If a right triangle's height is 5 times the length of its base and the area of the triangle is 160, then the height of the triangle is 40 units
A right triangle's height is 5 times the length of its base
Consider the length of the base as b and the height as h
h = 5b
The area of the triangle = 160 square units
The area of the triangle = 1/2 × b × h
Where b is the base of the triangle
h is the height of the triangle
Substitute the values in the equation
1/2 × b × h = 160
1/2 × b × 5b = 160
1/2 ×5b^2 = 160
5b^2 = 320
b^2 = 320/5
b^2 = 64
b = [tex]\sqrt{64}[/tex]
b = 8 units
Then the height of the triangle h = 5b
= 5 × 8
= 40 units
Therefore, the height of the triangle is 40 units
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Preceding the attack at the Somme on July 1, 1916, the British bombarded the German trenches for eight days. Some 1,537 British guns fired 1,723,873 rounds without letting up. In round figures, what was the average number of rounds fired each day? _________ What was the average number of rounds fired by each gun during the eight days? ___ _
The average number of rounds fired each day is 140.
The average number of rounds fired by each gun during the eight days is 1122.
What is a mean?A mean simply means the average of the set of numbers. It is calculated by adding the numbers and then dividing.
In this situation, the British bombarded the German trenches for eight days and some 1,537 British guns fired 1,723,873 rounds without letting up. The average will be:
= 1,723,873 / 1,537
= 1122 rounds .
The average per day will be
= Average / Number of days
= 1122 / 8
= 140 per day.
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If a categorical independent variable contains 4 categories, then ________ dummy variables will be needed to uniquely represent these categories. a. 1 b. 2 c. 3 d. 4
If a categorical independent variable contains 4 categories, then four dummy variables will be needed to uniquely represent these categories. a. 1 b. 2 c. 3 d. 4
How many dummy variables are needed to represent the categorical variable?
We need 1 less dummy variable than outcomes for the categorical variable.
categorical variable has 2 outcomes
So, we need 2-1 = 1 dummy variable.
Note: If our categorical variable had 5 outcomes, we would need 5-1 = 4 dummy variables.
b. Write the multiple regression equation relating the dependent variable to the independent variables.
Note: Depending your your professor, this can be written one of the following ways...
yhat = a + b1 x1 + bx2
yhat = b0 + b1 x1 + b2 x2
yhat = beta0hat + beta1hat x1 + betahat2 x2
where x1 is the ratio variable
and x2 is the dummy variable
c. Interpret the meaning of the coefficients in the regression equation.
b0 = the predicted value of y when x1 and x2 both equal 0.
b1 = the change in y when x1 increases by 1 unit holding x2 constant.
b2 = the predicted difference in y between the two possible outcomes of the categorical variable holding x1 constant
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The values for random variables in a Monte Carlo simulation are
a. selected manually.
b. generated randomly from probability distributions.
c. taken from forecasting analysis.
d. derived secondarily using formulas.
The correct option is (B) generated randomly from probability distributions.
The values for random variables in a Monte Carlo simulation are generated randomly from probability distributions.
A frequency distribution that has been idealized is a probability distribution. An individual sample or dataset is described by its frequency distribution. It's the number of times in the dataset that each possible value of a variable appears. The probability of occurrence of a value determines how frequently it appears in a sample.
A random variable can have any number of alternative values and likelihoods within a particular range, and a probability distribution is a statistical function that captures all of these possibilities. This range will be constrained by the minimum and maximum possible values, but the location of the possible value on the probability distribution will rely on a number of other variables.
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An anchor 15 3/5 m below the surface of the ocean is lowered 4 1/5 m Then it is pulled up 12 3/5 m what is the anchors new position
The new position of the anchor is 7 1/5 below the surface of the ocean
How to find the new position of the anchorInitially the anchor is located 15 3/5 m below the surface of the ocean, this is same as = -15 3/5 m
The anchor is further lowered and the position now is
= -15 3/5 m - 4 1/5 m
= -99 /5 m
Then the anchor is pulled up 12 3/5 m the new position now is
= -99 /5 m + 12 3/5 m
= -36/5
= -7 1/5
= -7.2
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choose the statement that is false.group of answer choicesa 95% confidence interval is wider than a 90% confidence intervalwhen sampling for means and thinking about the central limit theorem, the n should always be >30.when estimating the standard deviation in calculating confidence intervals, make sure you use the t tables.reducing the variation of a process will increase the width of a given confidence interval relative to that process.
