El problema que tiene una relación de proporcionalidad es el siguiente: la distancia en kilómetros recorrida por un deportista y el tiempo en minutos que se tardó.
En este caso, se establece una relación directamente proporcional entre la distancia recorrida y el tiempo empleado. Esto significa que a medida que aumenta la distancia recorrida, también aumenta el tiempo necesario para completarla, y viceversa.
La proporcionalidad se refleja en el hecho de que si se duplica la distancia, también se duplicará el tiempo empleado para recorrerla. Del mismo modo, si se reduce a la mitad la distancia, también se reducirá a la mitad el tiempo necesario.
Este tipo de problema de proporcionalidad es común en actividades físicas, como correr, caminar o montar en bicicleta, donde la velocidad y el ritmo determinan el tiempo necesario para cubrir una determinada distancia.
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jack bought 24 apples out of farmstand he divided the apples between his brother his friend and himself in a ratio of 2:1:3 how many apples does each person receive
Answer: 8:4:12 I believe...
Step-by-step explanation: If the order is 2-his brother 1-his friend- and 3- himself, then I believe his brother would get eight, his friend 4, and he would have twelve.
Answer:
8:4:12
Step-by-step explanation:
Which relation in the below table(s) represents a function?
The relation 2 represents a function.
In order to determine which relation in the below table represents a function, we need to first understand what a function is.A function is a relationship in which each input value corresponds to exactly one output value.
To put it another way, each x-value has one and only one y-value. The most typical method to determine whether a relation is a function is to use the vertical line test.
The vertical line test is a way to determine if a relation is a function graphically. To test if a graph is a function, we draw a vertical line through each x-value on the graph. If a vertical line crosses the graph more than once, it is not a function.
If, on the other hand, the graph passes the vertical line test and no vertical line crosses the graph more than once, it is a function.Now let's look at the table below to determine which relation is a function.
We will first plot the x and y values of each relation on a coordinate system and then apply the vertical line test to each relation.
Relation 1: x | y0 | 10 | 11 | 22 | 23 | 34 | 35 | 4Relation 1 does not represent a function since we can draw a vertical line through x = 3 and the line will cross the graph more than once.
Relation 2: x | y2 | 33 | 34 | 45 | 46 | 57 | 5Relation 2 represents a function since we can draw a vertical line through each x-value on the graph and it will only cross the graph once.
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A worker earns a 3% increase in her annual salary for each of 5 years. They plan to continue working in their position for an additional n years. If they continue to earn a 3% increase in their annual salary, what statement could describes the expression that can be used to calculate the total percent increase in their annual salary from the first year to the last year
Answer:
Given that a worker earns a 3% increase in her annual salary for each of 5 years, and they plan to continue working in their position for an additional N years, if they continue to earn a 3% increase in their annual salary, to determine what statement could describe the expression that can be used to calculate the total percent increase in their annual salary from the first year to the last year the following calculation should be performed:
1 + 0.03 (interest rate) ^ N (number of years) = final interest rate
1.03 ^ N = Final interest rate
Thus, for example, if it were invested for 5 years, the equation would operate as follows:
1.03 ^ 5 = X
1.16 = X
The total percent increase in their annual salary from the first year to the last year is \((1.03)^n\).
What is Percentage?A percentage is a way to describe a part of a whole. such as the fraction 1/4 can be described as 0.25 which is equal to 25%.
To convert a fraction to a percentage, convert the fraction to decimal form and then multiply by 100 with the '%' symbol.
As it is given that the annual salary of the worker increases at a rate of 3%. therefore, the salary of the worker increases compounded at a rate of 3% annually. Therefore, the salary of the worker after n number of years can be written as,
\(A = P(1+\dfrac{r}{100})^n\)
where A is the final salary of the worker, P is the initial salary of the worker, r is the rate at which the salary is increasing, and n is the number of years.
Substituting the values in the formula,
\(A = P(1+\dfrac{3}{100})^n\\\\A = P(1.03)^n\)
Hence, the total percent increase in their annual salary from the first year to the last year is \((1.03)^n\).
