The possible values of [tex]$a_{10}$[/tex] are [tex]$-\frac{263}{4}$[/tex]and [tex]$-\frac{13}{5}$[/tex].
Since [tex]$a_1, a_2, a_3,\dots$[/tex] is an arithmetic sequence, we can write[tex]$a_3 = a_1 + d$[/tex] and [tex]$a_5 = a_1 + 2d$[/tex] where [tex]$d$[/tex] is the common difference between consecutive terms. Then the given equations become[tex]$3a_1 + 4d = -12$ and $a_1(a_1 + d)(a_1 + 2d) = 80$.[/tex] Simplifying the second equation gives $a_[tex]1^3 + 3da_1^2 + 2d^2a_1 - 80 = 0$.[/tex]
We can solve for [tex]$d$[/tex] in the first equation: [tex]$d = \frac{-3a_1-12}{4} = -\frac{3}{4}a_1 - 3$[/tex]. Substituting this into the second equation yields a cubic equation in terms of[tex]$a_1$[/tex]:
[tex]a\frac{3}{1}-[/tex] [tex]\frac{9}{4} a\frac{2}{1} -[/tex] [tex]\frac{15}{4} a_{1}- 80=0[/tex]
Using synthetic division or another method, we can find that [tex]$a_1 = -5$[/tex] is a root of this equation. Dividing by [tex]$a_1 + 5$[/tex] yields the quadratic [tex]$a_1^2 - \frac{1}{4}a_1 - 16 = 0$[/tex], which has roots [tex]$a_1 = -4$[/tex] and [tex]$a_1 = 4/5$[/tex].Therefore, the possible values of the common difference [tex]$d$[/tex] are [tex]$-\frac{27}{4}$[/tex] and [tex]\frac{4}{5}$[/tex]
Using [tex]$a_1 = -5$[/tex] and [tex]$d = -\frac{27}{4}$[/tex], we find that [tex]$a_{10} = a_1 + 9d = -5 - \frac{243}{4} = -\frac{263}{4}$.[/tex]
Using [tex]$a_1 = -5$[/tex] and [tex]$d = \frac{4}{5}$[/tex], we find that [tex]$a_{10} = a_1 + 9d = -5 + \frac{36}{5} = -\frac{13}{5}$.[/tex]
Therefore, the possible values of [tex]$a_{10}$[/tex] are [tex]$-\frac{263}{4}$[/tex]and [tex]$-\frac{13}{5}$[/tex].
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what is the range of data?
40
42
54
96
what is the median of the data?
64.5
72.5
74.5
75
what is the mode of the data?
5
70
75
88
The range, median and mode of the data-set are given as follows:
Range: 42.Median: 74.5.Mode: 75.How to obtain the features?Considering the stem-and-leaf plot, the data-set is given as follows:
54, 55, 60, 66, 69, 72, 73, 74, 75, 75, 81, 82, 88, 89, 95, 96.
The range of a data-set is calculated as the difference between the highest value and the lowest value in the data-set, thus:
96 - 54 = 52.
The data-set has an even cardinality of 16, hence the median is calculated as the mean of the two middle elements as follows:
Median = (74 + 75)/2
Median = 74.5.
The mode of a data-set is the observation that appears the most times in the data-set, hence it is of 75, which is the only observation that appears twice in the data-set.
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The amount of money in a savings account increases by 0.2% every month.
Part A
Write a function for the amount of money in the account, B, after t months with an initial deposit of $100.
B(t) =
(
)t
Part B
By what factor does the amount in the account increase every month? Every year? Every 5 years? Round answers to the nearest thousandth.
each month:
each year:
every five years:
a) A function for the amount of money in the account, B, after t months with an initial deposit of $100 isB(t) = [tex]100(1 + 0.002)^t[/tex]
b) The amount in the account increases by a factor of approximately 1.002 every month, approximately 1.025 every year and approximately 1.099 every five years.
a) The function for the amount of money in the account after t months with an initial deposit of $100 and an increase of 0.2% per month can be written as:
B(t) = [tex]100(1 + 0.002)^t[/tex]
where t is the number of months.
b) To determine the factor by which the amount in the account increases every month, year, and five years, we can calculate the value of the function for t = 1, t = 12, and t = 60, respectively, and then divide each value by the previous one.
