Graph 4x + y = 6x − 1.
Show your work and explain the method used to determine the graph.

Answers

Answer 1

Answer:
Graph the line using the slope and y-intercept, or two points.

Slope: 2
y-intercept: (0, -1)

x | y
0| -1
1 | 1

Step-by-step explanation:

Graph 4x + Y = 6x 1.Show Your Work And Explain The Method Used To Determine The Graph.
Answer 2

A(0,-1) and B(0.5,0) of 4x+y = 6x-1 help us to get two coordinates to determine the graph is a straight line.

What is graph?

" A graph is defined as the representation of two variables on the coordinate plane to determine the relation between the two variables."

According to the question,

Given,

  4x + y = 6x - 1

Find the value of 'y' in form of 'x' we get,

⇒y =6x - 4x -1

⇒ y = 2x - 1

Calculate the value of 'x' and 'y' for y-intercept and x-intercept respectively on the graph we have,

When x = 0 ⇒y = -1

When y = 0 ⇒x = 0.5

From the graph we can find,

y = 2x - 1 represents graph of  the straight line passing through y-intercept A(0,-1) and x-intercept B(0.5,0).

Hence,  A(0,-1) and B(0.5,0) of 4x+y = 6x-1 help us to get two coordinates to determine the graph is a straight line.

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Graph 4x + Y = 6x 1.Show Your Work And Explain The Method Used To Determine The Graph.

Related Questions

plss help Simplify: 29/4

Answers

Answer: 7.25/1

I think you are simplifying fractions so this should be the answer

Answer:

just do 4+2 then 6x9 the you get your top number then put 4 as the bottem number

Step-by-step explanation:

Expand the linear factors of f(x), where f(x) = (x - 10)(x + 2).

Answers

Multiply X in the second parentheses then multiply -10 in the second parentheses.

X^2 + 2x -10x -20 (now simplify)

X^2 -8x -20 is the answer.

A study is designed to test the effects of location (island vs. mainland) and squirrels (present or absent) on the cone sizes of lodgepole pines. Which of the following interaction plots is consistent with this combination of main effects and interactions? A main effect of location is present. A main effect of squirrels is present. An interaction between squirrels and location is present.

Answers

The interaction plot consistent with the combination of main effects and interactions described is Plot D, which shows an interaction between squirrels and location.

An interaction occurs when the effect of one independent variable (in this case, squirrels) on the dependent variable (cone sizes) depends on the level of another independent variable (location).

Based on the given information, we have the following main effects and interactions:

1. Main effect of location: This means that the location (island vs. mainland) has an independent effect on cone sizes. It suggests that there is a difference in cone sizes between the two locations.

2. Main effect of squirrels: This means that the presence or absence of squirrels has an independent effect on cone sizes. It suggests that the presence of squirrels may influence cone sizes.

3. Interaction between squirrels and location: This means that the effect of squirrels on cone sizes depends on the location. In other words, the presence or absence of squirrels may have a different impact on cone sizes depending on whether the trees are on an island or the mainland.

Among the given interaction plots, Plot D is consistent with these main effects and interactions. It shows that the effect of squirrels on cone sizes differs between the island and mainland locations, indicating an interaction between squirrels and location.

Therefore, Plot D is the interaction plot that aligns with the combination of main effects and interactions described in the question.

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Plz answer picture included

Plz answer picture included

Answers

Answer:

C

Step-by-step explanation:

also close ur tabs bro, u will lag ur computer that way

Answer:

holy sh- thats alot brainly tabs

Step-by-step explanation:

In the figure shown at right, the area of the large rectangle is (5x)(8x+1) and the area of the small rectangle is (4x)(2x) which of the following expression represents the area of the shaded region?

In the figure shown at right, the area of the large rectangle is (5x)(8x+1) and the area of the small

Answers

Given:

Area of large rectangle = (8x + 1)(5x)

Area of small rectangle = (4x)(2x)

To find area of the shaded region, subtract the area of the small rectangle from the large rectangle.

