creamer to their coffee.
The question given is:
Vanilla Chocolate
Age 18 - 30 2 6
Age 30 + 4 8
2 + 4 + 6 + 8 Equals 20 clients in this instance.
6 + 8 = 14 is the number of clients who select chocolate creamer.
Customers that used chocolate creamer made up: [14/20] / 100 = 70%
As a result, 70% of consumers at that time add chocolate creamer to their coffee.
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The complete question is:
The manager of a coffee shop recorded the number of customers who put vanilla creamer or chocolate creamer in their coffee during one hour and classified them by age. The results are shown in the table. Coffee Creamer. Vanilla. Chocolate. Age 18 to 30. 2, 6. Age 31 plus. 4, 8 What percentage of these customers put chocolate creamer in their coffee during this hour?
Answer:
70%
Step-by-step explanation:
i did the quiz lol
The Quick Meals Diner served 288 dinners. A child's plate cost $2.50 and an adult's plate cost $8.20. A total of $1,614.90 was collected. How many of each type of plate was served?
Round answers to the nearest whole person.
____ child plates were served.
___ adult plates were served.
The Quick Meals Diner served 131 child plates and 157 adult plates.
Let's use a system of two equations to represent the given information:
c + a = 288 (1) // The number of child and adult plates served add up to 288
2.5c + 8.2a = 1614.9 (2) // The total amount collected is the sum of the prices of all plates served
where c represents the number of child plates served and a represents the number of adult plates served.
We can use equation (1) to solve for c in terms of a:
c = 288 - a
Substituting this expression for c into equation (2), we get:
2.5(288 - a) + 8.2a = 1614.9
720 - 2.5a + 8.2a = 1614.9
5.7a = 894.9
a = 157
So, 157 adult plates were served. Substituting this value into equation (1), we get:
So, 157 adult plates were served. Substituting this value into equation (1), we get:
So, 131 child plates were served.
Therefore, The result is 131 child plates and 157 adult plates.
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Express the product of ((4)/(3)x-6) and ((5)/(6)x+(5)/(3)) as a trinomial in simplest form.
The product of ((4)/(3)x-6) and ((5)/(6)x+(5)/(3)) as a trinomial in simplest form is (10/9)x^2 + (-10/9)x + (-10).
To express the product of ((4)/(3)x-6) and ((5)/(6)x+(5)/(3)) as a trinomial in simplest form, we need to multiply the two expressions together and then simplify. Here are the steps:
1. Distribute the first term of the first expression to the second expression: (4/3)x * (5/6)x + (4/3)x * (5/3) = (20/18)x^2 + (20/9)x
2. Distribute the second term of the first expression to the second expression: -6 * (5/6)x + -6 * (5/3) = (-30/6)x + (-30/3)
3. Combine the like terms: (20/18)x^2 + (20/9)x + (-30/6)x + (-30/3) = (20/18)x^2 + (-10/9)x + (-30/3)
4. Simplify the fractions: (10/9)x^2 + (-10/9)x + (-10)
So the product of ((4)/(3)x-6) and ((5)/(6)x+(5)/(3)) as a trinomial in simplest form is (10/9)x^2 + (-10/9)x + (-10).
The product of ((4)/(3)x-6) and ((5)/(6)x+(5)/(3)) as a trinomial in simplest form is (10/9)x^2 + (-10/9)x + (-10).
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Write a sinusoidal function with amplitude 4, period 3???? and
vertical shift down 8 units.
A sinusoidal function is a type of periodic function that can be written in the form y = a sin(bx + c) + d, where a is the amplitude, b is the frequency, c is the phase shift, and d is the vertical shift.
Given the parameters in the question, we can plug them into the general form of a sinusoidal function to find the specific function.
Amplitude = 4
Period = 3π
Vertical shift = -8
The period of a sinusoidal function is related to the frequency by the equation period = (2π)/b. Therefore, we can solve for b to find the frequency:
3π = (2π)/b
b = (2π)/(3π)
b = 2/3
Plugging in the given values for amplitude, frequency, and vertical shift, we get the sinusoidal function:
y = 4 sin((2/3)x) - 8
This is the sinusoidal function that satisfies the given conditions. It has an amplitude of 4, a period of 3π, and a vertical shift down 8 units.
