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?
Answers
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
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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Answer:
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13. 12008.
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Answer:
1). Simplify the expression.
Exact Form:
( [tex]\frac{37}{25}[/tex] )
Decimal Form:
1.48
Mixed Number Form:
( [tex]1\frac{12}{25}[/tex] )
2). Simplify the expression.
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Exact Form:
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Decimal Form:
0.7083 ( bar notation)
4). Simplify the expression.
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solve the equation please
142=10+4x+7x
x= what
Answers
Answer:
11
Step-by-step explanation:
142=10+12x
132=12x
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Answer:
x=12
Step-by-step explanation:
A recipe requires 2/5 cup of sugar for 1 batch of brownies enter the number of batches of brownies that can be made using 3 1/5 cups of sugar
Answers
Answer:
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Step-by-step explanation:
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Answers
Answer:
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Step-by-step explanation:
if f(x)= -13, find x
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Find the area of the composite shape.
Answers
Answer:
For the one on the far left its 104 m2
Step-by-step explanation:
u split the shape in a square and rectangle
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x
x
−
6
9
=
−
5
Answers
- BRAINLIEST answerer
Answer:
64
Step-by-step explanation:
Read the excerpt from the poem "Hide and Seek":
(21) I examine my hideout, the contours of the leaves,
(22) The blades of grass, a crawling caterpillar.
(23) The minutiae fascinate me, a world within my world.
(24) One touch from me, and the caterpillar lies curled.
(25) Isn't this a metaphor for life?
(26) I'm in a game within another game.
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(28) How often do we acknowledge others' trouble and strife?
How does the point of view influence the description in lines 22-28?
A deeper connection is made and uses the setting to relate to life by the speaker.
A quick description of the hiding place is given at the end of the game by the speaker.
The other children's hiding spots are described by someone, not in the poem.
The setting is being described by someone who was not playing the game.
Answers
Answer:
A
Step-by-step explanation:
PLS HELP FAST FIRST ANSWER GETS BRAINLYEST 35 POINTSSSSS
Elena borrowed some
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the same amount every
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much she owes after each
week.
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Answer:
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Step-by-step explanation:
DUDE PUT THE GRAPH WHERE IS iT
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Answer:
73
Step-by-step explanation:
In the diagram below segment AC is congruent to segment CE and segment BC is congruent to segment DC.
Why is triangle BCA congruent to triangle DCE?
See picture for full problem. Please and thank you!
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Step-by-step explanation:
By reflection
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Calculate the volume of a cylinder with height 14cm and diameter 10cm. Give your answer rounded to 3 SF.
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Un significant figured Volume=1099.56
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A drilling crew dug to a height of -45 1/4 feet during their first day of drilling. On the second day, the crew dug down 9 1/3 feet more than on the first day. Describe the height of the bottom of the hole after the second day.
Answers
The height of the bottom of the hole after the second day is -35 11/12 feet
Given:
Day 1 height = -45 1/4 feet
Day 2 height = -45 1/4 + 9 1/3
= - 181/4 + 28/3
= (-543 + 112) / 12
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Therefore, the height of the bottom of the hole after the second day is -35 11/12 feet
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Answers
Answer:
12
Step-by-step explanation:
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Simplify. 54+4(3/4−1/2)2
Answers
Answer:
56
Step-by-step explanation:
54 + 4(3/4 − 1/2)2
=> 54 + 4(1/4)2
=> 54 + (1)2
=> 54 + 2
=> 56
Therefore, 56 is our answer.
Hoped this helped.
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Answers
Using the trigonometry ratio and Pythagorean Theorem, the value of b in the triangle is: 4.
Recall:
The trigonometry ratio is used in solving a right triangle, having, hypotenuse, adjacent, and the opposite side, given a reference angle.Trigonometry ratios are: SOH CAH TOAPythagorean Theorem is given as: [tex]c^2 = a^2 + b^2[/tex], where c is the longest side (hypotenuse).Given the trigonometry ratio of sin A = 3/5
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[tex]b = \sqrt{c^2 - a^2}[/tex] (Pythagorean Theorem)
Substitute[tex]b = \sqrt{5^2 - 3^2}\\\\\mathbf{b = 4}[/tex]
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SOMEONE PLEASE HELP I will give you brainliest it’s due in 11:59 pm TODAY!! Please
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basically get the equations for area and perimeter which will be
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P: l + 2w
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What is the value of y when the value of x is 1?
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urgently
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Rewrite x2 - 8x + 13 = 0 in the form (x -a)2= b, where a and b are integers, to determine the a and b values.
O a = 4 and b = 3
O a = 3 and b = 2
O a= 2 and b = 1
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Answers
Answer:
a =4 and b= 3
Step-by-step explanation:
Stare at it for a bit. You have the squre of x, then(ignoring the minus sign) 2 times x times 4. What's left is the square of 4, which is 16; you have 13, you are 3 short. Let's add them to both sides:
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Answers
Answer:
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Step-by-step explanation:
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evaluate the function h(x) = |-2x|-9 for the given values of x a) h(4)=. b) h(-5)=. c) h(0) =
Answers
Answer:
h(4) = -1 ; h(-5) = 1 h(0) = -9
Step-by-step explanation:
a) h(x) = |-2x| - 9 Substitute x = 4
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h(x) = | -8| - 9
h(4) = 8 - 9
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b) h(x) = |-2x| - 9 Substitute x = -5
h(-5) = |-2 · -5| - 9
h(-5) = |-10| - 9
h(-5) = 10 - 9
h(-5) = 1
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h(0) = |0| - 9
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Answers
Step-by-step explanation:
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vertex: 9/2, 121/4
Explanation Write properties of function: Write properties of function:
x intercept/zero: ; t1=-1, and t2=10
vertex form: (t-9/2)^2, (-121/4)
vertex: 9/2, 121/4
hope this helped
Simplify (5p+1.49)-(2p+6.49)
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Combine like terms
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what are the four functions that are increasing on the interval
Answers
Answer:
Tbh i don’t really know
Step-by-step explanation:
Ask someone else
Cubing function
Reciprocal function
Sine function
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Answers
the answer is t<-48
i hope this helped you if you need the explanation lmk
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Enter your answer as a whole number or a fraction in simplest form in the box.
Answers
Answer:
1/4
Step-by-step explanation:
use 2 points from the graph (-4,5) and (0,6) and put them in the distance equation.
(y2-y1)
----------
(x2-x1)
6-5
-------
0-(-4)
1/4
read sddddddddd
dxfcgvhbjnkml,
Answers
Answer:
1/5
Step-by-step explanation:
rise = 2 ft
run = 10 ft
slope = rise/run = 2/10 = 1/5
Answer: 1/5
Answer:
1/5
Step-by-step explanation:
The slope is the rise over the run
Y / x
2/10
1/5