Reducing the variation of a process will increase the width of a given confidence interval relative to that process.
Option C is correct .
What is a confidence interval?
In statistics, the probability that a population parameter will fall between a set of values for a predetermined percentage of the time is referred to as a confidence interval. By employing the dimensions of values used in the computation of the intervals, it is simple to establish the link between components of two confidence intervals. The width is a fundamental component in these range estimates, which are affected by sample size, etc.
Hence, reducing the variation of a process will increase the width of a given confidence interval relative to that process is false.
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Help me out please
answers:
-1/3
3
1/3
-3
please do x to
Answer:
slope = 3
y-intercept = 0
Step-by-step explanation:
Help me on these please!. Thank you whoever. 13 points!!
Answer:
1. $105
2. $144
Step-by-step explanation:
For the first question:
4.20 × 25 = 105
For the second question:
4.80 × 30 = 144
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Two components of a minicomputer have the following joint pdf for their useful lifetimes X and Y. (If an answer doesn't exist enter DNE.) f(x, y) = xe−x(1 + y) x ≥ 0 and y ≥ 0 0 otherwise Determine E(XY).
The value of E(XY) is equivalent or equal to -1 according to the joint pdf having function f(x, y) = xe^−x(1 + y) x ≥ 0 and y ≥ 0 0.
Given that:
f(x,y) = xe^-x(1+y), where x ≥ 0 and y ≥ 0 0.
E(XY) = ∫∞ ∫∞ xy. xe^−x(1 + y) dx dy
0 0
E(XY) = ∫∞ ∫∞ x^2y . e^−x(1 + y) dx dy
0 0
E(XY) = ∫∞ x^2 . e^−x (∫∞ y e^-xy dy) dx
0 0
E(XY) = ∫∞ x^2 . e^−x (-1/x) dx
0
E(XY) = - ∫∞ x . e^−x dx
0
E(XY) = - 1
Two components of a minicomputer have the following joint pdf for their useful lifetimes X and Y are equal to i.e. E(XY) = -1.
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when the null hypothesis is not rejected, it is possible a type i error has occurred. possible a type ii error has occurred. possible either a type i or a type ii error has occurred. not possible a type ii error has occurred.
When a null hypothesis is not rejected, a type ii error has occurred.
What is a null hypothesis?A null hypothesis being a statistical hypothesis, states that no statistical significance can be present in a set of observations. Usually, hypothesis testing is a method used to judge the veracity of a given sample.
Sometimes, it is called just null, or even it has a symbol, viz, [tex]H_0[/tex].
We consider generally 4 cases:
[tex]H_0[/tex] is accepted when [tex]H_0[/tex] is true ⇒ A correct decision[tex]H_0[/tex] is rejected but is true⇒ Type i error has occurred and is rejected by us, null hypothesis is present[tex]H_0[/tex] is false but is accepted by us⇒ Type ii error has occurred, null hypothesis is not present. [tex]H_0[/tex] is false and is rejected⇒ A correct decision.According to the given question, we have not rejected the null hypothesis.
Thus, we have two options present, either the type ii error has occurred and null hypothesis is not present, or the null hypothesis is present.
Concluding, when a null hypothesis is accepted, it is possible that a type ii error has occurred.
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Akira is redecorating her bedroom. She misread the markings on her ruler and thought a picture frame she bought was 5.2 centimeters wide. The frame's actual width was 4.8 centimeters. What is the percent error for her measurement?
The percentage error is 8.3%
What is percentage?A percentage is a portion of a whole expressed as a number between 0 and 100 rather than as a fraction.
Given that, Akira is redecorating her bedroom. She misread the markings on her ruler and thought a picture frame she bought was 5.2 centimetres wide. The frame's actual width was 4.8 centimetres.
Percentage Error = ((Estimated Number – Actual Number)/ Actual number) x 100.
