Given:
The series is
[tex]2x+2x^2+2x^3+...+2x^n[/tex]
To find:
Whether the given series is arithmetic, geometric, both, or neither.
Solution:
We have,
[tex]2x+2x^2+2x^3+...+2x^n[/tex]
Difference between consecutive terms are:
[tex]d_1=a_2-a_1[/tex]
[tex]d_1=2x^2-2x[/tex]
[tex]d_1=2x(x-1)[/tex]
And,
[tex]d_2=a_3-a_2[/tex]
[tex]d_2=2x^3-2x^2[/tex]
[tex]d_2=2x^2(x-1)[/tex]
Here, [tex]d_1\neq d_2[/tex].
So, the given series is not an arithmetic series.
Ratio between consecutive terms are:
[tex]r_1=\dfrac{a_2}{a_1}[/tex]
[tex]r_1=\dfrac{2x^2}{2x}[/tex]
[tex]r_1=x[/tex]
And,
[tex]r_2=\dfrac{a_3}{a_2}[/tex]
[tex]r_2=\dfrac{2x^3}{2x^2}[/tex]
[tex]r_2=x[/tex]
Similarly upto last pair of consecutive terms.
[tex]r_{n-1}=\dfrac{a_n}{a_{n-1}}[/tex]
[tex]r_{n-1}=\dfrac{2x^n}{2x^{n-1}}[/tex]
[tex]r_{n-1}=x[/tex]
Since, [tex]r_1=r_2=...=r_{n-1}[/tex], so the given series have a common ratio.
Therefore, it is a geometric series.
Find C.
Round to the nearest tenth.
90 ft
55 ft
A
В
50 ft
C = [? ]°
YLaw of Cosines: c2 = a+ b2 - 2ab cos C
9514 1404 393
Answer:
29.4°
Step-by-step explanation:
The equation can be rearranged to give C directly.
C = arccos((a^2 +b^2 -c^2)/(2ab))
C = arccos((90^2 +55^2 -50^2)/(2·90·55))
C = arccos(8625/9900) ≈ 29.4002°
C ≈ 29.4°
25% of 96 is what number round to the nearest tenth of necessary
Answer:
y = .25 x 96
y = 24
This is the answer.
Step-by-step explanation:
25% is the same as 0.25
25% = 25/100 = 0.25
Multiply 0.25 with 96
0.25 x 96 = 24
24 is your answer
hope this helps
If a^m=a^n , what can you determine about m & n?
Answer:
m=n
Step-by-step explanation:
i am not 100% sure what the answers would be but it would me m=n
evaluate the expression when c=2. 6c/2
Answer:
6Step-by-step explanation:
Given the expression g(c) = 6c/2, we are to find the value when c = 2
Substitute c = 2 into the expression
g(2) = 6(2)/2
g(2) = 12/2
g(2) = 6
Hence the result when c = 2 is 6
HELP ASAP An office employee ears $600 weekly. Find the equivalent earnings if paid biweekly, semimonthly, monthly, and annually
1200~bi-weekly
1200~semimonthly
2400~monthly
31,200~annually
Four copies of the triangle shown are joined together, without gaps or overlaps, to make a parallelogram. measurements= 5cm, 13cm, 12cm What is the largest possible perimeter of the parallelogram?
Answer:
Highest Possible Perimeter = 52cm
Step-by-step explanation:
The triangle is not shown. But, the question can still be solved.
The given sides (5cm,12cm and 13cm) of the triangle shows that the triangle is a right angled triangle as proven below:.
[tex]13\² = 5\² + 12\²[/tex]
[tex]169 = 25 + 144[/tex]
[tex]169 = 169[/tex]
Having shown that;
The next step is to determine the highest possible value of the perimeter.
To get the highest possible perimeter;
The 4 triangles have to be joined at the 12cm and 5cm part of each triangle (see attachment).
