Answers
Answer:
a. Explicit: f(x) = 2x² +3. Recursive: f(-3) = 21; f(x) = f(x -1) +4x -2
b. Explicit: g(x) = 3x² -2x. Recursive: g(5) = 65; g(x) = g(x -1) +6x -5
Step-by-step explanation:
Given two tables of values, you want to find the explicit and recursive formulas for those values.
General approachWhen the x-values are consecutive integers, as they are in these tables, it is usually useful to look at the first difference of the y-values. If those are constant, the table represents a linear function.
When the first differences are not constant, the exercise can be repeated. If the second differences are constant (as here), then the explicit formula will be a second-degree polynomial. The coefficients of the polynomial can be found different ways. We will describe one way here.
2nd degree explicit formulaThe constant second differences are double the leading coefficient of the quadratic that describes the relation between x and y. Knowing this, we can see how well the 2nd degree term by itself represents the relation. To that end, we have added to the table columns for the difference between the y-value and the 2nd degree term (y1 -ax^2), and the difference of those differences (diff).
Explicit formula, Table AThe attachment shows the first second difference of the values of Table A is 4. That means our first approximation of the sequence will be (4/2)x². The next column shows us this is always 3 less than the value of y, so our explicit formula can be ...
f(x) = 2x² +3
Explicit formula, Table BThe attachment shows the first second difference of the values of Table B is 6. That means our first approximation of the sequence will be (6/2)x². Subtracting this from the value of y, we find an arithmetic sequence that has a common difference of -2, and a value of -10 when x=5.
The explicit formula for an arithmetic sequence with a first term a1 and a common difference d is ...
an = a1 +d(n -1) . . . . . . where 1 is the x-value of the first term
Our sequence of differences doesn't start with x=1, but with x=5. This means our explicit formula will be ...
g(x) = 3x² +(-10 +(-2)(x -5))
g(x) = 3x² -2x
2nd degree recursive formulaA recursive formula is one that expresses a given term as a function of previous terms of the sequence. When the sequence is 2nd degree, as here, we know the difference from one term to the next is an arithmetic sequence. Thus we can write the formula for a term as the sum of the previous term and a value that depends on the term number.
The explicit formula for the arithmetic sequence of differences has the form shown above. For the purpose here, the difference from the previous term is shown on the line above the x-value.
Recursive formula, Table AThe applicable sequence of first differences has first term -10 and common difference 4. The first of the differences of consequence corresponds to x=-2, so can be written ...
d(x) = -10 +4(x -(-2)) = 4x -2
Then the recursion relation is
f(x) = f(x -1) +d(x) = f(x -1) +4x -2
And the recursive formula is ...
f(-3) = 21; f(x) = f(x -1) +4x -2
Recursive formula, Table BThe applicable sequence of first differences has first term 31 and common difference 6. The first of the differences of consequence corresponds to x=6, so can be written ...
d(x) = 31 +6(x -6) = 6x -5
Then the recursive formula is ...
g(5) = 65; g(x) = g(x -1) +6x -5
Related Questions
How many chicks will hatch from 4,500 eggs if on average 87 chicks hatch from 100 eggs?
Answers
Answer:
33915
Step-by-step explanation:
87% is the average, so you have to find 87% of 4500.
3. Find the circumference of the circle. Use 3.14 for the value of . Round your answer to the nearest tenth. 64.1 in 63.4 in 19.9 in 62.8 in 20 in
Answers
Answer:
62.8 in
Step-by-step explanation:
The circumference, C. of a circle with diameter d is given by the formula
[tex]C = \pi d[/tex]
Here [tex]\pi = 3.14[/tex] and [tex]d = 20[/tex] in
So circumference = 3.14 x 20 = 62.8 inches
The complement of an angle is 90 degrees less than the supplement of the angle. What is the angle?
Answers
The angle which is as described in the task content is; 0°.
Complementary and Supplementary anglesIf we assume the angle in discuss is; x.
It's complement is therefore; (90-x).
Therefore, since the complement of the angle is 90° less than the supplement; we have;
90 - x = 180 - 90
90 - x = 90
x = 0°
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Two dozen eggs and a loaf of bread cost K4.94. Half a dozen eggs and two loaves of bread cost K2.32. Find the cost of a dozen eggs.
Answers
The cost of a dozen of eggs is $3.
Given two dozen eggs and a loaf of bread cost K4.94 and
Half a dozen of bread cost K2.32
Cost of a dozen of eggs = ?
we know that, 24E ₊ B = 8.50 and
6E ₊ 2B = 6.50
multiply the first equation by 2 and substract
48E ₊ 2B = 17
6E ₊ 2B = 6.50
after solving both equations we get:
42E = 10.50
we are searching for the value of a dozen eggs, which is 12E
multiply 42E = 10.50 by 12/42 = 6/21
and you get
12E = 10.50 × (6/21) \\ 10.50 = 21/2
12E = (21×6)/(2×21)
12E = 3
so a dozen eggs cost 3 dollars.
Hence we get the cost of a dozen of eggs as $3
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If Andrew's batting average is exactly 0.400 going into the series, and that value is based on exactly 2000 career hits out of 5000 previous times at bat, what is the least his average could possibly be when he
goes up to bat the tenth time of the series?
Answers
The least Andrew's average could possibly be when he goes up to bat the tenth time of the series is 0.399.
Here, we are given that,
Andrew's batting average = 0.400
Number of career hits for 0.400 batting average = 2000
Previous bat times for 0.400 batting average = 5,000
Now,
For the least possible average, he must have zero career hits in every match he bats.
Before the tenth time of the series, he will bat in 9 times
He must have 0 career hits in these 9 matches he bats in
therefore,
The total number of career hits = 2000
Total number of bat times = 5,000 + 9 = 5,009
Hence,
Average = (Total career hits) ÷ (Total number of times he bats)
= 2000 ÷ 5,009
= 0.399
Thus, the least his average could possibly be when he goes up to bat the tenth time of the series is 0.399.
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Jade is stranded downtown with only $10 to get home. Taxis cost $0.75 per mile, but there is an additional $2.35 "hire" charge. Write a formula and use it to calculate how many miles Jade can travel with her money.
Answers
She starts with 10 dollars and when she get a taxi they will charge 0.75 per mile (x) and this will add a 2.35 fee at the end
If we solve for x formula ends as:
X=(10-2.35)/0.75
How do you solve for x if x/5 = 7/3
Answers
We get that, the value of x is 11.67 when the equation is x / 5 = 7 / 3.
An equation is a combination of two expressions connected by an equal sign.
We are given an equation:
x / 5 = 7 / 3
We need to find the value of x.
Multiply both sides by 5
x / 5 × 5 = 7 / 3 × 5
x = 35 / 3
Now, we will divide 35 by 3 and round off the result to two decimal places:
x = 11.67
Therefore, we get that, the value of x is 11.67 when the equation is x / 5 = 7 / 3.
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Evaluate this 5 2/3 + 11/12 =
pls tell me the answer ASAP
Answers
Answer:
6[tex]\frac{3}{4}[/tex]
Step-by-step explanation:
Another way to write 5 2/3 is to change this into an improper fractions. Another names for 1 is 3/3. I am going to add 5, 3/3 to 2/3
3/3 + 3/3 + 3/3 + 3/3 + 3/3 + 2/3 = 17/3
We want to add this to 11/12, but to do that we need a common denominator. I need to make an equivalent fraction of 17/3 where 12 is the denominator
[tex]\frac{17}{3}[/tex] x [tex]\frac{4}{4}[/tex] = [tex]\frac{68}{12}[/tex] Now we can add the two fractions together.
[tex]\frac{68}{12}[/tex] + [tex]\frac{11}{12}[/tex] = [tex]\frac{79}{12}[/tex] = 6[tex]\frac{3}{4}[/tex]
The image below has the following translation: (x, y) → (x +4, y - 1)
Determine the ordered pair for F' after the translation.
a. F' (-1, 3)
b. F' (-9, 5)
c. F' (8, -6)
d. F' (4, -1)
Answers
Some college advisors noticed the following breakdown of majors for the incoming freshman at their school: 3% math, 22% nursing, 16% psychology, 11% criminal justice, and 48% business. Suppose a first-year student was chosen at random. Which of the following is the probability distribution for that student’s major?
Answers
Answer:
The correct answer is B, I took the test :)
You just turn the percentages into decimals
The probability distribution table is formed clearly in the answer part.
What is probability?Probability is the branch of Mathematics that deals with the measurement of the chance of occurrence of a random event.
The probability of any event always lie in the close interval of 0 and 1 [0,1].
The probability for all the elements in the sample space can be shown in one table known as distribution table.
Suppose X be the event of choosing a major.
Then, its probability can be given as P(X).
Here, the percent value of a given event is equivalent to their probability.
It can be represented in the form of table as,
X (Major chosen by student) P(X) (Probability)
Math 3% = 0.03
Nursing 22% = 0.22
Psychology 16% = 0.16
Criminal justice 11% = 0.11
Business 48% = 0.48
This table is known as the probability distribution table.
Hence, the probability distribution table is formed by calculating the probability for each of the events.
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Your club is baking vanilla and chocolate cakes for a bake sale. They need at most 25 cakes. You cannot have more than 10 chocolate cakes. Write a system of inequalities to model this system. Let x be the number of vanilla cakes and y be the number of chocolate cakes.
Answers
The inequalities are x + y <= 15 and y <= 10.
How to express the inequality?It should be noted that inequality are used to how the relationship between expressions that are unequal.
Let x = the number of vanilla cakes.
Let y = the number of chocolate cakes.
They need at most 25 cakes. This will be x + y <= 15.
They cannot have more than 10 chocolate cakes. This will be:
y <= 10.
Therefore, the inequalities are x + y <= 15 and y <= 10.
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Hi ~
I need help please...
I know this is a simple question.
but- I just want to know if someone can solve this without cheating at all... and make into your own words.
[tex]\rightarrow{\sf{{What \: is \: -26x \: - \: 12 \: = 15?[/tex]
Thanks~
Answers
Answer:
x would equal -1.03(1 DP)
"-26x - 12 = 15, solve for x."
Step-by-step explanation:
Start with adding 12 to both sides of the expression. Sides were switched purposely.
[tex]15 + 12 = -26x - 12 + 12[/tex]
Next, simplify your addition process. You do this by using a specific rule.
[tex](-a) = a\:\:\mathrm{if\:a\neq 0}\\-26x = 26x\\26 + (x)\\= 26 + 1\\= 27\\= -26x=27[/tex]
Lastly, we are going to divide both sides by -26(x was cancelled).
[tex]\frac{-26x}{-26}=\frac{27}{-26}[/tex]
Thus,
[tex]x= -1.03[/tex]
➲ Hope this helps, address any concerns if needed.
Answer:
x = -1.038
Step-by-step explanation:
- 26x - 12 = 15
- 26x = 15 + 12
- 26x = 27
x = - 27/26
x = - 1.038
__________
hope this helps!
Find the missing side length, s.
help!!
Answers
Answer:
The missing side length is 11.
Step-by-step explanation:
On the smaller figure the AB side is 6 and on the bigger figure the XY side is 9. There was an increase of 3 so that means there will be an increase of 3 on the XZ side compaered to the AC sdie witch is 8. 8 + 3 = 11.
Amanda is framing her pool for resurfacing. The pool began with 14,340 gallons of water and it is draining at a rate of 880 gallons per hour. How long has the pool been draining if currently there are 8,840 gallons in the pool.
Answers
The number of hours that the the pool been draining if currently there are 8,840 gallons in the pool is 6.25 hours.
How to calculate the time?Let the time taken be represented by h.
Therefore, the appropriate expression will be:
14340 - 880h= 8840
Collect like terms
880h = 14340 - 8840
880h = 5500
h = 5500/880
h = 6.25 hours
The number of hours is 6.25 hours.
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Can someone please find x ?
Answers
Answer:
Step-by-step explanation:
There are 31 horses competing in a show, how many ways can the blue,red,and yellow ribbons be awarded
Answers
If there are 31 horses competing in a show, then the blue, red, and yellow ribbons can be awarded in 26970 different ways.
As per the question statement, 31 horses are competing in a show.
We are required to calculate the number of ways in which the blue, red and yellow ribbons can be awarded.
To solve this question, first, we need to know a basic rule of horse shows, which is the 1st place or the winner is awarded with a blue ribbon, the second place or the runners-up is awarded with a red ribbon and the third place or the second runners-up is awarded with a yellow ribbon.
That is, in simpler terms, we have to calculate the number of different ways, in which the first, second and third places can be achieved between 31 different horses, each having equal probability of winning.
To solve this question, we just need to know the formula of permutation which goes as [tex][(nPr)=\frac{n!}{(n-r)!} ][/tex], i.e., we are to select an ordered set or "r" from a set of "n".
As per our question, (n = 31) and (r = 3), and using these in the above mentioned formula of permutation, we get
[tex](31C)=\frac{31!}{(31-3)!}=\frac{31!}{28!} =\frac{28!*29*30*31}{28!}=(28*29*30)=26970.[/tex]
That is, the blue, red and yellow ribbons can be awarded in a show with 31 horses as contestants in 26970 different ways.
Probability: In mathematics, probability of an event is the extent to which it is likely to occur, measured by the ratio of the favorable cases to the whole number of cases possible.Permutation: In mathematics, a permutation of a set is an arrangement of its members into a particular sequence, or if the set is already ordered, a rearrangement of its elements.To learn more about permutations, click on the link below.
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describe the translation from figure A to figure B
Answers
Answer:
The figure A is translated from the third quadrant to the second quadrant thus the formula used is P(x,y) = T(a,b) = Image of P(x+a, y+b). The object A and its image B are congruent and the direction and magnitude of the displacements are given by the direction and magnitude of translation vector t = ( a,b ). Where, a is the horizontal displacement ( along x-axis ) and b is the vertical displacement ( along y-axis ).
Debbie has 340 dimes in three boxes. she says that there are 4 times as many dimes in the first box as in the second and 3 times as many in the third box as in the first how much money in dollars does she have in each box
Answers
The amount of money in the first box is 8 dollars
The amount of money in the second box is 2 dollars
The amount of money in the third box is 24 dollars
Solving equationsFrom the question, we are to determine how much money there are in each box
From the given information,
"Debbie has 340 dimes in three boxes"
Let x represents the number of dimes in the first box
y represent the number of dimes in the second box
and z represent the number of dimes in the third box
Thus,
x + y + z = 340
Also, from the given information
"she says that there are 4 times as many dimes in the first box as in the second"
x = 4y
and
"3 times as many in the third box as in the first"
z = 3x
Substitute the second and third equations into the first equation
x + y + z = 340
4y + y + 3x = 340
4y + y + 3(4y) = 340
4y + y + 12y = 340
17y = 340
y = 340/17
y = 20
Substitute the value of y into the second equation
x = 4y
x = 4(20)
x = 80
Substitute the value of x into the third equation
z = 3x
z = 3(80)
z = 240
Thus,
There are 80 dimes in the first box
80 dimes = 8 dollars
There are 20 dimes in the second box
20 dimes = 2 dollars
There are 240 dimes in the third box
240 dimes = 24 dollars
Hence,
The amount of money in the first box is 8 dollars
The amount of money in the second box is 2 dollars
The amount of money in the third box is 24 dollars
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Figure A is a scale image of Figure B.
What is the value of x?
FAST!!! 20 POINTS AND THE BRAINLIEST FOR THE FIRST CORRECT ANSWER
Answers
Answer:
21
Step-by-step explanation:
If A 45 translates to be 35, then x can be given by (35×27)÷45 =21
(4x+5)+(-5x-1) help me solve this I’m struggling
Answers
Answer:[tex]-x+4[/tex]
Step-by-step explanation:
Combine like terms:
[tex](4x+-5x)+(5+-1)[/tex]
[tex]= -x+4[/tex]
455 miles traveled in 7 hours find the unit rate
Answers
Answer:
Step-by-step explanation:
This is a fraction equal to
455 miles ÷ 7 hours
We want a unit rate where
1 is in the denominator,
so we divide top and bottom by 7
455 miles ÷ 7
7 hours ÷ 7
=
65 miles
1 hour
=
65 miles
hour
= 65 miles per hour
Please help 2 questions with details and work out please
Answers
From properties of parallel lines the value of the indicated angle is 84° and the value of x is 4°.
Parallel lines are two lines that are equidistant from one another.
Parallel lines in geometry are coplanar, straight lines that don't cross at any point. In the same three-dimensional space, parallel planes are any planes that never cross.A line that intersects both the parallel lines is called a transversal.A set of angles on the inner side of each of the two lines but on the opposing sides of the transversal are known as alternate interior angles.Alternate external angles are those outside the two lines that the transversal is intersecting.For the question 7 the two lines are parallel and the indicated angle is an alternate interior angle to the given angle. Hence the indicated angle is also 84°.
For question 8, the two angles are alternate exterior angles.
Hence they are equal. Therefore we can write a linear equation in x to solve for x.
21x+6=90
or, 21x=84
or, x=4°
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Which number produces an irrational number when added to 1/3
Answers
Answer: 2pi thats all the answer is
Step-by-step explanation:
i dont have one just enjoy the answer, brainliest please
3. Mr. Brown bought some new shoes for $76.34. If he paid with $100 bill, how much change did he get?
please explain in number form and as little as possible but still explaining
Answers
Answer:
23.66
Step-by-step explanation:
you just subtract the two.
100.00 - 76.34 = 23.66
Is a = 8 a solution to 6 = a/4 + 2
Answers
Sheila is baking cookies. The radius of each cookie is 4 centimeters.
What is the circumference of each cookie (use 3.14 for pi and round to
the nearest tenth)?
Answers
The circumference of each cookie is 25 cm.
Circumference is usually referred to the outer length of a circle.
If 'r' is the radius of a circle, then the circumference of the circle is given by 2πr, where π = 3.14.
Here, the radius of the each cookie, r = 4 cm
Then the circumference of each cookie = 2πr
= 2 x 3.14 x 4
= 25.12
= 25 cm
[Rounding to the nearest tenth, as 1 and 2 are less than 5, 25.12 will be 25]
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The sum of a number and 7 is less than 15
Answers
The words translate into algebra as
n + 7 < 15
Subtract 7 from both sides to find n.
n = 15 - 7 = 8
A parking lot has 65 spaces total. If 30 of the spaces have cars in them, what is the ratio of empty spaces to filled spaces?
Answers
Answer: 35:30, because 65-30 equals 35 and if you do the empty spaces which there are 35 to the filled spaces which there are 30 it will become your answer of 35:30.
Hope this helps!
The solution is 7 : 6
The ratio of proportion of the empty spaces to the filled spaces is 7 : 6
What is Proportion?
The proportion formula is used to depict if two ratios or fractions are equal. The proportion formula can be given as a: b::c : d = a/b = c/d where a and d are the extreme terms and b and c are the mean terms.
Given data ,
Let the total number of parking spaces be = P
The value of P = 65 spaces
Now , the number of spaces that are filled with cars = 30 spaces
So , the remaining number of spaces = the empty spaces
The remaining number of spaces = total number of parking spaces - number of spaces that are filled with cars
Substituting the values in the equation , we get
The remaining number of spaces = 65 - 30
The remaining number of spaces = 35 spaces are empty
Now , the ratio of empty spaces to filled spaces is given by
Ratio of empty spaces to filled spaces = 35 : 30
On simplifying , we get
Ratio of empty spaces to filled spaces = 7 : 6
Therefore , the proportion is 7 : 6
Hence , The ratio of the empty spaces to the filled spaces is 7 : 6
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Which of the following is NOT a voluntary response sample?
***
Choose the correct answer below.
A. A local dentist asks her patients to fill out a questionnaire and mail it back to determine the quality of the care received during an office
visit.
B. Quiz scores from a college level statistics course are analyzed to determine student progress.
C. A radio station asks for call-in responses to a question concerning city recycling.
OD. A survey is taken at a mall by asking passersby if they will fill out the survey.
Answers
Of the given options, the one that is NOT a voluntary response sample is B. Quiz scores from a college level statistics course are analyzed to determine student progress.
What is a voluntary response sample?A voluntary response sample refers to a sampling method where those who are to be in the sample are asked to be in the sample. They will have a choice on accepting the offer to be in the sample.
When quiz scores from a college level statistics course are used as the sample, this is not a voluntary response sample as the students who had the scores were not consulted.
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por que es nesesario expresar un numero mixto como 1 fraccion impropia?
Answers
Es preciso transformar un número mixto en una fracción impropia cuando se requiere calcular la cantidad asociada al número en formato decimal.
¿Qué es un número mixto y una fracción impropia?
En esta pregunta vamos a abordar dos tipos de notación utilizadas entre los números racionales, esto es, números reales de la forma m / n, donde m y n son números enteros y n es distinto de cero.
Tanto los números mixtos como las fracciones impropias son utilizadas para representar números reales mayores que 1, cuyas diferencias se enumeran a continuación:
El número mixto emplea tanto números enteros como fracciones, es de hecho la suma de un número entero y una fracción. (i.e. 1.5 = 1 1 / 2)La fracción impropia es solamente una fracción, en la cual el valor del numerador es mayor que el valor del denominador. (i.e. 1.5 = 3 / 2)Es preciso transformar un número mixto en una fracción impropia cuando se requiere calcular la cantidad asociada al número en formato decimal.
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