We have:

Area of large rectangle =

\(\begin{gathered} (8x+1)(5x) \\ \\ =8x(5x)+1(5x) \\ \\ =40x^2+5x \end{gathered}\)

Area of small rectangle =

\(\begin{gathered} (4x)(2x) \\ \\ =8x^2 \end{gathered}\)

Area of shaded region =

\(\begin{gathered} (40x^2+5x)-(8x^2) \\ \\ 40x^2+5x-8x^2 \\ \\ \text{Combine like terms:} \\ 40x^2-8x^2+5x \\ \\ =32x^2+5x \end{gathered}\)

Therefore, the area of the shaded region is = 32x² + 5x

ANSWER:

\(32x^{2}+5x\)

Find the sum of squares of the deviations from the mean of a series of ACT scores listed below.31, 22, 24, 15, 23The sum of squares is(Type an integer or a decimal.)

Answers

Solution

Given the following scores below

\(31,22,24,15,23\)

To find the sum of squares of the deviations,

Firstly, we find the mean, the formula to find the mean of ungrouped data is

\(\begin{gathered} \bar{x}=\frac{\sum_X}{n} \\ Where\text{ n is the number of terms} \end{gathered}\)

Where n = 5

Substitute the given data into the formula to find the mean of ungrouped data

\(\begin{gathered} \bar{x}=\frac{31+22+24+15+23}{5} \\ \bar{x}=\frac{115}{5}=23 \\ \bar{x}=23 \end{gathered}\)

Secondly, we subtract the mean from each of the values given as shown below

\(\begin{gathered} 31-23=8 \\ 22-23=-1 \\ 24-23=1 \\ 15-23=-8 \\ 23-23=0 \end{gathered}\)

Then, to find the sum of squares of the deviations

We add the square of each of the deviations deduced above

\(\begin{gathered} =(8)^2+(-1)^2+(1)^2+(-8)^2+(0)^2 \\ =64+1+1+64+0 \\ =130 \end{gathered}\)

Hence, the sum of squares is 130

A population of beavers decreases exponentially at a rate of 7.5% per year. What is the equivalent monthly rate to the nearest hundredth of a percent

Answers

Answer:

0.65%

Step-by-step explanation:

i took the test

The average age in a sample of 90 students at City College is 20. As a result of this sample, it can be concluded that the average age of all the students at City College:

Answers

If the sample is not truly representative, the conclusion may not accurately reflect the actual average age of all the students at the college.

Based on the given information, it can be concluded that the average age of all the students at City College is likely around 20. However, it's important to note that this conclusion is only valid if the sample of 90 students is representative of the entire student population at City College. If the sample is not truly representative, the conclusion may not accurately reflect the actual average age of all the students at the college.

The average age in a sample of 90 students at City College is 20. However, based on this sample alone, it cannot be conclusively determined that the average age of all the students at City College is also 20. This is because the sample may not be fully representative of the entire student population. More information or a larger sample would be needed to make a more accurate conclusion about the average age of all students at City College.

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If the sample of 90 students is representative of the entire student population at City College, then we can conclude that the average age of all students is approximately 20 years old.

Based on the given information, the average age in a sample of 90 students at City College is 20.

To determine if this sample can be used to conclude the average age of all students at City College, we need to consider these terms:
Sample:

A subset of a population, which in this case is the group of 90 students at City College.
Population:

The entire group of students at City College that we want to make a conclusion about.
Average (Mean) Age:

The sum of ages divided by the total number of students, in this case, 20 years.
Representativeness:

How well the sample reflects the characteristics of the entire population.
If the sample of 90 students is representative of the entire student population at City College, then we can conclude that the average age of all students is approximately 20 years old.

However, if the sample is not representative, the conclusion may not be accurate.

To make a more accurate conclusion, it is important to ensure that the sample is representative by using a larger sample size or random sampling methods.

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3. Lim
x-infinity
x² +6x²+1/
x²+3
[AP]

3. Limx-infinityx +6x+1/x+3[AP]

Answers

Answer:  0

=======================================================

Explanation:

Let n be the degree of the numerator

Let d be the degree of the denominator

If n < d, then the limit at infinity is always 0. This is because the denominator is growing faster compared to the numerator. I suggest looking at a table of values to see this in action.

In this case, n = 3 and d = 4, so we see that n < d is the case here. So that's why the answer is 0.

----------------------

Side notes:

If n = d, then the limit at infinity is equal to a/b, where a and b are the leading terms of the numerator and denominator. If n > d, then the numerator is growing faster than the denominator, meaning the ultimate result is infinity.

Solve the trigonometric equation for all values -5 sinπ/3x=0

Solve the trigonometric equation for all values -5sin/3x=0

Answers

The solutions to the equation sin(πx/3) = 0 in the interval -5 < x < 5 are x = -3, 0, and 3.

