The nth term of a sequence is 3n2 - n + 10 where n is a positive integer. Which term in the sequence is equal to 54?​

The Nth Term Of A Sequence Is 3n2 - N + 10 Where N Is A Positive Integer. Which Term In The Sequence

Answers

Answer 1

Answer:

4th term

Step-by-step explanation:

Equate the nth term formula to 54 and solve for n

3n² - n + 10 = 54 ( subtract 54 from both sides )

3n² - n - 44 = 0

Consider the factors of the product of the n² term and the constant term which sum to give the coefficient of the n- term.

product = 3 × - 44 = - 132 and sum = - 1

The factors are - 12 and + 11

Use these factors to split the n- term

3n² - 12n + 11n - 44 = 0 ( factor the first/second and third/fourth terms )

3n(n - 4) + 11(n - 4) = 0 ← factor out (n - 4) from each term

(n - 4)(3n + 11) = 0

Equate each factor to zero and solve for n

n - 4 = 0 ⇒ n = 4

3n + 11 = 0 ⇒ 3n = - 11 ⇒ n = - [tex]\frac{11}{3}[/tex]

Since n > 0 then n = 4

Answer 2

The 4th term of the sequence is 54.

What is a sequence ?

A sequence is a set of numbers with a constant difference or a constant ratio or it have a certain relation with the next and previous term.

According to the given question the nth term of a sequence is 3n² - n + 10.

We have to determine which term is equal to 54 or the value of and it must be an integer.

So, 3n² - n + 10 = 54.

3n² - n - 44 = 0.

3n² - 12n + 11n - 44 = 0.

3n(n-4) +11(n-4) = 0.

(3n+11) = 0 OR (n-4) = 0.

n = - 11/3 OR n = 4.          ( given the term no. is a positive integer ).

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Related Questions

Which value of m is a counterexample for the following statement?

If m is an odd prime number, then m + 2 is also prime.

7

3

5

9

11

Answers

Answer: 7

The prime numbers here are 3, 5, 7, and 11. This means that 9 is not prime. Since 7 +2 is 9, this disproves that m + 2 is also prime.

Would appreciate brainly <3

Answer:

true

Step-by-step explanation:

because you can start at zero and go on forever adding twos but it'll still be the same

Determine if y=3⋅2z+12 is linear, quadratic, or exponential.

Answers

Answer:

Exponential

Step-by-step explanation:

2z

A total of 10 families participate in a car wash. Each family brings two cars. Mr. Gonzales notices that 35% of the cars are minivans. How many minivans are washed?

Answers

Answer:

Step-by-step explanation:

Answer:

14 minivans

Step-by-step explanation:

From the question

A total of 20 families participate in a car wash. Each family brings two cars.

Hence, the total number of cars brought to the car wash is:

20 × 2

= 40 cars.

Mr. Gonzales notices that 35% of the cars were minivans.

The number of minivans were washed is :

35% of the total number of cars

= 35/100 × 40

= 14 minivans

Answer:

14 minivans

Step-by-step explanation:

From the question

A total of 20 families participate in a car wash. Each family brings two cars.

Hence, the total number of cars brought to the car wash is:

20 × 2

= 40 cars.

Mr. Gonzales notices that 35% of the cars were minivans.

The number of minivans were washed is :

35% of the total number of cars

= 35/100 × 40

= 14 minivans

How would a child use addition to find 8 X 2?

Answers

Answer:

16

Step-by-step explanation:

They would do 8+8 to get their answer

14. Explain why a step in solving the equation 4n = -36 is to divide both sides by 4. Then
solve the equation.

Answers

Answer:

Because you cant combine unlike terms. And the goal is to get X by itself.

-9 is the answer

Step-by-step explanation:



2. Explain the relationship between depression and heart disease.

Answers

Answer:

People with depression may have uncommonly sticky platelets, the tiny cells that cause blood to clot. In patients with heart disease, this can accelerate atherosclerosis (hardening of the arteries) and increase the chance of heart attack. Some studies show that treating depression make platelets less sticky again.

Answer:

People with depression may have uncommonly sticky platelets and tiny cells that cause blood to clot.

Patients with heart disease can accelerate atherosclerosis (hardening of the arteries) and increase the chance of heart attack.

For people with heart disease, depression can increase the risk of an adverse cardiac event such as a heart attack or blood clots.

