A polynomial term is an expression composed of constants, variables, and exponents.
A polynomial term is an expression composed of constants, variables, and exponents. Constants are the numerical values that don't change, while variables are values that can change. Exponents are numbers that indicate how many times a number is multiplied by itself. For example, 2^3 means 2 multiplied by itself 3 times, or 8. A polynomial term is an expression that combines constants, variables, and exponents, such as 6x^2 - 3x + 5. In this expression, 6, -3, and 5 are constants, x is a variable, and 2 and 1 are exponents. A polynomial term can also contain fractions, such as (2x + 1)/3. In this case, 2, 1, and 3 are constants, and x is a variable. Polynomial terms are the building blocks of polynomials, which are equations that consist of multiple polynomial terms.
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the price of an item is $90.after the sales tax is added, the final cost is &94.5. which percent of sales tax has been applied to the item?
The percent of sales tax that has been applied to the item is 5%.
What is sales tax?A sales tax is a consumption tax imposed on the sale of items. It is often applied to the selling price of an item.
Here, the original cost is $90 and the final cost is $94.5.
Let, the sales tax rate is r%.
Calculate the percentage of sales tax.
Final price after sales tax = Selling Price×(1 + Rate of sales tax/100)
94.5 = 90(1+r/100)
94.5 = 90 + 0.9r
0.9r = 4.5
r = 5
Therefore, the obtained answer is 5%.
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A wholesaler sells 1 kg of green tea leaves for $8 and 600 g of assam black tea leaves for $7.20. A tea merchant wants to mix these two types of tea leaves to form 100 kg of classic blend. Determine the amount of each type of tea leaves he should order from the wholesaler such that his cost price is $10/kg.
Answer:
50 kg of green tea leaves and 50 kg of assam black tea leaves.
Step-by-step explanation:
Let x kg be the amount of green tea and y kg be the amount of Assam tea.
x+y=100 (1) [mass]
price for 1 kg of assam tea= 7.20/600×1000g
= $12/kg
total cost= 100×10
= $1000
8x+12y= 1000 (2) [cost]
(1)×8: 8x+8y= 800 (3)
(2)-(3): (8x+12y)-(8x+8y)= 1000-800
4y= 200
y= 50 (4)
sub (4) into (1):
x+50= 100
x= 50
Which of the following is the surface area of the right cylinder below?
radius 7
height 2
Answer:
395.8406(answer depends on what place you round to)
Step-by-step explanation:
The equation is A=2πrh+2πr^2. Plug it what you know, and it'd look like this: A=2π(7)(2)+2π(7)^2. Use your calculator and you get the answer.
In parallelogram ABCD, AB = 5x * 3 and CD = 15 * x. FInd the value of x
In a parallelogram, opposite sides are equal. Therefore, AB = CD.
5x * 3 = 15 * x
15x = 15
x = 1
Therefore, the value of x is 1.
If the height of parallelogram ABCD is 6, what is the area of the parallelogram?To find the area of parallelogram ABCD, we can use the formula A = base x height, where the base is the length of side AB and the height is the perpendicular distance between side AB and the opposite side CD. Since the height of parallelogram ABCD is given as 6, we need to find the length of side AB.
From the given information, we know that AB = 5x * 3, where x = 1. Therefore, AB = 15. Now we can calculate the area of parallelogram ABCD as:
A = base x height
A = 15 x 6
A = 90 square units
Therefore, the area of parallelogram ABCD is 90 square units.
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Rewrite in simplest rational exponent form square root of x times the fourth root of x. Show each step of your process.
We can simplify the expression to get:
[tex]\sqrt[4]{x^3}[/tex]
How to simplify the expression?Here we want to simplify the following expression:
[tex]\sqrt[]{x} *\sqrt[4]{x}[/tex]
Remember that a square root is equivalent to a power of 1/2, and the fourth root is equivalent to a power of 1/4.
