Factoring, utilizing square roots, completing the square, and the quadratic formula are the four ways to solve a quadratic equations.
What is Quadratic Equation ?An algebraic equation of the second degree in x is a quadratic equation. The quadratic equation is written as ax² + bx + c = 0, where x is the variable, a and b are the coefficients, and c is the constant term. First, there must be a term other than zero in the coefficient of x² (a ≠ 0) for an equation to be a quadratic equation. The x² term is written first when constructing a quadratic equation in standard form, then the x term, and finally the constant term. The numerical values of a, b, and c are often expressed as integral values rather than fractions or decimals.
Factoring, utilizing square roots, completing the square, and the quadratic formula are the four ways to solve a quadratic problem.
To factor an equation with quadratic terms:
Convert the equation to standard form with a zero on one side.Factor the non-zero sideReset each component to zero (Remember: a product of factors is zero if and only if one or more of the factors is zero).Solve each of the ensuing equations.To learn more about Quadratic Equation refer to :
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a) Input this table of values into Desmos to write a quadratic regression equation that best fits the
data set. Hint: use yz-axi + bx2 + c
b) Use your regression equation and estimate the y value if x is 23. Show your work.
х
15
17
19
20
у
423
398
308
255
297
365
401
29
The equation would become y = -3.99(23)2 + 37.2(23) - 102 which can then be simplified to y = -2213.71 + 755.6 and further simplified to y = -1458.11. This rearrangement and simplification can be completed to find the estimated y value when x is 23, which is y = 227.8.
A) y = -3.99x2 + 37.2x - 102
B) y = -3.99(23)2 + 37.2(23) - 102 = 227.8
y = -3.99(23)2 + 37.2(23) - 102
y = -3.99(529) + 857.6 - 102
y = -2213.71 + 755.6
y = -1458.11
y = 227.8
Using the given data set of x and y values, a quadratic regression equation can be written in Desmos as y = -3.99x2 + 37.2x - 102. To estimate the y value if x is 23, the equation can be rearranged and all values plugged in. The equation would become y = -3.99(23)2 + 37.2(23) - 102 which can then be simplified to y = -2213.71 + 755.6 and further simplified to y = -1458.11. This rearrangement and simplification can be completed to find the estimated y value when x is 23, which is y = 227.8.
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88 63at a certain stage of a criminal investigation, the inspector in charge is 60% convinced of the guilt of a certain suspect. suppose, however, that a new piece of evidence which shows that the criminal has a certain characteristic (such as left-handedness, baldness, or brown hair) is uncovered. if 20% of the population possesses this characteristic, how certain of the guilt of the suspect should the inspector now be if it turns out that the suspect has the characteristic? you may suppose that the probability of the suspect having the characteristic if they are, in fact, innocent is equal to 0.2, the proportion of the population possessing the characteristic.
The probability that the inspector in-charge is convinced that the suspect is guilty given he/she has brown hair is 0.882.
P(C) = P(C∣G)P(G) + P(C∣Gc)P(Gc) = (1)(0.6)+(0.2)(0.4) = 0.68
Simply put, probability is the likelihood that something will occur. When we don't know how an event will turn out, we can discuss the likelihood or likelihood of several outcomes. Statistics is the study of events that follow a probability distribution.
This is then used to update the inspector's belief in the suspect's guilt posterior to discovering that the suspect does have that characteristic.
P(G∣C) = (P(G)P(C∣G))/P(C)
=1(0.6)/0.68
=0.882
So the probability that the inspector in-charge is convinced that the suspect is guilty given he/she has brown hair is 0.882.
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The probability that the inspector in charge is convinced that the suspect is guilty given he/she has brown hair is 0.882.
P(C) = P(C∣G)P(G) + P(C∣Gc)P(Gc) = (1)(0.6)+(0.2)(0.4) = 0.68
Simply put, the probability is the likelihood that something will occur. When we don't know how an event will turn out, we can discuss the likelihood or likelihood of several outcomes. Statistics is the study of events that follow a probability distribution.
This is then used to update the inspector's belief in the suspect's guilt posterior to discovering that the suspect does have that characteristic.
P(G∣C) = (P(G)P(C∣G))/P(C)
=1(0.6)/0.68
=0.882
So the probability that the inspector in charge is convinced that the suspect is guilty given he/she has brown hair is 0.882.