= (5.2-4.8)/4.8x100 = 8.3%
Hence, The percentage error is 8.3%
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if you draw square abcd and extend the sides by equal lengths to form square efgh, what must be the measure of angle heb so that the area of abcd is half the area of efgh?
The measure of angle < HEB = 60 degrees.
Given:
if you draw square abcd and extend the sides by equal lengths to form square efgh.
so that the area of abcd is half the area of efgh.
Let AB = x and HA = x
so area of square ABCD = x * x
= x^2
< HEB = 60 so < BHE = 30
EB = y
HE = 2y
HB = x + y
so x + y = [tex]\sqrt{3}[/tex] y
x = [tex]\sqrt{3}[/tex] y - y
x = ([tex]\sqrt{3}[/tex] - 1 ) y
y = x / ([tex]\sqrt{3}[/tex] - 1 )
squaring on both sides
y^2 = x^2 / ([tex]\sqrt{3}[/tex] - 1 )^2
= x^2 / 3 - 1
= x^2 / 2
Area of EFGH = (2y)^2 = 4y^2 = 2x^2 = 2 * area of ABCD.
Therefore < HEB = 60 degrees.
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1. If AABC is an equilateral triangle, solve for both x and y.
B
A...
3x + 1
18y-41
49 m
Solving for Sides with OOGEE
A
C
Ind
2. If ARST is an equilateral triangle, find x and the measure of each side
its the second oneee
Let R be an equivalence relation on a set A. Prove the following statement directly from the definitions of equivalence relation and equivalence class. For every a and b in A, if [a] = [b] then a Rb. Some of the sentences in the following scrambled list can be used to prove the statement. By definition of equivalence class, a E[b]. Let b E[a]. Then by definition of equivalence class, b Ra. Since R is symmetric, if b R a then a R b. | Thus, a Ra, and so, by definition of equivalence class, a E [a]. Since [a] = [b] and a E [a], then a E [b] by definition of set equality. | Hence, by definition of equivalence class, a Rb. By definition of equivalence relation, R is reflexive. Proof: Construct a proof by selecting appropriate sentences from the list and putting them in the correct order. 1. Suppose R is an equivalence relation on a set A, a and b are in A, and [a] = [b]. 2. ---Select--- 3. ----Select--- 4. ---Select--- 5. ---Select---
If the R is an equivalence relation then for every a and b in set R , if a = b then aRb exists.
If R is an equivalence relation on set A, a and b are in A and [a]=[b]
By the definition of the equivalence relation we can say that R is reflexive
Hence aRa and so by definition of equivalence class a ∈ [a] .
Since [a] = [b] and a ∈ [a] we can say that a ∈ [b] by the definition of set equality.
Now we will use the definition of equivalent class we can say that aRb .
An equivalence relation is a reflexive, symmetric, transitive binary link. The relationship of equipollence between line segments in geometry is one example of an equivalence relation.
Each equivalence relation separates the underlying set into distinct equivalence classes. Two items in the given set are only comparable to one another if and when they belong to the same equivalence class.
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Which expression would be easier to simplify if you used the associative property to change the grouping?
The expression that would be easier to simplify if you used the associative property to change the grouping is D. (160 + 40) + 27.
What is the associative property?The associative property of some binary operations in mathematics means that rearranging the parentheses in an expression will not change the result. Associativity is a valid rule of replacement for expressions in logical proofs in propositional logic.
This law simply states that when adding and multiplying numbers, you can change the grouping of the numbers in the problem and the answer will not change.
Addition and multiplication are both affected by the associative property. The reason for this is that you are combining numbers to get a total in both of these operations. You are combining values with addition. It makes no difference how you group these to put them together. The associative property of addition states that the addends can be grouped in various ways without changing the outcome.
In this case, (160 + 40) + 27 can simply be (40 + 160) + 27.
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at what rate per annum should p2400 be invested so that it will earn an interest of p800 in 8 years?
The interest rate is 4.17%, according to the question.
What do you mean by interest rate?
An amount that a borrower must pay to a lender as interest during the course of a loan, stated as a percentage of the loan amount is called interest rate.
According to data in the given question,
We have the given values:
Amount to be invested/Principal: 2,400
Amount of Interest: 800
Time: 8 years
Now, we will calculate the rate,
Solve for the rate:
Interest = Principal × Rate × Time
Derive the equation for rate:
Rate = [Interest ÷ (Principal × Time)] × 100
Substitute the given values:
Rate = [800 ÷ (2,400 × 8)] × 100
Rate = [800 ÷ 19,200] × 100
Rate = 0.04167 × 100
Rate = 4.17 %
Therefore, the rate is 4.17%.
Check:
800 = 2,400 × 8 × 0.04167
800 = 800.064
800 = 800
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Alex rides his bike to visit two friends and returned home. Interpret the graph to answer questions about his activities.
1. How long did it take Alec to get to his friends house?
2. How long did he stay at his first friends house?
3. How long did it take alec ti ride his bike from his first friends house to his second friends house?
4. How much longer did alec stay at his first friends house than at his second friends house?
5. In which parts of the graph is alec riding his bike toward his home?
6. In which parts of the graph is alec traveling the fastest?
7. How long was alec away from his house?
The required question of the given problem are solved below.
Explain is distance vs time graph?A distance-time graph shows how far an item has gone in a given time. It is a straightforward line diagram that signifies distance versus time discoveries on the chart. Distance is plotted on the Y-pivot. Time is plotted on the X-pivot.
According to question:1) he take 20 minutes to get to his friends house.
2) he stayed 60 - 20 = 40 minutes at his first friends house.
3) he take 70 - 60 = 10 minutes to ride his bike from his first friends house to his second friends house.
4) 30 minutes, he stayed his second friend
Then
Difference = 40 - 30 = 10 minutes
So, he stay 10 minutes longer than first friend.
5) In part E, he is riding towards his home.
6) In part A of the graph he is travelling faster.
7) he went 10 kilometer away from his house.
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To weigh your cat, you hold it while you step on the scale. By yourself, you weigh 130. 6 130. 6 pounds. Holding your cat, you weigh 142. 5 142. 5 pounds. How much does your cat weigh?.
Answer: 11.9 pounds
Step-by-step explanation:
142.5 - 130.6 = 11.9
Please help :') ty ty ty ty ty
Please show your work too! :)
Answer:
I don’t know
Step-by-step explanation:
a bin contains 4 items: 1 a, 1 b, 2 c and 6 d. a person randomly selects 3. how many different types of items will be selected
The 4 different types of items will be selected.
What is the combination?
Combinations are mathematical operations that count the number of possible configurations for a set of items where the order of the selection is irrelevant. In combinations, you can select the items in any order.
[tex]nCr = \frac{n!}{(n - r)! \ r!}[/tex]
This formula to find the number of combinations by using r objects from the n objects is also referred as the ncr formula.
so, we have 4 items and a person randomly selects 3.
[tex]nCr = (n, r) = (4, 3)[/tex]
[tex]= \frac{4!}{3!(4 - 3)!}[/tex]
= 4! / 3!
= 4
Hence, The 4 different types of items will be selected.
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In a test of the equality of the percent defectives from two populations when the sample sizes are large (> 30), which of the following approximation methods is appropriate?
Poisson approximation
Hypergeometric approximation
Fisher's approximation
Normal approximation
Chi-square approximation
The number of defectives follows binomial distribution with parameters (n,p) and if n>30 then binomial distribution goes to the Normal' approximation.
Given that,
We have to find which of the following approximation approaches is adequate in a test of the equality of the percent defectives from two populations when the sample sizes are big (> 30).
We know that,
What is a normal approximation?The normal curve is roughly followed by the sample distribution of averages or proportions from numerous independent experiments. The population value that corresponds to a sample proportion or average is its expectation.
Therefore, the number of defectives follows binomial distribution with parameters (n,p) and if n>30 then binomial distribution goes to the Normal' approximation.
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a test has a mean of 85 with a standard deviation of 5. which of the following scores is within one standard deviation of the mean?
A test's standard deviation is 5 and its mean is 85. scores is within one standard deviation of the mean is 25/n^12.
The square root of the variance of a random variable, sample, mean ,statistical population, data set, or probability distribution is that variable's standard deviation. Although less robust in practice, it is algebraically simpler than the average absolute deviation.The fact that the standard deviation is expressed in the same unit as the data, as opposed to the variance, is a useful characteristic of the statistic.
variance = 5^2 = 25
standard deviation of the mean = ( variance / n )^1/2
= (25/n)^1/2
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a confidence interval for a population mean has a margin of error of 6.4. determine the length of the confidence interval.
the length of the confidence interval is 12.8
What 95% confidence interval means?You have a 5% chance of being incorrect with a 95% confidence interval. You have a 10% chance of being incorrect with a 90% confidence interval. A 95% confidence interval is narrower than a 99% confidence interval.
How do you interpret a confidence interval?The likely location of the population parameter is shown by a confidence interval. For instance, the population mean is between 9 and 11, according to the 95% confidence interval of the mean [9 11].
According to the question,
Length of confidence interval = 2*(6.4)
Length of confidence interval = 12.8
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A very large study showed that aspirin reduced the rate of first heart attacks by %. A pharmaceutical company thinks they have a drug that will be more effective than aspirin, and plans to do a randomized clinical trial to test the new drug. What is the null hypothesis the company will use?.
the null hypothesis the company will use p =0.44.
What is z test?
If the data is distributed normally, a z test can be used to determine whether the means of two populations differ from one another. The z test statistic's value must be determined, together with the null hypothesis and alternative hypothesis setups, for this reason. On the z critical value, the decision criterion is based. The distribution graph is divided into acceptance and rejection zones during hypothesis testing by the z critical value. The null hypothesis can be rejected if the test statistic lies inside the rejection region; otherwise, it cannot.
Here the data is normally distributed and using the sample mean.
This is the right-tailed test.
The null hypothesis is
H0 : p =0.44
Hence, the null hypothesis the company will use p =0.44.
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One leg of a right triangle is 6 units long, and its hypotenuse is 12 units long. What is the length of the other leg? Round to the nearest whole number.
10 units
13 units
18 units
4 units
The length of the other leg of the right triangle, rounded to the nearest whole number, is 10 units.
To find the length of the other leg of the right triangle, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.
Let's denote the length of the other leg as x. Given that one leg is 6 units long and the hypotenuse is 12 units long, we can set up the equation:
6^2 + x^2 = 12^2
Simplifying this equation, we have:
36 + x^2 = 144
Subtracting 36 from both sides, we get:
x^2 = 108
Taking the square root of both sides, we find:
x = √108
Rounding this value to the nearest whole number, we have:
x ≈ 10.392
The length of the other leg of the right triangle, rounded to the nearest whole number, is 10 units.
The correct option is: 10 units.
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the u.s. energy information administration claimed that u.s. residential customers used an average of 10,400 kilowatt hours (kwh) of electricity this year. a local power company believes that residents in their area use more electricity on average than eia's reported average. to test their claim, the company chooses a random sample of 163 of their customers and calculates that these customers used an average of 10,782kwh of electricity last year. assuming that the population standard deviation is 2768kwh, is there sufficient evidence to support the power company's claim at the 0.01 level of significance?
There is not sufficient evidence to support the power company's claim.
According to the information given in the question, we can frame the hypothesis as follows-
Null hypothesis ⇒ : H = 10400
Alternate hypothesis ⇒ Ha: > 10400
This is the right-tailed test.
Test statistic = z
[(x - μ)√n]/ σ
where x ⇒ sample mean = 10,782
σ ⇒ standard deviation = 2768
= (10782 - 10400)√163/ (2768)
= 382* 12.76/(2768)
= 1.76
⇒ Test statistic z = 1.76
Now, P( z > 1.76) = 1 - P( z < 1.76)
= 1 - 0.9608
= 0.0392
using z tables-
p-value = 0.0392
a = 0.01
we see that p-value > a
Thus, we fail to reject our null hypothesis.
Therefore, there is not sufficient evidence to support the power company's claim.