Please helppppp


Reagan solved 5.25 = 5 and got 105. What did Reagan do wrong?

Answers

Answer:

He did not simplify correctly and forgot to place the decimal point correctly.

Step-by-step explanation:

To simplify the equation, one needs to divide both sides of the equal sign by 5.

i.e 5.25/5=5/5

Here we find 1.05=1

Note the placement of the decimal point.

Write an equation in slope-intercept form of the line please help me

Answers

Answer:

The formula is generally represented equationally as ( y - Y1 ) = m( X - X1 ) so now let's substitute the points plotted on the graph.

it is equal to (y - 4) = m(x - 0)

and now we look for the slope

m = y2 - y1/ x2 - x1

which can be directly substituted according to every line connecting each x value to a certain y value.

make y the subject of the formula
x=13(t-4y) over y

Answers

Answer:

make y the subject of the formula

x=13(t-4y)

Step-by-step explanation:

y=mx+c  

⟹(y)−c=(mx+c)−c  

⟹y−c=mx+(+c−c)  

⟹y−c=mx+0  

⟹y−c=mx  

⟹mx=y−c  

⟹mx×(1m)=(y−c)×(1m)  

⟹x×(mm)=1m(y−c)  

⟹x×1=1m(y−c)  

⟹x=1m(y−c)

The subject of the formula for y is y = 13t / x(1 + 52/x).

What is the equation?

The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.

We have been given the equation as:

x = 13(t - 4y) / y

We have to make y the subject of the formula

x = 13(t - 4y) / y

Cross multiplication to get,

y = 13(t - 4y) / x

y = (13t - 52y) / x

y = 13t / x - 52y / x

Now group the y terms together and we get

y + 52y / x = 13t / x

The factor out the y to get

y(1 + 52/x) = 13t / x

y = 13t / x(1 + 52/x)

Therefore, the subject of the formula for y is y = 13t / x(1 + 52/x).

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How to get slope from standard form.

Answers

Answer:

Solve the equation for y. See example.

Step-by-step explanation:

I'll use 3x + 5y = 15. First subtract 3x from both sides since it is positive.

[tex]3x + 5y = 15 \\ - 3x \: \: \: \: \: \: \: \: \:\: \: \: \: \: \: - 3x[/tex]

[tex]5y = - 3x + 15[/tex]

Now solve for y by dividing each term by 5.

[tex] \frac{5y}{5} = \frac{ - 3}{5} x + \frac{15}{5} [/tex]

Now simplify.

[tex]y = \frac{ - 3}{5} x + 3[/tex]

The slope is

[tex] - \frac{3}{5} [/tex]

help me please I don't wanna fail his ​

Answers

D I think I have not done that in a long time
answer; c
explanation;
if 3 | 3 = 3.3, then the line must mean that the | is a decimal point.
so for 1 | 88 , the line is the decimal point so it should be 1.88.
same explanation for the rest, 2 | 025 = 2.025, 3 | 0115 = 3.0115

Shreyas went to the fair and played a game with three spinners. He spins each spinner once and wins a prize if he gets 2 blues and 1 red.

Answers

Using the principle of probability, the likelihood that Shreya wins by getting 2 blues and 1 red is 0.416

Creating an area model for the first two spinners :

___ G _ B _ B _ R _R _R

R_RG_RB_RB_RR_RR_RR

R_RG_RB_RB_RR_RR_RR

B_BG_BB_BB_BR_BR_BR

B_BG_BB_BB_BR_BR_BR

B_BG_BB_BB_BR_BR_BR

B_BG_BB_BB_BR_BR_BR

G_GG_GB_GB_GR_GR_GR

G_GG_GB_GB_GR_GR_GR

Creating an area model or tree diagram for the third spinner would result in a sample space of (48 × 12) = 576 combinations.

However, the probability that Shreya would win can be obtained thus :

To win he needs to pick get 2 blues and 1 red in any order :

3! = 3 × 2 × 1 = 6 ways

P(BBR) = 1/3 × 4/8 × 5/12 = 0.0694444

P(winning) = 6 × 0.0694444 = 0.416

Therefore, the probability that Shreya wins is 0.416.

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Conducting numerous, separate statistical analyses increases the chance that one or more of the results appear to be statistically significant, but are actually attributable to random variation or measurement error. The problem is referred to as:

Answers

A family-wise inflation of error rate is the increase in the probability that one or more results of a numerous, independently (separately) conducted statistical analyses to become statistically significant, but these results can actually be attributed to random variation or measurement error.