From the attachment, the perimeter is then calculated as:
Perimeter = 13cm + 13cm + 13cm+ 13cm
Perimeter = 52 cm
Answer: 76
Step-by-step explanation:
how much is 21 hundreds
Answer:
21,000
Step-by-step explanation:
Jodie spent 25% less buying her English reading books thank Claudia. .Gianna spent 9% less than Claudia. Gianna spent more than Jodie by what percent? If your using decimal round to the nearest tenth
Answer:
21.3%
Step-by-step explanation:
Given that:
Money spent by Jodie for buying English reading books = 25% lesser than that of Claudia
and
Money spent by Gianna is 9% lesser than that of Claudia.
To find:
By what percent, Gianna spent more than Jodie ?
Solution:
Let the money spent by Claudia on her English books = 100
Now, as per question statement:
Money spent by Jodie = 100 - [tex]\frac{9}{100}\times 100[/tex] = 75
Money spent by Gianna = 100 - [tex]\frac{25}{100}\times 100[/tex] = 91
Now, to find the answer:
[tex]\dfrac{\text{Difference between money spent by Gianna and Jodie}}{\text{Money spent by Jodie}}\times 100[/tex]
[tex]\Rightarrow \dfrac{91-75}{75}\times 100\\\Rightarrow \dfrac{16}{75}\times 100\\\Rightarrow \bold{21.3\%}[/tex]
Therefore, Gianna spent 21.3% more than the amount that was spent by Jodie.
if Efx=300+30p and N=10+p, find the valu of mean
mean=30
Step-by-step explanation:
mean=Efx/n
=300+p/10+p
= 30(10+p)/10+p
=30
(1, 1) and (4, 3) slope
Answer:
[tex] \huge \boxed{ \boxed{ \frac{2}{3} }}[/tex]
Step-by-step explanation:
The slope of a line given two points can be found by using the formula
[tex]m = \frac{ y_2 - y _ 1}{x_ 2 - x_ 1} \\[/tex]
From the question we have
[tex]m = \frac{3 - 1}{4 - 1} = \frac{2}{3} \\ [/tex]
We have the final answer as
[tex] \frac{2}{3} \\ [/tex]
Hope this helps you
Divide. Write your answer in fraction form.
(5x+ + 18x+ 15) / (x+2)
Answer:
what? it seems like you just spammed anything from the web O_o
Step-by-step explanation:
Can i have some help plz
Answer:
a) 15 + 25x ≤ 70
b) 60 + 15x ≤ 500
Step-by-step explanation:
a) Let x represent the number of calculators that Ms. Burgos can buy. since each calculator cost $25, then the total cost of calculator = $25 * x = $25x
She bought three notebooks costing $5 each. Money spent on notebooks = 3 * $5 = $15
Hence the total money spent = $15 + $25x = 15 + 25x
She has only $70, therefore:
15 + 25x ≤ 70
b) Cayla initially has $60.
Cayla is saving $15 per week. Let us assume she saves for x weeks, hence money saved by Cayla = 15x
Therefore the total money saved = 60 + 15x
Since Cayla needs to save atleast $500, hence:
60 + 15x ≤ 500
what is the volume of the cone to the nearest cubic centimeter?
Answer:
301.44
Step-by-step explanation:
How come nobody answers my questions? Like wth, I'm stuck but everyone else is getting their questions answered left and right.
Answer:
That is a good question and it might be your question you are trying to find the answer and maybe your question looks hard
Hope this help :)
Step-by-step explanation:
HELP
Please don’t answer if you don’t know it.
Answer:
d=5
Step-by-step explanation:
Answer: d= 5
Step-by-step explanation:
I did this test on edgunity if you need a step by step I can leave it in the comments below. Good luck
What is the value of x?