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A manufacturer of refrigerators must ship at least 100 refrigerators to its two West coast warehouses. Each warehouse holds a maximum of 100 refrigerators. Warehouse A holds 25 refrigerators already, while warehouse B has 20 on hand. It costs $12 to ship a refrigerator to warehouse A and $10 to ship one to warehouse B. Union rules require that at least 300 workers be hired. Shipping a refrigerator t warehouse a requires 4 workers, while shipping a refrigerator to warehouse b requires 2 workers. How many refrigerators should be shipped to each warehouse to minimize costs? what is the minimum cost? How many refrigerators should be shipped to each warehouse to minimize cost? What is the minimum cost?
The manufacturer should ship 0 refrigerators to warehouse A and 80 refrigerators to warehouse B to minimize costs. The minimum cost is $800.
The objective of the problem is to minimize the cost of shipping the refrigerators to the two warehouses while also meeting the requirements of shipping at least 100 refrigerators and hiring at least 300 workers. This can be formulated as a linear programming problem with the following decision variables:
x1 = the number of refrigerators shipped to warehouse A
x2 = the number of refrigerators shipped to warehouse B
The objective function is the total cost of shipping the refrigerators:
minimize 12x1 + 10x2
The constraints are the requirements of shipping at least 100 refrigerators, hiring at least 300 workers, and the maximum capacity of each warehouse:
x1 + x2 >= 100
4x1 + 2x2 >= 300
x1 <= 75 (100 - 25)
x2 <= 80 (100 - 20)
Using the graphical method, we can plot the constraints and find the feasible region. The optimal solution will be at one of the corner points of the feasible region.
After plotting the constraints and finding the feasible region, we can evaluate the objective function at each of the corner points to find the minimum cost. The corner points and their corresponding costs are:
(75, 0) -> 12(75) + 10(0) = $900
(0, 80) -> 12(0) + 10(80) = $800
(50, 100) -> 12(50) + 10(100) = $1700
(60, 90) -> 12(60) + 10(90) = $1740
The minimum cost is $800, which occurs when 0 refrigerators are shipped to warehouse A and 80 refrigerators are shipped to warehouse B.
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Given sin A = and that angle A is in Quadrant I, find the exact sec A in simplest radical form using a rational denominator
For 50pt
Answer: Read the step by step explanation
Step-by-step explanation:
Since sin A = , we can use the Pythagorean identity to find cos A:
cos A = √(1 - sin²A) = √(1 - ( )²) = √(1 - ) = √()
Since A is in Quadrant I, both sin A and cos A are positive. Therefore, we can use the definition of secant to find sec A:
sec A = 1/cos A = 1/√() = √()/
To simplify the expression, we can rationalize the denominator by multiplying both the numerator and denominator by √():
sec A = (√()/)(√()/√()) = √()/ =
Therefore, the exact secant of A in simplest radical form using a rational denominator is .
Please help meeeeeeeeee
The answer of the given question based on the Equation is given the solution to the given equation is n = 21/4.
What is Quadratic equation?A quadratic equation is type of equation in an algebra that involves variable (usually represented by x) that raised to the second power (i.e., squared). The general form of the quadratic equation are given,
[tex]ax^2+bx+c = 0[/tex]
The highest power of variable is 2, hence , name "quadratic".
To solve this equation, we can start by simplifying each of the terms on both sides of the equation:
3n + √(n² + 8) + 3√(n² + 8) - √(n² + 8) = 8
Combining like terms, we get:
3n + 3√(n² + 8) = 8
Subtracting 3√(n² + 8) from both sides, we get:
3n = 8 - 3√(n² + 8)
Dividing both sides by 3, we get:
n = (8/3) - (√(n² + 8)/3)
Now, we can rearrange this equation to isolate the radical term on one side of the equation:
√(n² + 8)/3 = (8/3) - n
by Squaring both the sides of equation, we get:
n² + 8 = 64/9 - (16n/3) + n²
Simplifying this equation, we get:
16n/3 = 56/9
Dividing both sides by 16/3, we get:
n = 21/4
Therefore, the solution to the given equation is n = 21/4.
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100 POINTS IF YOU CAN HELP ME!!
Use the equation below to calculate the total cost of a payday loan for #6-8.
\Total Cost = Loan amount + finance charge ( 1 + Number of rollovers or renewals). Keep in mind, this does not include the initial loan cost, just the interest.
