(1 point) Find a formula for the nth term in the sequence: 17,−17/8,17/27,−17/64,17/125,…
Given:
The sequence is:
[tex]17,-\dfrac{17}{8},\dfrac{17}{27},-\dfrac{17}{64},\dfrac{17}{125},...[/tex]
To find:
The formula for the nth term in the given sequence.
Solution:
We have,
[tex]17,-\dfrac{17}{8},\dfrac{17}{27},-\dfrac{17}{64},\dfrac{17}{125},...[/tex]
The given sequence can be written as
[tex]\dfrac{17}{1^3},-\dfrac{17}{2^3},\dfrac{17}{3^3},-\dfrac{17}{4^3},\dfrac{17}{5^3},...[/tex]
The sign are alternative and the absolute value of each term can be defined by the expression [tex]\dfrac{17}{n^3}[/tex], where n is a natural number.
So, the required formula is:
[tex]a_n=(-1)^{n+1}\dfrac{17}{n^3}[/tex]
Therefore, the formula for nth term in the given sequence is [tex]a_n=(-1)^{n+1}\dfrac{17}{n^3}[/tex].
Compare and contrast expanding and simptying
algebraic expressions with simplifying numeric
expressions. For example, compare simplifying 3(x - 2) +
(x - 1) with 3(5 - 2) + (5 – 1)
Answer:
With algebraic expressions, you can’t add and subtract any terms like you can add and subtract numbers. Terms must be like terms in order to combine them. So, you can’t always simplify an algebraic expression by following the order of operations. You have to use the distributive property to rewrite the expression and then combine like terms to simplify. With numeric expressions, you can either simplify inside the parentheses first or use the distributive property first.
Step-by-step explanation:
Welcome for the answer. This answer is for good intentions only, report if necessary. Thank you and have a good rest of your day!Answer:
Algebraic expressions have terms, Terms must be like to add and subtract, You can’t always follow the order of operations with algebraic expressions.
Step-by-step explanation:
James earns $22.00/hour. One week, he worked 40 regular hours and 5 hours of overtime. What is his GROSS pay?
Answer:
$1,045
Step-by-step explanation:
40×22=880
22÷2=11
11+22=33
33×5=165
165+880=1,045
Can someone please explain the answer step by step pls.
Answer:
a) x= 29, y= 87
b) x= 19, y= 45
Step-by-step explanation:
Q5. a) Let the first number be x and the second number be y.
The sum of 2 integers is 116.
x +y= 116 -----(1)
The second number is three times the first number.
y= 3x -----(2)
Substitute (2) into (1):
x +3x= 116
4x= 116
x= 116 ÷4
x= 29
Substitute x= 29 into (2):
y= 3(29)
y= 87
b) Let the smaller number be x and the larger number be y.
x +y= 64 -----(1)
y -x= 26 -----(2)
Since we have to use substitution to solve the equations, let's first rewrite an equation to make one of the variables the subject of the equation.
From (1):
x= 64 -y -----(3)
Substitute (3) into (2):
y -(64 -y)= 26
y -64 +y= 26 (expand bracket)
2y= 26 +64 (simplify, +64 on both sides)
2y= 90
y= 90 ÷2
y= 45
Substitute y= 45 into (3):
x= 64 -45
x= 19
Please help please help please
Answer:
566
Step-by-step explanation:
566
solve 9x-10÷2=x+9
explain how
Answer:
x = 4
Step-by-step explanation:
PLEASE HURRY PLEASE :(
Answer:
Step-by-step explanation:
height after x seconds = -16x² - 2x + 600
-16x² - 2x + 600 = 450
16x² + 2x - 150 = 0
8x² + x - 75 = 0
Quadratic formula
x = [-1 ± √(1² – 4·8(-75))] / [2·8]
= [-1 ± √2401] / 16
= [-1 ± 49] /16
= 3, -3⅛
-3⅛ is an extraneous solution, so x = 3 seconds.
Solve for x in the equation x2 + 4x-4-8.
O x= -6 or x = 2
O x--2+/- 2_/2
O x=-2 or x = 6
O x-2+/-2_/3
The solution of the equation is x= -6 or x = 2.
What is Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given:
We have the Equation x²+ 4x -4 - 8 or x² + 4x - 12.
Now Factorizing the equation we get
x² + 4x - 12
= x² + 6x - 2x - 12.
= x (x+ 6) - 2( x+ 6)
= (x -2) (x+ 6)
So, x-2 = 0 or x+ 6= 0
x= 2 or x= -6
Thus, the solution of the equation is x= -6 or x = 2.