Then we can write:
[tex]\sqrt[]{x} *\sqrt[4]{x} = x^{1/2}*x^{1/4}[/tex]
Now in the product we just add the exponents:
[tex]\sqrt[]{x} *\sqrt[4]{x} = x^{1/2}*x^{1/4} = x^{1/2 + 1/4} = x^{3/4} = \sqrt[4]{x^3}[/tex]
That is the expression si,plified.
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You deposit $9000 in a savings account that earns 3.6% annual interest compounded monthly.
Answer:
A(t) = 9000(1 + 0.036/12)^12t
[Function formula for the compound interest]
A = 9000(1 + 0.036/12)^12t
[General formula for the compound interest]
A(1) ≈ 9329.40 $
[Compound interest over 1 year]
Step-by-step explanation:
Compound interest formula:
A = P(1 + r/n)^nt.
P is the principal or starting amount.
r is the interest rate.
n is the number of times compounded per year.
t is the period of time.
Given P is 9000, r is 3.6% or 0.036, n is 12 or monthly, and t is variable.
The following function represents the relationship over time:
A(t) = 9000(1 + 0.036/12)^12t
Newington Town Manager Tanya Lane proposed a $124.2 million budget Monday night -- a 4.7 percent increase over the previous year." [R141] What was Newington's budget in the "previous year"?
Newington's budget in the "previous year" is $119.2 million
The term "budget" refers to a financial plan for a given period that outlines expected expenses and revenues. The previous year's budget for Newington is the financial plan that the town had for the previous fiscal year.
Assuming the previous year's budget refers to the fiscal year that ended just before the current fiscal year, we can find the amount by looking at the town's financial statements for that period. These statements will show the town's revenues and expenses for that fiscal year, and the difference between the two will be the budget.
If the town had $100 million in revenues and $95 million in expenses in the previous fiscal year, then the budget for that year would be $5 million. This means that the proposed $124.2 million budget for the upcoming year is a 4.7% increase from the $119.2 million budget of the previous year.
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PLEASE HURRY!! Which of the following statements are true regarding the graph of this linear function? Select all that apply.
The slope of the line, 9.75, is the amount of money she makes per hour of work. The y-intercept of the line, -25, is the amount of money she starts with, since she owes her sister $25 and has worked 0 hours.
The definition of amount?Extent, volume, and supply are all nouns. the sum of two or more amounts; the complete worth, impact, or importance of anything.
What is an example of a number?A number is a mass or accumulation, especially of something impossible to count: amount of The appropriate quantity of sand wasn't delivered. Animals were kept on a small amount of land. He donated money on a regular basis to a charity.
We know that slope =
[tex]$m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Here, slope m is
[tex]$m=\frac{53 -14}{8 -4 }[/tex]
[tex]$m=\frac{39}{4 }[/tex]
m = 9.75
And putting the value in y-intercept form we have
y = 9.75x – 25
Therefore, The slope of the line, 9.75, is the amount of money she makes per hour of work. The y-intercept of the line, -25, is the amount of money she starts with, since she owes her sister $25 and has worked 0 hours.
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90 points for helping! Need a explanation as well.
keeping in mind that perpendicular lines have negative reciprocal slopes, let's check for the slope of the equation above
[tex]2y+3x=1\implies 2y=-3x+1\implies y=\cfrac{-3x+1}{2} \\\\\\ y=\stackrel{\stackrel{m}{\downarrow }}{-\cfrac{3}{2}}x+\cfrac{1}{2}\qquad \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\stackrel{~\hspace{5em}\textit{perpendicular lines have \underline{negative reciprocal} slopes}~\hspace{5em}} {\stackrel{slope}{ \cfrac{-3}{2}} ~\hfill \stackrel{reciprocal}{\cfrac{2}{-3}} ~\hfill \stackrel{negative~reciprocal}{-\cfrac{2}{-3} \implies \cfrac{2}{ 3 }}}[/tex]
so we're really looking for an equation whose slope is 2/3
[tex]{\Large \begin{array}{llll} y=\stackrel{\stackrel{m}{\downarrow }}{\cfrac{2}{3}}x+\cfrac{5}{2} \end{array}} \qquad \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}[/tex]
Use a graphing calculator to find an equation of the line of best fit for the data. Round the slope to the nearest tenth and the y-
intercept to the nearest integer.