For each month:
B(1) = 100(1 + 0.002) = $100.20
B(2) = 100(1 + 0.002)² = $100.40
B(2)/B(1) = $100.40/$100.20 = 1.001993
The amount in the account increases by a factor of approximately 1.002 every month.
For each year:
B(12) = 100(1 + 0.002)¹² = $102.44
B(24) = 100(1 + 0.002)²⁴ = $105.01
B(24)/B(12) = $105.01/$102.44 = 1.0249
The amount in the account increases by a factor of approximately 1.025 every year.
For every five years:
B(60) = 100(1 + 0.002)⁶⁰ = $110.41
B(120) = 100(1 + 0.002)¹²⁰ = $121.20
B(120)/B(60) = $121.20/$110.41 = 1.0991
The amount in the account increases by a factor of approximately 1.099 every five years. Therefore, the amount in the account increases by a small factor every month, a moderate factor every year, and a larger factor every five years.
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 Cooper can purchase a item for $45.00, Which store has the best buy?
A. Store 1: 25% off coupon
B. Store 2: $15 dollars off
C. Store 3: 10% off
I’ll give brainly please help me
a 10 x 10 x 10 cub is painter red on all faces and then cut into ten 10 x 10 x 1 slices each slice is then cut into twenty five 2 x 2 x 1 blocks how many of the 250 blocks have exactly on face painted red
There are exactly 250 blocks with exactly one face painted red.
What is cube ?
A cube is a three-dimensional solid shape with six square faces of equal size that meet at 90-degree angles. It is a special case of a rectangular prism, where all of the edges have the same length.
When the 10 x 10 x 10 cube is painted red on all faces, it means that all of the 1000 unit cubes inside the large cube are red.
When the cube is cut into ten 10 x 10 x 1 slices, each slice will contain 100 unit cubes. When each slice is cut into twenty-five 2 x 2 x 1 blocks, each block will contain 4 unit cubes.
Therefore, each 2 x 2 x 1 block will come from 4 unit cubes, and each unit cube will contribute to 4 different blocks.
To count the number of blocks with exactly one face painted red, we can focus on the blocks that have a red face on the bottom (or top) and three unpainted faces on the other sides. Each such block will correspond to one of the 100 unit cubes in a slice, and there are 10 slices, so there are 1000 such blocks in total.
However, each of these blocks has four unit cubes, so we need to divide by 4 to get the number of blocks. Therefore, the answer is:
1000 ÷ 4 = 250
Therefore, there are exactly 250 blocks with exactly one face painted red.
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At which values in the interval [0, 2π) will the functions f (x) = cos 2x + 1 and g(x) = sin x + 2 intersect?
x equals 0 comma pi over 6 comma 5 times pi over 6 comma pi
x equals 0 comma pi comma 7 times pi over 6 comma 11 times pi over 6
x equals pi over 2 comma 7 times pi over 6 comma 3 times pi over 2 comma 11 times pi over 6
x equals pi over 6 comma pi over 2 comma 5 times pi over 6 comma 3 times pi over 2
The functions f(x) = cos 2x + 1 and g(x) = sin x + 2 intersect at x = pi/6, pi/2, 5pi/6, and 3pi/2 in the interval [0, 2π).
To find the intersection points, we set f(x) equal to g(x) and solve for x.
cos 2x + 1 = sin x + 2
Rearranging, we get:
cos 2x = sin x + 1
Using the identity cos 2x = 1 - 2sin²x, we can rewrite this as:
1 - 2sin²x = sin x + 1
Simplifying and factoring, we get:
2sin²x + sin x = 0
sin x(2sin x + 1) = 0
Therefore, sin x = 0 or sin x = -1/2. Solving for x in the interval [0, 2π), we get x = pi/6, pi/2, 5pi/6, and 3pi/2. These are the values at which f(x) and g(x) intersect.
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Find the measure of the angle between the two vectors. u = -7i and v = -4i + 4j
If it takes 15 minutes for water in a pot to boil, the expression 20x+ 15 can be used to find the total time needed to cook x batches of boiled cornbread. Which expression can also be used to determine the total time needed to cook x batches of boiled cornbread? PLS ANSWER ASAPP I REALLY NEED TO ANSWER THIS QUESTION
A 18x + 4x + 6 + 7
B 10x + 10x + 20 - 5
C 6(5x + 5) - 10x + 15
D 3(x + x + x + 3)+ 2x + 15
the correct expression which can also be used to determine the total time needed to cook x batches of boiled cornbread is,
B) 10x + 10x + 20 - 5.