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A random sample of size 17 is taken from a normal population with meanmu. If the sample mean is 85 and the sample standard deviation is 6, then a 95% upper confidence bound formuis87.8588.0687.1982.15
The 95% upper confidence bound for the population mean μ, given a sample size of 17 and a sample mean of 85 with a sample standard deviation of 6, is 87.85.
87.85
The 95% confidence interval for the population mean is given by
CI = Sample mean ± (t-score) * (Standard Error)
where t-score can be obtained from the t-table with degrees of freedom as n-1 and confidence level as 95%.
Therefore, for a sample size of 17, the t-score is 1.711 and the standard error is 6/√17 = 1.5.
So, the 95% upper confidence bound for μ is
87.85 = 85 + (1.711)*(1.5)
The 95% upper confidence bound for the population mean μ, given a sample size of 17 and a sample mean of 85 with a sample standard deviation of 6, is 87.85.
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Which of these is a coefficient?
A. The 5 in (4t – 5)
B. The 6 in (6 – 9x)
C. The 12 in 12x + 3
D. The 15 in [15(28y)/]
The 12 in 12x+13
Reason:
A coefficient is the number to the left of a variable. The 12x has a coefficient of 12 and variable of x. We multiply the two items together.
12x = 12 times x = 12*x
How much is 100 grams to cups?
100 grams to convert the cups is 1/2 cup.
How do you weigh 100 g?Utilizing a scale is the only accurate technique to measure in grammes. Kitchen spoons and cups, for example, offer an approximate approximation. Additionally, always have a conversion calculator or chart on hand so you can measure grammes without a scale.There are 240 grammes in a cup when measuring using a typical U.S. measuring cup.Using a calculator, you may convert between cups and grammes. You have a choice of 20 well-liked kitchen ingredients or may just write in the product density.You may calculate grammes using this method without a scale. Three teaspoons are equal to one soup spoon.To learn more about grams refer to:
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I need to know how long my shadow would be
Your height and the length of your shadow are related by the formula 1/Tangent (height of the sun). Your shadow would be 5.67 times longer than you if the sun were to be at its lowest point in the sky (10 degrees). At 5 degrees, the proportion is 11.43. (A person of average height (5.8 feet) would therefore cast a shadow that is 66 feet long.)
How would one describe a shadow's length?The length of the shadow is influenced by the Sun's position in the sky. The shadows are long when the Sun is low in the horizon. The shadows are substantially shorter when the Sun is high in the sky.
How far does your morning shadow extend?Because the sun's rays are slanted in the morning and evening but are directly overhead at noon, the shadows are longer in the morning and evening and shorter in the noon. The distance of the object from the light source affects how big the shadow is.
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suppose that the point (x, y) is in the indicated quadrant. decide whether the given ratio is positive or negative. recall that in quadrant i, is positive or negative?
The ratio of x/y is then 2/3, which is a positive number.
In quadrant I, both the x and y coordinates are positive. Therefore, a ratio of x/y will be positive. To illustrate this, let's say that the point (x, y) is located at (2, 3). This means that x=2 and y=3. The ratio of x/y is then 2/3, which is a positive number.
To calculate the ratio, we divide the x coordinate by the y coordinate: x/y = 2/3. This will give us the ratio of the point (x, y) in the indicated quadrant. If the result is a positive number, then the ratio is positive. If the result is a negative number, then the ratio is negative. In this example, the result is a positive number, so the ratio is positive.
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When The Exponential Distribution Probability Is Given As P(X ≤ 9 ) = 1 − E−9/18 The Average Value For X Is A. 18 B. 1/2 C. 9/18 D. 9
The average value for X is 9/18. Hence, the answer is D. 9.
The exponential distribution probability is given as P(X ≤ 9 ) = 1 − E−9/18. The average value for X is calculated as follows.
The expected value (mean) of an exponential distribution of a random variable X with rate parameter λ is given by E[X] = 1/λ.
In the given problem, λ = 18. Thus, the expectation of the random variable X is 1/18.
The calculation for the expected value of X can be represented as:
E[X] = 1/λ = 1/18
Thus, the average value for X can be represented as:
Average Value of X = E[X] = 1/18 = 9/18
Therefore, the average value for X is 9/18. Hence, the answer is D. 9.
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write a situation for algebraic expression 7-s
There are many possible answers for this.
One example is below.
S = the number of stations included when a person canceled orders basic cable, write an expression for the number of stations a person has if he at first ordered 7 basic cable.
What is Subtraction?Subtraction is the process of taking away a number from another. It is a primary arithmetic operation that is denoted by a subtraction symbol (-) and is the method of calculating the difference between two numbers.
here, we have,
algebraic expression 7-s
We can represent this as = 7 - s
now,
The value that we don't know is the number of
stations included when a person canceled orders basic cable.
So we can represent that as s.
Then, since the person at first ordered 7 premium channels, that means he is adding an 7 basic channels with out s basic channels.
So we can represent this as 7-s.
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It is often useful to find the ___ of a polynomial in order to find its roots.
It is often useful to find the constant term of a polynomial in order to find its roots.
Roots of polynomials are the solutions for any given polynomial for which we need to find the value of the unknown variable. If we know the roots, we can evaluate the value of polynomial to zero.
The polynomials are the expression written in the form of:
[tex]$$a_n x^n+a_{n-1} x^{n-1}+\ldots . .+a_1 x+a_0$$[/tex]
The formula for the root of linear polynomial such as ax+b is x=-b / a
The general form of a quadratic polynomial is[tex]$a x^2+b x+c$[/tex] and if we equate this expression to zero, we get a quadratic equation, i.e. [tex]$a x^2+b x+c=0$[/tex]
The roots of quadratic equation, whose degree is two, such[tex]$ a x^2+b x+c=0$[/tex] are evaluated using the formula; [tex]$x=\left[-b \pm \sqrt{ }\left(b^2-4 a c\right)\right] / 2 a$[/tex]The formulas for higher degree polynomials are a bit complicated.
Hence, it is often useful to find the constant term of a polynomial in order to find its roots.
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use analytical methods and/or a graphing utility to identify the vertical asymptotes (if any) of the function.
Analytical techniques or a graphing tool can be used to locate the function's vertical asymptotes.
On a function graph, a vertical asymptote is a line that the graph approaches but never crosses. It can be discovered by examining the function's equation and how it behaves as it gets closer to infinity. By resolving the equation and determining the values of x that cause the denominator to equal 0, one can use analytical techniques to determine the vertical asymptotes of the function. For instance, the function will have a vertical asymptote at x = 5 if the equation is f(x) = (x-3)/(x-5), as the denominator of the equation equals 0 at this point. Vertical asymptotes can also be found using graphing tools. One can observe the behavior of the equation by charting its graph.
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For finding median in continuous series, which amongst the following are of importance?Select one:a. all of theseb. Particular frequency of the median classc. Lower limit of the median classd. cumulative frequency preceeding the median class
For finding median in continuous series, all of the four factors are important.
The median is a central value in a data set that separates the upper and lower halves of the data.
In a continuous series, it is important to find the median because it gives us a good indication of the typical value in the series.
To find the median in a continuous series, four factors are important:
a. Particular frequency of the median class: This refers to the number of observations that fall into the median class.
b. Lower limit of the median class: The lower limit of the median class defines the start of the interval in which the median falls.
c. Upper limit of the median class: The upper limit of the median class defines the end of the interval in which the median falls.
d. Cumulative frequency preceding the median class: This refers to the total number of observations that fall into classes before the median class.
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How are position vs time graph useful ?
An object's distance from its beginning point during the course of its motion is displayed as a position-time graph. A line's slope increases with its steepness, and an object's motion changes more quickly as a result.
How would you explain a time graph?We can see how the speed of a moving object varies over time by looking at a speed-time graph. The acceleration is larger the steeper the graph is. The object is moving steadily if there is a horizontal line. An object is said to be slowing down when a line dips downward.The vertical axis (y-axis) of a distance-time graph will display the distance (in meters, kilometers, miles, etc.) and the horizontal axis will display the time (in seconds, minutes, hours, etc). ( x-axis). On this page, we will examine some distance-time graphs, all of which will be drawn using straight lines. The velocity of the object is shown on a time graph. Therefore, the slope's value at a particular instant indicates the object's velocity at that instant.To learn more about time graph, refer to:
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A nontoxic furniture polish can be made by combining vinegar and olive oil. The amount of oil should be three times the amount of vinegar. How much of each ingredient is needed in order to make 46 oz of furniture polish?
Here, the 11.5 oz of vinegar ingredient is needed in order to make 46 oz of furniture polish .
So in this problem it says a furniture polish can be made containing or combining vinegar and olive oil and the amount of oil should be three times the amount of vinegar. So I'm gonna make vinegar X. And oil three X. How much of each ingredient is needed in order to make 46 oz of furniture Polish. So I'm gonna go ahead and add these together. Okay. Yes. Which means that four x. equals 46 and divide by four So X. is 11.5. So that means that for vinegar we need 11.5 oz. And then I'm going to multiply that by three to get 34.5 oz for the oil. And if you can find those together just to check you get 46. So this would be the amount of both ingredients.
To make 46 oz of furniture polish, you will need 3 times as much olive oil as vinegar.
So, you need 46 oz / 4 = 11.5 oz of vinegar.
And 11.5 oz * 3 = 34.5 oz of olive oil.
Therefore,the 11.5 oz of vinegar ingredient is needed in order to make 46 oz of furniture polish .
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given the standard deviation of 3.7 for a data set, what is the approximate value of the variance?
In this case, the standard deviation is 3.7, so the variance is 3.7², or 13.69. This means that the data points in the data set are, on average, 13.69 units away from the mean.
The variance of a data set is a measure of how the data points are distributed around the mean. It is calculated by squaring the standard deviation, which is the average distance of the data points from the mean.
Variance is a useful measure for quantifying the spread and variability of the data points in a data set. By knowing the variance, it is possible to make predictions about how likely it is that a given data point will fall within a certain range from the mean.
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how to complete the equation
Answer: 3
Step-by-step explanation:
What is the sum of the rational expressions below? 3x + 2 / x-1 + 2x - 5 / x-1 ASAP please
To add the two rational expressions, we need to find a common denominator:
3x + 2 / x - 1 + 2x - 5 / x - 1 = (3x + 2)(x - 1) / (x - 1)(x - 1) + (2x - 5)(x - 1) / (x - 1)(x - 1)
Now that we have a common denominator, we can add the numerators and simplify:
= (3x^2 - x + 2x - 5) / (x - 1)(x - 1)
= (3x^2 + x - 5) / (x - 1)(x - 1)
This is the simplified sum of the two rational expressions.
what proportion of the area is in each tail? enter your answer to 3 decimal places.
The proportion of the area in each tail is 0.025, or 2.5%. This means that 2.5% of the area of the normal distribution lies in each of the two tails.
The total area of the normal distribution is 1.
The area of the left tail is 0.3413.
The area of the right tail is 0.3413.
Therefore, the proportion of the area in each tail is 0.341.
The normal distribution is a symmetric probability distribution that has a single peak and two tails extending outwards from the peak. The proportion of the area in each tail of the normal distribution is 0.025, or 2.5%. This proportion is the same for both tails and is determined by the fact that the normal distribution is symmetric. This means that 2.5% of the area of the normal distribution lies in each of the two tails. This area can be calculated by multiplying the total area of the normal distribution by 0.025. The total area of the normal distribution is equal to 1, and so the area in each tail is equal to 0.025. This proportion is constant regardless of the mean and standard deviation of the normal distribution. The proportion of the area in each tail of the normal distribution is an important concept in statistics, as it is used to calculate probabilities of certain events occurring.
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The complete question is
What proportion of the area is in each tail of a normal distribution with mean 0 and standard deviation 1? Enter your answer to 3 decimal places.
The radiu of a circle i 6 centimeter. What i the circle' area?
Ue 3. 14 for . Quare centimeter
The Area of the circle is = 3.14 x (6 cm)^2
Area = 113.04 cm^2
What is the area of circle?The theory used in this question is the formula for the area of a circle, which states that the area of a circle is equal to π multiplied by the square of the radius.
given below
Step 1: Use the formula A = πr^2 to calculate the area of the circle.
Step 2: Identify the radius, r, which is equal to 6 cm.
Step 3: Substitute the values into the formula, A = πr^2.
Step 4: Calculate the area by multiplying 3.14 (π) by the square of 6 cm (6 cm x 6 cm).
Step 5: The area of the circle is 113.04 cm^2.
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consider the following porgram segment where i j and k are integer variables
For the program segment where i , j and k are integer variables , then the print statement is executed 576 times .
The program is : for i : 1 to 12 do
for j [tex]:[/tex] 5 to 10 do
for k : = 15 down to 8 do
print (i - j ) × k
This is because the program has three nested loops, each of which run a specific number of times.
The innermost loop is executed 15 - 8 + 1 = 8 times, for each value of k.
The middle loop is executed 10 - 5 + 1 = 6 times, for each value of j.
And the outermost loop is executed 12 times, for each value of i.
the total number of times print statement is executed is 8×6×12 = 576.
Therefore , The print statement will be 576 times .
The given question is incomplete , the complete question is
Consider the following program segment where i , j and k are integer variables ,
for i : 1 to 12 do
for j : 5 to 10 do
for k : = 15 down to 8 do
print (i - j ) × k
How many times the print statement is executed ?
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What is 145.65 divided by 21.2?
Answer: 6.87
Step-by-step explanation:
21.2 / 145.65
Move to the decimal to the right 1 time to make 21.2 to 212 and 145.65 to 1456.5.
Then you want to look for a number you can multipl 212 into the 1456.
In this case, 212 times 6 because it equals 1272.
If you multiply 212 times 7, you get 1484 (which is over the number of 1456 { we dont want that}).
Then you continue multiplying the number until you get to 0, or in other words, a remainder. In which I got, 6.870
a1=(1,3,-1) , a2=(-5,-8,2) and b=(3,-5,h). For what values of h is b in plane spanned by a1 and a2?
The value of h for which b in plane spanned by a1 and a2 is 3.
If b is spanned by a1 and a2, then for some constant x and y
b = x*a1 + y*a2
(3, -5, h) = x(1, 3, -1) + y(-5, -8, 2)
So we get equations
x - 5y = 3
3x - 8y = -5
-x + 2y = h
Solving x - 5y = 3 and 3x - 8y = -5
(3x - 8y) - 3(x - 5y) = -5 - 3*3
7y = -14
y = -2
Also x = 3 + 5y = 3 + 5*-2
So x = -7
Now h = -x + 2y
= -(-7) + 2*(-2)
= 7 - 4
= 3
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Which operation is NOT used in the phrase "three times a number, decreased by 2, divided by 6" ?
Answer:
Addition (+)
Step-by-step explanation:
If we were to take the problem and form an expression, it would look like this:
3 times a number (3 ×?) decreased by 2 (- 2) divided by 6 (÷ 6)
Putting it all together it forms:
3 ×? - 2 ÷ 6The four operations are addition, subtraction, multiplication and division.
We can see the multiplication, subtraction, and division, but not addition.
Therefore, the operation that is missing is Addition.
True or False: An observational study itself can never establish cause and effect.
We are unable to establish causation or cause-and-effect correlations using observational data. Observational studies are fantastic for describing a particular group, contrasting groups, or looking at the patterns or relationships between variables.
What is an observational study?Observational research Without making any attempts to change the value of the explanatory or response variables, this measurement only considers the response variable's value. To put it another way, in an observational study, the researcher just watches how the participants behave without attempting to sway the results.Observational studies involve observing the results of a risk factor, diagnostic test, treatment, or other intervention without attempting to alter who is or is not exposed to it.Observational studies are less reliable than experimental research, are more subject to bias and confounding, and cannot be used to prove causation.To Learn more About Observational studies Refer To:
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Priya writes the equation y=-1/2x-7. Write an equation that has: a. Exactly one solution in common with Priya's equation
There are other equations that have the same number of solutions as Priya's equation, y = -1/2x - 7. For instance:
y = -1/2x - 7 + k (where k would be any constant value)
or
y equals mx plus b, where m is -1/2 and b is -7.
Single Solution Equation Y=-1/2x-7The slope and y-intercept of the equations are the same as Priya's equation. This means that the equations will meet Priya's equation at exactly one point, giving them the same solution. However, it is important to note that the constant value (k) or the y-intercept (b) can be changed to make the equation different from Priya's equation, but as long as the slope (m) remains the same, the two lines will intersect at exactly one point.
I determined that because both equations have the same slope (-1/2) and the same y-intercept (-7). This means that they will intersect at exactly one point on the coordinate plane, resulting in one solution in common.
The slope of a line is represented by the coefficient of x in the equation, and the y-intercept is represented by the constant term. In both equations, the slope is -1/2 and the y-intercept is -7, so they are the same line, and therefore will have exactly one solution in common.
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state whether the following statement is true or false. the law of sines can be used to solve triangles where three sides are known.
The statement "the law of sines can be used to solve triangles where three sides are known" is false.
A triangle is a three-sided polygon, with each side representing a line segment connecting two vertices. To fully determine a triangle, we need to know at least three pieces of information about it, such as the lengths of its sides, or the measures of its angles.
The law of sines is a mathematical formula that relates the ratios of the lengths of the sides of a triangle to the angles opposite those sides. It states that the ratio of the length of a side of a triangle to the sine of the angle opposite that side is constant for all three sides of the triangle.
However, the law of sines cannot be used to solve a triangle if all three sides are known. To solve a triangle, we need to have additional information, such as the angles or some side-angle pairs. The law of sines can only be used to find missing side lengths or angle measures if we have at least one side length and one angle measure, or two side lengths and an angle not contained between them.
In conclusion, the statement "the law of sines can be used to solve triangles where three sides are known" is false. To solve a triangle, we need additional information in the form of angles or side-angle pairs.
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Find the diagonal of a square whose sides are of the given measure.
Given = 7√3
Step-by-step explanation:
Use the Pythagorean theorem: a^2 + b^2 = c^2. In this case, sides a and b are each 7sqrt(3), and c is the diagonal of the square.
a^2 + b^2 = c^2
(7sqrt3)^2 + (7sqrt3)^2 = c^2
294 = c^2
c = sqrt(294) = 7sqrt(6)
The table shows the circumference of a tree in centimeters, y, at x years. Choose the function that represents the data. Y = y = 2. 7xy = 2. 7xy = 2. 7x2.
The function that best represents the data in the table is y = 2.7x. This is because the circumference of the tree is directly proportional to the number of years it has been alive, which can be represented by a linear equation.
The circumference of a circle is the total length of the edge of the circle. It is calculated using the formula C = 2πr, where r is the radius of the circle. This formula is based on the fact that the circumference of a circle is equal to the length of the perimeter of the circle, which is equal to the product of the circumference and the radius. The circumference is an important measure used in many areas of mathematics and geometry, including area and volume calculations.
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How to use Recursive formula calculator?
There are a few recursive formulas that can be used to calculate the nth term based on the pattern of the given data. For n 2, they are the nth term of the mathematical progression a = a - 1 + d. Geometric Progression nth term a = a - 1 r for n > 2.
What is meant by Recursive formula?Given that each phrase, an, goes back to the term before it, an1, the formula an=2an1+3 is recursive. According to this equation, the term we are looking for is equal to the previous term multiplied by two and then added to three. 4,11,25 make up the first three terms in this chain.
Almost identical to reading one, writing recursive functions:
Create a regular function with a base case that can be satisfied by its inputs.Give the function arguments that immediately cause the base case to be executed.Just once should be passed for the subsequent arguments that start the recursive call.A recursive sequence, also called a recurrence sequence, is a series of numbers that are indexed by integers and produced by solving a recurrence equation.
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100 POINTS AND BRAINLIEST!!!!!!
Find the equation of the linear function represented by the table below in slope-intercept form.
(Table below)
x y
1 0
2 5
3 10
4 15
Answer:
e
Step-by-step explanation:
e
Answer:
Step-by-step explanation:
The slope of the line can be found by finding the rise over the run between two points on the line. Using the points (1,0) and (2,5), the slope can be found as follows:
m = (5-0)/(2-1) = 5
Now that we have the slope, we can use the point-slope form of a line to find the equation of the line in slope-intercept form. Using the point (1,0) and the slope (5), we have:
y - 0 = 5(x - 1)
Simplifying and solving for y, we have:
y = 5x - 5
So the equation of the linear function represented by the table is:
y = 5x - 5.