X
y
y =
5 6
12 -2
r=
7
00
8 9 10 11 12
3
-1-4
6
0
Identify the correlation coefficient. Round to the nearest thousandth if necessary.
An equation of the line of best fit for the data is y = -0.9x + 13.6.
The correlation coefficient (r) for the data to the nearest thousandth is -0.964.
How to determine an equation of the line of best fit for the data?In order to determine a linear equation in slope-intercept form for the line of best fit that models the data points described above, we would use a scatter plot (graphing calculator).
On the Excel worksheet, you should right click on any data point on the scatter plot, select format trend line, and then tick the box to display a linear equation for the line of best fit (trend line) on the scatter plot.
From the scatter plot (see attachment) which models the relationship between the data set, a linear equation for the line of best fit is given by:
y = -0.895x + 13.600.
Rounding up as required, we have:
y = -0.9x + 13.6.
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Complete Question:
Use a graphing calculator to find an equation of the line of best fit for the data in the table. Round the slope and y-intercept to the nearest tenth. Then Identify and interpret the correlation coefficient.
X- 10.1 9.8 9.7 9.4 8.9 8.7 8.4 8.1
Y- 4.3 4.8 5.3 5.2 5.6 5.8 6.1 6.3
The equation of the line of best fit is y=
To the nearest thousandth, the correlation coefficient is r=
If you are obtaining a $195,000 loan and the bank charges 4.1%
plus $250 and 2½ points, what are the one-time charges?
Answer:
5125
Step-by-step explanation:
I was have it in my practice today
how many pattern block trapezoids would create 5 hexagons
There would be 30 trapezoids to create 5 hexagons.
An hexagon is a six-sided polygon. It is made up of six equilateral triangles and six trapezoids. To create an hexagon using pattern blocks, you need 10 equilateral triangles and 20 trapezoids. Therefore, to create 5 hexagons
The exact number of trapezoids needed to create three hexagons depends on the size and shape of the hexagons. However, in general, you would need at least 18 trapezoids.
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To create 5 hexagons using pattern block trapezoids, you would need 15 trapezoids. This is because 3 trapezoids form one hexagon.
Explanation:In geometry, a hexagon can be divided into 6 equilateral triangles. In the context of pattern blocks, these triangles are often used to construct other shapes. Now, considering that a trapezoid in pattern blocks is usually made up of 2 of these triangles, it takes 3 trapezoids to create one hexagon. Hence, to create 5 hexagons, you would need 5 x 3 trapezoids, which equals 15 trapezoids.
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Michael took his three kids to get haircuts the haircuts cost $57. 50 he also gave the stylist a 20% tip what was the total cost including tip for Michael’s three kids to get haircuts
The total cost of haircuts for Michael's three children, including tip, would be $207.00.
If Michael gave a 20% tip and the haircuts cost $57.50, the tip would be:
Tip = 0.20 * $57.50 = $11.50
The total cost of the haircuts, including the tip, is as follows:
Total cost = haircut cost + tip
The total cost is $57.50 + $11.50.
The total cost is $69.00.
Since Michael took his three children to get haircuts, the total cost for all three children, including tip, would be:
Total cost for three children = three times the total cost
Total cost for three children = three times $69.00
The total cost for three children is $207.00.
As a result, the total cost of haircuts for Michael's three children, including tip, would be $207.00.
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suppose that the proportions of blood phenotypes in a particular population are as follows: a b ab o 0.42 0.14 0.05 0.39 assuming that the phenotypes of two randomly selected individuals are independent of one another, what is the probability that both phenotypes are o? (enter your answer to four decimal places.)