In Statistics, a family-wise inflation of error rate is also referred to as family-wise error rate (FWER) and it can be defined as the probability of making at least one false conclusion or type I errors in numerous, separate statistical analyses or hypothesis tests.

Hence, a family-wise inflation of error rate increases the probability that one or more of the results among groups within an independent data set to be statistically significant, especially due to random variation or measurement error.

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A square tile has a side length of 12 cm. What is the area of the tile?

48 square centimeters

72 square centimeters

24 square centimeters

144 square centimeters

Answers

Answer:

144 cm²

Step-by-step explanation:

Remember: If you are finding the area of a square and are given a side, you can simply square it and it will be the area. Thus:

12 x 12 cm = Area of tile.

=> 144 cm² = Area of tile.

Therefore, 144 cm² is the area.

Hoped this helped.

At 1:40 PM, the temperature is 99˚F. For the rest of the evening, the temperature drops an average of 4˚F per hour. Write an equation in slope-intercept form to represent the temperature y after x hours.

Answers

Answer:

Y=-4x+99

Step-by-step explanation:

Your y intercept is always the last number in the equation

The equation in slope-intercept form to represent the temperature y after x hour is Y=-4x+99

What is the slope?

The slope is the ratio of the vertical changes to the horizontal changes between two points of the line.

The slope of the line is calculated as follows:

m = Δy/Δx

Given that At 1:40 PM, the temperature is 99˚F. For the rest of the evening, the temperature drops an average of 4˚F per hour.

Therefore, the slope of the line is;

m = Δy/Δx

m = 4

The equation in slope-intercept form is;

Y=-4x+99

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3) Solve this system using elimination method. Upload your work
8x + 14 y = 4
-6x - 7y=-10

Answers

Answer:

y = -2 and x = 4

Step-by-step explanation:

8x + 14y = 4

-6x - 7y = -10

First, find the lowest common multiple of 8 and 6 (which is 24). Multiply the first equation by 3:

8x + 14y = 4

3(8x + 14y) = 3(4)

24x + 42y = 12

Multiply the second equation by 4:

-6x - 7y = -10

4(-6x - 7y) = 4(-10)

-24x - 28y = -40

Now, add the two equations together:

24x + 42y = 12

-24x - 28y = -40

24x + -24x = 0

42y + -28y = 14y

12 + -40 = -28

14y = -28

Divide both sides by 14:

14y ÷ 14 = -28 ÷ 14

y = -2

Plug this known variable back into the first equation:

8x + 14(-2) = 4

8x + (-28) = 4

8x - 28 = 4

Add 28 to both sides:

8x - 28 + 28 = 4 + 28

8x = 32

Divide both sides by 8:

8x ÷ 8 = 32 ÷ 8

x = 4

So y = -2 and x = 4.

Hope this helps!

3. Expand. 3(8 - 6j)

Answers

[tex]3(8-6j) = 24 - 18j[/tex]

Juan joins a movie club. He pays $10 to join and each movie costs $5. Which equation represents the relationship between the total cost, y, and the number of movies, x?

Answers

you’re answer is 5x-10=y i think.

123, 472 to two decimal places​

Answers

Answer:

123.00 and 472.00

Step-by-step explanation:

can't really do much except add 0's since those numbers are whole numbers

Jimmy is interested in purchasing some yellow and red flowers for his mother's birthday. He visits a local floral shop and gift shop. Both businesses have a variety of flowers from which he can choose. Which answer best describes the sample and population

Answers

Answer:

ll available yellow and red flowers at the two businesses

Population: all available flowers at the two businesses

Step-by-step explanation:

The sample and population should be sample represents all yellow and red flowers while the population represents all flowers.

What are the sample and population?

The entire group about whom you want to make conclusions is referred to as a population. The particular group from which you will gather data is known as a sample. The sample size is always smaller than the population as a whole. A population in research doesn't usually refer to humans.

An entire group from which a conclusion should be derived is referred to as a population. The sample, on the other hand, refers to the population from which the data is drawn.

So based on this, we can say that the sample represents all yellow and red flowers while the population represents all flowers.

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Halppppppppppppp..............

