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

What is the simplified expression for the expression belov
4(x + 8) + 5(x - 3)
O 9x + 5
O 9x + 11
O 9x + 17
O 9x + 47

Answers

Answer: 9x + 17

Step-by-step explanation: Add 4x and 5x and you get 9x. Next take away 15 from 32 and you get 17 therefore the answer wuld be 9x + 17.

plz help. what is the simplified expression for ​

Answers

Answer:

Step-by-step explanation:

3³x3³=3^6

3^6÷3^4=3²

Help me with math!!!!

Answers

Answer:

-4

Step-by-step explanation:

so t is greater than -5, and for negatives, you need to get nearer zero.

3. Expand. 3(8 - 6j)

Answers

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

How to find number of combinations.

Answers

Answer: Remember, the formula to calculate combinations is nCr = n! / r! * (n - r)!, where n represents the number of items, and r represents the number of items being chosen at a time.

Step-by-step explanation:

1. What is the vertex for the following quadratic function, y = 2x^2 - 4x + 5?
A). (1,3)
B). (3, 1)
C) (0,5)
D). (2,5)

Answers

Answer:

A

Step-by-step explanation:

Given a quadratic in standard form

y = ax² + bx + c ( a ≠ 0 )

Then the x- coordinate of the vertex is

x = - [tex]\frac{b}{2a}[/tex]

y = 2x² - 4x + 5 ← is in standard form

with a = 2 and b = - 4 , then

[tex]x_{vertex}[/tex] = - [tex]\frac{-4}{4}[/tex] = 1

Substitute x = 1 into the equation for corresponding value of y

y = 2(1)² - 4(1) + 5 = 2 - 4 + 5 = 3

vertex = (1, 3 ) → A

Martha, Brett, and Mike are competing in a cooking competition. They all used different amounts of oil from a can containing 8 gallons of oil.

Martha used 17% of the total oil in the can.
Brett used 0.18 of the total oil in the can.
Mike used 0.7 gallon of the total oil in the can.
Who used the greatest amount of oil from the can? Show your work and explain your answer in words. (10 points)

Answers

Answer:

Mike

Step-by-step explanation:

17% = .17

.7 = .70

All that's left is to compare the amounts of oi for each person and decide who has the most, which would be Mike. Hope this helps! (Rate brainliest!)

Answer:

Brett used the most

Step-by-step explanation:

Martha used = 17%

Brett used = 0.18 = 18/100 = 18%

Mike used = 0.7 × 100/8 = 8.75% (he only used 0.7 of ONE of the gallons in the can, not of the total oil in the can)

Therefore, Brett used the greatest amount of oil.

There are 1580 adults and children on a ship. 60% of them are adults. When the ship arrives are harbour, some of the students alight and the percentage of adults remaining on the ship decreases by 20%. What is the ratio of the children to adults remaining on the ship?

Answers

Answer:

379 : 62

Step-by-step explanation:

Let’s gather the info from the problem.

1580 adults and children on a ship.

60% of them are adults.

percentage of adults and students remaining on the ship decreases by 20%

60% of 1580 is 948 so there are 948 adults onboard

leaving the remaining children which is 632

948 Adults

632 Children

Adults decreases by 20% so 758 adults

Children decreases by 20% so 124 children

the ratio is 758:124 simplified would be 379 : 62

Mitchell solves the following system of equations using the elimination method.

−2x+3y=6
4x−6y=−6

He chooses to eliminate the variable x.

Which statement correctly describes his process and solution?

Answers

Multiply the first equation by 2 or divide the second one my 2, to get the #X opposites, to cancel each other out

-4x+6y=12
4x-6y=-6

Or

-2x+3y=6
2x-3y=-3

there’s no solution either way

Answer:

Mitchell multiplies  −2x+3y=6 by 2 and then adds the equations. He finds the result is a contradiction, so there is no solution.

Step-by-step explanation:

4 + 4 + 4 + 4 + 4 if it is converted into multiplication form it becomes​

Answers

The answer would be 5x4

(Pythagorean theorem) find the missing side length. Round to the nearest hundredth (show steps)

Answers

Answer:

The missing length is 10.44

Step-by-step explanation:

a^2 + b^2 = c^2

3^2 + 10^2 = c^2

9 + 100 = c^2

109 = c^2

√c^2 = √109

c = √109

c ≈ 10.440307

c ≈ 10.44

Answer:

10.44

Step-by-step explanation:

Pythagorean theorem equation is a²+b²=c²

3²+10²=c²

9+100=c²........simplify

109=c².............add

√109=c

10.44031

10.44................round to the nearest hundredth

You are organizing books on the shelf. Each book has a width of 3/4 inches. write and solve an equality for the numbers of books b can fit on the shelf

Answers

3/4 = 0.75 inches

24 inches / 0.75 inches

= 32 books

Which of these groups of values plugged into the TVM Solver of a graphing
calculator will return the same value for PV as the expression
($415)((1 +0.003)24 – 1)?
(0.003)(1 +0.003)24

Answers

The TVM solver is a tool found in graphing calculators, that solve Time

Value of Money problems.