The probability that both phenotypes are o is 0.1600
Events classified as independent do not depend on other events for their occurrence. For instance, if we toss a coin in the air and it lands on head, we can toss it again and this time it will land on tail. Both instances include independent occurrences of the two events.
In a probability notation, events and are independent if ( ∣ ) = ( ) . Events and are independent if and only if ( ∩ ) = ( ) × ( ) . If and are dependent events, then ( ∩ ) = ( ∣ ) × ( ) .
the proportions of blood phenotypes in a particular population are as follows: a b ab o 0.42 0.14 0.05 0.39 so for o the value is 0.40 so we put it and slolve .
The samples are independents, so:
P(O1∩O2) = P(O1).P(O2) = 0.40*0.40=0.1600
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Find the area of the shaded region. The graph to the right depicts IQ scores of adults, and those scores are normally distributed with a mean of 100 and a standard deviation of 15.
The area of the shaded region is
The area of the shaded region is given as follows:
0.0475.
How to obtain probabilities using the normal distribution?The z-score of a measure X of a variable that has mean symbolized by [tex]\mu[/tex] and standard deviation symbolized by [tex]\sigma[/tex] is obtained by the rule presented as follows:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score represents how many standard deviations the measure X is above or below the mean of the distribution, depending if the obtained z-score is positive or negative.Using the z-score table, the p-value associated with the calculated z-score is found, and it represents the percentile of the measure X in the distribution.The mean and the standard deviation for the IQ scores are given as follows:
[tex]\mu = 100, \sigma = 15[/tex]
The shaded region is the area to the right of 125, hence it's area is one subtracted by the p-value of Z when X = 125, hence:
Z = (125 - 100)/15
Z = 1.67
Z = 1.67 has a p-value of 0.9525.
Hence:
1 - 0.9525 = 0.0475.
Missing InformationThe shaded region is the area to the right of 125.
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what is the problem from y=x+1
Answer: Change x to a number, and that number + 1 will be y
Step-by-step explanation: the reason for this is simple, change the independent variable, which is always in the problem, and you can figure out the dependent variable.
Answer:
X +1
Step-by-step explanation:
the graph is x +1.....
Need help with this for school
Answer:
135
Step-by-step explanation:
The max value is where the far right point of the "whisker" is.
please help meeeeh:
Find the first four terms and stated term given the arithmetic sequence, with a, as the 1" term.
an = 25 - 10n, a5
an = 11 + 9n, a6
an = 65 - 35n, a9
Answer:
The nth term of an arithmetic sequence is given by an = a + (n – 1)d ... Step 1: First, calculate the difference between each pair of adjacent terms.
Step-by-step explanation:
Hope this help's you
one card is randomly selected from a standard deck of 52 cards. what is the probability of randomly selecting a(n) jack or 4? enter your answer as a reduced fraction.
the probability of randomly selecting a jack or 4 from a standard deck of 52 cards is 2/13.
In a standard deck of 52 cards, there are four jacks and four 4s, for a total of 8 cards that are either a jack or a 4. The probability of selecting a jack or 4 can be found by dividing the number of favorable outcomes (8) by the total number of possible outcomes (52): P(jack or 4) = 8/52. This fraction can be reduced by dividing both the numerator and denominator by 4: P(jack or 4) = 2/13. Therefore, the probability of randomly selecting a jack or 4 from a standard deck of 52 cards is 2/13. Probability is a measure of the likelihood of an event occurring, expressed as a number between 0 and 1. The probability of an event is calculated by dividing the number of favorable outcomes by the total number of possible outcomes. Probability is used in a wide range of fields, from gambling and sports to scientific research and data analysis. Understanding probability is important for making informed decisions, predicting outcomes, and assessing risks.
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Too tired to do it. please answer it for me
The regular price for a certain bicycle is
$125.00. If that price is reduced by 20%, what is the new price?
Answer:
The new price is $100.
Step-by-step explanation:
20% of $125 = 0.2 × 125 = $25
New price = Regular price - Discount
New Price = $125 - $25 = $100
What is the perimeter, p, of a rectangle that has a length of x 8 and a width of y − 1? p = 2x 2y 18 p = 2x 2y 14 p = x y − 9 p = x y 7
The perimeter of the given rectangle is option (b) 2x + 2y + 14.
Perimeter is a mathematical term used to describe the distance around the boundary of a two-dimensional shape.
In this case, we are given a rectangle with a length of x+8 and a width of y-1, and we are asked to find its perimeter, p.
To find the perimeter of a rectangle, we need to add up the lengths of all four sides. In a rectangle, opposite sides are equal in length, so we can simplify the calculation by multiplying the sum of the length and width by two. This gives us the formula:
perimeter = 2(length + width)
Substituting the given values for the length and width of our rectangle, we get:
p = 2(x+8 + y-1)
p = 2(x+y+7)
Simplifying further, we get the answer:
p = 2x + 2y + 14
Therefore, the correct option is (b).
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Complete Question:
What is the perimeter, p, of a rectangle that has a length of x + 8 and a width of y − 1?
a) p = 2x + 2y + 18
b) p = 2x + 2y + 14
c) p = x + y − 9
d) p = x + y + 7
Point B is located at (-4, -6) on the coordinate plane. Point B is reflected over the x-axis to create point B'. Point B' is then reflected over the y-axis to create point
B". What ordered pair describes the location of B"?
Answer:
The ordered pair for point B after it has been reflected over both the x and y-axis is (4, 6).
This is due to the rule for reflecting over the x-axis, which is to negate the value of the y-coordinate of each point, but leave the x-value the same. This means that after reflecting point B over the x-axis, it's new coordinates would be (-4, 6).
The rule for reflecting over the y-axis is to negate the value of the x-coordinate of each point, but leave the y-value the same. This means that after reflecting point B' over the y-axis, it's new coordinates would be (4, 6).
make a venn diagram for the following situation and answer the questions below. a recent poll states that 48% of us teenagers had read harry potter and the half blood prince, 58% had seen the movie and that 22% both read the book and saw the movie. find the probability that a randomly selected us teenager
The probability that a randomly selected US teenager has either read Harry Potter and the Half Blood Prince or seen the movie is 84%.
To create a Venn diagram for this situation, you would need two circles that overlap in the middle. One circle would represent the 48% of teenagers who read the book, and the other circle would represent the 58% of teenagers who saw the movie. The overlap between the two circles would represent the 22% of teenagers who both read the book and saw the movie.
+-----------------------------------------+
| |
| Read |
| 48% (R) |
| |
+--------------------+-------------------+
| | |
| | |
| | |
| Both (B∩R) | Movie (M) |
| 22% (B) | 58% (M) |
| | |
| | |
| | |
+---------------------+------------------+
Not Read
30% (N∩M)
Here, R represents the event of reading the book, M represents the event of watching the movie, and B represents the event of both reading the book and watching the movie. The numbers in parentheses represent the percentage of US teenagers in each event. The area of each circle represents the total number of US teenagers.
To find the probability that a randomly selected US teenager has either read the book or seen the movie, you need to find the total area of the two circles (the 48% who read the book plus the 58% who saw the movie) and subtract the overlap (the 22% who both read the book and saw the movie). This gives you:
P(read or saw) = 48% + 58% - 22% = 84%
So the probability that a randomly selected US teenager has either read Harry Potter and the Half Blood Prince or seen the movie is 84%.
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superior segway tours gives sightseeing tours around chicago, illinois. it charges a one-time fee of $45, plus $25 per hour. what is the slope of this situation?
If they charges a one-time fee of $45, plus $25 per hour, then the the slope of this situation is $25 per hour.
The situation described can be represented by the linear equation
Cost = $45 + $25 × hours
where "Cost" is the total cost of the tour and "hours" is the number of hours for which the tour is taken.
The slope of this equation represents the rate of change in the cost of the tour with respect to the number of hours.