#6. Toby takes out a payday loan to pay for a medical bill that costs $450. The payday lender charges him $50 every two weeks. Toby has to roll over the loan 4 times before he can finally pay it off. What was the total cost of his loan?
7. Tabitha takes out a payday loan to pay for her son's emergency room bill that costs $300. The payday lender charges her $40 every two weeks. She has to roll over the loan 6 times before she can finally pay it off. What is the total cost of her loan?
8. Sariah takes out a payday loan to get a new set of tires in order to pass inspection. The bill is $500. She needs her car to get to and from work but does not have enough money in her savings to cover the bill so she takes out a payday loan. The payday loan will cost her $45 every two weeks. She has to roll over 7 times. What was the total cost of her loan?
Step-by-step explanation:
Toby's loan amount is $450 and the finance charge is $50 every two weeks. He rolls over the loan 4 times.
Total cost = $450 + ($50 x (1 + 4))
Total cost = $450 + ($50 x 5)
Total cost = $450 + $250
Total cost = $700
Therefore, the total cost of Toby's payday loan is $700.
Tabitha's loan amount is $300 and the finance charge is $40 every two weeks. She rolls over the loan 6 times.
Total cost = $300 + ($40 x (1 + 6))
Total cost = $300 + ($40 x 7)
Total cost = $300 + $280
Total cost = $580
Therefore, the total cost of Tabitha's payday loan is $580.
Sariah's loan amount is $500 and the finance charge is $45 every two weeks. She rolls over the loan 7 times.
Total cost = $500 + ($45 x (1 + 7))
Total cost = $500 + ($45 x 8)
Total cost = $500 + $360
Total cost = $860
Therefore, the total cost of Sariah's payday loan is $860
Answer:
#6.
Loan amount = $450
Finance charge = $50 every two weeks
Number of rollovers or renewals = 4
Total Cost = 450 + (50 x (1 + 4))
Total Cost = 450 + 250
Total Cost = $700
The total cost of Toby's loan is $700.
#7.
Loan amount = $300
Finance charge = $40 every two weeks
Number of rollovers or renewals = 6
Total Cost = 300 + (40 x (1 + 6))
Total Cost = 300 + 280
Total Cost = $580
The total cost of Tabitha's loan is $580.
#8.
Loan amount = $500
Finance charge = $45 every two weeks
Number of rollovers or renewals = 7
Total Cost = 500 + (45 x (1 + 7))
Total Cost = 500 + 360
Total Cost = $860
The total cost of Sariah's loan is $860.
Please help I’ll give brainliest
Answer:
[tex](5x-1)(x+4)[/tex]
Step-by-step explanation:
Given:
[tex]5x^2 +19x-4[/tex]
Factor the expression by grouping. First, the expression needs to be rewritten as [tex]5x^2 +ax+bx-4[/tex]. To find a and b, set up a system to be solved.
[tex]a+b=19[/tex]
[tex]ab=5(-4)=-20[/tex]
Since [tex]ab[/tex] is negative, a and b have the opposite signs. Since [tex]a+b[/tex] is positive, the positive number has greater absolute value than the negative. List all such integer pairs that give product [tex]-20[/tex].
[tex]-1,20[/tex]
[tex]-2,10[/tex]
[tex]-4,5[/tex]
Calculate the sum for each pair.
[tex]-1+20=19[/tex]
[tex]-2+10=8[/tex]
[tex]-4+5=1[/tex]
The solution is the pair that gives sum [tex]19[/tex].
[tex]a=-1[/tex]
[tex]b=20[/tex]
Rewrite [tex]5x^2+19x-4[/tex] as [tex](5x^2-x)+(20x-4)[/tex].
Factor out x in the first and 4 in the second group.
[tex]x(5x-1)+4(5x-1)[/tex]
Factor out common term [tex]5x-1[/tex] by using distributive property.
[tex](5x-1)(x+4)[/tex]
Therefore, [tex](5x-1)(x+4)[/tex].
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Solve the system of equations by graphing. Graph both equations on the coordinate plane even if they represent the same line.
The point where the two lines come together (1,1). Hence, x = 1 and y = 1 are the answers to the system of equations.
What are the names of equations?Algebraically speaking, an equation is a statement that shows the equality of two mathematical expressions. For instance, the two equations 3x + 5 and 14, which are separated by the 'equal' sign, make up the equation 3x + 5 = 14.