What is Trigonometric equation?

A trigonometric equation is an equation that involves trigonometric functions such as sine, cosine, tangent, or their inverses. Trigonometric equations arise in a variety of mathematical and scientific contexts, from solving geometric problems involving angles and triangles to modeling periodic phenomena in physics, engineering, and other fields.

Solving a trigonometric equation typically involves finding the values of the unknown variable that satisfy the equation within a certain interval. For example, the equation sin(x) = 0 has infinitely many solutions, but if we restrict the interval to [0, 2π], then the solutions are x = 0, π, 2π, which correspond to the x-intercepts of the sine function in that interval.

Here the equation sin(πx/3) = 0 has solutions whenever πx/3 is an integer multiple of π, since the sine function is zero at these values. Thus, we need to find all integers n such that πx/3 = nπ, or equivalently x = 3n for some integer n.

Since -5 < x < 5, we need to find all integers n such that -5 < 3n < 5. Dividing all sides by 3, we get -5/3 < n < 5/3. The only integers in this range are -1, 0, and 1. Therefore, the solutions to the equation sin(πx/3) = 0 in the interval -5 < x < 5 are x = -3, 0, and 3.

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Rent is VERY expensive in Garden City, but after you graduate, you know you want to move into
your own apartment. You have been working the last 2 years and have saved $5,000. If rent is $750
a month, how many months could you pay full rent with your savings?

Answers

Answer:

70000

Step-by-step explanation:

provide an example of a one-way anova that could be done as both a between-subjects and repeated-measures design. for your example, indicate which would be better to use and why.

Answers

An example of a one-way ANOVA that could be conducted as both a between-subjects and repeated-measures design is a study comparing the effectiveness of three different teaching methods on student performance. Conducting the ANOVA as a repeated-measures design would be more appropriate in this case.

Suppose a researcher wants to investigate the impact of three teaching methods (A, B, and C) on student performance in a specific subject.

In a between-subjects design, different groups of students would be assigned to each teaching method, and their performance scores would be measured and compared.

This would involve independent groups of participants, with each participant experiencing only one teaching method.

On the other hand, in a repeated-measures design, the same group of students would receive all three teaching methods in a random order, and their performance scores would be measured after each method.

This allows for a direct within-subject comparison of the three teaching methods, as each participant serves as their control.

In this example, a repeated-measures design would be more appropriate.

It eliminates the individual differences between participants, making the comparison more accurate and reducing the variability in the data.

Additionally, using a repeated-measures design requires a smaller sample size compared to a between-subjects design, which can be more cost-effective and efficient.

By using a repeated-measures design, the researcher can directly observe the effect of each teaching method on the same group of students, leading to a more robust and precise analysis of the teaching methods' effectiveness.

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What’s the answer?????

Whats the answer?????

Answers

Answer:

19.3

Step-by-step explanation:

d=m/v

d=2316/120

d=19.3 g/cm^3

Answer:

19.3g/cm^3

Step-by-step explanation:

find missing measure​

find missing measure

Answers

Answer:

Step-by-step explanation:

∠Q = 180-∠T = 89°

∠S = 360-∠T-∠Q-∠R = 360-91-89-27 = 153°

assume that when adults with smartphones are randomly selected, 59% use them in meetings or classes. if 12 adult smartphone users are randomly selected, find the probability that fewer than 3 of them use their smartphones in meetings or classes

Answers

The probability that fewer than 3 out of 12 randomly selected adult smartphone users use their smartphones in meetings or classes is approximately 0.0539.

To find the probability that fewer than 3 out of 12 randomly selected adult smartphone users use their smartphones in meetings or classes, we can use the binomial probability formula.

The binomial probability formula is given by:

P(X = k) = C(n, k) * p^k * (1 - p)^(n - k)

where:

- P(X = k) is the probability of exactly k successes,

- n is the number of trials,

- k is the number of successes,

- p is the probability of success in a single trial, and

- C(n, k) is the combination of n choose k.

In this case, n = 12, k can be 0, 1, or 2, and p = 0.59 (the probability of using smartphones in meetings or classes).

