What is the 6th term of the geometric sequence?
3,6, 12, 24, ...
A. 36
B. 27
C. 48
O D. 96
Answers
Answer:
96 is the 6th term of the geometric sequence
Step-by-step explanation:
The sequence is just adding the number twice to get the nect sequence.
So,
3+3 = 6
6+6 = 12
12+12 = 24
24+24 = 48
48+48 = 96 this is the 6th term
Hope this is helpful
Related Questions
prove the following [tex]\bold{algebraically}[/tex]:
[tex] \displaystyle \frac{ {29}^{3} + {29}^{2} + 30 }{ {29}^{4} - 1} = \frac{1}{28} [/tex]
Answers
Answer:
see below
Step-by-step explanation:
we are given
[tex] \displaystyle \frac{ {29}^{3} + {29}^{2} + 30 }{ {29}^{4} - 1} = \frac{1}{28}[/tex]
we want to prove it algebraically
to do so rewrite 30:
[tex] \displaystyle \frac{ {29}^{3} + {29}^{2} + 29 + 1}{ {29}^{4} - 1} \stackrel{ ? }{= }\frac{1}{28}[/tex]
let 29 be a thus substitute:
[tex] \displaystyle \frac{ {a}^{3} + {a}^{2} + a + 1}{ {a}^{4} - 1} \stackrel{ ? }{= }\frac{1}{28}[/tex]
factor the denominator:
[tex] \rm\displaystyle \frac{ {a}^{3} + {a}^{2} + a + 1}{ ({a}^{2} + 1) (a- 1)(a + 1)} \stackrel{ ? }{= }\frac{1}{28}[/tex]
Factor out a²:
[tex] \rm\displaystyle \frac{ {a}^{2} ({a}^{} + 1)+ a + 1}{ ({a}^{2} + 1) (a- 1)(a + 1)} \stackrel{ ? }{= }\frac{1}{28}[/tex]
factor out 1:
[tex] \rm\displaystyle \frac{ {a}^{2} ({a}^{} + 1)+1( a + 1)}{ ({a}^{2} + 1) (a- 1)(a + 1)} \stackrel{ ? }{= }\frac{1}{28}[/tex]
group:
[tex] \rm\displaystyle \frac{ ({a}^{2} +1)( a + 1)}{ ({a}^{2} + 1) (a + 1)(a - 1)} \stackrel{ ? }{= }\frac{1}{28}[/tex]
reduce fraction:
[tex] \rm\displaystyle \frac{ \cancel{({a}^{2} +1)( a + 1)}}{ \cancel{({a}^{2} + 1) (a + 1)}(a - 1)} \stackrel{ ? }{= }\frac{1}{28}[/tex]
[tex] \displaystyle \frac{1}{a - 1} \stackrel {?}{ = } \frac{1}{28} [/tex]
substitute back:
[tex] \displaystyle \frac{1}{29 - 1} \stackrel {?}{ = } \frac{1}{28} [/tex]
simplify substraction:
[tex] \displaystyle \frac{1}{28} \stackrel { \checkmark}{ = } \frac{1}{28} [/tex]
hence Proven
Answer:
Step-by-step explanation:
Identity to use:
1+N+N^2+N^3 = (N^4-1)/(N-1)
Let N=29
1+29+29^2+29^3 = (29^4-1) / (29-1)
30+29^2+29^3 = (29^4-1) / 28
Transpose and re-arrange
(29^3+29^2+30) / (29^4-1) = 1 / 28 QED
f(x) = 3x – 5. Find the average rate of change of the function between x = 3 and x = 7.
Answers
Given:
The function is:
[tex]f(x)=3x-5[/tex]
To find:
The average rate of change of the function between x = 3 and x = 7.
Solution:
We have,
[tex]f(x)=3x-5[/tex]
For [tex]x=3[/tex],
[tex]f(3)=3(3)-5[/tex]
[tex]f(3)=9-5[/tex]
[tex]f(3)=4[/tex]
For [tex]x=7[/tex],
[tex]f(7)=3(7)-5[/tex]
[tex]f(7)=21-5[/tex]
[tex]f(7)=16[/tex]
The average rate of change of the function f(x) between x = a and x = b is:
[tex]m=\dfrac{f(b)-f(a)}{b-a}[/tex]
The average rate of change of the function between x = 3 and x = 7 is:
[tex]m=\dfrac{f(7)-f(3)}{7-3}[/tex]
[tex]m=\dfrac{16-4}{4}[/tex]
[tex]m=\dfrac{12}{4}[/tex]
[tex]m=3[/tex]
Therefore, the average rate of change of the function between x = 3 and x = 7 is 3.