The group of values that will return the same value as the given expression is; D. N = 24; I% = 3.6; PV =; PMT = -415; FV = 0; P/Y = 12; C/Y = 12; PMT :END

Reasons:

In the TVM solver, we have;

I = The annual percentage rate

N = n × t

t = The number of years

PV = Present value

PMT = Payment

P/Y = Number of payments per year = n

C/Y = Number of compounding periods per year = n

The formula for monthly payment is presented as follows;

[tex]M = \mathbf{\dfrac{P \cdot \left(\dfrac{r}{n} \right) \cdot \left(1+\dfrac{r}{n} \right)^{n \times t} }{\left(1+\dfrac{r}{n} \right)^{n \times t} - 1}}[/tex]

Which gives;

[tex]P = \mathbf{\displaystyle \frac{M\cdot \left(\left(1+\dfrac{r}{n} \right)^{n \times t} - 1 \right) }{\left(\dfrac{r}{n} \right) \cdot \left(1+\dfrac{r}{n} \right)^{n \times t}}}[/tex]

Therefore, we get;

Where;

M = PMT = -415

P = PV

r = I

P/Y = n = 12

Therefore;

[tex]\displaystyle 0.003 = \frac{I}{12}[/tex]

I = 0.003 × 12 = 0.036 = 3.6%

N = n × t = 24

[tex]P = \displaystyle \frac{(415)\cdot \left(\left(1+\dfrac{I}{12} \right)^{24} - 1 \right) }{\left(\dfrac{I}{12} \right) \cdot \left(1+\dfrac{I}{12} \right)^{24}} = \mathbf{\displaystyle \frac{(415)\cdot \left(\left(1+0.003\right)^{24} - 1 \right) }{\left(0.003\right) \cdot \left(1+0.003 \right)^{24}}} = ?[/tex]

The value of the equation is the present value, PV = ?

When payment are made based on the PV, we have FV = 0

The group of values the same value as the expression[tex]\displaystyle \frac{(\$415)\cdot (1 + 0.003)^{24} - 1}{(0.003) \cdot (1 + 0.003)^{24}}[/tex], when plugged into the TVM solver of a calculator is; D. N = 24; I% = 3.6; PV =; PMT = -415; FV = 0; P/Y = 12; C/Y = 12; PMT :END

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There are 35 students in the elementary band. The band is doing a fundraiser, and each student must sell 12 items. How many items will be sold altogether? Use a different multiplication strategies in each of the short answer questions.

Answers

Answer:

Altogether, 420 items will be sold.

Step-by-step explanation:

12 · 35 = 420

Choose the correct answer to 7,215 divided by 34 with a remainder

Answers

7,215: 34 = 0,212205882352941

Answer:

0,212205882352941

Step-by-step explanation:

Consider the figure below and mark the line segments and angles that are congruent, given that H is the incenter of the triangle.

Answers

21

2+1=21

is the answer good hqahahahahahah

tim drives at an average speed of 80km per hour for 3 hours 35 minutes work out how many kilometres tim drives

Answers

Answer:

286 2/3 km

Step-by-step explanation:

Recalling that 1 hour = 60 minutes, we convert '3 hours 35 minutes' to

3 + (35/60) hours, or 3 35/60 hours, or 3.5833 hours.

Since distance = (rate)(time),

the distance driven by tim is (80 km/hr)(3.5833 hrs) = 286 2/3 km

Can you pls help.
If you do I will give you brain list but only if it’s right

Answers

Answer:

y=-2x-7

Step-by-step explanation:

To find the slope intercept form:

y+mx+b

m is the slope and b is the y-intercept.

We can take the first two points and find the slope by:

[tex]\frac{y2-y1}{x2-x1}[/tex] ->

[tex]\frac{-5-3}{-1- - 5}[/tex] = -2.

That’s the slope.

For the y-intercept we solve the equation:

y=−2(−5)+b -> b = -7

now we have the slope and y-intercept so the equation is:

y=-2x-7

Hope that helps!

Pls help fast
What is the recursive rule for the sequence shown in the graph

Answers

Answer:

[tex]a_{n} =a_{n-1} -4[/tex]

explanation:

The recursive rule for the given graph will be [tex]a_{n} = a_{n-1}-4[/tex] thus, option (A) is correct.

What is a graph?

A graph is a diametrical representation of any function between the dependent and independent variables.

For example y = x² form a parabola now by looking at only the graph we can predict that it has only a positive value irrespective of the interval of x.

In the given graph, as n increases [tex]a_{n}[/tex] decreases.