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which statement is false someone pls answer
solve for x -12 ≤ 44+ x
Answer:
x can be all real numbers
Step-by-step explanation:
x - 12 ≤ 44 + x
Subtract x from both sides.
-12 ≤ 44
This statement is true, so the inequality is true for all values of x.
Now let's see how this makes sense. Look at the original inequality.
x - 12 ≤ 44 + x
Rewrite as:
x - 12 ≤ x + 44
What does there inequality mean? Subtract 12 from a number, and compare that with adding 44 to the same number. Of course, a number minus 12 is always less than the same number plus 44. It makes sense that this inequality is true for all values of x.
Answer:
\(\large \boxed{\mathrm{All \ real \ numbers}}\)
Step-by-step explanation:
\(x -12 \leq 44+ x\)
Subtract x from both parts.
\(x -12 -x\leq 44+ x-x\)
\(-12\leq 44\)
This is true.
The value of \(x\) is all real numbers.
Are you smart to answer this question?
The order of the quantity from least to the greatest will be π²/8 < √2 < √3 < π²/4 and the order of quantities, as in the numeric labels, is 2341.
What is number?A number is a mathematical entity that can be used to count, measure, or name things. For an example, 1, 2, 56 etc. are the numbers.
We have a quantity shown in the table with label 1 to 4
π²/4 = 2.467 → 1
π²/8 = 1.2337→ 2
√2 = 1.4142 → 3
√3 = 1.7320 → 4
The order of the quantity from least to the greatest will be:
π²/8 < √2 < √3 < π²/4
The order of quantities, as in the numeric labels:
= 2341
Thus, the order of the quantity from least to the greatest will be π²/8 < √2 < √3 < π²/4 and the order of quantities, as in the numeric labels, is 2341.
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A classroom can accommodate less than 24 students.
Which of the following inequalities represents the number of students the classroom can
accommodate?
A.
O
19
30 31
20
21
22
23
24
25 26 27 28 29
B.
O
29
30
31
28
24
25
23
26
27
19 20 21 22
O
C.
25 26
27
28 29 30 31
24
22
23
21
19
20
O
D.
28
25
27
29 30 31
28
19 20 21 22 23 24
The inequalities represents the number of students the classroom can
accommodate is Number line C.
What is Inequality?Mathematical expressions with inequalities are those in which the two sides are not equal. Contrary to equations, we compare two values in inequality. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign.
We have,
A classroom can accommodate less than 24 students.
For less than we use the inequality as '<'.
let the x be the number of students than the condition is
x < 24.
Now, For '<' inequality the arrow should head towards left side of 24 which means for x= 23, 22, 21, .....
Thus, the number line for the situation is C.
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in what number base was the addition 1+nn=100 where n >0, done
\(3x + 2y = 19 \: and \: \: x + y = 8 \: find \: y\)
For the given system of equations 3x + 2y = 19 and x + y = 8 , the value of y is equal to 5.
As given in the question,
Given system of equations are :
3x + 2y = 19 ___(1)
x + y = 8 ___(2)
Simplify the given system of equations to get the value of y we have,
Multiply equation (2) by 3 and eliminate variable x by subtracting (1) from it and get the value of y ,
3x + 3y = 24
3x + 2y = 19
0x + 1y = 5
This implies y is equal to 5.
Therefore, for the given system of equations 3x + 2y = 19 and x + y = 8 , the value of y is equal to 5.
The complete question is :
Simplify the given system of equations to find the value of y:
3x + 2y = 19 and x + y = 8.
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HELPPPPPPPPP 10 poingts
Answer:45
Step-by-step explanation: So the total measure of an exterior would be 360 so you divide the number of sides on the polygon be 360 and you get 45. (I hoped that helped.)
Answer:
45 degrees
Step-by-step explanation:
A octagon is 360 degrees total and since there is 8 sides you would do 360/8 which gives you 45 degrees
HOPE THIS HELPS
Using the Triangle Sum Theorem. Determine the angle measure
of <1.
38
31
(78 and 31 degrees)
Answer:
71 degrees
Step-by-step explanation:
Hi there!
The sum of the interior angles of a triangle is always 180 degrees.
Knowing this, to solve for the measure of angle 1, subtract 78 and 31 degrees from 180:
180-78-31
= 71
Therefore, angle 1 measure 71 degrees.
I hope this helps!
Use the Error Bound to find a value of n for which the given inequality is satisfied. Then verify your result using a calculator.
|e^-0.1 –T_n (-0.1)| ≤ 10 ^-6 , a=0
The calculated absolute difference is smaller than 10^(-6), the result verifies that n = 3 is indeed the correct value for the minimum n that satisfies the inequality.
To find a value of n for which the inequality |e^(-0.1) - T_n(-0.1)| ≤ 10^(-6) is satisfied, we need to use the error bound for Taylor polynomials. The error bound formula for the nth-degree Taylor polynomial of a function f(x) centered at a is given by:
|f(x) - T_n(x)| ≤ M * |x - a|^n / (n+1)!
where M is an upper bound for the (n+1)st derivative of f on an interval containing the values being considered.
In this case, we have a = 0 and f(x) = e^(-0.1). We want to find the value of n such that the inequality is satisfied.
For the function f(x) = e^x, the (n+1)st derivative is also e^x. Since we are evaluating the error at x = -0.1, the upper bound for e^x on the interval [-0.1, 0] is e^0 = 1.
Substituting the values into the error bound formula, we have:
|e^(-0.1) - T_n(-0.1)| ≤ 1 * |-0.1 - 0|^n / (n+1)!
Simplifying further:
|e^(-0.1) - T_n(-0.1)| ≤ 0.1^n / (n+1)!
We want to find the minimum value of n that satisfies:
0.1^n / (n+1)! ≤ 10^(-6)
To find this value of n, we can start by trying small values and incrementing until the inequality is satisfied. Using a calculator, we can compute the left-hand side for various values of n:
For n = 0: 0.1^0 / (0+1)! = 1 / 1 = 1
For n = 1: 0.1^1 / (1+1)! = 0.1 / 2 = 0.05
For n = 2: 0.1^2 / (2+1)! = 0.01 / 6 = 0.0016667
For n = 3: 0.1^3 / (3+1)! = 0.001 / 24 = 4.1667e-05
We can observe that the inequality is satisfied for n = 3, as the left-hand side is smaller than 10^(-6). Therefore, we can conclude that n = 3 is the minimum value of n that satisfies the inequality.
To verify this result using a calculator, we can calculate the actual Taylor polynomial approximation T_n(-0.1) for n = 3 using the Taylor series expansion of e^x:
T_n(x) = 1 + x + (x^2 / 2) + (x^3 / 6)
Substituting x = -0.1 into the polynomial:
T_3(-0.1) = 1 + (-0.1) + ((-0.1)^2 / 2) + ((-0.1)^3 / 6) ≈ 0.904
Now, we can calculate the absolute difference between e^(-0.1) and T_3(-0.1):
|e^(-0.1) - T_3(-0.1)| ≈ |0.9048 - 0.904| ≈ 0.0008
Since the calculated absolute difference is smaller than 10^(-6), the result verifies that n = 3 is indeed the correct value for the minimum n that satisfies the inequality.
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Please help! (70 Max points!)
Answer:
10 ft
Step-by-step explanation:
It mentions they are congruent.
Hence, according to the property of CPCT, corresponding parts of congruent triangles are equal.
Hence,
AC = EGf = 10 ftthe ratio of peter's age to richard's age is $5:8.$ the ratio of john's age to peter's age is $7:12.$ none of the three are over $100$ years old. what is the sum of their ages?
The sum of Peter, Richard, and John's ages is 191.
We know that the ratio of Peter's age to Richard's age is = 5/8 --(i)
The ratio of John's age to Peter's age is = 7/12 --(ii)
Similarly, the ratio of John's age to Richard's age is = (5*7)/(8*12)= 35/96 -(iii)
Using the value of (i),(ii),(iii), we get -
Age of Peter = (5*12)/(8*12) = 60/96
= 60 years of age
Age of John = (7*5)/(12*5) = 35/60
=35 years of age
From the value of (iii), since no one is over 100 years of age, the age of Richard= 96 years of age
Hence the sum of their ages is = 96+35+60
= 191
Therefore, we know that the sum of their ages is 191.
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The Edison Lightbulb Company tests 5% of their daily production of lightbulbs. If 500 bulbs were test on Tuesday, what was the total number of bulbs produced that day?
Answer:
1,000 lightbulbs that day were tested
Step-by-step explanation:
Which set of rational numbers is arranged from least to greatest? 1 over 5, −1.4, negative 1 over 2, 3
Answer:
\(-1.4, -\frac{1}{2}, \frac{1}{5}, 3\)
Step-by-step explanation:
Given
\(\frac{1}{5}, -1.4, -\frac{1}{2}, 3\)
Required
Order from least to greatest
We have:
\(\frac{1}{5}, -1.4, -\frac{1}{2}, 3\)
Convert all fractions to decimal
\(0.2, -1.4, -0.5, 3\)
Now order from least to greatest
\(-1.4, -0.5, 0.2, 3\)
Replace fractions
\(-1.4, -\frac{1}{2}, \frac{1}{5}, 3\)
Find the center of the equation 4x2 + y2 + 8x-5= 0.
Answer:
(-1,0)
Step-by-step explanation:
Plug it into desmos graphing calculator exactly how it is.
Suppose f has absolute minimum value m and absolute maximum value M. Between what two values must 7 3 f(x) dx lie? (Enter your answers from smallest to largest.)
The integral of 7/3*f(x) dx will lie between (7/3)*m and (7/3)*M. So the two values are (7/3)*m and (7/3)*M, and the answer from smallest to largest is: (7/3)*m, (7/3)*M.
Hi! I'd be happy to help you with this question. Suppose f has an absolute minimum value m and an absolute maximum value M. We need to find the range between which the integral 7∫3 f(x) dx must lie.
Step 1: Identify the minimum and maximum values of f(x).
Since f has an absolute minimum value m and an absolute maximum value M, we can write:
f(x) ≥ m and f(x) ≤ M for all x in the interval [3, 7].
Step 2: Determine the bounds for the integral.
Now, let's multiply both sides of these inequalities by the width of the interval, which is (7 - 3) = 4.
4m ≤ 4f(x) ≤ 4M
Step 3: Integrate both sides of the inequalities.
Now, integrate each part of the inequalities from 3 to 7:
4m(7 - 3) ≤ ∫7∫3 f(x) dx ≤ 4M(7 - 3)
Step 4: Simplify the inequalities.
16m ≤ 7∫3 f(x) dx ≤ 16M
So, the integral 7∫3 f(x) dx must lie between 16m and 16M, with 16m being the smallest value and 16M being the largest value.
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Please Help 1 24 + r ; r = 9 2 2a + 3 ; a = 10 3 Bc + 12.3 ; b = 9, c = 4 4 p ÷ q ; p = 24, q = 8 5 4c - 7.8 ; c = 4 6 c - a ; a = 3, c = 17 7 a ÷ 2c ; a = 20, c = 2 8 3x - 14 ; x = 5 9 1.5 + y² ; y = 6 10 t/5 + 6 ; t = 45
Answer:
See solution below
Step-by-step explanation:
Given the following expression
1) 24+r
If r = 9
24 + r = 24+9
= 33
2) 2a+3
If a = 10
Substitute
2(10)+3
= 20+3
= 23
3) BC+12.3
b = 9
c = 4
Substitute
= 9(4)+12.3
= 36+12.3
= 48.3
4) p÷q
Given p = 24 and q = 8
p÷q = 24÷8
p÷q = 3
5) 4c-7.8
If c = 4
Substitute
= 4(4)-7.8
= 16-7.8
= 8.2
6) c-a
a = 3
c = 17
Substitute
= 17-3
= 14
Hence c-a = 14
7) a ÷ 2c ; a = 20, c = 2
Substitute
a÷2c
= a/2c
= 20/2(2)
= 20/4
= 5
8) 3x-14
If x = 5
Substitute
= 3(5)-14
= 15-14
= 1
9) 1.5 + y² ; y = 6
Substitute
= 1.5+6²
= 1.5+36
= 37.5
10) t/5 + 6 ; t = 45
substitute the value of t given into the expression
= 45/5 + 6
= 9 + 6
= 15
4×5+-8÷(7×9) what is the answer?
Answer:
19.87301587
Step-by-step explanation:
Answer:
Step-by-step explanation:
Ok, so you would use PEMDAS, which is the correct order in which you would need to solve an equation. The idea is that the operations that come first would have to be solved first.
If you don't know it, PEMDAS is:
Parentheses
Exponents
Multiplication/division
Addition/subtraction
In this case, you would need to solve the parentheses. (7x9) is 63.
It would be rewritten as 4x5-8/63
There are no exponents, so you can skip the next operation.
Then you would do multiplication next, which would be 4x5 = 20
The equation would be rewritten as 20-8/63
-0.126984127 is -8/63
Lastly, 19.8730159 is the result of 20-0.126984127
Hope this helps!
Determine whether the given value is a solution of the equation: x + 15 = 10; x=5 *
Answer:
It is not correct, x = -5
Step-by-step explanation:
Answer:
no
Step-by-step explanation:
because 5+15=10
-15=15
x= -5
which means its NOT a solution because it equals -5
The volume of the cone shown is 6 cubic inches. What is the height of a cone with the same base diameter but a volume of only 3 cubic inches?
Answer:
9
Step-by-step explanation:
6=3
Side A B is parallel to Side D E in the map below. Triangle A B C. Side A B is 15 feet and side B C is 9 feet. Triangle C D E. Side C D is 6 feet and side D E is x feet. Which proportion solves for the distance between D and E? Start Fraction 9 Over 6 End Fraction = Start Fraction x Over 15 End Fraction Start Fraction 6 Over x End Fraction = Start Fraction 15 Over 9 End Fraction Start Fraction 9 Over 6 End Fraction = Start Fraction 15 Over x End Fraction Start Fraction 6 Over 15 End Fraction = Start Fraction 9 Over x End Fraction
The proportion that solves for the distance between D and E is x/15 = 6/9
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Triangle ABC and CDE are similar triangles, hence the ratio of their corresponding sides are in the same proportion.
Hence:
x/15 = 6/9
The proportion that solves for the distance between D and E is x/15 = 6/9
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Simplify √63x10y15 to the form a√b.
Answer:
49
Step-by-step explanation:
Add then subtract
(edge) The linear function that is represented by which table has the same slope as the graph?
On a coordinate plane, a line goes through points (0, negative 3) and (2, 1).
A 2-column table with 5 rows. Column 1 is labeled x with entries negative 25, negative 21, negative 17, negative 13, negative 9. Column 2 is labeled y with entries negative 9, negative 7, negative 5, negative 3, negative 1.
A 2-column table with 5 rows. Column 1 is labeled x with entries negative 25, negative 21, negative 17, negative 13, negative 9. Column 2 is labeled y with entries 9, 7, 5, 3, 1.
A 2-column table with 5 rows. Column 1 is labeled x with entries negative 9, negative 7, negative 5, negative 3, negative 1. Column 2 is labeled y with entries negative 25, negative 21, negative 17, negative 13, negative 9.
A 2-column table with 5 rows. Column 1 is labeled x with entries 1, 3, 5, 7, 9. Column 2 is labeled y with entries negative 9, negative 13, negative 17, negative 21, negative 25.
Answer: is 3
Step-by-step explanation:
Very easy man !!!
The United States Census collects data on many variables about individuals and households.
Which variables are quantitative?
Select all that apply.
Years living in the U.S.
How many adults are registered to vote in the upcoming election?
Number of adults over 18.
Number of minors in the household
Family role of respondent
Number of family members residing at the address
Ethnicity
Zip code
Answer:
Years living in the U.S.
How many adults are registered to vote in the upcoming election?
Number of adults over 18
Number of minors in the household
Number of family members residing at the address
Zip code
Step-by-step explanation:
Given the following :
Select the variables which are quantitative :
Quantitative variables may be explained as those variables which are represented numerically or possess numerical attributes. The are usually expressed in numbers. Quantitative variables in the options below are those which will take Numeric inputs.