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Based on recent demand for single family homes in a growing city, it is recommended potential home buyers put 20 percent down when making an offer. A mortgage loan officer would like to test the claim that the average percent down on a single family home purchase is greater than the recommended 20 percent. To test this claim, at the 5% significance level, the mortgage loan officer collects the following data on a sample of 22 recent home purchases and records the percent down. The following is the data from this study: Sample size =22 recent home purchases Sample mean =24 percent down Sample standard deviation =9 percent down Identify the null and alternative hypothesis for this study by filling in the blanks with the correct symbol (=,≠,<, or > to represent the correct hypothesis.)
This enabled the borrower to obtain 90 percent financing while avoiding the additional cost of pmi. these loans are more commonly referred to as piggyback mortgage loans.
A loan is the lending of cash via one or more individuals, organizations, or different entities to other individuals, corporations, etc. The recipient incurs a debt and is normally susceptible to pay hobby on that debt till it is repaid as well as to repay the foremost amount borrowed.
A mortgage is a shape of debt incurred by using an character or different entity. The lender—commonly a business enterprise, economic organization, or authorities—advances a amount of money to the borrower. In return, the borrower agrees to a sure set of phrases together with any finance charges, hobby, repayment date, and different situations.
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Emma has a rain gauge on her deck to measure the amount of rain that falls in the area. After a storm with steady rain, there were 4.23 inches of water in the rain gauge. If the storm lasted 3 hours, how much water did the rain gauge collect every hour?
Answer:
1.41 inches per hour
Step-by-step explanation:
volume of water for 3 hrs=4.23 inches
v of water for 1 hours=4.23/3=1.21inches
what is the quotient of 1/4 divided by 3/5
Answer:
[tex]\frac{5}{12}[/tex]
Step-by-step explanation:
1/4 / 3/5
To divide fractions we flip the second one and then multiply them both and this method works for any number
1/4 x5/3
5/12
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suppose a license plate that has 2 length of 7 characters can only contain digits and upper-case vowels and must contain at least one digit and at least one vowel. how many different legitimate license plates are available?
The total number of possible legitimate license plate numbers possible are (15)⁵.
The license plate has a length of 7 character for the legitimate license plates.
So, there are a total 7 position, in these positions, on has to be a upper case vowel and one has to be an integer digit.
Now, we have only 5 position are left.
There are only 5 vowels and 10 integers digits.
So, we are assuming that the repetition is allowed because nothing else is mentioned.
So, total possible combinations are 1 x 1 x 15 x 15 x 15 x 15 x 15.
Because repetition is allowed, we don't have to consider the factor of internal arrangement.
So, the total number of legitimate license plates possible are (15)⁵.
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A function f (x) is graphed on the coordinate plane. What is the function rule in slope-intercept form? Afunction f (>) is graphed on the coordinate plane What is the function rule in slope-intercept fom? Enter your answer in the box f(r) Basic x2
The required function of the line would be y = 2x + 1.
Function rule in slope-intercept form:The slope-intercept form is one rule to represent linear function rules.
f(x) = mx+b is sometimes used. In any scenario, m and b describe the line's overall features. The slope is denoted by m, while the y-intercept is denoted by b.
Linear equations, or straight-line equations, can be quickly recognized as they have no terms with exponents in them. For example, you will find an x or a y , but never an x². Each linear equation describes a straight line, which can be expressed using the slope intercept form equation.
According to the given question,
The coordinates of the y-intercept would be (0, 1).
The value of the x-coordinate is 1 when y-coordinate is 3.
Here the line passes through points (0, 1) and (1, 3).
Let the required linear function would be
y - y₁ = (y₂ - y₁)/(x₂ -x₁ )[x₂ -x]
x₁ = 0, y₁ = 1
x₂ = 1, y₂ = 3
⇒ y - y₂ = (y₂ - y₁)/(x₂ -x₁ )[x -x₂]
⇒ y - 3 = (3 - 1)/(1 - 0 )[x -1]
⇒ y - 3 = (2)[x -1]
⇒ y - 3 = 2x - 2
⇒ y = 2x - 2 + 3
⇒ y = 2x + 1
Therefore, the required function of the line would be y = 2x + 1 which is shown in the given question.
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