-4n + 1/3m + 4n - 4/5m
Answer:
[tex]-4n+\frac{1}{3m}+4n-\frac{4}{5m}=-\frac{7}{15m}[/tex]
Step-by-step explanation:
Given the expression
[tex]-4n\:+\:\frac{1}{3m}\:+\:4n\:-\frac{4}{5m}[/tex]
Group like terms
[tex]-4n\:+\:\frac{1}{3m}\:+\:4n\:-\frac{4}{5m}=-4n+4n+\frac{1}{3m}-\frac{4}{5m}[/tex]
Adding similar elements: -4n + 4n = 0
[tex]=\frac{1}{3m}-\frac{4}{5m}[/tex]
L.C.M of 3m and 5n will be: 15m
so adjusting fractions based on the LCM
[tex]=\frac{5}{15m}-\frac{12}{15m}[/tex]
Since, the denominators are equal, combine the fractions: [tex]\frac{a}{c}\pm \frac{b}{c}=\frac{a\pm \:b}{c}[/tex]
[tex]=\frac{5-12}{15m}[/tex]
[tex]=\frac{-7}{15m}[/tex]
[tex]=-\frac{7}{15m}[/tex]
Therefore, we conclude that:
[tex]-4n+\frac{1}{3m}+4n-\frac{4}{5m}=-\frac{7}{15m}[/tex]
In psychological theory, there are 66 types of basic instincts in a human being, and personality is determined by the presence or absence (2(2 choices) of these 66 basic instincts. How many different types of personalities can be identified
Answer:
2145
Step-by-step explanation:
Given that:
Number of basic instincts present = 66
Number of choices = 2
Using combination :
nCr = n! / (n - r)! r!
66C2 = 66! / (66 - 2)!2!
66C2 = 66! / 64!2!
66C2 = (66 * 65) / 2
66C2 = 2145 different personalities
Multiply 2.3. (-1.2)
Answer:
-2.76
Step-by-step explanation:
2.3x(-1.2)
= -2.76
Find the value of 5x - 4x^2 for x=2
Answer:
=10
Step-by-step explanation:
5x-4x². (x=2)
5(2)-4(2)²
=10-0
=10
Which method would you choose to solve the following system?
-5x + 2y = 15
y = - 3x - 20
Equal Values Method
O Substitution Method
O Graphing Method
Elimination Method
Answer: combining like terms
Step-by-step explanation:
Rob is saving to buy a new iPad. For every $15 he earns babysitting, he saves $6. On Saturday, Rob earned $75 babysitting. How much money did he save?
ion understand this one
Answer:
angle 7 = angle 3 because corresponding angles r equal
help please i dont understand this chile-
Answer:
37.5%
60%
75% and .75
Step-by-step explanation:
Four bottles of Powerade cost $3.88. Find the unit price of each bottle.
If I buy 5 plants from the garden centre at £3.00 a plant how much do the plants cost? If I have a £20 note how much change will I get?
Answer:
They will cost you £5.00 total
Step-by-step explanation:
If the plants each cost £3.00
You multiply the amount of plants, in this case is 5 by the price :-
5×3.00
= £15.00
You then subtract the total from the cash
15.00 - 20.00
= £5.00
Determine the intercept of the line.
Y-intercept : ( ) , ( )
X- intercept : ( ) ( )
Answer:
Y: (0) (0.4)
X: (0.3) (0)
Step-by-step explanation:
prove me wrong
(HELP URGENT TWO VARIABLE INEQUALITIES)
(SEE ATTACHED PICTURE)
Which of the following inequalities matches the graph?
A) The correct inequality is not listed.
B) 5x + y ≥ 1
C) 5x + y ≤ 1
D) 5x − y ≥ 1
Answer:
D)
Step-by-step explanation:
Line: y = 5x - 1
The shaded space is less than or equal to the line.
So it is y [tex]\leq[/tex] 5x - 1
This is the same as D)
Solve the equation below for x.
cx- 4 = 7
A. x=11/c
B. x=c/3
C. x=3/c
D. x= c/11
Answer:
a. x = 11/c
Step-by-step explanation:
cx - 4 = 7 [add 4 to both sides of the equation]
cx = 11 [divide by c to isolate x]
x = 11/c
Can I get the answer please
Answer:
C
Step-by-step explanation:
first equation is y=3/4x+2
second equation is -2x+17