Now we can calculate the probabilities for each value of k and sum them up:

P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2)

P(X = 0) = C(12, 0) * 0.59^0 * (1 - 0.59)^(12 - 0)

P(X = 1) = C(12, 1) * 0.59^1 * (1 - 0.59)^(12 - 1)

P(X = 2) = C(12, 2) * 0.59^2 * (1 - 0.59)^(12 - 2)

Calculating these probabilities and summing them up will give us the desired probability that fewer than 3 out of 12 users use their smartphones in meetings or classes.

Let's calculate the probabilities.

P(X = 0) = C(12, 0) * 0.59^0 * (1 - 0.59)^(12 - 0)

Using the combination formula, C(12, 0) = 1, and simplifying the equation:

P(X = 0) = 1 * 1 * (1 - 0.59)^12 = 0.0003159

P(X = 1) = C(12, 1) * 0.59^1 * (1 - 0.59)^(12 - 1)

Using the combination formula, C(12, 1) = 12, and simplifying the equation:

P(X = 1) = 12 * 0.59^1 * (1 - 0.59)^11 = 0.0065294

P(X = 2) = C(12, 2) * 0.59^2 * (1 - 0.59)^(12 - 2)

Using the combination formula, C(12, 2) = 66, and simplifying the equation:

P(X = 2) = 66 * 0.59^2 * (1 - 0.59)^10 = 0.0470972

Now, let's sum up these probabilities to find P(X < 3):

P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2)

P(X < 3) = 0.0003159 + 0.0065294 + 0.0470972 = 0.0539425

Therefore, the probability that fewer than 3 out of 12 randomly selected adult smartphone users use their smartphones in meetings or classes is approximately 0.0539.

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|1.3x+7.8|>0 what would be the answer in this inequality.

Answers

Answer:

inequality form would be x<-6 or x>-6

1. Find the volume of the shape below:
3 i
5.8 in
12 in

1. Find the volume of the shape below:3 i5.8 in12 in

Answers

Answer:

208.8 inches is the answer

Based on concepts related to the volume of prisms, the volume of the shape depicted with the dimensions shown in the figure is equal to 208.8 square inches. #SPJ2

How to calculate the volume of a prism-like element

Prisms are tridimensional elements whose volume is equal to the product of area of its base, in square inches, and its height, in inches. The base of the shape is certainly a rectangle, whose area is equal to the product of its width and length, both in inches.

Therefore, the volume of shape is:

V = (12 in) · (5.8 in) · (3 in)

V = 208.8 in³

Based on concepts related to the volume of prisms, the volume of the shape depicted with the dimensions shown in the figure is equal to 208.8 square inches. #SPJ2

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Expand and simplify
3(2m + 1) + 5m

Answers

Answer:

The simplified answer is 8m+3.

Step-by-step explanation:

3(2m+1)+5m

(6m+3)+5m

8m+3

Answer:

11m + 3

Step-by-step explanation:

First you distribute:

3 ( 2 + 1 )  +  5

6m + 3 + 5m

Next, you combine like terms:

6m + 5m + 3 = 11m + 3

The bell tower of the cathedral in Pisa, Italy, leans 5.6\deg from the vertical. A tourist stands 105m from Its base, with the measures the angle of elevation to the top of the tower to be 29.2\deg . Find the length of the tower to the nearest meter.

Answers

The length of the tower is approximately 55 meters to the nearest meter.Hence, the correct option is B. 55.

Given that the bell tower of the cathedral in Pisa, Italy, leans 5.6° from the vertical and a tourist stands 105m from its base, with the measures the angle of elevation to the top of the tower to be 29.2°.

We have to find the length of the tower to the nearest meter.We can find the length of the tower using the tangent function of the angle of elevation and the Pythagorean theorem. Let the length of the tower be x meters. Therefore, the height of the tower

= x sin 5.6°and t

he distance of the tourist from the tower = x cos 5.6° + 105 m.

Now, according to the given information:

x sin 5.6° = height of the tower

= (x cos 5.6° + 105) tan 29.2°x sin 5.6°

= (x cos 5.6° + 105) tan 29.2°⇒ x sin 5.6°

= x tan 29.2° cos 5.6° + 105 tan 29.2°⇒ x [sin 5.6° − tan 29.2° cos 5.6°]

= 105 tan 29.2°⇒ x = 105 tan 29.2° ÷ [sin 5.6° − tan 29.2° cos 5.6°]

≈ 55.86 m

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Which statement is true?
A.
4.22 = 4.022
B.
12.51 < 12.439
C.
0.808 > 0.088
D.
10.672 > 10.762

Answers

Answer: C. 0.808 > 0.088

Step-by-step explanation:

A is wrong because 4.22 and 4.022 are different numbers. 4.022 is less because it has a 0 in the tenths place, whereas 4.22 has a 2 in the tenths place, which is more.

B is wrong because 12.51 is more than 12.439. It has a 5 in the tenths place, whereas 12.439 has a 4 in the tenths place, which is less.

C is right because 0.808 is more than 0.088. It has a 8 in the tenths place, whereas 0.088 has a 0 in the tenths place, which is less.

D is wrong because 10.672 is less than 10.762. It has a 6 in the tenths place, whereas 10.762 has a 7 in the tenths place, which is more.

The tenths place is the number right after the decimal, which gives a good indication of which number is bigger or smaller. Remember the greater or less than signs (< and >) always face open towards the bigger side. (Crocodile wants to eat the bigger number).

Answer: C
Explanation: for A if the zero is on the left side after the decimal point it’s significant but when it’s on the end for example 2.340 it wouldn’t be significant or it wouldn’t matter so it’s wrong and for B the 5 in 12.51 is greater than the 4 in 12.439 and for D the 7 in 10.762 is greater than the 6 in 10.672 hope it helps

find the complexity function for each of these algorithms and explain why algorithm b is more efficient assume that mulitppication is the basic operation

Answers

Therefore , due to the following above reasons we find algorithm b is more efficient function.

Function is what?

You've been playing about with equations of the type "y=" for a while now. You've also observed that the equations that are "nice" to solve for "y=" and then input into your graphing calculator are those that have straight lines rather than ellipses. These equations with "y=" are functions.

Here,

To determine how each of these algorithms' complexity functions

To summarize, regardless of the type of machine an algorithm runs on, temporal complexity predicts how well it performs.

By "counting" the amount of operations your code executes, you can determine the temporal complexity.

The Big-O notation is used to define this temporal complexity as a function of the input size n. The input size is indicated by n, and the worst-case growth rate function is represented by O.

thus, algorithm b is more efficient

Therefore , due to the following above reasons we find algorithm b is more efficient function.

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1. Estimate
Square root 5

Answers

Answer: 25

Step-by-step explanation: 5^2 = 25, 5x5 = 25

Hope this helps!

2.2

did that help at all

when he applied to y combinator (see case exhibit 3), what hypotheses did houston have about dropbox’s strategy? be specific. as of june 2010, which of them turned out to be wrong? be specific.

Answers

He defined quality as a speedy procedure and document security through the use of a web interface, and the data was safely backed up to Amazon S3.

Houston determined that his potential customers, who would be his target demographic, were already technically savvy, but that because of the product's simplicity and the advent of the internet, it could fast increase.

The user-friendly application and product accessibility are important aspects of his business approach. This idea was proven by developing a solution that is simple to use and allows users to work on the most recent version of a particular document via an automated update. Houston wants to ensure that one of the most important aspects of his product is its quality. He defined quality as a speedy procedure and document security through the use of a web interface, and the data was safely backed up to Amazon S3.Houston determined that his potential customers, who would be his target demographic, were already technically savvy, but that because of the product's simplicity and the advent of the internet, it could fast increase. As a result, his next major aspect was the distribution of a single version for all users, as well as the deployment of the "Trojan Horse" technique to expand. Dropbox employed the Freeware model to generate income, which meant that the first 2 GB were provided for free and the remaining GB had to be paid for on a monthly basis.

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16 x 7 x 15 + 11 + 17​

Answers

Answer:

1,708

Step-by-step explanation: does it need an explanation?

if so tell me

1,708

if you multiply 16 by 7 and by 15 equal 1,680. Then you add 11 then add 17 which would give you 1,708

Uncle Saul's car goes 42 3/10 miles on a gallon of gas. There are 2 1/2 gallons of gas remaining in his gas tank.
3. How many miles can he drive before running out of gas?
4. Saul drives a total of 19 9/10 miles each day during his 5-day workweek. Will he need to buy more gas for the upcoming week? explain your answer.
please help asap tysm <33

Answers

Answer:

Step-by-step explanation:

quit

if −x+5y=7 is a true equation, what would be the value of -2(-x+5y)

Answers

Answer:

-14

Step-by-step explanation:

Given -x+5y=7

Now we substitute x+5y into -2(-x+5y)

-2(-x+5y) = (-2)(7)

= - 14

find the current i(t) if the resistance is 0.1 ohm, the impressed voltage is e(t) = 5, and i(0) = 0.
i(t) =

Answers

If the resistance is 0.1 ohm, the impressed voltage is e(t) = 5, and i(0) = 0. The current i(t) is 50t.