At n = 4 , a₄ = a₃ - 4 = 5 - 4 = 1

Thus, [tex]a_{n} = a_{n-1}-4[/tex]  will be the recursive rule.

Hence "The recursive rule for the given graph will be [tex]a_{n} = a_{n-1}-4[/tex]".

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Although mercury is a metal, it is a liquid at room temperature. Mercury melts at about "-39°C." If the temperature of a block of mercury starts at "-54°C." and increases by 22°C, does the mercury melt?
Explain your answer! Please make sure it’s valid.

Answers

Yes, the Mercury will melt

-54 °C + 22 °C = -32 °C

The very minimum temperature for Mercury to melt is -38 °C, so that additional few degrees will only speed up the process of Mercury melting.

whats the GCF of 77 and 55

Answers

Answer:

GCF= 11

Step-by-step explanation:

Find the perimeter. Simplify the answer.

Answers

Answer:

34p-16

Step-by-step explanation:

Perimeter of parallelogram

= 2(9p-10)+2(8p+2)

= 18p-20+16p+4

= 34p-16

The cost of Matt and Natalie's dinner was $27.35. They want to leave a 20% tip. Which of the following is the closest to the amount of the tip they want to leave?
A. $4.00
B. $4.50
C. $5.00
D. $5.50

Answers

Answer:

Option D is correct.

Step-by-step explanation:

27.35 x 20/100

=> 2.735 x 2/1

=> $5.47

=> $5.50 (Rounded)

Therefore, Option D is correct.

Hoped this helped.

1. (2x+5)+(3x-2)=
2. (3x-2)-(2x+5)=
3. (2x+5)-(3x-2=

Answers

Answer:

5x+3x -7-x +7

Step-by-step explanation:

Combine like terms. The associative and commutative properties of addition apply, as does the distributive property.

__

1. (2x+5)+(3x-2) = (2x +3x) +(5 -2) = 5x +3

__

2. (3x-2)-(2x+5) = 3x -2 -2x -5 = (3x -2x) +(-2 -5) = x -7

__

3. (2x+5)-(3x-2) = 2x +5 -3x +2 = (2x -3x) +(5 +2) = -x +7

_____

Additional comment

Note that swapping the order of operands in a subtraction problem (problems 2 and 3) will cause the sign of the result to reverse.

Answer:

1. = 5x+3

Step-by-step explanation:

Kal decides to open a home-based cupcake business. His cost is an initial value of $10 in operating expenses plus $0.25 to make each cupcake. He will sell each cupcake at $1.50 to try and make a profit. How many cupcakes will he need to sell before he makes a profit?

Also need an equation

Answers

Answer:

4

Step-by-step explanation:

I need help pls
ASAP

Answers

Answer:

look at the picture ..........

Find The Slope of Each Line

Answers

Answer: 2/8 first answer, 6/2 second answer, 3/2 last answer

Step-by-step explanation: The slope should be the rise over the run, so the answer to the first question would be 2/8 which is rise/run which equals the slope the second answer would be 6/2=slope and the the answer to the last question is 3/2 you start from one point, rise until you get next to the other point on the graph, then you run until you get on that point, the you count your rise which will be the top number of your fraction and then you count your run which will be the bottom number of your fraction. I hope this helped if you could even make sense of all of this.


Two vertical angles have measures (4x-21)° and (x+6)°. Find the measures of the angles




Answers

The measure of the two vertical angles is 15°

The two vertical angles have measures (4x-21)° and (x+6)°

Note that:

The measure of two vertical angles are equal

Therefore, equate  (4x-21)° and (x+6)° and solve for x

(4x-21)° =  (x+6)°

4x  -  21   =  x   +  6

Collect like terms

4x  -  x   =   6  +  21

3x    =  27

x   =  27/3

x    =   9

Substitute x = 9 into 4x - 21

4x - 21 = 4(9)  -  21

4x  -  21  = 15°

Substitute x = 9  into x + 6

x  +  6  =  9  +  6

x  +  6  =  15°

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A recipe calls for 40 ounces of rice. how many grams of rice does the recipe require

Answers

Answer:

So you can convert e.g. 1 cup of rice or rice flour into grams or ounces etc. easily. Other even more exotic rice varieties converters menu page. You may enter whole numbers, decimals or fractions

Step-by-step explanation:

What is 9/10 divided by 3/4

Answers

Answer:

1.5

Step-by-step explanation:

Find the reciprocal of the divisor

Reciprocal of  

3

4

:  

4

3

Now, multiply it with the dividend

So,  

9

10

÷  

3

4

=  

9

10

×  

4

3

=  

9 × 4

10 × 3

=  

36

30

After reducing the fraction, the answer is  

6

5

In mixed form: 1

1

5

Answer: 0.075 (decimal form) or (fraction form) 3/40 or 7.5% (percentage form)

Step-by-step explanation:

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