(a) We see that it can be written as y' = (y²/(22+y²)) - (x/(22+y²))*y. (b) The equation -22ln|y| + ln|y² - xy| = x + C.
(a)
(1) The given equation is not separable, Bernoulli or homogeneous. To check if it is linear, we see that it contains a term y multiplied by x, which means it is not linear. Therefore, the equation is none of the above.
(2) The given equation is not linear, separable or homogeneous. To check if it is Bernoulli, we see that it can be written as y' = (y²/(22+y²)) - (x/(22+y²))*y. Here, the power of y is 2 which means it is not a Bernoulli equation. Therefore, the equation is none of the above.
(b) To find the general solution of equation (2), we first need to convert it into a separable equation. We can do this by multiplying both sides of the equation by (22+y²) and rearranging the terms, which gives us:
(22+y²)dy/dx = y² - xy
Now, we can separate the variables and integrate both sides as follows:
∫(22+y²)dy/(y² - xy) = ∫dx
To solve this integral, we can use partial fraction decomposition and write the left-hand side as:
∫(22/ y² - xy)dy + ∫(y²/ y² - xy)dy
After integrating, we get the following equation:
-22ln|y| + ln|y² - xy| = x + C
where C is the constant of integration. This is the general solution of the given equation (2).
In conclusion, the solution to the given problem involves determining the type of differential equation and then finding the general solution. It is important to show the work and steps involved in solving the problem in order to receive full credit. Failure to do so may result in point deductions.
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please help for points
Answer:
the answer is A
Step-by-step explanation:
did it not the long ago
Label the following rational/irrational phrases as Always (A), Sometimes (S) or Never (N). Enter your answers in numerical order w/ no spaces (ex:123).
How do I enter in this answer? I’ve tried both letters and numbers but it isn’t working & I’m getting frustrated. It tells me to use letters but in numerical order. I’m going to break this laptop in half.
On solving the provided question, we can say that The product of a rational number and an irrational number is an irrational number = > is always irrational
what is rational numbers?Any number that can be expressed as a ratio (or fraction) of two integers is said to be rational. A rational number is a fraction that has a nonzero denominator. 1/2, 1/5, and 3/4 are examples of rational numbers. Additionally a rational number, "0" may be expressed in a variety of ways, including 0/1, 0/2, and 0/3.
the answer of data from figure are -
The product of a rational number and an irrational number is an irrational number = > is always irrational, [tex]2 * \sqrt{2} = 2\sqrt{2}[/tex] is a irrational
the sum of a rational and an irrational is a rational number. => is always irrational [tex]2 + \sqrt{2} = (2+\sqrt{2})[/tex] is a irrational
The product of two irrational numbers is an irrational number. = > is always rational[tex]\sqrt{2}*\sqrt{2} = 2[/tex] is rational
The difference of a rational and a rational number is a rational number. => is always irrational [tex]3-\sqrt{2} = ( 3 - \sqrt{2} )[/tex] is a irrational
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Assignment
The values in the table represent a function.
f(x)
x
-6
7
4
3
-5
8
3
-5
.
-2
12
Use the drop-down menus to complete the
statements.
The ordered pair given in the first row of the table can
be written using function notation as
î
f(3) is
f(x) = -5 when x is
So on solving the provided question we cans ay that function f(3) is f(x) = -5 so x = 3
what is function?The subject of mathematics includes quantities and their variations, equations and related structures, shapes and their locations, and places where they can be found. The term "function" refers to the relationship between a set of inputs, each of which has an associated output. A connection between inputs and outputs in which each input leads to a single, distinct result is known as a function. Each function is given a domain and a codomain, or scope. Usually, f is used to denote functions (x). input is an x. There are four main types of functions accessible. based on the following factors: on functions, one-to-one functions, many-to-one functions, inside functions, and on functions.
here, we have
f(3) is f(x) = -5
so x = 3
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Solve the inequality for U.
65> 4u-11
The term "inequality" refers to a relationship between two expressions or values that is not equal to one another.
What is called inequality?Inequality is the relationship between two expressions or values that are not equal to one another.
The five inequality symbols used in mathematics are greater than symbol (>), less than symbol (), greater than or equal to symbol (), less than or equal to symbol (), and not equal to symbol ().
