(A). Yes, overdetermined systems can be consistent.
As, the system of equations below is consistent because it has a solution
x1 = 2 , x2 = 4 , x1 + x2 = 6.
We have,
'Over-determined system is a system of linear equations, in which there are more equations than unknowns'.
If we have m equations and n variables where m>n (more equations than variables), then system can be consistent if last m−n equations are linear combinations of previous ones.
For e.g. Let us consider the system,
x + y = 1
x - y = 1
3x + y = 3
solving these equations, we can see
The only intersection point is (1,0). Thus, x= 1 and y= 0 is the solution of this system.
Thus, over-determined system can be consistent.
According to the options,
Hence, option A is correct.
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Kylli began a trip with 18 1/2 gallons of gas in the gas tank of her car. If she used 17 3/4 gallons on the trip, how many gallons did she have left when she finished the trip?
Answer:
3/4 of a tank of gas
Step-by-step explanation:
18 1/2-17 3/4= 3/4
or the easiest way for me is to change the faction to decimals
18.5-17.75= 0.75 which is 3/4
Solve the inequality and the graph the solution
An inequality with two variables has a graph, which is a collection of points that shows all possible solution is x≤ 5 3/10.
How to find the calculation?The boundary line between the coordinate plane's two halves, one of which represents the inequality's solutions, is created by a linear inequality.
x + 1 1/2 ≤ 6 8/10 :
Solution : x ≤ 5 3/10
Decimal : x ≤ 5.3
Interval notation : (-∝ , 53/10)
Steps:
x + 1 1/2 ≤ 6 8/10 :
Convert mixed Number to improper Fraction : 1 1/2 = 3/2
1 1/2
Convert mixed numbers to improper fraction ; a (b/c ) = a. c +b /c
1 1/2 = 1.2 + 1 /2
=3/2.
x + 1 1/2 ≤ 6 8/10 :
Convert mixed Number to improper Fraction : 6 8/10 = 68/10
6 8/10
Convert mixed numbers to improper fraction ; a (b/c ) = a. c +b /c
6 8/10 = 6.10 + 8 /10
=68/10
x+ 3/2 ≤ 68/10
Cancel the Common factor :2
x + 3/2 ≤ 34/5
Move 3/2 to the right side
x ≤ 53/10
Convert improper Fraction to mixed Numbers: 53/10 = 5 3/10
53/10 = 5 Reminder 3
Convert to mixed Number : Quotient (Remainder / Divisor)
53/10 = 5 3/10
x≤ 5 3/10
x≤ 5 3/10.
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Please helppp with this question
On solving the system of linear equations 3x + 3y = 45 and x + 2y = 24, the cost for each shirt is obtained as $6, and cost for each pair of pants is obtained as $9.
What is a linear equation?
A linear equation is one that has a degree of 1 as its maximum value. No variable in a linear equation, thus, has an exponent greater than 1. A linear equation's graph will always be a straight line.
Let the cost of shirts be x and the cost of pair of pants be y.
The number of shirts bought by person A = 3
The number of pair of pants bought by person B = 3
The total cost for person A = $45
The equation for person A is -
3x + 3y = 45....(1)
The number of shirts bought by person B = 1
The number of pair of pants bought by person B = 2
The total cost for person B = $24
The equation for person B is -
x + 2y = 24....(2)
Multiply equation (2) by 3 -
3(x + 2y) = 24 × 3
3x + 6y = 72....(3)
Subtraction equation (1) from equation (3) -
3x + 6y - (3x + 3y) = 72 - 45
3x + 6y - 3x - 3y = 27
3y = 27
y = 9
Substitute the value of y in equation (2) -
x + 2(9) = 24
x + 18 = 24
x = 24 - 18
x = 6
Therefore, the cost of shirts and pants is x = 6 and y = 9 respectively.
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please help will mark BRAINLIEST
Answer:
100
Step-by-step explanation:
total angles of any triangle is 180
it tells you one of the base angles is 40, so 2 of them are 80
so the top one is 180-80 =100
big lake bob spends his time carving fishing lures and duck decoys. if big lake bob spends all of his time carving fishing lures he can carve 125 lures in a week. if he spends all of his time carving duck decoys he can carve 20 decoys in a week. for every 4 duck decoys big lake bob carves he must give up 25 fishing lures. Fill in the values in the table below to complete Big Lake Bob's production possibilities schedule. Fising Lures Duck Decoys 100 0 0 30
50 fishing lures are carved in a week.
A) Big Lake Bob
Production Possibilities Schedule:
Fishing Lures Duck Decoys
100 0
90 5
80 10
70 15
60 20
50 25
40 30
30 35
20 40
10 45
0 50
50 fishing lures are carved in a week.
25 duck decoys are crafted in a week.
This implies that Big Lake Bob forgoes 10 fishing lures for every 5 duck decoys he carves.
Large Lake Schedule of Bob's productivity potentials
B) Bob's potential for production The schedule is a table of numbers that shows the various combinations of two items that can be created using the restricted resources (labor hours, capital, materials, etc.) and technology in Bob's economy.
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It is reported that the wild tiger population has declined by 97%
over the last 20 years.
There are now 3200 tigers left in the wild.
To the nearest thousand, how many wild tigers were there 20 years ago?
The nearest thousand, there were an estimated 116,000 wild tigers 20 years ago.
Determine Percentage decrease theory.The percentage decrease theory suggests that a decrease in the price of a product or service will lead to an increase in demand for that product or service.
This theory is based on the idea that consumers are more likely to buy a product or service if its price is lower. This theory can be applied to both new and existing products or services.
For example, a retailer may decide to decrease the price of a product in order to attract more customers and increase sales. Similarly, a company may choose to reduce the cost of a service in order to make it more attractive to potential customers.
This question is using the percentage decrease theory. According to this theory,
you can calculate the percentage decrease by subtracting the current value from the original value and then dividing by the original value.
Step 1: Subtract the current number of wild tigers (3200) from the original number of wild tigers (20 years ago).
Original - Current = Change
120,000 - 3200 = 116,800
Step 2: Divide the change (116,800) by the original number of wild tigers (120,000)
Change / Original = Percentage Change
116,800 / 120,000 = 97%
Step 3: Multiply the percentage change (97%) by the original number of wild tigers (120,000)
Percentage Change x Original = Estimated Original
97% x 120,000 = 116,400
Therefore, to the nearest thousand, there were an estimated 116,000 wild tigers 20 years ago.
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(-1.2) (-3.5) (-2.7) (-0.4) a positive product?
We have the product of 4 negative numbers, by the rule of signs, we can see that the product is positive.
Is the product positive?Here we need to reember the rule of signs for the product, it is:
(-)*(-) = +
(+)*(+) = +
(+)*(-) = -
(-)*(+) = -
So the product between two negative numbers is positive, now let's look to our product.
(-1.2)*(-3.5)*(-2.7)*(-0.4)
We can rewrite this as:
(-1.2*-3.5)*(-2.7*-0.4)
The negative sings cancell, then we get:
(-1.2*-3.5)*(-2.7*-0.4)
(4.2)*(1.08)
Now we have the product of two positive numbers, this will be positive.
(4.2)*(1.08) = 4.536
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What is a perimeter of a rectangluar drive way measuring 20 feet long and 15 feet wide?
Answer:
Step-by-step explanation:
P = 2l+b)
P = 2(20 + 15)
P = 2(35)
P = 70 feet
Answer:
70 feet
Step-by-step explanation:
Perimeter of rectangle:length = 20 feet
width = 15 feet
[tex]\sf \boxed{\text{Perimeter of rectangle = 2* ( length * width)}}[/tex]
[tex]\sf = 2* (20 + 15)\\\\ = 2 * 35\\\\= 70 \ feet[/tex]
The sum of two numbers is 62. 3 times the smaller number exceeds twice the larger number by one. What are the numbers.
The smaller number is 25 and larger number is 37
What are linear equations?Linear equations help in representing the relationship between variables such as x, y, and z, and are expressed in exponents of one degree. In these linear equations, we use algebra, starting from the basics such as the addition and subtraction of algebraic expressions.
Given here; The sum of two numbers is 62 and 3 times the smaller number exceeds twice the larger number by one.
let the smaller number be x and the larger number be y then we have
x+y=62
3x-2y=1
Thus solving this system of linear equations by method of elimination we get
5y=185
y=37
∴ x=25
Hence, The smaller number is 25 and larger number is 37
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What is 67% of 800? ,ms
Answer:
536
Step-by-step explanation:
Answer: 536
Step-by-step explanation:
Step 1: As we know, a whole of something is equal to 100%. In this case, we want to find what 67% of 800 is. We know that 100% of 800 is, well, just 800.Step 2: If 100% of 800 is 800, then we can get 1% of 800 by dividing it by 100. Let's do 800 / 100. This is equal to 8.0. Now we know that 1% is 8.0.Step 3: Now that we know what 1% of 800 is, we just need to multiply it by 67 to get our solution! 8.0 times 67 = 536. That's all there is to it!
Suppose you are assigned the number 1, and the other students in your statistics class call out consecutive numbers until each person in the class has his or her own number.
Explain how you could get a random sample of four students from your statistics class. (Select all that apply.)
A. Randomly choose four of the students that are sitting in the back row.
B. Use a computer or random-number table to randomly select four students after numbers are assigned.
C. Randomly choose four of the first students that walk into the classroom.
D. Randomly choose four of the tallest students in the classroom.
E. Randomly choose four of the last students that walk into the classroom.
The most suitable method to obtain a random sample of four students from the statistics class would be to use a computer or random-number table to randomly select four students after numbers are assigned.
This method ensures that every student has an equal chance of being selected and that the sample is truly random. This is the only method that guarantees that the sample is random and representative of the entire class.
The other methods listed (A, C, D, and E) do not ensure randomness, as they are based on non-random criteria (such as seating arrangement, height, or time of arrival). These methods might introduce bias into the sample and lead to incorrect conclusions about the population.
Hence, the correct answer is B.
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f(x) = 3x and g(x)=x-2, find f(g(4))
If f(x) = 3x and g(x)=x-2, then the value of f(g(4)) is 6.
What is a function?
A function is a mathematical object that assigns exactly one output to each input of a specified type. In other words, a function is a rule that takes in certain inputs (or "arguments") and produces a unique output. The inputs to a function are called the domain, while the set of possible outputs is called the range.
The given functions are f(x) = 3x and g(x)=x-2.
To find f(g(4)), we first need to evaluate g(4). The function g is defined as g(x) = x - 2, so g(4) = 4 - 2 = 2.
Next, we need to evaluate f(2), where f is defined as f(x) = 3x. So, f(2) = 3 * 2 = 6.
Therefore, f(g(4)) = f(2) = 6.
Hence, if f(x) = 3x and g(x)=x-2, then the value of f(g(4)) is 6.
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Graph the inequality below on the number line.
y>-10
The graph of the inequality y > -10 is given by the image presented at the end of the answer.
What are the inequality symbols?The four inequality symbols, along with their meaning, are presented as follows:
> x: greater than x.< x: less than x.≥ x: at least x.≤ at most x.The inequality for this problem is given as follows:
y > -10.
Which means that the solution is the numbers that are greater = to the right of -10, with an open interval.
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Given
sec
�
=
−
73
8
secA=−
8
73
and that angle
�
A is in Quadrant II, find the exact value of
csc
�
cscA in simplest radical form using a rational denominator.
The exact value of csc(A) is csc(A) = 7/20[√10]
How to determine the value of csc(A)From the question, we have the following parameters that can be used in our computation:
sec(A) = 7/3
Take the inverse of both sides
cos(A) = 3/7
Using the following trigonometry identity, we have
sin²(A) + cos²(A) = 1
Substitute the known values in the above equation, so, we have the following representation
sin²(A) + (3/7)² = 1
So, we have
sin²(A) = 40/49
Take the square roots
sin(A) = ±√(40/49)
The angle is in quadrant II
So, we have
sin(A) = √(40/49)
Take the inverse
csc(A) = √(49/40)
So, we have
csc(A) = 7√(1/40)
This gives
csc(A) = 7/[2√10]
Rationalize
csc(A) = 7/20[√10]
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Complete question
Given sec(A) = 7/3 and that angle A is in Quadrant II, find the exact value of csc(A)
Any one help me please the question is in the screenshot.
The answers include the following below:
The sale price is 85% of the regular price.The equation which can be used to find the sale price, s, of an oil change is s = 0.85(30).What is Sale price?This is referred to as the discounted price at which goods or services are being sold.
Since we were told that the discount is 15%, then the sale price will be (100-85)% of $30 which is 85% of $30.
This therefore means that the equation to find the sale price will be 85/100 × 30 = 0.85(30).
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item 18 time remaining 4 hours 13 minutes 48 seconds 04:13:48 ebook item 18 time remaining 4 hours 13 minutes 48 seconds04:13:48 if bob can produce more donuts in one day, if
If Bob is able to produce more donuts than Sue in one day, that means that Bob has an absolute advantage in the production pf donuts.
Absolute advantage is when a particular person is able to produce more amount of product than the other with the same amount of input of resources, for example, time. Comparative advantage on the other hand is based on the opportunity cost.
Comparative advantage is basically the ability to produce a good or a service for an opportunity cost which is lower than that of a competitor. Since, Bob is able to produce more donuts than Sue, Bob has an absolute advantage over Sue.
--The given question is incomplete, the complete question is
If Bob can produce more donuts in one day than Sue can produce in one day, then:
a. Bob has a comparative advantage in the production of donuts.
b. Sue has a comparative advantage in the production of donuts.
c. Bob has an absolute advantage in the production of donuts.
d. Sue has an absolute advantage in the production of donuts."--
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a group of students take hundreds of digital photos for a science project about weather patterns. each photo file contains data representing the level of red, green, and blue for each pixel in the photo. the file also contains metadata that describes the date, time, and geographic location where the photo was taken. for which of the following goals would analyzing the metadata be more appropriate than analyzing the data? select two answers.
The metadata be more appropriate than analyzing the data is a series of binary digits called bits.
The term called metadata can be defined as the data that provides information about one or more aspects of a given data and it also provide a structured reference that helps to sort and identify all of its attributes such as Author, created Date, modified date, type of the file and the size of the file.
Here we have given that a group of students take hundreds of digital photos for a science project about weather patterns.
And also each photo file contains data representing the level of red, green, and blue for each pixel in the photo.
Where the file also contains metadata that describes the date, time, and geographic location where the photo was taken.
In this scenario, we have to analyze the metadata would be more appropriate than analyzing the data when determining the likelihood that the photo was taken or created at a particular public event.
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A biologist is studying the plant diversity in 15 million acres of the Sierra Nevada Mountains. He will count the number of species in 150 acres. Match the strategies to their corresponding sampling techniques.
The biologist goes to his 150 favorite hiking places and looks at an acres along each trail.
The biologist orders the 15 million acres by latitude and then surveys every 100000th acre on the list.
The biologist classifies the Sierras into 10 different ecological types and then makes sure that the proportion of each ecological type from the sample is the same as the proportion of that of the population.
The biologist goes to 15 diverse locations that have 10 acres each and surveys all 10 acres for each of these 15 locations.
The biologist enters the 15 million acres into a data base and had a computer randomly select 150 of these acres.
Cluster Sampling
Systematic Sampling
Convenience Sampling
Stratified Sampling
Simple Random Sampling
Answer:
The biologist goes to his 150 favorite hiking places and looks at an acre along each trail: Random Sampling.
The biologist orders the 15 million acres by latitude and then surveys every 100000th acre on the list: Stratified Sampling.
The biologist classifies the Sierras into 10 different ecological types and then makes sure that the proportion of each ecological type from the sample is the same as the proportion of that of the population: Stratified Sampling.
The biologist goes to 15 diverse locations that have 10 acres each and surveys all 10 acres for each of these 15 locations: Cluster Sampling.
The biologist enters the 15 million acres into a data base and had a computer randomly select 150 of these acres: Random Sampling.
give me brainiestFind the Area of the figure below, composed of a rectangle with a semicircle removed from it. Round to the nearest tenths place.
Answer:
39.9
Step-by-step explanation:
Rectangle: area = length × width
Semicircle: area = 0.5πr²
total area = 9 × 6 - 0.5 × 3.14159 × 3²
total area = 39.9
The dating web site oollama requires its users to create profiles based on a survey in which they rate their interest (on a scale from 0 to 3) in five categories: physical fitness, music, spirituality, education, and alcohol consumption. a new oollama customer, erin o'shaughnessy, has reviewed the profiles of 40 prospective dates and classified whether she is interested in learning more about them. based on erin's classification of these 40 profiles, oollama has applied a logistic regression to predict erin's interest in other profiles that she has not yet viewed. the resulting logistic regression model is as follows: for the 40 profiles (observations) on which erin classified her interest, this logistic regression model generates that following probability of interested. Probability of Probability ofObservation Interested Interested Observation Interested Interested35 1 1.000 13 1 0.41221 1 0.999 2 0 0.28529 1 0.999 3 0 0.21925 1 0.999 7 0 0.16839 1 0.999 9 0 0.16826 1 0.990 12 0 0.16823 1 0.981 18 0 0.16833 1 0.974 22 1 0.1681 0 0.882 31 1 0.16824 1 0.882 6 0 0.12828 1 0.882 20 0 0.12836 1 0.882 15 0 0.02916 0 0.791 5 0 0.02027 1 0.791 14 0 0.01530 1 0.791 19 0 0.01132 1 0.791 8 0 0.00834 1 0.791 10 0 0.00137 1 0.791 17 0 0.00140 1 0.791 4 0 0.00138 0 0.732 11 0 0.000(a) Using a cutoff value of 0.5 to classify a profile observation as Interested or not, construct the confusion matrix for this 40-observation training set.PredictedActual 0 10 1 Compute sensitivity, specificity, and precision measures and interpret them within the context of Erin's dating prospects.If required, round your answers to two decimal places. Do not round intermediate calculations.The sensitivity of the model is . This suggests that the model is reasonably - Select your answer -goodbadItem 6 at identifying the profiles that Erin is interested in.The specificity of the model is . This suggests that the model is reasonably - Select your answer -goodbadItem 8 at avoiding recommending profiles to Erin that she will not be interested in.The precision of the model is . This suggests that the model is reasonably - Select your answer -goodbadItem 10 at suggesting profiles of interest to Erin.(b) Oollama understands that its clients have a limited amount of time for dating and therefore use decile-wise lift charts to evaluate their classification models. For the training data, what is the first decile lift resulting from the logistic regression model? Interpret this value.The first decile lift of this classification is . It means that the first decile of the logistic regression model - Select your answer -halvesdoublestriplesdoes not changeItem 12 the number of profiles that Erin is interested in versus random selection.(c) A recently posted profile has values of Fitness = 3, Music = 1, Education = 2, and Alcohol = 1. Use the estimated logistic regression equation to compute the probability of Erin's interest in this profile.If required, round your answers to three decimal places. Do not round intermediate calculations.Log odds =Probability of Interest =(d) Now that Oollama has trained a logistic regression model based on Erin's initial evaluations of 40 profiles, what should its next steps be in the modeling process?Oollama should use their model to suggest profiles - Select your answer -of interestwith lack of interestof interest and with lack of interestItem 15 to Erin in order to compute classification accuracy measures on a validation set.
The dating web site Oollama.com requires its users to create pro les based on a survey in which they rate their interest (on a scale from 0 to 3) in positive categories: physical fitness, music, spirituality, education, and alcohol consumption.
A new Oollama customer, Erin O'Shaughnessy, has reviewed the pro les of 40 prospective dates and classi ed whether she is interested in learning more about them. Based on Erin's classi cation of these 40 pro les, Oollama has applied a logistic regression to predict Erin's interest in other pro les that she has not yet viewed. The resulting logistic regression model is as follows:
Log odds of Interested = −0.920 + 0.325 × Fitness − 3.611 × Music
+5.535 × Education − 2.927 × Alcohol
The detailed solution is attached below.
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Ian travels 225 km in 2.5 hours. At what speed does he travel?
Answer:
90 km/h
Step-by-step explanation:
speed = distance/time
speed = 225 km / 2.5 h
speed = 90 km/h
Answer:
90km/hr
Step-by-step explanation:
To find the speed, take the distance and divide it by the time.
225 km/ 2.5 hours
90km/hr
Find the value of x PLEASE HELP FOR BRAINLIEST
Answer:
31.81
Step-by-step explanation:
the dotted line ² = (22²-16²)
x = sq root of [dotted line² +(44-16)² ]
= sq root of [22²-16²+28²]
31.81
please help will mark BRAINLIEST
We can see here that Side AC is the longest side. A. Side AC.
What is an angle?An angle is a figure in Euclidean geometry made up of two rays that share a common terminal and are referred to as the angle's sides and vertices, respectively. Angles created by two rays are in the plane where the rays are located. The meeting of two planes also creates angles. Dihedral angles are these.
We see here that triangles that have an angle of 90° are usually known to be right angle. The angles in a triangle are equal to 180°.
We see here that the above answer. This is because the side opposite to the largest angle is the longest angle.
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Need help with question attached below in an image.
We can apply the order of four transformations to the graph of f(x) in order to sketch the graph of g(x): A 3-unit horizontal shift to the left : The graph becomes f(x-3 ) as a result, with a vertical asymptote at x = 0 rather than x = 3.
A ( -2 ) stretch in the vertical direction: The graph is now -2f(x-3), with a slope of -2 for x greater than 3 and 2 for x less than 3.An observation regarding the x-axis: The graph is now -2|f(x-3)|, which is the x-axis-reflecting graph of f(x-3) as a result of this change.A shift up one unit in the vertical: The result of this transformation is the final graph of g(x) = -2|x-3|+1, which is -2|f(x-3)|+1.2. To move from f(x) to g(x), four transformations are used:
A three-unit horizontal shift to the left: The graph thus shifts by a factor of -2 three units in the direction of the left A vertical stretch.
How does one plot a graph?You must first define the function and its domain before you can plot its graph. We can begin by sketching the piecewise linear graph of f(x) = |x|, which has a slope of 1 for x greater than 0 and -1 for x less than 0 in order to sketch the graph of g(x) = -2|x-3|+1. The vertical asymptote is shown by the x axis. For all real numbers, the definition of the f(x) graph exists.
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suppose you have a street light at a height . you drop a rock vertically so that it hits the ground at a distance from the street light. denote the height of the rock by . the shadow of the rock moves along the ground. let denote the distance of the shadow from the point where the rock impacts the ground. of course, and are both functions of time. to enter your answer into webwork use the notation to denote : then the speed of the shadow at any time while the rock is in the air is given by
The speed of the shadow at any time while the rock is in the air is given by v(1-s) / (H-h).
By the AAA congruency theorem, the two triangles are formed and are similar. Here, the ratio of their sides must be equal, and thus -
= H/d+s = h/s
= Hs = h(d+s)
= Hs = hd + hs
= Hs - hs = hd
= s(H-h) = hd
Differentiating both sides with respect to t -
= {s' (H- h)} + {sh'} = h'
Since we know that h' = v -
= {s' (H- h)} + {sv} = v
= s'(H-h) = v - sv
= s'(H-h) = v(1-s)
= s' = v(1-s) / (H-h)
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using a table or diagram write an equation that represents the linear function shown in the table or mapping diagram
An equation that represents the linear function shown in the table or mapping diagram is y = -x/4 - 3.
How to write an equation that represents the linear function?In order to write an equation that represents the linear function, we would use the point-slope form. Mathematically, the point-slope form of a straight line can be calculated by using this mathematical expression:
y - y₁ = m(x - x₁) or y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)
Where:
m represents the slope.x and y are the points.Next, we would determine the linear function representing the line which passes through the data points (-4, 6) and (8, 3) by using the point-slope form as follows:
y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)
y - 6 = (3 - 6)/(8 - (-4))(x - (-4))
y - 6 = (3 - 6)/(8 + 4)(x + 4)
y - 6 = -3/12(x + 4)
y - 6 = -x/4 - 9
y = -x/4 - 9 + 6
y = -x/4 - 3
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Need help with 9,10,13,14 also explain
The rule for divisibility by 9 is similar to divisibility rule for 3. That is, if the sum of digits of the number is divisible by 9, then the number itself is divisible by 9.
What is divisibility?the capacity of being divided. Math. the capacity of being evenly divided, without remainder.
Divisibility rules or Divisibility tests have been mentioned to make the division procedure easier and quicker. If students learn the division rules in Math's or the divisibility tests for 1 to 20, they can solve the problems in a better way. For example, divisibility rules for 13 help us to know which numbers are completely divided by 13. Some numbers like 2, 3, 4, 5 have rules which can be understood easily. But rules for 7, 11, 13, are a little complex and need to be understood in-depth.
Divisibility rule for 10 states that any number whose last digit is 0, is divisible by 10.
Example: 10, 20, 30, 1000, 5000, 60000, etc.
For any given number, to check if it is divisible by 13, we have to add four times of the last digit of the number to the remaining number and repeat the process until you get a two-digit number. Now check if that two-digit number is divisible by 13 or not. If it is divisible, then the given number is divisible by 13.
For example: 2795 → 279 + (5 x 4)
→ 279 + (20)
→ 299
→ 29 + (9 x 4)
→ 29 + 36
→65
Number 65 is divisible by 13, 13 x 5 = 65.
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you and friends go to the state fair . it costs $6 to get into the fair and $2 each time you go on a ride consider the relationship between number of rides (x) and total cost (y)
It costs $6 to enter the fair, and each ride costs $2, thus the equation is x = 6+ 2y.
what is equation ?Its core idea is understood to be the number's minimal equivalent fraction. How to determine the simplest form. A fractional figure can be checked to discover if it is a prime number. A phrase having two equal sides and now an equal sign in the middle is referred to as a mathematical equation. Every variable's degrees are listed in ranking in the general form of any equation. Its general form of a two-variable linear equation is an x + b y + c = 0. (or something similar). Perhaps conditional equations of identities are categories for equations.
given
Suppose the total cost is x and there are y rides.
Each ride costs two dollars. Thus, the price of the rides will be:
= Number of rides * Price per ride
=> y * 2
=> 2 y
Thus, the final price will be:
Total price = Admission price + ride prices
Total cost: $6 plus $2. (Number of rides)
x = 6 + 2y
It costs $6 to enter the fair, and each ride costs $2, thus the equation is x = 6+ 2y.
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Write a recursive rule for the sequences:
1,3,-2,5,-7,12,...
and 1,2,2,4,8,32,...
The recursive formula for each sequence is given as follows:
1,3,-2,5,-7,12: [tex]a_n = a_{n - 2} - a_{n - 1}, a_1 = 1, a_2 = 3[/tex]1,2,2,4,8,32: [tex]a_n = a_{n - 1} \times a_{n - 2}, a_1 = 1, a_2 = 2[/tex]How to define the recursive formulas?
The first sequence is given as follows:
1,3,-2,5,-7,12...
The pattern is that each term is the subtraction of the second to last term by the last term, hence the formula is given as follows:
1,3,-2,5,-7,12: [tex]a_n = a_{n - 2} - a_{n - 1}[/tex]
The second sequence is given as follows:
1,2,2,4,8,32,...
The pattern is that each term is obtained by the multiplication of the two previous terms, hence the formula is given as follows:
[tex]a_n = a_{n - 1} \times a_{n - 2}, a_1 = 1, a_2 = 2[/tex]
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Evaluate the given function as required.
Calculate R(0) and R(30) if R(t) is as shown below. (Round your answer to two decimal places.)
R(t)=328-296e⁻o.oo4t
The numeric values of the function R(t) = 328 - 296e^(-0.004t) at t = 0 and t = 30 are given as follows:
R(0) = 32. R(30) = 65.47.How to find the numeric value of a function or of an expression?To find the numeric value of a function or of an expression, we replace each instance of the variable in the function or in the expression by the value at which we want to find the numeric value.
The function for this problem is defined as follows:
R(t) = 328 - 296e^(-0.004t)
At t = 0, the numeric value is found replacing the lone instance of t by zero, hence:
R(0) = 328 - 296e^(-0.004(0))
R(0) = 32.
At t = 30, the numeric value is found replacing the lone instance of t by 30, hence:
R(30) = 328 - 296e^(-0.004(30))
R(30) = 65.47.
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