How Do You Solve an Equation System?The technique of solving a system of equations involves calculating the unknown variables while maintaining the equations balanced on both sides. We solve an equation system by identifying the value of the variable that makes the condition of all the provided equations true.
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5+5 x 5 is whattt EASY MATH 20 points
Answer:50
Step-by-step explanation:5+5=10 and 5 groups of 10 is 50
Answer:30
Step-by-step explanation:
5x5=25
25+5
30
O RATIONAL EXPRESSIONS Adding rational expressions with common der Subtract. (z)/(z^(2)+4z-12)-(2)/(z^(2)+4z-12) Simplify your answer as much as possible.
The solution to the given rational expressions is (z - 2)/(z^(2)+4z-12).
To subtract rational expressions with common denominators, we simply subtract the numerators and keep the same denominator.
In this case, our common denominator is (z^(2)+4z-12), so we can subtract/add the numerators:
So, we will subtract the numerators, (z) - (2), and keep the same denominator:
(z)/(z^(2)+4z-12)-(2)/(z^(2)+4z-12) = (z - 2)/(z^(2)+4z-12)
Now, we can simplify the numerator by combining like terms:
(z - 2)/(z^(2)+4z-12) = (z - 2)/(z^(2)+4z-12)
Since the numerator and denominator cannot be simplified any further, this is our final answer:
(z - 2)/(z^(2)+4z-12)
Therefore, the solution to the subtraction of the given rational expressions is (z - 2)/(z^(2)+4z-12).
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Find three consecutive odd integers such that the product of the second and third minus the product of the first and second is 34. (If there is no solution, enter NO SOLUTION.)
There is no solution to this problem.
To find the three consecutive odd integers, we need to use algebra. Let's first represent the three consecutive odd integers as x, x+2, and x+4. Then we can set up an equation based on the given information:
(x+2)(x+4) - (x)(x+2) = 34
Simplifying the equation gives:
x^2 + 6x + 8 - x^2 - 2x = 34
Combining like terms gives:
4x + 8 = 34
Subtracting 8 from both sides gives:
4x = 26
Dividing by 4 gives:
x = 6.5
However, since we are looking for odd integers, there is no solution to this problem. Therefore, the answer is NO SOLUTION.
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Is 5x^2+y=0 a direct variation
No, 5x^2+y=0 is not a direct variation.
What is a direct variation?Direct variation is a relationship between two variables, x and y, where y is directly proportional to x, meaning that as x increases, y increases in proportion to x, and as x decreases, y decreases in proportion to x.
The equation 5x^2+y=0 does not satisfy this relationship since y is not directly proportional to x. As x increases or decreases, y may change in a non-proportional manner due to the presence of the constant term.
An example of a direct variation equation is y = kx, where k is a constant. In this equation, y is directly proportional to x, with a constant of proportionality k.
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100 POINTS!! HELP!! MATH!!
Arrange in order from least to greatest (Radicals)
a. 4√3
b. 3√5
c. 5√2
d. 2√10
e. 2√13
f. 3√6
1. Classify each triangle by its side lengths and angle measurements. Circle the correct names.
Classify Using
Side Lengths
m
b.
Equilateral Isosceles
Math Day Or
Scalene
Classify Using
Angle Measurements
Acute Right Obtuse. Angel mea
There are three types of triangle according to sides and angles each.
What is a triangle?The triangle is a type of polygon having three sides, angles and vertices.
Classification of triangles :-
Based on sides :-
1) Scalene triangle :- A triangle with all different measurements of sides and angles are called a Scalene triangle.
2) Isosceles triangle :- A triangle with two of the sides and angles are congruent called an Isosceles triangle.
3) Equilateral triangles :- A triangle with all the same measurements of sides and angles is called an Equilateral triangle.
Based on angles :-
1) Acute angled triangle :- A triangle with all the angles less than 90°, are called acute angled triangle.
2) Obtuse angled triangle :- A triangle with all the angles greater than 90° and less than 180°, are called Obtuse angled triangle.
3) Right angled triangle :- A triangle with one angle equals 90° is called a Right angled triangle.
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7th grade math question pls answer a s a p will give brainlist thingy
Answer:
it’s 159 sorry
Step-by-step explanation:
10 to the second power is 10x10 which is 100 then 8 to the second power is 8x8 which is 64. 164-5 is 159, I apologize.
Evaluate the expression without using a calculator.
sin(2arccos(1/3))
Exact Form of the expression is mathematically given as
[tex]\sin \left(2 \arccos \left(\frac{1}{3}\right)\right)[/tex]
What is an expression?Generally, An expression is a combination of variables, numbers, operators, and/or functions that represent a value.
[tex]\sin \left(2 \arccos \left (\frac{1}{3}\right)\right)[/tex]
Evaluate[tex]$\arccos \left(\frac{1}{3}\right)$.[/tex]
sin (2 *1.23095941)
Multiply 2 by 1.23095941.
sin (2.46191883)
The result can be shown in multiple forms.
Exact Form:
[tex]\sin \left(2 \arccos \left(\frac{1}{3}\right)\right)[/tex]
Decimal Form:
0.62853936
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if you help me I will make another question with 300 points
a.) Use the table below to calculate the average percent change in population in California from 2000-2009.
b.) If California's population in 2009 was 37,000,000 and the population trend were to continue, what would the population be in the year 2015?
The exponential growth equation is x ( t ) = 37,000,000 ( 1 + 1.3567% )⁶ , where x ( t ) is the population in the year 2015 = 40,115,896
What is exponential growth factor?The exponential growth or decay formula is given by
x ( t ) = x₀ × ( 1 + r )ⁿ
x ( t ) is the value at time t
x₀ is the initial value at time t = 0.
r is the growth rate when r>0 or decay rate when r<0, in percent
t is the time in discrete intervals and selected time units'
Given data ,
Let the exponential growth equation be represented as x ( t )
Now , the average percentage change from the year 2000 - 2009 is calculated by
The total percentage = ( 1.97+1.71+1.65+1.42+1.22+1.02+1.07+1.22+0.93 )
The total number of years = 9 years
So , the average percentage change = total percentage / number of years
On simplifying , we get
The average percentage change = 12.21 / 9 = 1.35667 %
b)
The population in 2009 was 37,000,000
So , the population growth rate r = 1.35667 %
And , the population in the years 2015 is given by
The number of years n = 6 years
x ( t ) = 37,000,000 ( 1 + 1.3567% )⁶
On simplifying , we get
x ( t ) = 37,000,000 ( 1.013567 )⁶
x ( t ) = 40,115,896
Hence , the population in the year 2015 is 40,115,896
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The compound shape below is formed from rectangle ABDE and right-angled triangle BCD. What is the area of this shape? Give your answer in cm² and give any decimal answers to 1 d.p. A 4cm B 9 cm E 4 cm D 15 cm C Not drawn accurately
The area of the shape formed from rectangle ABDE is 78 cm².
How to find area of a rectangle?To find the area of the compound shape, we need to find the area of rectangle ABDE and triangle BCD separately and then add them.
The rectangle ABDE has a length of 15 cm (DE) and a width of 4 cm (AB). Therefore, its area is:
Area of rectangle = length x width = 15 cm x 4 cm = 60 cm²
The triangle BCD has a base of 4 cm (BC) and a height of 9 cm (BD). Therefore, its area is:
Area of triangle = 1/2 x base x height = 1/2 x 4 cm x 9 cm = 18 cm²
Now, add the areas of the rectangle and the triangle to find the total area of the compound shape:
Total area = Area of rectangle + Area of triangle = 60 cm² + 18 cm² = 78 cm²
Therefore, the area of the compound shape is 78 cm².
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A follow-up question will appear once you have correctly answered the ques Since p(-1)=0, write p(x) in the form p(x)=(x+1)q(x).
The polynomial p(x) in the form p(x) = (x+1)q(x), where q(x) is a polynomial of degree n-1.
Algebraic expressions called polynomials include coefficients and variables. Indeterminates are another name for variables. For polynomial expressions, we can do mathematical operations like addition, subtraction, multiplication, and positive integer exponents but not division by variables.
x2+x-12 is an illustration of a polynomial with a single variable. There are three terms in this example: x2, x, and -12.
Since we know that p(-1)=0, we can use this information to substitute -1 into p(x), giving us:
p(-1) = 0
We can then rearrange this equation to get:
0 = p(-1) = (x+1)q(x)
This gives us the form of p(x) that we are looking for:
p(x) = (x+1)q(x)
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whats the first step tp solve n/4=-12
PLEASE HELP PLSSS
a sequence of transformations that maps DOG to D'O'G' is a (answer choice) followed by a (answer choice)
answer choices:
1. rotation of about 180 degrees of the origin
2.rotation of about 90 degrees of the origin
3. translation 5 units right
4. translation 5 units left
The sequence of transformations that maps DOG to D'O'G' is a rotation of about 90 degrees of the origin, followed by a translation of 5 units right.