The equation of the circuit is given as;v = L di/dt + R iThe initial current is zero, and the capacitor has no charge. As a result, the total voltage is equal to the impressed voltage.

e(t) = L di/dt + R i

Differentiate both sides with respect to time.

t(e(t)) = d(L di/dt)/dt + d(R i)/dt

t(e(t)) = L d²i/dt² + R di/dt + i(dR/dt)

Substituting the given values,R = 0.1, L = 0.02

Therefore;e(t) = 0.02(d²i/dt²) + 0.1(di/dt)

The equation is a second-order linear homogeneous differential equation. The auxiliary equation is given by;0.02m² + 0.1m = 0m(0.02m + 0.1) = 0m = 0 or -5

Taking m = 0;

Let i(t) = A + Bt

Substituting in equation (1);

e(t) = 0.02(d²i/dt²) + 0.1(di/dt)0 = 0.02d²i/dt² + 0.1di/dt

Substituting i(t) = A + Bt0 = 0.02B0 + 0.1A5 = 0.1B0.1B = 5B = 50

Using the values of A and B, i(t) can be calculated as;i(t) = 50t

Hence, the current i(t) is 50t.

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Question 10 of 13
by visual inspection, determine the best-fitting regression model for the
scatterplot.
o a. no pattern
o b. quadratic
o c. exponential
o d. linear


please help!

Answers

The best-fitting regression model for the scatter plot is exponential curve , Option C is the right answer.

The missing graph is attached with the answer.

What is an exponential graph ?

An exponential graph is given by y = aˣ , the graph for an exponential growth is also attached with the answer,

From the graph given in the question it can be concluded that it is not linear , not quadratic and it is not true that it doesn't have a pattern , It is an exponential growth graph, Therefore Option C is the right answer.

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Question 10 of 13 by visual inspection, determine the best-fitting regression model for the scatterplot.
Question 10 of 13 by visual inspection, determine the best-fitting regression model for the scatterplot.

& represents 29 students in a class
B represents students who have a brother
S represents students who have a sister
В.
S
7
4
2x
x + 3
7+4+2x+x+3=29
a) One student from the class is chosen at random.
What is the probability that the student has a sister? 14+3x=29
3x=15
X=5
29-8=21​

Answers

Answer:

a) 14/ 29

b) 4/11

Step-by-step explanation:

x = 5


Find the 32 nd term of each sequence. 101,105,109,113, ...........

Answers

The arithmetic sequence AP's 32nd term is calculated to be 225.

What is the definition of an AP arithmetic sequence?

An arithmetic progression (AP) in mathematics is a list and maybe sequence of numbers with each term is obtained by adding a sequence to the term before it.

With the exception of arithmetic progression, the fixed number is denoted by the letter 'd.'Common difference => d = a2 - a1 = a3 - a2 = a4 - a3 =...... = a - an-1.nth term of an AP: an = a + (n - 1) dThe sum of n terms of an AP's => Sn = n/2(2a+(n-1)d) = n/2(a + l), where l = last term of the AP.

Finally, the solution to the question is as follows:

The numbers in the displayed sequence are as follows:

101,105,109,113, ...........

We must explore the 32nd number in the series because it contains 32 terms.

The common difference with both two consecutive terms of an AP which are equal is denoted by 'd.'

Let's assume the first term is'a₁' = 101.

Let's assume 'a₂' = 105 is the second term.

Let's assume the third term is 'a₃' = 109

Substitute the values the preceding equation; the 32nd term is-

d = a₂ - a₁  

Obtain the common difference;

d = 105 - 101

d = 4

Put the values in the preceding formula; the 32nd term is

The formula finds the nth term equation;

nth term of an AP: an = a + (n - 1) dTotal number of terms is; n = 32Initial term is a = 101Common difference d = 4

Put the given values in nth term formula;

a₃₂ = a + (n - 1) d

a₃₂ = 101 + (32 - 1)(4)

a₃₂ = 101 + 128 - 4

a₃₂ = 225

Thus, the 32nd term value of the arithmetic sequence is calculated to be 225.

More information on the arithmetic sequence can be found here.

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