Answers

Answer:

1 2/3, and -1 2/3

Step-by-step explanation:

Im wondering how old you are, and since you seem young just based off the math you're asked to do, please listen to the explanation and teach yourself this. This skill in particular is SOOO important to the rest of the math world. So since your number line is already divided into thirds, there are two ways you could find your answer. One, you can count 5 thirds away from zero, or two, you could simplify 5/3 from an improper fraction to a mixed number (1 2/3) and find your spot from there. "and the opposite" means not only the point 5/3 Away from zero on the Right, but also 5/3 away from zero on the Left. start from zero again and count the same amount away but in the opposite direction. With negatives it can help to think of how all numbers are just descriptions of how far left or right a number is from zero. i hope this helped lol, negatives are a confusing batch, but they're so so important to math as a whole.

my bibi’sister need a answer she don't know the answer, she need your help​

Answers

13. 12008.

14. 59286.

15. 21459.

16. 80478.

17. 130567.

18. 11100.

19. Seventy-two thousand, one hundred eighty.

20. Eighty thousand, seven hundred eighty-six.

Hope This Helps...:)

Mr.Thomson wants to protect his garage by installing a flood barrier. He connects 2 barriers side by side. Each barrier is 9 feet high. What is the combined area of the barriers

Answers

Answer:

300 ft

Step-by-step explanation:

NEED HELP ASAP ON A TEST WILL GIVE YOU BRAINLIST

A fishing rental company charges $25.75 for a small boat rental, plus an additional $6.20 per hour that the boat is rented. Partial hour
rentals are allowed. The total charge for a certain rental is $53.65
How long was the boat rented?
Enter your answer in the box

Answers

Answer:

ok so first you do this 25.75 + 6.20 = 31.95 and then you just do like this 53.65 - 31.95 = 21.7 that would be the answer and the answer is 21.7

Step-by-step explanation:

hope this help and if this is wrong i am very sorry

4.5

I just took the test hope this helped ;)

Help me with this very confused

Answers

Answer:

[tex] \frac{3 - 5x}{2} [/tex]

Step-by-step explanation:

Set g(x)=y

y=-2/5x+3

5y=-2x+3

2x=3-5y

x=3-5y/2

So g^-1(x)=

[tex] \frac{3 - 5x}{2} [/tex]

D) No, you are too afraid of sharks to even attempt the dive!
8) You are interested in retrieving a souvenir from a shipwreck located 115 feet below the water. You
do not have diving equipment, so your dive is limited by the equation y=0.05x2 - 4x – 38
Assumming you are able to retrieve your souvenir, how long do you have to hold your breath until
you resurface?
A) almost 90 seconds B) 38 seconds
C) almost 2 minutes D) a minute and 10 seconds

Answers

Answer:

B. 38 seconds

a point on the circumference of the circle with the equation (x+10)^(2)+(y+1)^(2)=25 is?

Answers

The point on the circumference of the circle with the equation (x+10)^(2)+(y+1)^(2) = 25 is (-6 , 2).

What is the equation of the circle with radius r units, centered at (x,y) ?

If a circle O has radius of r units length and that it has got its center positioned at (h, k) point of the coordinate plane,

then, its equation is given as:

(x-h)^2 + (y-k)^2 = r^2

The given equation is

(x+10)^(2)+(y+1)^(2)=25

Where,

h = - 10

k = -1

r = 5

If x = -6 and y = 2

then the given equation of circle is stidfy the given points.

Hence, the point on the circumference of the circle with the equation (x+10)^(2)+(y+1)^(2) = 25 is (-6 , 2).

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Carlos bought 17 boxes of cereal. This is 20% of the total boxes at the store. In order to find the total number of boxes at the store, what do you need to find?


A) the part

B) the whole

C) the percent

D) benchmark percent

Answers

Answer:

The whole

Step-by-step explanation:

If the part is 20% then you already have a part of a whole, now you need to find the entire thing

Ophelia has 5 flower less than Daisy. Together they have 20 flowers. How many flowers have each of them?

Answers

20 divided by four is 5 so maybe it is four.


I tried

Write an algebraic expression to represent the verbal statement: The product of the difference of m and 7 and 6.

Answers

Answer:

(m-7) * 6

Step-by-step explanation:

you follow the statement from left to right. You see that there's a product so you write a product sign

*

then you know its the difference of m-7 on one side and 6 on the other getting

(m-7) * 6

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