What is rotation?Rotation is a physical phenomenon where an object spins around an axis. It is a type of circular motion where an object moves in a circular path around a central point.
To accomplish this transformation, first, the point representing the letter D is rotated 90 degrees clockwise around the origin so that it is now pointing in the same direction as the letter O. After that, the point representing the letter D is translated 5 units to the right, resulting in the final transformation of DOG to D'O'G'.
Thus, the sequence of transformations that maps DOG to D'O'G' is a rotation of about 90 degrees of the origin, followed by a translation of 5 units right.
For more questions related to circular motion,
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1. In a dart tournament, the probabilities John,Sam and Grey will hit the target are 3/4, 1/2 and 4/5, respectively. Assuming the events each of them hits the target are independent, find the probability that
a) all three of them hit the target
b) none of them hit the target
c) only John hits the target
2. Plastic X has four red and two white marbles. Plastic Y has one green, two red and two white marbles. In a game, a die is thrown first and if the outcome is a number less than 3, a marble is chosen at random from plastic X. Otherwise, a marble is randomly chosen from plastic Y.
Draw a tree diagram to show all the possible outcomes of the game. Hence, find the probability that
a) a red marble is chosen from plastic X.
b) a white marble is chosen from plastic Y.
c) a red marble is chosen.
d) a marble is chosen from plastic Y if it is known that it is red.
1) the probability that all three of them hit the target is 3/10, none of them hit the target 1/40, only John hits the target 3/40, 2) a red marble is chosen from plastic X is 2/9, a white marble is chosen from plastic Y is 4/15, a red marble is chosen is 2/9, a marble is chosen from plastic Y if it is known that it is red is 2/5.
1. a) The probability that all three of them hit the target is the product of their individual probabilities:
P(all three hit the target) = P(John hits the target) × P(Sam hits the target) × P(Grey hits the target)
= (3/4) × (1/2) × (4/5)
= 12/40
= 3/10
b) The probability that none of them hit the target is the product of their individual probabilities of not hitting the target:
P(none hit the target) = P(John doesn't hit the target) × P(Sam doesn't hit the target) × P(Grey doesn't hit the target)
= (1 - 3/4) × (1 - 1/2) × (1 - 4/5)
= (1/4) × (1/2) × (1/5)
= 1/40
c) The probability that only John hits the target is the product of his probability of hitting the target and the other two's probabilities of not hitting the target:
P(only John hits the target) = P(John hits the target) × P(Sam doesn't hit the target) × P(Grey doesn't hit the target)
= (3/4) × (1 - 1/2) × (1 - 4/5)
= (3/4) × (1/2) × (1/5)
= 3/40
2. The tree diagram for this game is as follows:
Die
/ \
/ \
/ \
/ \
/ \
/ \
<3 >=3
/ \ / \
X Y X Y
/ \ / \ / \ / \
R W R W R W R W
a) The probability that a red marble is chosen from plastic X is the product of the probability of the die outcome being less than 3 and the probability of choosing a red marble from plastic X:
P(red from X) = P(die < 3) × P(red from X)
= (2/6) × (4/6)
= 8/36
= 2/9
b) The probability that a white marble is chosen from plastic Y is the product of the probability of the die outcome being greater than or equal to 3 and the probability of choosing a white marble from plastic Y:
P(white from Y) = P(die >= 3) × P(white from Y)
= (4/6) × (2/5)
= 8/30
= 4/15
c) The probability that a red marble is chosen is the sum of the probabilities of choosing a red marble from plastic X and from plastic Y:
P(red) = P(red from X) + P(red from Y)
= (2/9) + (4/15)
= 10/45
= 2/9
d) The probability that a marble is chosen from plastic Y if it is known that it is red is the probability of choosing a red marble from plastic Y divided by the probability of choosing a red marble:
P(Y | red) = P(red from Y) / P(red)
= (4/15) / (2/9)
= 12/30
= 2/5
To learn more about probability here:
https://brainly.com/question/13604758#
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[SOLVED!]
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[tex] \frac{ \sqrt{7} }{ \sqrt{3x} } [/tex]