Given that;
The expression 20x + 15 represents the total time needed to cook x batches of boiled cornbread.
We can simplify this expression by factoring out the common factor of 5: = 20x + 15
= 5(4x + 3)
Therefore, the expression that can also be used to determine the total time needed to cook x batches of boiled cornbread must have a factor of 5 in it.
Option A:
18x + 4x + 6 + 7 does not have a factor of 5,
so it cannot be the correct answer.
Option B:
10x + 10x + 20 - 5
= 20x + 15,
which is the same as the original expression.
Therefore, Option B is equivalent to the original expression and can also be used to determine the total time needed to cook x batches of boiled cornbread.
Option C:
6(5x + 5) - 10x + 15 = 30x + 15 - 10x + 15 = 20x + 30,
which does not have a factor of 5.
Therefore, Option C is not correct.
Option D:
3(x + x + x + 3) + 2x + 15 = 9x + 6 + 2x + 15 = 11x + 21,
which does not have a factor of 5.
Therefore, Option D is not correct.
Therefore, the correct answer is,
B) 10x + 10x + 20 - 5.
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In 2011 Staci invested $14,500 in a savings account for her newborn son. The account pays 3.5% interest each year. Determine the accrued value of the account in the year 2029, when her son will go to college. Round your answer the nearest cent.
The accrued value of Staci's investment in the account in the year 2029 is $26933.59
Calculating the accrued value of the accountThe statements in the question can be sumarrized as
Invested amount = $14,500Rate of interest = 3.5% compounded annually.The formula to calculate amount on investment is
Amount = P * (1 + r)ⁿ
Where
P = Principal = 14,500r = Rate = 3.5%n = time = 2029 - 2011 = 18When the values are substituted in the amount equation, we have
Amount = 14500 * (1 + 3.5%)¹⁸
Evaluate
Amount = 26933.59
Hence, the amount after the investment is $26933.59
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Find the critical points of the function f (x) = x − 1 /x^2 + 3
there is no real number that can be raised to the third power to give a negative number, there are no real solutions to this equation. Therefore, there are no critical points of the function f(x) = x - 1/x² + 3.
what is critical points ?
In calculus, critical points are points on a function where its derivative is either zero or undefined. These points are important because they can indicate the location of maximum or minimum values of the function or points of inflection where the concavity of the function changes.
In the given question,
To find the critical points of the function f(x) = x - 1/x² + 3, we need to find the values of x where the derivative of the function is equal to zero or undefined.
First, we need to find the derivative of the function:
f'(x) = 1 + 2/x³
Next, we set the derivative equal to zero and solve for x:
1 + 2/x³ = 0
2/x³ = -1
x³ = -2
Since there is no real number that can be raised to the third power to give a negative number, there are no real solutions to this equation. Therefore, there are no critical points of the function f(x) = x - 1/x² + 3.
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The sum of two numbers is 49. One number is 23 more than the other. Find the numbers.
The larger number is:
The smaller number is:
Answer:
Larger number: 36
Smaller number: 13
Find the missing side lengths. Leave your answers as radicals in simplest form.
The value of m and n are 2√3 and 4√3/3 respectively.
What is trigonometric ratio?The trigonometric functions are real functions which relate an angle of a right-angled triangle to ratios of two side lengths.
Sin(tetha) = opp/hyp
cos(tetha) = adj/hyp
tan(tetha) = opp/adj
There are special angles in trigonometry, examples are; 60° , 30° and 90°. This angles have exact values and can be calculated without using calculator.
Tan 60 = n/2
√3 = n/2
n = 2√3
cos 60 = 2/m
√3/2 = 2/m
m√3 = 4
m = 4/√3
= 4√3/3
Therefore the value of m and n are 2√3 and 4√3/3 respectively.
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Please solve this for me!
Answer: 1; 520/9 number 2: 9/2 number 3: d number 4:d number 5: 151.7
Step-by-step explanation:
100 POINTS
Question:
read the paragraph and then you’d have all the information that you need
Answer:
First braclets coast 3$ and necklaces coast 6$ so now in the box you can put 3in the first one then 6 in the next and keep going its like multiples of 3 and 6 :) Hope this helps.
Step-by-step explanation:
I would love some help please 11-13
(11) The value of expression 3/y + 2y/4 when y = 4 is [tex]2\frac{3}{4}[/tex].
Hence the correct option is (b).
(12) The value of expression 12/y + 3y/4 when y = 8 is [tex]7\frac{1}{2}[/tex].
Hence the correct option is (c).
(13) 2x/3 + 4 = 10 equation does x = 9.
Hence the correct option is (b).
(11) The given expression is,
3/y + 2y/4 = 3/y + y/2
Substituting the value of y = 4 we get,
3/4 + 4/2 = 3/4 + 2 = [tex]2\frac{3}{4}[/tex].
Hence the correct option is (b).
(12) The given expression is,
12/y + 3y/4
Substituting y = 8 in the given equation we get,
12/8 + (3*8)/4 = 3/2 + 6 = 1 + 1/2 + 6 = [tex]7\frac{1}{2}[/tex].
Hence the correct option is (c).
(13) Given the solution is x =9.
For first option: (2/3)*9 - 6 = 6 - 6 = 0
2x/3 - 6 = 12 does not satisfied by x = 9.
For second option: (2/3)*9 + 4 = 6 + 4 = 10
So, x = 9 satisfies 2x/3 + 4 = 10.
For third option: 3*9 - 12 = 27 - 12 = 15
So x = 9 does not satisfy 3x - 12 = 21.
For fourth option: 3*9 + 12 = 27 + 12 = 39
So x = 9 does not satisfy 3x + 12 = 19.
Hence the correct option is (b).
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When a retired police officer passes away, he leaves $300,000 to be divided among his three children and six grandchildren. The will specifies that each child is to get twice as much as each grandchild. How much does each get?
Answer:
so first off if its six grandchildren and 3 children then that means 9 people but if the children get double the amount distributed then lets treat it like 12 people so 25,000 each meaning each child of the police officer gets 50 thousand and each grandchild gets 25 thousand
Step-by-step explanation:
hope this helps !
please help with this question!
Answer:
The true statements:
6 is an element of D
12 is an element of D
1. A rectangular block of wood has dimensions 24 cm by 9 cm by 7 cm. It is cut up into children's bricks. Each brick is a cube of side 3 cm.
(a) Find the largest number of bricks that can be cut from the block.
(b) Find the volume of wood that is left.
The dimensions of the rectangular block indicates;
(a) The largest number of bricks that can be cut from the block is 48 bricks
(b) The volume of the wood left is 216 cm³
What is the volume of a rectangular block?The volume of the rectangular block is the product of the length, L, width, W, and height, H.
1. The dimensions of the rectangular block indicates that the block volume is; V = 24 cm × 9 cm × 7 cm = 1,512 cm³
The largest number of bricks that have side lengths of 3 cm that can be cut from the block is therefore;
Number of cubes; (24)/3 × (9)/3 × (7)/3 ⇒ 8 × 3 × 2 = 48
48 cube bricks can be cut from the block(b) The volume of wood left = 1512 - 48 × 3 × 3 × 3 = 216
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If the number 48700 is written in scientific notation, it will be in the form 4.87×10n. What is the value of n?
If the number 48700 is written in scientific notation, it will be in form 4.87×10ⁿ, and the value of n is 4.
What is scientific notation?Scientific notation describes the shorthand way of writing very large or very small numbers in standard forms.
Writing in scientific notation, a number between 1 and 10 is multiplied by a power of 10.
48700 = 4.87×10ⁿ = 4.87×10⁴
Thus, the n represents the exponent of power 10 to which the number is reduced.
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The administrator of a county's museum is considering increasing the price of an annual pass by 1% from $25 to $25.25. At the current price, the museum sells 2500 annual passes and the point of elasticity is 0.73. What effect would the increase in price have on the museum's annual pass revenue?
Answer: the increase in price from $25 to $25.25 would result in a small increase in annual pass revenue of $178.50 or about 0.3%.
Step-by-step explanation: we can calculate the modern yearly pass income by increasing the modern amount requested by the unused cost of $25.25:
Unused yearly pass income = Modern cost x Modern amount requested
Unused yearly pass income = $25.25 x 2482 = $62,678.50
We as of now know that the ancient yearly pass income is $62,500 (since 2500 passes were sold at $25 each), so ready to calculate the alter in yearly pass income:
Alter in yearly pass income = Unused yearly pass income - Ancient yearly pass income
Alter in yearly pass income = $62,678.50 - $62,500 = $178.50
express 7 min 30 sec. as a percentage of 1 hour
Answer:
12.5 is the answer
Step-by-step explanation:
7 × 60 ( 7 being the minutes, 60 being the hour )
= 420
+ 30
= 450
450 ÷ 3600 × 100
45000 ÷ 3600
450 ÷ 30
= 12.5
12.5 being the answer
A political pollster wants to know what proportion of voters are planning to
vote for the incumbent candidate in an upcoming election. A poll of 150
randomly selected voters is taken from the more than 2,000 voters in the
population, and 78 of those selected plan to vote for the incumbent
candidate.
Based on this sample, which of the following is a 90% confidence interval
for the proportion of all voters who plan to vote for the incumbent
candidate?
Choose 1 answer:
780.067
78±0.080
0.520.067
The confidence interval is 0.52±0.067.(option c)
What is confidence interval?
In statistics, confidence interval means that the probability in which a population parameter will fall between a set of values for a certain proportion of times.
A political pollster wants to know what proportion of voters are planning to
vote for the incumbent candidate in an upcoming election. A poll of 150
randomly selected voters is taken from the more than 2,000 voters in the
population, and 78 of those selected plan to vote for the incumbent
candidate.
The formula for confidence interval(CI) is given by:
CI= p ± z √{p(1-p)/n} ----------------(1)
Here from the given data p= 78/150= 0.52
n= 150
For 90% confidence interval the value of z= 1.645.
Putting all the values in equation (1) we get,
CI= 0.52± 1.645√{(0.52×0.48)/150}
= 0.52±1.645×0.04
= 0.52±0.067
Hence, the confidence interval is 0.52±0.067.
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This is a picture of a cube and the net for the cube.
What is the surface area of the cube?
Responses
The surface area of the cube is 384 mm².
What is a cube:A cube is a solid three-dimensional figure, which has 6 square faces, 8 vertices and 12 edges.
Since there are six square that makes up a cube, to find the surface area of the cube, we find the area of one of the square and multiply by six
A = 6L²...................... Equation 1Where:
A = Surface area of the cubeL = Length of the side of the cubeFrom the question,
Given:
L = 8 mmSubstitute this value into equation 1
A = 6×8²A = 6×64A = 384 mm²Hence the right option is D. 384 mm².
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A company may acquire property, plant, equipment, and intangible assets for cash, in exchange for a deferred payment contract, by exchanging other assets, or by a combination of these methods. Identify six types of costs that should be capitalized as the cost of a parcel of land. For your answer, assume that the land has an existing building that is to be removed in the immediate future so that a new building can be constructed on the site. At what amount should a company record an asset acquired in exchange for a deferred payment contract? In general, at what amount should assets received in exchange for other nonmonetary assets be valued? Specifically, at what amount should a company value a new machine acquired by exchanging an older, similar machine and paying cash?
Six types of costs are:
Closing costsPurchase costBrokerage commissionsSurveying feesDemolition costsSite preparation costsHow the asset is to be recordedFor assets attained in exchange for a deferred payment contract, the asset should be documented at its fair worth, which is the prevailing market rate. If establishing the fair value of the asset proves to be impracticable, the asset should be recorded based on the current value of upcoming payments due under the deferred payment agreement, stated using an apposite interest rate.
Generally, assets acquired in exchange of other non-monetary commodities should be appraised at their fair worth. If the truthful appraisal of the exchanged assets is uncertain, the assets should be noted down according to the seized amount of the items provided, including any received or paid cash during the transaction.
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Man I don’t even know how to solve this, can y’all help me???
Answer:
3
Step-by-step explanation:
The inverse function returns the original value for which a function gave the output.