In other words, it tells us how much the cost increases for each additional hour of the tour.
The slope of this equation is simply the coefficient of the "hours" variable, which is $25.
Therefore, the slope of this situation is $25 per hour.
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Answer:
$25 per hour.
Step-by-step explanation:
Bella has volunteered to feed the dogs at a shelter. The table shows the number of cups of dog food that each dog should be fed each day. What does the number of observations in this data set signify
It signifies the number of dogs that Bella feeds. The number of observations in dataset is an important characteristic that helps to determine the size of data and potential variability of data.
The table of the number of cups of dog food that each dog should be fed each day is a dataset that contains multiple observations. Each row in the table represents one observation for one dog, with information about the number of cups of dog food that the dog should be fed each day.
The number of observations in this data set is equal to the number of dogs that Bella will be feeding at the shelter. Each observation in the dataset represents a single unit of information, in this case, the number of cups of dog food that a particular dog should be fed.
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Matt says the expressions 12 divided by p and p divided by 12 are equivalent. Darla says they are not equivalent. who is correct? explain.
Two expressions p/12 and 12/p gives different values, and thus they are not equivalent so Darla is correct and Matt is incorrect.
What is Fraction?A fraction represents a part of a whole.
To Check if Matt or Darla is correct, we need to check if the expressions 12 ÷ p and p ÷ 12 are equivalent.
To see whether the two fractions equivalent or not, we can choose a specific value of p
Compare the two expressions.
let p = 6, then:
12 ÷ p
12 ÷ 6 = 2
p ÷ 12
6 ÷ 12 = 1/2
The two expressions give different values, and thus they are not equivalent.
Hence, Two expressions p/12 and 12/p gives different values, and thus they are not equivalent so Darla is correct and Matt is incorrect.
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For some reason, Brainly keeps saying that the question I'm asking hurts their feelings though I am just typing out the question from the screenshot. please take a look
There is part A and Part B.
Based on the information in the graph, we can infer that the area of the three triangles is the same. In this case the area would be 45 cm².
How to calculate the area of triangles?To calculate the area of the triangles we must calculate the area of one of them taking into account that all three have the same dimensions. According to the above, we must apply the following formula:
a = b * h / 2Then we must replace the values of the base and the height:
a = 9 * 10 / 2a = 90 / 2a = 45So the area of the triangles would be 45cm.
Note: This question is incomplete. Here is the complete information:
question
What is the area of the triangles?
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the multiple linear regression predictive model is thus: and the least squares optimization target is we can find the least squares solution by finding the gradient of with respect to and setting it to zero: what kind of object is ? a real number a vector with the same size as . a matrix of the same size as . a vector with the same size as . unanswered what is ? . . . unanswered savesave your answer submit you have used 0 of 3 attempts
Object is kind of a vector with the same size as the coefficients in the linear regression model.
In the least squares optimization target, the sum of squared errors (SSE) is typically minimized with respect to the coefficients of the linear regression model. The gradient of the SSE with respect to the coefficients is a vector that provides the direction of steepest ascent, or the direction in which the SSE increases the most rapidly. Setting this gradient vector to zero and solving for the coefficients yields the least squares solution to the linear regression problem.
Therefore, in this context, " " is likely a vector of coefficients that are being optimized to minimize the SSE.
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1. Find f(4)
f(1)=8
f(n)=-2f(n-1)-4
The fourth term in the sequence is:
f(4) = -76
How to find the value of f(4)?Here we have a sequence where we know the first term:
f(1) = 8
And the recursive formula is:
f(n) = -2*f(n - 1) - 4
Using the recursive formula we can get the next terms:
f(2) = -2*f(2 - 1) - 4
= -2*f(1) - 4 = -2*8 - 4 = -20
f(3) = -2*f(3 - 1) - 4
= -2*-20 - 4 = 40 - 4 = 36
f(4) = -2*f(4 - 1) - 4
= -2*36 - 4 = -76
That is the value of the fourth term.
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