Which best describes the vertex of this parabola?
Answers
Answer:
The correct option is (2,1);maximum. The explanation is given below. The vertex of the parabola is the point where the parabola crosses its axis of symmetry. the vertex will be the lowest point on the graph, the point at the bottom of the " U "-shape.
Step-by-step explanation:
thank me later
A coach divided 13 liters of water into water bottles so that each bottle contained 0.65 liter of water how many water bottles are there
Answers
Answer:
there would be 20 bottles.
Step-by-step explanation:
13 divided by .65 = 20
A city held a bike parade. 52 bikers rode in the parade, and 8 of them rode a fixed-gear bicycle.
What is the probability that a randomly chosen bike in the parade was a fixed-gear bicycle?
Write your answer as a fraction or whole number.
P(fixed-gear bicycle) =
Answers
Answer:
[tex]\frac{2}{13}[/tex]
Step-by-step explanation:
Find the probability by dividing the number of fixed gear bikers by the total number of bikers in the parade.
Since there are 8 fixed gear bikers and 52 bikers in total, this will be found by dividing 8 by 52.
So, the probability as a fraction is [tex]\frac{8}{52}[/tex]
This can be simplified by dividing both the numerator and denominator by 4:
= [tex]\frac{2}{13}[/tex]
So, the probability is [tex]\frac{2}{13}[/tex]
An ice cream store sells 2 drinks, in 4 sizes, and 6 flavors. In how many ways can a customer order a drink?
Answers
- 3/10h = 15 what does h =
Answers
Answer:
h = -50
Step-by-step explanation:
- 3/10h = 15
Multiply each side by -10/3 to isolate h
-10/3 * - 3/10h = 15 * -10/3
h = -150/3
h = -50
Answer:
h = -50
Step-by-step explanation:
3. If 2x +9 32, then x could be
11.5?
Answers
2x= 32-9
2x= 23
x= 23:2
x= 11.5
Answer:
Yes
Step-by-step explanation:
We can see step by step how to solve for x, and get 11.5:
2x+9=32
Subtrract the 9 from both sides. You should always try to get the number on one side, and the variable on the other:
2x+9-9=32-9
=
2x=23
In the end, once the number values are on one side, and the variable value on the other, you want you varaible to be 1.
When I mean 1, I mean you want 1x, or just x.
Here we see 2x=23, meaning we need to divide both sides by 2, to get 1x:
2x/2=23/2
=
x=11.5
So x equals 11.5, and you were correct.
Hope this helps!
Simplify. pls pls help
-2 √35
-24 √35
24 √35
Answers
See image for question.
Answers
Answer:
#7(a)
Sample space:
1*1, 1*2, 1*3, 1*4,2*1, 2*2, 2*3, 2*4,3*1, 3*2, 3*3, 3*4,4*1, 4*2, 4*3, 4*4Total 16 outcomes
(b)
(i) P(even) = 12/16 = 3/4(ii) P(3x) = 7/16(iii) P(perfect square) = 4/16 = 1/4#8(a) Sample space:
1T, 1H, 2T, 2H, 3T, 3H, 4T, 4HTotal 8 outcomes
(b)
(i) 1T, 3T
P(T and odd) = 2/8 = 1/4(ii) 1H, 4H
P(H and square) = 2/8 = 1/4(iii) 1H, 2H, 3H, 4H
P(H) = 4/8 = 1/2describe fully the single transformation which takes shape A to shape B
Answers
Answer:
Clockwise rotation of 90 degress around the
point (4,3)
Answer:
Clockwise rotation of 90 degress around the point (4,3)
Step-by-step explanation:
what is the midpoint of this point (-4,2) and (8,0)?
Answers
Answer:
Mid - point = ( 2 , 1 )
Step-by-step explanation:
Let A = ( - 4 , 2 ) and B = ( 8 , 0 )
Let P = ( x , y ) be the mid-point of AB
Then,
[tex]P = (\frac{x_A + x_B}{2} , \frac{y_A + y_B}{2} ) \\\\P =(\frac{-4+8}{2} , \frac{2+0}{2}) \\\\P = ( \frac{4}{2} , \frac{2}{2} )\\\\P = ( 2 , 1)[/tex]
Answer:
(2,1)
Step-by-step explanation:
Hi there!
Midpoint: [tex](\frac{x_1+x_2}{2} , \frac{y_1+y_2}{2} )[/tex] where two endpoints of a line segment are [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]
Plug in the given points (-4,2) and (8,0)
[tex](\frac{-4+8}{2} , \frac{2+0}{2} )\\(\frac{4}{2} , \frac{2}{2} )\\(2, 1)[/tex]
Therefore, the midpoint of the line segment is (2,1).
I hope this helps!
Solve for w -8.5 = 3.46
Answers
Done done done, W=3.46+8.5
W=11.96!
Hit the heart if it was helpful!
Answer:
11.96
Step-by-step explanation:
A 6-foot diameter circle is divided
into six congruent sectors. What
is the area of each sector in square
inches? (Use 3.14 for 2.)
Answers
Answer:
the area is 1235
Step-by-step explanation:
Answer:
2714.33 sq in
explanation-
since circle is divided into 6 congruent sectors, area of each sector is 1/6th of area of circle.[tex]ar \: of \: sector \: = ar \: of \: circle \: \div 6 \\ = \pi \times 72 \times 72 \div 6 \\ = 2714.33[/tex]Find the volume of this cone.
Use 3 for pi
Answers
Answer:
81 cm^3
Step-by-step explanation:
We know that we have to use 3 for pi.
Formula given for formula of cone is:
πr^2h ÷3
Use formula with the given pi and dimensions:
3(3^2)(9) ÷ 3
= 3(9)(9) ÷ 3
= 243 ÷ 3
= 81
Volume is measured in cubic centimeters.
FINAL ANSWER:
81 cm^3
Hope this helps!
The sum of four consecutive numbers equals b+6. What are the numbers?
Answers
Answer:
0,1,2 and 3
Step-by-step explanation:
let the first number be b
therefore the second,third and fourth numbers are b+1,b+2 and b+3
b+b+1+b+2+b+3=b+6
4b+6=b+6
4b-b=6-6
3b=0
b=0
If x = 47, what is the value of the expression x + 24?
Answers
Answer:
71.
Step-by-step explanation:
If x = 47, you would add 24 to 47, which equals 71.
After filling the first sandbox to a height of 6 inches, the groundskeeper had 24 cubic feet of sand left
over. She used all the leftover sand to fill the second sandbox.
. The second sandbox has a base in the shape of a rectangle.
The base of the second sandbox has a perimeter that is less than 35 feet.
The groundskeeper filled the second sandbox to a height of 6 inches.
What could be the length and width, in feet, of the second sandbox?
Answers
Answer:
Length could be 14.05 ft and width 3.41 ft.
Step-by-step explanation:
The volume of the sand in the second box = 24 ft^3.
Let its base be x feet wide and y feet long.
Then 2(x + y) < 35.
The volume of sand = 0.5xy ft^3.
So 0.5xy = 24
xy = 48.
x = 48/y
Substituting ih the above inequality:
2(48/y + y) < 35
96/y + 2y < 35
2y^2 - 35y + 96 < 0
Solving 2y^2 - 35y + 96 = 0 gives y = 3.41, 14.09.
So the length could be 14.05 ft and the width 48/14 = 3.41 ft.
The length could be 14.05 ft and the width will be 3.41 ft.
What is volume?The volume of the sand in the second box = 24 ft³.
Let its base be x feet wide and y feet long.
Then 2(x + y) < 35.
The volume of sand = 0.5xy ft^3.
So 0.5xy = 24
xy = 48.
x = 48/y
Substituting the above inequality:
2(48/y + y) < 35
96/y + 2y < 35
2y² - 35y + 96 < 0
Solving 2y² - 35y + 96 = 0 gives y = 3.41, 14.09.
So the length could be 14.05 ft and the width 48/14 = 3.41 ft.
To know more about volume follow
https://brainly.com/question/15607324
#SPJ2
write a proportion and find the missing side lengths. show work!! 30 points.
Answers
Answer:
Step-by-step explanation:
34 . since the given two figure are similar their corresponding sides are proportonal.
let the missing side be x
take these ratios
15/18 = x/30
do cross multiplication
18*x = 30*15
18x = 450
x = 450/18
x = 25
therefore missing side is 25
35.since they are also similar their corresponding sides are proportional.
let the missing side be x
for this take these ratios
8/12 = 10/x
do cross multiplication
12*10 = 8*x
120/8 =x
15 =x
therefore missing side is 15.
Which graph is likely to have a leading coefficient value of -1/8?
Answers
Answer:
The second graph: only this one opens downward.
In the diagram of △EHG below, JF ∥HG, EJ=12, JH=24, and EF=6. What is the length of EG?
Answers
FG = JHxEF/EJ = 12 + 6 = 18
Consider this composite figure.
Shape B is a cone and shape B is a cylinder.
Examine the composite figure to determine what two three-dimensional geometric shapes make up the figure.
What shape does A represent?
What shape does B represent?
Answers
Answer:
Shape A: cone
Shape B: cylinder
Shape C: cone
the sum of two cones and a cylinder
Step-by-step explanation:
On edge- 2021 :)
Answer:
Step-by-steShape A: cone
Shape B: cylinder
Shape C: conep explanation:
Given the table below, determine the initial value/y intercept. PIC IS ABOVE! ANSWER!
Answers
Answer:
The initial value is the y value when x is zero. Look at the table to help you determine the y value when x is zero and that is your answer.
Step-by-step explanation:
Please help me it’s important for me
Answers
Answer:
Step-by-step explanation:
8
A snow cone is a tasty treat with flavored ice and a spherical bubble gum ball at the bottom, as shown below:
Snow cone with spherical bubble gum ball at the bottom
The radius of the cone is 1.25 inches, and its height is 2.75 inches. If the diameter of the bubble gum ball is 0.5 inches, what is the closest approximation of the volume of the cone that can be filled with flavored ice? (4 points)
Group of answer choices
4.43 in3
0.07 in3
13.50 in3
4.50 in3
Answers
==========================================================
Explanation:
The volume of the cone is...
V = (1/3)*pi*r^2*h
V = (1/3)*3.14*(1.25)^2*2.75
V = 4.49739583333333
which is approximate.
-----------
The volume of the sphere is
V = (4/3)*pi*r^3
V = (4/3)*3.14*(0.25)^3 ... note the radius is half the diameter
V = 0.06541666666667
which is approximate as well
-----------
Subtract the two volumes to finish things up
4.49739583333333-0.06541666666667 = 4.43197916666667
The result 4.43197916666667 then rounds to 4.43
This is the approximate amount of empty space in the cone that isn't taken up by the spherical gum. The units are in "cubic inches" or "in^3" for short.
#42 urgent please be certain
Answers
Answer:
Its D
Step-by-step explanation:
HELP‼️‼️‼️‼️‼️‼️‼️‼️
Answers
Answer:
a. x^(5/6) + 2x^(7/3)
Step-by-step explanation:
____
joseph cao bao nhiêu, nếu anh ấy cao 72 inch? Nếu anh ta là bao nhiêu feet, thì anh ta là bao nhiêu thước? nếu anh ta là bao nhiêu thước, anh ta là bao nhiêu cm?
Answers
Answer:
im not sure
Step-by-step explanation:
Answer:
joseph là 6 feet hoặc 2 thước Anh hoặc 182 cm.
A test is worth 30 points. Multiple-choice questions are worth 7 point and
short-answer questions are worth 2 points. If the test has 20 questions, how
many multiple-choice questions are there?
Answers
Answer:cvg
Step-by-step explanation:
Given that√7=2.65 and √70=8.37,find the value of
(a)√0.07
(b)√0.0007
(c)√0.7
(d)√0.007
(e)√0.000007
(f)√0.00007
Answers
Answer:
A) 0.265
B) 0.0265
C) 0.837
D) 0.0837
E) 0.00265
F) 0.00837
Step-by-step explanation:
We are given;
√7 = 2.65 and √70 = 8.37
A) √0.07 can be rewritten as;
√(7 × 1/100)
Let's deal with the digits in the bracket.
Square root of 100 is 10. Thus;
√(7 × 1/100) = (1/10)√7 = (1/10) × 2.65 = 0.265
B) √0.0007
Rewrite to get;
√(7 × 1/10000)
Square root of 1/10000 is 1/100
Thus;
√(7 × 1/10000) = (1/100)√7 = (1/100) × 2.65 = 0.0265
C) √0.7
Like above;
√0.7 = √(70 × (1/100))
>> (1/10)√70 = (1/10) × 8.37 = 0.837
D) √0.007
Like above;
Rewrite to get;
√(70 × 1/10000)
Square root of 1/10000 is 1/100
Thus;
√(70 × 1/10000) = (1/100)√70 = (1/100) × 8.37 = 0.0837
E) √0.000007
Rewritten to;
√(7 × (1/1000000))
√(1/1000000) = 1/1000
Thus; √(7 × (1/1000000)) = 1/1000 × √7 = 1/1000 × 2.65 = 0.00265
F)√0.00007
Rewritten to;
√(70 × (1/1000000))
√(1/1000000) = 1/1000
Thus; √(70 × (1/1000000)) = 1/1000 × √70 = 1/1000 × 8.37 = 0.00837