Use the steps below to resolve an inequality: Step 1: Remove all fractions by multiplying every phrase by the fractions' lowest common denominator. Step 2 Consolidate like terms on both sides of the inequality to simplify. Step 3: Add or subtract amounts to get the unknown on one side and the numbers on the other.
Therefore, the answer is [tex]$u \in(-\infty, 19)$[/tex].
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What is the area of the right triangle with base 5 cm and altitude 4cm?
The area of the right triangle with base 5 cm and altitude 4 cm will be 10 cm².
The area of right triangle is calculated using the formula -
Area = 1/2 × b × h. In the formula, the b is base of triangle and h is height of triangle.
Keep the values in formula to find the area of the right triangle.
Area = 1/2 × 5 × 4
Performing division on Right Hand Side of the equation
Area = 5 × 2
Performing division on Right Hand Side of the equation
Area = 10 cm²
Therefore, the area of right hand triangle will be 10 cm².
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got moved to a new class, no intro no subject, i dont know what kind of problem this is or how to solve it,, help pls!!!
Answer:94
Step-by-step explanation:
English is not my first language, so I don't know if you understand what I meant in the explanation.
A metalworker has a metal alloy that is 30% copper and another alloy that is 60% copper. How many kilograms of each alloy should the metalworker combine to create 50 kg of a 48% copper alloy?
If a metalworker has a metal alloy that is 30% copper and another alloy that is 60% copper. The amount of kilograms of each alloy is: 20kg of 30% copper alloy must be combined with 30kg of 60% copper alloy to obtain 50 kg of 48% copper alloy.
How to find the amount of kilograms?Let a be the amount of 30% copper alloy and b be the amount of 60% copper alloys. The combined alloys must be 50 kilograms.
a + b = 50 kg
The total copper in the mixture:
0.30a + 0.60b = 0.48(50)
Substitute by making use of the first equation
0.30(50-b) + 0.60b = 24
15 -0.30b + 0.60b =24
0.30b= 9
Divide both side by 0.30b
b = 9/0.30
b = 30
The amount of 30% copper alloy needed is:
a= 50-b
a = 50 -30
a = 20
Therefore 20 kg of 30% copper alloy must be combined with 30 kg of 60% copper alloy to obtain 50 kg of 48% copper alloy.
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Tonia eats 2 meals each day, breakfast and dinner. For breakfast, she always eats the same thing, and the total calories for each breakfast are 500. The total calories she ate for 5 days was 9,000.
What was the average number of calories Tonia consumed for dinner each day over the 5 days?
Answer: We know that Tonia eats 2 meals each day, breakfast and dinner. We also know that the total calories for each breakfast are 500.
If Tonia ate breakfast for 5 days, the total calories for breakfast would be 500 x 5 = 2500 calories.
We know that the total calories she ate for 5 days was 9000 and the number of calories for breakfast is 2500.
The number of calories for dinner over 5 days is 9000 - 2500 = 6500 calories.
To find the average number of calories Tonia consumed for dinner each day over the 5 days, we need to divide the total number of calories for dinner by the number of days:
average number of calories = 6500 / 5 = 1300 calories per day.
So Tonia consumed an average of 1300 calories per day for dinner over the 5 days.
Step-by-step explanation:
When the area in square units of an expanding circle is increasing twice as fast as its radius in linear units, the radius is.
1/π is the radius of an expanding circle that grows twice as fast as its radius in linear units.
What is area?The size of a region on a surface is measured in area. Surface area refers to the area of an open surface or the border of a three-dimensional object, whereas area of a plane region or plane area refers to the area of a form or planar lamina.
Here,
The area of a circle is: Ac = π×r² where r is the radius of the circle
If this area is expanding that mean Ac and r are a function of time and the speed is dA/dt and dr/dt can be found from the equation of the area
Then:
Ac = π×r²
dA/dt = 2×π×r×dr/dt
According to the problem statement
dA/dt = 2×dr/dt
By substitution
2×dr/dt = 2×π×r×dr/dt
Simplifying
1 = π×r
and
r = 1/π
The radius of expanding circle that is increasing twice as fast as its radius in linear units is 1/π.
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A word problem that can be olved by finding the number that have a 11 a a factor
Let the question be,
A group of friends raised money for a charity by selling 11 packs of cookies. They sold a total of 546 cookies. How many 11-packs of cookies did they sell?
The act of charity is the selfless, voluntary assistance provided to those in need as a humanitarian act. There are several charitable ideologies, many of which are religious in nature.
In this problem, we can find the number of 11-packs of cookies by dividing the total number of cookies by the number of cookies in each pack.
We know that:
The number of 11 cookies pack can be determined by:
546 cookies / 11 cookies/pack = 49.63636...
So the number of packs of cookies is 49. This means that 49 is the number that has 11 as a factor.
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If two sides of a triangle are 5 and 7 which would be the third side
Answer:
2 < x < 12
Step-by-step explanation:
given 2 sides of a triangle then the third side x is in the interval
difference of 2 sides < x < sum of 2 sides , that is
7 - 5 < x < 7 + 5
2 < x < 12
third side could be 3, 4, 5, 6, 7, 8, 9, 10, 11
The table below represents the number of power boats registered in the
given year. Using the equation for the line of best fit, which is a
good prediction for the number of powerboat registrations in 2013?
Answer:
provide the table please
How many Bijective functions can be defined from A to B if A |= N and B |= M?
A bijective function is a function that is both one-to-one and onto, meaning that it assigns a unique output to each input, and every output in the codomain is assigned by some input in the domain.
If A has N elements and B has M elements, and we want to find the number of possible bijective functions from A to B, we can use the following formula:
Number of bijective functions = (Number of functions from A to B) / (Number of one-to-one functions from A to B)
The number of functions from A to B is given by the number of ways to assign each element of set A to set B, which is [tex]M^N[/tex].
The number of one-to-one functions from A to B is given by the number of ways to assign a unique element from set B to set A, which is[tex]M!/(M-N)![/tex]
So, the number of bijective functions is:
[tex]M^N[/tex] / (M!)/(M-N)!
When A and B have the same cardinality, N = M, the number of bijective functions will be M!/(M!)/(M-M)! = 1, that is only one bijective function can be defined.When A and B have different cardinality, N ≠ M, the number of bijective functions will be[tex]M^N / (M!)/(M-N)! = 0[/tex], which means that no bijective function can be defined.Read more about the Bijective function:
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What are the 5 algebraic properties of equality?
The five algebraic properties of equality are: Reflexive, Symmetric, Transitive, Addition, and Multiplication properties
Reflexive property: For any real number a, a = a.Symmetric property: For any real numbers a and b, if a = b, then b = a.Transitive property: For any real numbers a, b, and c, if a = b and b = c, then a = c.Addition property of equality: For any real numbers a, b, and c, if a = b, then a + c = b + c.Multiplication property of equality: For any real numbers a, b, and c, if a = b, then a * c = b * c.These properties are the foundation of algebraic manipulation and are used to solve equations and simplify expressions.
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Macy made a 220 grooming dogs one day in her mobile grooming business she charges 60 per appointment and 40 earned in tips write an equation to represent the situation and solve the equation to determine how many appointments Messi had part B Logan made a profit of 300 as a mobile groomer he charge $70 per appointment and received $50 in tips but he had to pay a rental fee for the truck of $20 per appointment write an equation to represent the situation and solve the situation to determine how many appointments Logan had (32 points)
We can see that:
Part A: 3 appointments
Part B: 5 appointments
What is an equation?A mathematical equation is a formula that uses the equals sign to represent the equality of two expressions.
Part A
Let x = number of dog grooming appointments Macy had in one day.
Given information:
Charge per appointment = $60
Total amount earned = $220
Total amount of tips earned = $40
Create an equation with the given information:
⇒ 60x + 40 = 220
Solving the equation:
Subtracting 40 from bothsides, we have:
⇒ 60x + 40 - 40 = 220 - 40
⇒ 60x = 180
⇒ 60x ÷ 60 = 180 ÷ 60
⇒ x = 3 appointments.
Part B
Let x = number of dog grooming appointments Logan had.
Given information:
Charge per appointment = $70
Total amount earned = $300
Total amount of tips earned = $50
Rental fee per appointment = $20
Create an equation with the given information:
⇒ 70x - 20x + 50 = 300
Solve the equation:
⇒ 50x + 50 = 300
⇒ 50x + 50 - 50 = 300 - 50
⇒ 50x = 250
⇒ 50x ÷ 50 = 250 ÷ 50
⇒ x = 5 appointments.
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Point A has coordinates A(2,1). What is the image after a dilation centered at the origin with a scale factor of 2?
The coordinate of point A(2,1) after dilation of 2 will be (4,2).
What is dilation?Resizing an item uses a transition called dilation. Dilation is used to enlarge or contract the items. The result of this transformation is an image with the same shape as the original. However, there is a variation in the shape's size.
A coordinate plane is a 2D plane that is formed by the intersection of two perpendicular lines known as the x-axis and y-axis. A coordinate system in geometry is a method for determining the positions of the points by using one or more numbers or coordinates.
Given that Point A has coordinates A(2,1). The dilation of the point will be calculated as,
A(2,1) = A' ( 2 x 2, 2 x 1 ) = A'( 4,2)
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i need help pls!!!!!!!
The equation Y=3/4x+3/2 is a slope intercept form equation for line AB.
What is equation?An equation is a mathematical statement that two expressions are equal. It consists of two expressions separated by an equals sign and can contain numbers, variables, and operators. Equations are used to solve problems, make predictions, and describe relationships between different quantities. Equations can also be used to represent physical laws and other phenomena.
This equation is written in the form y=mx+b, where m is the slope of the line and b is the y-intercept of the line. In this equation,
the slope m is equal to 3/4 and the y-intercept b is equal to 3/2. The slope of the line AB is 3/4, so the line has a positive slope, and the y-intercept of the line AB is 3/2.
This equation can be used to find the coordinates of any point on the line AB, as well as the equation of the line itself.
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adding probabilities common core algebra i
The Poisson law states that the probability of at least 2 different changes daily is 0.0263. Thus, 0.0263% of changes happen twice or more each day.
Define probability.The mathematical method it explains for calculating probability calculates all the probabilities of something occurring in the setting of specific random events. A probability's proximity to the unit value and, conversely, its distance from zero can make one less comfortable in the outcome. The confidence level is based on how close the probability value is, which is calculated using a range from 0 and 1
Here,
The conditional probability function for X is the amount of times the incident occurs over a specific period of time.
In this experiment, the frequency, or x, at which an event occurs is counted.
The likelihood of the event happening throughout each period is equal.
The number of events in one period is independent of the number in other intervals.
The first step is to set the discrete stochastic process X to the number of website content updates.
Let's say that there are on average x content changes every day.
The Poisson distribution law states that the probability of at least 2 changes each day is 0.0263.
0.0263% of changes occuring twice or more as a result per day.
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Help asap! Ive tried many different things!
Answer: that realy saadddddddddd
Step-by-step explanation: 4xx 6y 9x
Answer: The slope is -1/5
The function f(x) is defined below. What is the end behavior of f(x)?
f(x) = 80x* 2 + 640 - 400х - 52
The end behavior will be as x approaches infinity, and negative infinity, f(x) approaches infinity.
What is a function?Function is a type of relation, or rule, that maps one input to specific single output.
The function f(x) is defined as:
→ f(x)= 80x* 2 + 640 - 400x - 52
We need the degree and the leading coefficient to determine the behavior.
Since our leading coefficients has a leading even degree of 5, and a positive number,
The function will Rises to the left and falls to the right.
The end behavior will be as x approaches infinity, and negative infinity, f(x) approaches infinity.
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After picking apples at Fruitville Orchards, Sidney stops at the orchard's market to get some fresh apple cider. She wants to drink a pint of cider at the orchard. She also wants to bring a pint of cider to each of her 5 friends later in the day. How many 1-quart jugs of apple cider should she buy?
Sidney should buy 3 1-quart jugs of cider.
What is mean by pint?
The pint is a liquid amount that is equal to one eighth of a gallon and it is also equal to one half of a quart.
How many 1-quart jugs of apple cider should Sidney buy?
Sidney wants to drink a pint of cider. She also wants to bring a pint of cider to each of her 5 friends.
So, she needs total 6 pints of cider.
As per standard metric unit, 1 liquid pint = 0.5 liquid quart
6 liquid pints = (6 × 0.5) liquid quart = 3 quarts
So, Sidney should by 3 quarts of apple Cider that means 3 amounts of 1 -quart jugs of cider.
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What is the exponential form of 2 into 2 into a?
The Exponential form of the given expression "2 into 2 into a" is represented as [tex]2^{2} \times a[/tex] , and the value is 4a .
The Expression is given as : " 2 into 2 into a" ;
mathematically the given expression can be written as : ⇒ [tex]2\times 2\times a[/tex] ;
By using the Law Of Exponents , which states that : when the base of the exponents are same the power gets added ;
we see that , the base number 2 is same , So , we add the power of 2 ;
So , on adding the power ,
we get ;
⇒ [tex]2^{2} \times a[/tex] ;
So, the exponential form is [tex]2^{2} \times a[/tex] ;
and the value of this exponential expression is 4a .
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While playing a board game, Mary noticed that the die landed on the number 4 more often than usual. Please Hurry!!!!! Will mark brainliest for explanation of all parts.
Part A: Describe a simulation that could be run to test how many times out of 100 a fair die should land on the number 4. State the representations and possible outcomes. Be sure to give enough detail that another person could replicate your simulation. (7 points)
Part B: While running a simulation, the die landed on the number 4 a total of 32 times out of the 100 rolls. Construct and interpret a 95% confidence interval for the true proportion of rolls that will land on the number 4. Show all work. (7 points)
Part C: Does the confidence interval in part B support Mary's suspicions that the die is not fair? Explain your reasoning. (6 points)
Part A:
We want to see how often the number 4 comes up when we roll a fair dice 100 times. We will use a dice with numbers 1,2,3,4,5,6. We will keep track of how many times 4 comes up and we think it should be around 16 times because there are 6 numbers on the dice.
Part B:
We rolled the dice 100 times and got 4 32 times.
-We want to know if that is normal or if something is wrong with the dice.
-We use special numbers to check if this is normal, it's called the confidence interval
-The confidence interval tells us if 32 times is normal or not.
Part C:
The confidence interval tells us that 32 times is not normal, it's unlikely that it happened by chance. So, the dice might not be fair.
26. Workplace injuries (5.2, 5.4) Pick a nonfatal work- place injury in private industry at random. The table gives the probability model for the day of the week that the injury took place.
Day: Sunday Monday Tuesday Wednesday
Probability: 0.06 0.18 0.17 0.17
Day: Thursday Friday Saturday
Probability: x 0.15 0.09
(a) Find the probability that the randomly chosen injury took place on a Thursday.
This is Probability and Statistics!
(b) Find the probability that the injury took place on a weekday (Monday through Friday).
(c) Given that an injury took place on a weekday, what is the probability that it took place on a Monday?
a) The probability that the randomly chosen injury took place on a Thursday would be 0.17.
b) The probability that the injury took place on a weekday (Monday through Friday) would be 0.84.
c) The probability that it took place on a Monday would be 21.4%.
What is the probability?
Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, where 0 indicates that an event is impossible, and 1 indicates that an event is certain.
(a) To find the probability that the injury took place on a Thursday, we need to find the value of x in the probability table:
Day: Sunday Monday Tuesday Wednesday
Probability: 0.06 0.18 0.17 0.17
Day: Thursday Friday Saturday
Probability: x 0.15 0.09
The sum of the probabilities for each day must equal 1. So we can set up an equation to find x:
0.06 + 0.18 + 0.17 + 0.17 + x + 0.15 + 0.09 = 1
0.83 + x = 1
x = 0.17
The probability that the injury took place on a Thursday is 0.17.
(b) To find the probability that the injury took place on a weekday (Monday through Friday), we sum the probabilities for Monday, Tuesday, Wednesday, Thursday, and Friday:
0.18 + 0.17 + 0.17 + 0.17 + 0.15 = 0.84
The probability that the injury took place on a weekday is 0.84.
(c) Given that an injury took place on a weekday, we can use Bayes' Theorem to find the probability that it took place on a Monday. Let A be the event that the injury took place on a weekday, and B be the event that the injury took place on a Monday. Then:
P(B|A) = P(B and A) / P(A)
P(B and A) = P(B) = 0.18
P(A) = 0.84 (from (b))
So:
P(B|A) = 0.18 / 0.84 = 0.214 or 21.4%
The probability that the injury took place on a Monday, given that it took place on a weekday, is 21.4%.
Hence,
a) The probability that the randomly chosen injury took place on a Thursday would be 0.17.
b) The probability that the injury took place on a weekday (Monday through Friday) would be 0.84.
c) The probability that it took place on a Monday would be 21.4%.
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A rectangule ha a preimeter of 446 feet. The rectangle ha a length of (13x-1) feet and a width of (9x 4) feet. Find the length and width of the rectangle
The rectangle has a length of 222 feet and a width of 150 feet.
A quadrilateral with parallel sides equal to one another and four equal vertices is known as a rectangle. It is also known as an equiangular quadrilateral for this reason.
Rectangles can also be referred to as parallelograms since their opposite sides are equal and parallel.
We know that the perimeter of a rectangle is the sum of all four sides. So in this case:
Perimeter = 2(length) + 2(width)
Given that the perimeter is 446 feet, we can set up the equation:
446 = 2(13x-1) + 2(9x+4)
On Simplifying, we get:
446 = 44x + 6
Now we can solve for x by subtracting 6 from both sides:
440 = 44x
Finally, dividing both sides by 44:
x = 10 feet
Now that we know the value of x, we can substitute it back into the expressions for the length and width:
Length = (13x-1) = (13(10)-1) = 129 feet
Width = (9x+4) = (9(10)+4) = 94 feet
Therefore, the rectangle has a length of 129 feet and a width of 94 feet.
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A student randomly draws a card from a standard deck of 52 cards. He records the type of card drawn and places it back in the deck. This is repeated 20 times. The table below shows the frequency of each outcome.
Outcome Frequency
Heart 7
Spade 3
Club 6
Diamond 4
Determine the experimental probability of drawing a heart.
0.13
0.25
0.35
0.70
Answer:
.35
Step-by-step explanation:
Experimentally 7 hearts were drawn with 20 tries
7/20 = .35
Answer: A: 0.13
Step-by-step explanation:
find x when 7x-8 = 5x+24
Answer: 16
Step-by-step explanation:
7x - 8 = 5x + 24
2x = 32
x = 16 :>
Graph a right triangle with the two points forming the hypotenuse. Using the sides, find the distance between the two points, to the nearest tenth (if necessary).
(−3,−6) and (4,−8)
Pls help I need this
The distance between these two points is √53 units.
What is Triangle?A triangle is a three-sided polygon that consists of three edges and three vertices.
The two points of a triangle are (−3,−6) and (4,−8)
The length along a line or line segment between two points on the line or line segment.
Distance=√(x₂-x₁)²+(y₂-y₁)²
=√(4+3)²+(-8+6)²
=√7²+2²
=√49+4=√53
So the distance between these two points is √53 units
Hence, the distance between these two points is √53 units.
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Pizza Palace pays Tony $40 a night +2 dollars for every delivery he makes which number line shows how many pieces Tony must deliver them to make at least $70 an hour. Please answer quickly
Analyzing the question, Tony must deliver them 35 pieces to make at least $70 an hour.
What is algebra?Algebra is a branch of mathematics that deals with mathematical symbols and the rules for manipulating these symbols. It is used to study mathematical structures that include numbers, as well as variables and other abstract concepts. Algebraic concepts include operations such as addition, subtraction, multiplication, and division, as well as the properties of operations such as distributivity and associativity. Algebraic concepts also include equations, inequalities, and functions.
According the question,
tony make 2 dollars for each delivery,
so, he need to do 70/2 = 35 delivery
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How do you solve 2 ordered pairs?
An ordered pair is a set of two values, (x,y), that represents a point on a coordinate plane. To solve an ordered pair means to find the coordinates (x,y) of a point on a coordinate plane.
To solve two ordered pairs, you would need to know the coordinates of both points, and then you can graph them on a coordinate plane to visualize the relationship between the two points.
For example, if you have the ordered pairs (2,3) and (4,5), you can graph them on a coordinate plane with the x-axis and y-axis, where x represents the horizontal position and y represents the vertical position. The point (2,3) would be located at 2 on the x-axis and 3 on the y-axis, and the point (4,5) would be located at 4 on the x-axis and 5 on the y-axis.
Once you have plotted the points on a coordinate plane, you can use them to make a conclusion about the relationship between the two points, for example if they are in the same line, if the distance between them, if they form a slope, etc.