This means if there is a function f(x) and at x = a, f(a) = k then f⁻¹(k) = a
This may be difficult to grasp with variables but essentially returning to the specific question
if f(3) = 17
then
f⁻¹(17) = 3
And that is the answer
How large a sample is needed in order to be 90% confident that the sample proportion will not differ from the true proportion by more than 3%? a previous study indicates that the proportion is 21%
Using the data given such as the margin of error, sample size and z-score, the maximum sample size required is 499
How large a sample is needed in order to be 90% confident that the sample proportion will not differ from the true proportion by more than 3%?To solve this problem, we need to know the minimum sample size required. The formula for this is given as;
n = (z² * p(1 - p))/ E²
n = sample sizeE = Maximum margin of errorp = estimated proportion from the given previous studyz = z-scoreSubstituting the values into the formula;
n = (1.645² * 0.21(1 - 0.21))/ 0.03²
n = 498.8
The sample size should be at least approximately 499
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Write an equation that represents the line.
Answer:
y = (3/4)x + 2
Step-by-step explanation:
A line (or linear function) can be represented by the equation y = mx + b where "m" is the slope and "b" is the y-intercept.
The y-intercept is when x = 0 or when the line crosses the y-axis. In the graph, notice that the line crosses at (0, 2). Thus, the y-intercept is at y = 2 and "b" must be "2".
Next, we have to find the slope, "m". The slope is defined as a change in "y" divided by a change in "x". Lets use the two points which are marked on the graph already, (4, 5) and (0, 2). We first subtract the y-values, and then divide that by the difference between corresponding x-values:
(5 - 2)/(4 - 0) = 3/4 The slope is 3/4, so m = 3/4
Now, plug "m" and "b" into the equation:
y = (3/4)x + 2
Answer:
y=(3/4)x+2
Step-by-step explanation:
So first you need to find the slope (3/4). To find that you can use the rise over run method. In this case they have already chosen two points on the line, but you could use any exact points. Count how many up from 2 to 5 (in green), which is 3 then how many across (in red) which is 4. Then put the rise (3) over the run (4) so 3/4.
Then b (2) is equal to y in the y intercept which is (0,2)
sum of 213341 & 444233 base 5
Answer:
1213124
To add 213341 and 444233 in base 5, we need to line up the digits of the two numbers according to their place values, and then add them digit by digit, carrying over to the next place value if the sum of the digits is 5 or greater.
Here's how to do it:
2 1 3 3 4 1
+ 4 4 4 2 3 3
-----------------------
1 2 1 3 1 2 4
Therefore, the sum of 213341 and 444233 in base 5 is 1213124.
Please help with these two equations, and please show work as well, thank you!
The simplified polynomial for the area and perimeter of the rectangles are:
13). Area = 5x² + 40, Perimeter = 12x + 16
14). Area = x² + 10x + 12, Perimeter = 4x + 20
How to evaluate for the area and perimeter of the rectanglesArea of rectangle = Length × Width
Perimeter of rectangle = 2(Length + Width)
13). Area of the rectangle = 5x × (x + 8)
Area of the rectangle = 5x² + 40
Perimeter of the rectangle = 2[5x + (x + 8)]
Perimeter of the rectangle = 2(6x + 8)
Perimeter of the rectangle = 12x + 16
12). Area of the rectangle = (x + 3)(x + 7)
Area of the rectangle = x² + 7x + 3x + 21
Area of the rectangle = x² + 10x + 21
Perimeter of the rectangle = 2[(x + 3) + (x + 7)]
Perimeter of the rectangle = 2(2x + 10)
Perimeter of the rectangle = 4x + 20.
Therefore, the simplified polynomial for the area and perimeter of the rectangles are:
13). Area = 5x² + 40, Perimeter = 12x + 16
14). Area = x² + 10x + 12, Perimeter = 4x + 20
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Suppose a person were to breath an average of 13 times per minute. How many days would it take for them to breathe one billion times? Round your answer to the nearest single days.
Answer:
12 / min
720 / hr
17,280 / day
6,307,200 / yr
Now divide 1,000,000,000 by 6,307,200 (darn close to your 158!)
HELP MEEEEE PLEASEEE SOMEONEEEE :(
The function is not defined for x > 5, as a result ƒ(7) does not exist.
How did we arrive at this assertion?The given piece-wise function is:
f(x) = {x - 2}²- 1
1
-x+1
x < 2
x = 2
2 < x ≤ 5
Step 2
f(x) = (x-2)² - 1
1
-x+1
x < 2
x = 2
2 < x ≤ 5
Note that the function is not defined for x > 5.
Step 3
Since the function is not defined for > 5, therefore ƒ(7) does not exist.
The function is not defined for x > 5, therefore ƒ(7) does not exist.
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