Learn more about Equation here:
https://brainly.com/question/29657992
#SPJ7
What is the area of a circle that has a circumference of 31.4 feet, also I need to show my work
Answer:
78.46020384
Step-by-step explanation:
A=C^2/4π
A= 31.4^2/4π
A = 78.46020384
Can anyone help! I can’t figure out the answer.
what
is the quistion cause can't nobody see that
Simplify the following expressions and remember to pay attention to the signs
( -14) - ( -53) =
(18) - ( -2) =
( -84) / ( 12) =
(25) * (2) =
Answer:
(-14)-(-53) = 39
18-(-2)=20
(-84)/(12)=-7
25*2=50
Step-by-step explanation:
two minuses are plus
when numbers are on the minuses which number is higher their sign will have an answer
Answer:
A. 39
B. 20
C. -7
D. 50
Step-by-step explanation:
A. ( -14) - ( -53) =
53 - 14 = 39
B. (18) - ( -2) =
18 + 2 = 20
C. ( -84) / ( 12) =
-84/12 = -7
D. (25) * (2) =
25(2) = 50
please help!!!
i would really apreciate it
Answer:
it should be the graph on the bottom right
Step-by-step explanation:
The income should be more than the cost in order to make a profit and that happens for Leanne when she sells 8 quilts, so the 8 should be on the x-axis (the axis named "Quilts Sold")
The income should be 0 in the beginning bc when she sells 0 quilts she will be earning 0.
after selling 8 quilts her income will be higher than her costs
(Though naming the y-axis as "profit" is not accurate bc when she sells 0 quilts she will lose money since she will be spend money to make the quilts but not earn the money to compensate for the cost).
with all of these reasons combined the correct should be the one on the bottom right
you deposit $1600 in a bank account. find the balance after 3 years if the account pays 1.75% annual interest compounded quarterly
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Answer:
$1686.05
Step-by-step explanation:
The amount with compound interest is ...
A = P(1 +r/n)^(nt)
for principal P earning annual rate r compounded n times per year for t years.
A = $1600(1 +0.0175/4)^(4·3) = $1686.05
The balance after 3 years is $1686.05.
Answer:
the answer is $1686.05
Step-by-step explanation:
:))
What is the solution to the equation 2x+4-12-20?
X=0
x=1
X=2
X=9
Answer:
C : x=2
Step-by-step explanation:
Edge 2022
Caterpillar nitrogen assimilation and body mass. we explored the relationship between nitrogen assimilation and body mass (both on log scales) for data on a sample of caterpillars in Caterpillars. The Instar variable in the data codes different stages (1 to 5) of caterpillar development.
a. Fit a model to predict log nitrogen assimilation (LogNassim) using log body mass (LogMass). Report the value of for this model.
b. Fit a model to predict LogNassim using appropriate indicators for the categories of Instar. Report the value of for this model and compare it to the model based on LogMass.
c. Give an interpretation (in context) for the first two coefficients of the fitted model in (b).
d. Fit a model to predict LogNassim using LogMass and appropriate indicators for Instar. Report the value of and compare it to the earlier models.
e. Is the LogMass variable really needed in the model of part (d). Does the linear trend appear to be better when the caterpillars are in a free growth period? (Again, we are not ready to fit more complicated models, but we are looking at the plot for linear trend in the two groups.)
In a bowl, there are gum balls. There are 5 red, 7 blue, 3 yellow and 11 purple.
What is the ratio of the following?
10. Purple to Red _____
11. Blue to Yellow _____
12. Yellow to Red _____
13. Purple to Blue _____
A. 11 to 5
B. 11 to 7
C. 3 to 5
D. 7 to 3
Answer:
10 is A
11 is D
12 is C
and 13 is B
Can you help me solve this question
Answer:
t = 32
Step-by-step explanation:
The given equation is :
[tex]24=\dfrac{3}{4}t[/tex] ....(1)
Where
t is the number of guests attending the catered event.
The reciprocal of [tex]\dfrac{3}{4}[/tex] is [tex]\dfrac{4}{3}[/tex].
Multiplying both sides by the reciprocal of [tex]\dfrac{3}{4}[/tex].
[tex]24\times \dfrac{4}{3}=\dfrac{3}{4}\times \dfrac{4}{3}t\\\\t=8\times 4\\\\t=32[/tex]
Hence, 32 guests will attend the catered.
The bottom of a swimming pool is 10 feet below the surface of the water in the pool. The surface of the water is represented by the number 0, and the bottom of the pool is represented by the number -10. The pool’s diving board is the same distance above the surface of the water as the bottom of the pool is below the surface of the water. HELP I WLL GIVE THE CROWN THNG AND MORE POINTS
Answer:
I think its +10 above surface
Will give brainlst
Have a nice day
Answer:
x = 3.5
y = 8x + 12
Step-by-step explanation:
1) Given the equation
12x = 4(x+2)+20
Expand
12x = 4x+8+20
12x - 4x = 28
8x = 18
x = 28/8
x = 3.5
Hence the value of x is 3.5
2) The standard form of equation in slope intercept form is y = mx+c
m is the slope
c is the y intercept
Get the y-intercept
Substitute m = 8 and (0, 12) into y = mx+c
12 = 8(0)+c
12 = c
c = 12
Get the required equation
Recall that y = mx+c
y = 8x + 12
This gives the required equation
What is the graph of the function f(x) = the quantity of x squared plus 4 x minus 12, all over x plus 6 ? (1 point)
The scatterplot below shows a data set
and an approximate trend line for the
data.