Years living in the U.S. = quantitative
How many adults are registered to vote in the upcoming election? = quantitative
Number of adults over 18. = quantitative
Number of minors in the household = quantitative
Family role of respondent = not quantitative
Number of family members residing at the address = quantitative
Ethnicity = Not quantitative
Zip code = quantitative
Which table identifies the x-values, if any, of the relative extrema of f(x) = (x^3 – 5x^2 + 11x – 11)e^x
Answer:
Relative minimum: x=0
Relative maximum: None
Step-by-step explanation:
Relative extrema are going to be located where the first derivative changes sign. Therefore, we must first find the derivative of the function:
\(f'(x)=\frac{d}{dx}[(x^3-5x^2+11x-11)e^x]\\ \\f'(x)=(x^3-5x^2+11x-11)*\frac{d}{dx}(e^x)+[\frac{d}{dx}(x^3-5x^2+11x-11)]*e^x\\ \\f'(x)=(x^3-5x^2+11x-11)e^x+(3x^2-10x+11)e^x\\\\f'(x)=(x^3-2x^2+x)e^x\\\\f'(x)=xe^x(x^2-2x+1)\\\\f'(x)=xe^x(x-1)^2\)
Next, we set \(f'(x)=0\) where we determine our critical points:
\(0=xe^x(x-1)^2\)
\(x=0,x=1\)
We then test points around the critical points to find where the derivative changes sign. I will use the points \(x=1\), \(x=\frac{1}{2}\), and \(x=\frac{3}{2}\):
\(f'(-1)=(-1)e^{-1}((-1)-1)^2=-\frac{1}{e}(-2)^2=-\frac{4}{e}<0\\\\f'(\frac{1}{2})=\frac{1}{2}e^\frac{1}{2}(\frac{1}{2}-2)^2=\frac{\sqrt{e}}{2}(-\frac{1}{2})^2=\frac{\sqrt{e}}{8}>0\\\\f'(\frac{3}{2})=\frac{3}{2}e^\frac{3}{2}(\frac{3}{2}-2)^2=\frac{3\sqrt{e^3} }{2}(\frac{1}{2})^2=\frac{3\sqrt{e^3}}{8}>0\)
As you can see, the derivative changes sign from negative to positive at \(x=0\), but the sign stays positive at \(x=1\). Therefore, the only critical point that is an extreme point is \(x=0\), which is a relative minimum. This means that there is no relative maximum.
In conclusion, the 4th option is correct. Review the graph for a visual of how the derivative sign changes.
Given a polynomial f(x), if (x + 5) is a factor, what else must be true?
f(0) = 5
Ob
f(0) = -5
Ос
f(5) = 0
Od
f(-5) = 0
Answer:
As
\(p(-5) = 0\)
Thus, the correct option is 'd'.
Step-by-step explanation:
We know that the special theorem of remainder states that:
if
\(x-k\) is a factor of \(p(x)\)
then
\(p(k) = 0\)
so
\(x+5 = x-(-5)\)
\(k = -5\)
Thus,
\(p(k) = 0\)
\(p(-5) = 0\)
Thus, the correct option is 'd'.
Which expression is equivalent to 4f + f2 + 3?
Answer:
6f + 3
Step-by-step explanation:
so in order to get a equation that is equivalent to 4f + f2 + 3 is you have to simplify the expression by adding numbers to numbers and variables to variables.
so we are going to add 4f and 2f together:
(4f + f2) + 3
And you get the expression:
6f + 3
I hope this helps you!!
Suppose you are constructing a LEGO Technic Land Rover Defender with a total of 2573 pieces. You have already put together 253 pieces. Every minute you add 5 more pieces. Is the relationship linear? How do you know?
Answer: Yes it is
Step-by-step explanation:
A linear relationship simply put, is a relationship between variables that when constructed, forms a straight line. This happens when y changes at a constant rate if x changes by a constant rate as well for instance, 1.
From this question, assume x is minutes and y is the total number of pieces put together. This means that every time x (minutes) increases by 1, y increases by 5 pieces.
The formula would look like this;
y = 5x + 253
This is a formula for a straight line so indeed, this relationship is linear.
459, 450, 441, ...
Find the 38th term.
Answer:
I am pretty sure it is 351