7
6
5
3
1
0 10 20 30 40 50 60 70
Which is the best estimate of the value of
x that corresponds to y = 3? (8.18, 8.10,
SIE, SIF)
Where does
F 35
the line y = 3
G 25
intersect the
trend ine?
H 50
10
PLZ HELP ASAP (BRAINLIEST + 30 POINTS (show all work)
(7.03) Determine the missing term from the perfect square trinomial. Show ALL work.
x2 − ______+ 36
Write in factored form: ( )2
Answer:
x² - 12x + 36
factored: (x - 6)(x - 6)
Amir bought a camera 5 year ago for RM1500. He plans to sell his camera at a price of RM1800. What percentage of the profit or loss?
Answer:
20% profit
Step-by-step explanation:
Hope this helps
(5+2×8)/6=x(4+6) what is the value of x ?
Answer:
Step-by-step explanation:
Answer:
x= 7/20
Step-by-step explanation:
(5+2×8)/6=x(4+6)
(5+16) /6 = 4x+6x
21/6=10x (divide 21/6 by 3)
7/2=10x
7/2×1/10= x
x= 7/20
Hope this helps :)
Keep Smiling
profesor de Educación Física Oriente y occidente hacer Cada día los siguientes recorridos lunes 5,12 y kilómetros más de 6 koma 23 kilómetros miércoles 7,0 2 km y jueves 12,0 7 km y el viernes 15,0 1 kilómetros Cuántos kilómetros recorre cada estudiante a final de la semana datos operacion
Answer:
ask in English then only I will answer
[tex]533 {?}^{2} \times \frac{?}{?} [/tex]
Answer:
53
Step-by-step explanation:
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Pattern A follows the rule "subtract 3" and Pattern B follows the rule "subtract 4." Pattern A 20 17 14 11 8 Pattern B 24 20 16 12 8 Which ordered pairs are formed from combining a term in Pattern A with its corresponding term in Pattern B? Select all correct answers. (17, 20) (20, 24) (12, 11) (8, 8) (14, 20) (20, 16)
Answer:
(20,24) (17,20) and (8,8)
Hope this helps
Step-by-step explanation:
help please! by what fraction would you multiply 8 1/2 so that the proudct is about 5 explain your reasiong
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Answer:
5/8 or 5/9
Step-by-step explanation:
The fraction will be exactly ...
5/(8 1/2) = 10/17 ⇒ (8 1/2)×(10/17) = 5
__
The fraction will be approximately ...
5/8 or 5/9
The denominator will be a number that makes (8 1/2)/(denominator) ≈ 1. For that denominator, the numerator will be 5, so that we have ...
(8 1/2) × (5/denominator) ≈ 5
(8 1/2)/(denominator) ≈ 1 . . . . . . . . divide by 5
If we want the denominator to be an integer, we could choose either 8 or 9. If we choose 8, the result will be slightly more than 5; if we choose 9, the result will be slightly less.
(8 1/2) × (5/8) = 5.3125 ≈ 5
(8 1/2) × (5/9) = 4.722... ≈ 5
Either 5/8 or 5/9 will give a product of about 5.
Answer:
Step-by-step explanation:
Is the following relationship a function?
Answer:
yes it's a inverse function
Answer:
Yes it is
Step-by-step explanation:
To remeber, if none of the lines overlap or crosses each other, its a function.
1. Joshua has a ladder that is 12 ft long. He wants to lean the ladder against a vertical wall so that the top of the ladder is 11.8 ft above the ground. For safety reasons, he wants the angle the ladder makes with the ground to be no greater than 75°. Will the ladder be safe at this height? Show your work and draw a diagram to support your answer.
Answer:
So we'll use trig to solve this because it's a right triangle. The hypotenuse is the ladder (h) and the two smaller sides are the ground and the vertical wall (w).
That angle ladder makes with the ground = €
SOH: sin € = opposite/hypotenuse
No the ladder won't be safe!!!
Now let's make it safe:
The ladder's length (w) is constant, so stays 12
So now let's ask in an inequality what height will be safe (75° or less)
what does that mean?? well as long as you put the ladder against the wall so that the height from ground to top of the ladder is < 11.6 ft!!
Hope that helps! :-D
Step-by-step explanation:
Answer:
not safe it is 78.5 degrees
Step-by-step explanation:
In ΔSTU, the measure of ∠U=90°, the measure of ∠S=16°, and TU = 5.9 feet. Find the length of ST to the nearest tenth of a foot.
Answer:
21.4
Step-by-step explanation: