The first terms of a geometric sequence are as follows.
-810,-270,-90
Find the next two terms of this sequence.
Give exact values (not decimal approximations)
Answers
The fourth and fifth term of this sequence is -30 and -10 respectively.
Data;
first term (a) = -810common difference (r) = ?Common DifferenceThe common difference in a geometric progression is the ratio between two successive terms.
Let's find the common difference in this sequence
[tex]r = \frac{-270}{-810} \\r = \frac{1}{3}[/tex]
The nth term of a geometric sequence is given as
[tex]T_n = ar^n^-^1\\[/tex]
The next two terms of this sequence will be 4th and 5th term.
The fourth term of this sequence is
[tex]T_4 = ar^4^-^1\\T_4 = -810 * (\frac{1}{3})^3\\ T_4 = -810 * \frac{1}{27}\\ T_4 = -30[/tex]
The fifth term of this sequence is
[tex]T_5 = ar^5^-^1\\T_5 = -810 * (\frac{1}{3})^4\\T_5 = -810 * \frac{1}{81} \\T_5 = -10[/tex]
The fourth and fifth term of this sequence is -30 and -10 respectively.
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Related Questions
Mario paid $44in taxi fare from the hotel to the airport. the cab charged $2 for the first mile plus $3 for each additional mile. how many miles was it from the hotel to the airport
Answers
Answer: 50
Step-by-step explanation:
2+3=6+44=55
Factor completely 4x2 − 81. (1 point)
a
(4x − 9)(x + 9)
b
(2x + 9)(2x + 9)
c
(2x + 9)(2x − 9)
d
(2x − 9)(2x − 9)
Answers
Answer:
(2x-9)(2x+9)
Use the difference of square method. square root both sides and the answer has to be in postive and negative
what is 98 x 47 / 32 x 54?
Answers
Answer:
2837x/16
Step-by-step explanation:
hope this helps - NICK
Answer:
7772.625
Step-by-step explanation:
Given;
[tex]98\times47\div32\times54[/tex]
Solve;
[tex]\mathrm{Follow\:the\:PEMDAS\:order\:of\:operations}[/tex]
[tex]Multiply\:and\:divide\:\left(left\:to\:right\right)[/tex]
[tex]98\cdot \:47=4606[/tex]
[tex]=4606\div \:32\cdot \:54[/tex]
[tex]4606\div \:32=\frac{4606}{32}[/tex]
[tex]=\frac{4606}{32}\cdot \:54[/tex]
[tex]=\frac{62181}{8}[/tex]
= 7772.625
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which explains whether 18/24 and 63/84 are equivalent fractions
Answers
Answer:
Yes they are.
Step-by-step explanation:
18/24 * 3.5/3.5 (which equals 1) = 63/84
so yes
Luke bought one hundred thirty two calla lilies for vases to put on tables for a wedding. He needs to divide the lilies among twelve tables. How many calla lilies will be in each vase?
Answers
Answer:
11
Step-by-step explanation:
Why?
Lillies:132
132 divided by 12 is 11
So that means that each vase will give 11 calla lilies each
Graph the line with slope 3/4
passing through the point (5, -2).
Answers
Craig lives in a house that is 4 meters below sea level. Craig goes to school every day, which is 10 meters above sea level. How many meters does Craig travel, in altitude, when going from home to school?
Answers
Answer:
14 meters
Step-by-step explanation:
Craig starts at -4 meteres (4 below sea level and sea level is 0) so we add 4 to get to 0.
The school is +10 meters.
4 + 10 = 14 meters
what expression is equivalent to 1.2-(-8)
Answers
Answer:
is1.2-(8)+1.2.8
Step-by-step explanation:
the answer is1.2-(8)+1.2.8
convert 62 feet per second to (5280 = 1 mile)
Answers
Answer:
Step-by-step explanation:
if you want to convert to miles per hour, then
in 1 second distance covered=62 ft
In 60 seconds (1 minute) distance covered=62×60=3720 ft.
In 60 minutes (1 hour) distance covered=3720×60 ft=223200 ft
=223200/3=74400 yards
=74400/1760=7440/176=930/22=465/11 miles=42 3/11 miles
62 ft per second=42 3/11 miles per hour.
(2,4);slope=1/2
(-8,-1);slope=-3/4
Answers
Answer:
Step-by-step explanation:
1. y - 4 = 1/2(x - 2)
y - 4 = 1/2x - 1
y = 1/2x + 3
2. y + 1 = -3/4(x + 8)
y + 1 = -3/4x - 6
y = -3/4x - 7
HELP ME PLEASEeEeEeE
Answers
Answer:
7.5
Step-by-step explanation:
A club of 50 students is doing volunteer. Each student is volunteering at one of four location. 14 at the hospital, 15 at the pet shelter, 8 at tutoring, 13 at library. What is the probability that the first student volunteers at the library and the other two do not?
Answers
Answer:
The probability is 0.1473
Step-by-step explanation:
Given;
total number of students, n = 50
number at hospital, h = 14
number at pet shelter, p = 15
number at tutoring, t = 8
number at library, L = 13
If three students are chosen at random without replacement, the number of students that will be selected to work in other location is given by;
50 - 13 = 37 students
The probability that the first student volunteers at the library and the other two do not is given by;
P(13 students at library) x P(2 out of the 37 students did not)
[tex]= (\frac{13}{50})(\frac{37}{49})(\frac{36}{48} )\\\\ = 0.1473[/tex]
Anna has $2.53. How much money will Anna have left if she buys a bright yellow highlighter and a thin blue marker?
thin green highlighter $0.35
package of crayons $0.61
thin blue marker $0.80
bright yellow highlighter $0.74
Answers
Answer:
$0.99
Step-by-step explanation:
A thin blue marker = $0.80
A bright yellow highlighter = $0.74
First, find the total cost of these two products. Add the costs together:
0.80 + 0.74 = 1.54
Anna has $2.53 in all. Subtract 1.54 from 2.53:
2.53 - 1.54 = $0.99
Anna will have $0.99 left.
~
Just do it like this
2.53 - 0.80 - 0.74 = 0.99 and that’s it
A brand new smartphone costs $1200. It decreases in value by 13. 3% every year after its purchase. Which function models the value of the phone x years after its purchase?
Question 8 options:
f(x)=1. 133(1200)x
f(x)=1200(1. 133)x
f(x)=1200(0. 867)x
f(x)=0. 867(1200)x
Answers
The function that models the value of the phone x years after its purchase is y = 1200(0.867)^x
Exponential equationsThe standard exponential equation is given as:
y = ab^x
From the given question
a = 1200
b = 1 - 0.133
x is the time
Substitute to have:
y = 1200(1-0.133)^x
y = 1200(0.867)^x
Hence the function that models the value of the phone x years after its purchase is y = 1200(0.867)^x
Learn more on exponential equation here: https://brainly.com/question/2456547
whats the infinitely, one, no solution
Answers
Answer:
Step-by-step explanation:
The infinite solution is when the equation equals something like this:
10 = 10
2 = 2
586 = 586
One solution is when the answer to an equation is something like this
x = 4
x = 17
y = 657
y = 7
No solution is when the equation 'doesn't make sense' or something:
4 = 10
17 = 64
6 = 9
Hope I helped :)
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Noel is a computer repairman. To fix a computer, he charges a customer $40 per hour, plus a fixed fee of $15 for the service call, as represented by the function f(x) = 40x + 15. In the equation, what is represented by the variable x?
Answers
Step-by-step explanation:
4ox+15=60min
40x=60-15
40x=45
40 40
x=1.125
test it 40(1,125)+15=60
what is the area of this shape?
Answers
Width Bottom = 8 sq units
Width Top = 4 sq units
Height right = 9 sq units
Height left = about 13 sq units
Add the width and height to lessen the values.
[tex](8 + 4)\\(9 + 13 )\\8 + 4 = 12\\9 + 13 = 22[/tex]
Third, multiply height times width.
[tex]12 * 22 = 264[/tex]
Therefore, the area of this shape should be 264, according to my logic.
Please let me know if you need anything else!
Find the volume of this pyramid, Round to the nearest tenth if necessary.
Answers
pyramide volume = 1/3 x surface of the base x height
= 1/3 x 2 x 2 x 5 ≈ 6,7 ft³
square base
Work out the fraction that is halfway between 1/3
and
1 1/2
Write your answer in its simplest form.
Answers
Answer:
The fraction that is halfway between 1/4 and 1/2
= (1/4 + 1/2 )/2
= 3/4 ÷ 2
= 3/(4×2)
= 3/8 (final answer)
Answer:
17/12 or 1 5/12
Step-by-step explanation:
Fraction halfway between refers to the mean of the two fractions.
1/3 + 5/2 / 2
2/6 + 15/6 / 2
17/6 / 2
= 17/12 or 1 5/12
Leila was asked to solve the equation ļ (x + 5) = 29. The first step she did to solve the equation was į (x) + }(5) = 29. What property did she use in this step?
1 associative
2 commutative
3 distributive
4 reflexive
Answers
This question has been asked on Brainly!
https://brainly.com/question/19234403
Jonathon borrowed $700 from his grandparents to start a lawn mowing business in his neighborhood. After
mowing lawns for a month and paying his expenses, he was able to pay them $177.34. How much does
Jonathon still owe his grandparents?
Answers
Answer:
$522.66
Step-by-step explanation:
Subtract 177.34 from $700
700 - 177.34 = $522.66
Jonathon still owes his Grandparents' $522.66
Hope I helped :)
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A study on students drinking habits wants to determine the true average number of alcoholic drinks all uf underclassmen students have in a one week period. We know from preliminary studies that the standard deviation is around 2. 8. How many students should be sampled to be within 1. 5 drink of population mean with 90% probability?.
Answers
Answer: 16
Step-by-step explanation:
Standard deviation is 2
Margin error for the problem is 1
Probability 95%, that means thet the siginficance level α is 1 – p
α = 1 – 0.95 = 0.05
margin of error (ME) can be defined as follows
ME = Z(α/2) * standard deviation/ √n
Where n is the sample size
Z(0.05/2) = Z(0.025)
Using a z table Z = 1.96
Now, replacing in the equation and find n
1 = 1.96 * 2/ √n
1 = 3.92 / √n
√n = 3.92
n = 3.92^2
n = 15.36 = 16
i hope this work for you
TwT best answer gets brainliest. someone please help ;w; i would really appreciate it. And pls no links and dont answer if you dont actually know the answer
Answers
Answer:
A-B=6
C-D=4
Step-by-step explanation:
A ∪ B= {a,b,c,d,e,f} and B= {b,d,f} then, which set presents set A?
Answers
Answer:
set A presents {a,c,e}
I think of a number i multiple it by 5 i then subtract 19 finally i double the result the final number is 22 what number did i think of
Answers
To solve this problem, you read the problem backwards and to the opposite of that function.
if it says double --> divide by 2 22 / 2 = 11subtract by 19 --> add 19 11 + 19 =30multiply by 5 --> divide 5 30 / 5 = 6Thus the number that is thought of is 6
Hope that helps!
Unknown value: X
(5X-19)*2=22
5X-19=22/2
5X-19=11
5X=30
X=6
For a school drama performance, student tickets cost $5 each and adult tickets cost $10 each. The sellers collected $3,570 from 512 tickets sold. Which equation can be used to find c, the number of student tickets sold?
Answers
Step-by-step explanation:
let c be the number of students tickets and
y the number of adult tickets.
the equations to find these numbers are
c+y=512
5c+10y=3570
Given k Is parallel to l, what can you conclude about these triangles? Check all that apply. Vertical angles prove Angle1 Is congruent to Angle4. Alternate exterior angles prove Angle5 Is congruent to Angle3. Angle5 and Angle3 are alternate interior angles. The ratios of the corresponding angles are equivalent. The triangles are similar because all corresponding angles are congruent.
Answers
For the triangles made by the line k which is parallel to I, the option 1, 3 and 5 are correct.
Vertical angles prove Angle1 Is congruent to Angle4. Angle5 and Angle3 are alternate interior angles.The triangles are similar because all corresponding angles are congruent.What are the angles formed by the transverse line cut by the transversal?Angles formed by the transverse line cut by the transversal-
Corresponding angle- Corresponding angle keeps the same position on two different parallel line when cut by transverse.Alternate interior angle- This angle made inside the parallel lines cut by the transversal.Alternate exterior angle- This angle made outside the parallel lines cut by the transversal.Supplementary angle- Angle which made on the same line. The sum of the supplementary angle is equal to the 180 degrees.
Given, k Is parallel to l. The image for this problem is attached below.
Let's check all the options-
Vertical angles prove Angle1 Is congruent to Angle4- In the attached image the angle 1 and 4 are equivalent. Thus, this is the correct option.Alternate exterior angles prove Angle5 Is congruent to Angle3- No, they are interior angles.Angle5 and Angle3 are alternate interior angles-This option is also correct, as angle Angle5 and Angle3 are alternate interior angles.The ratios of the corresponding angles are equivalent-No the ratios are not equivalent for the corresponding angles.The triangles are similar because all corresponding angles are congruent-When the corresponding angles are congruent.Hence, For the triangles made by the line k which is parallel to I, the option 1, 3 and 5 are correct.
Vertical angles prove Angle1 Is congruent to Angle4. Angle5 and Angle3 are alternate interior angles.The triangles are similar because all corresponding angles are congruent.Learn more about the angles formed by the transverse line here;
https://brainly.com/question/13207832
Answer:
1 3 5
Step-by-step explanation:
Need help with both shown questions! Tysm!!
Answers
Answer:
8) y=10
9) z=4
Step-by-step explanation:
substitute and solve
Don and Linda would like to replace the hardwood flooring in their dining room. The flooring sells for $15.75 a square foot installed. The room size is 15 feet wide by 22 feet long. They can make a 20% down payment but will need to finance the rest at 12% for 42 months
a. What is the down payment?
b. What is the amount financed?
c. What is the monthly payment?
d. What is the total finance charge?
Answers
Answer:
a) Down payment = $1039.50
b) Amount financed = $4158
c) Monthly payment = $121.73
d) Total finance charge = $5112.66
Step-by-step explanation:
Area of rectangle = width × length
⇒ area of room = 15 × 22 = 330 ft²
Given:
cost of flooring = $15.75 per ft²⇒ Total cost of flooring = area × cost = 330 × 15.75 = $5197.50
a) Down payment = 20% of $5197.50
= 0.2 × 5197.50
= $1039.50
b) Amount financed = total cost - down payment
= 5197.50 - 1039.50
= $4158
c) Monthly payment = [tex]\dfrac{4158 \cdot \frac{0.12}{12}(1+\frac{0.12}{12})^{42}}{(1+\frac{0.12}{12})^{42}-1}[/tex]= $121.73
d) Total finance charge = monthly payment × number of months
= 121.73 × 42
= $5112.66
An algebra tile configuration. 0 tiles are in the factor 1 spot and 0 tiles are in the factor 2 spot. 20 tiles are in the product spot: 1 is labeled x squared, 8 are labeled negative x, and 16 are labeled . the geometric model represents a perfect square trinomial. use the drop-down menus to identify the two factors. factor 1 = factor 2 =
Answers
A quadratic equation is written in the form of ax²+bx+c. The factors of the given tile configuration are (x-4).
What is a quadratic equation?A quadratic equation is an equation whose leading coefficient is of second degree also the equation has only one unknown while it has 3 unknown numbers.
It is written in the form of ax²+bx+c.
In order to write the algebra tile configuration of the given problem, we need to convert sentences one by one. Therefore, the description can be converted as,
1 is labelled x squared, x²8 are labelled negative x, -8xand 16 are labelled. 16Now, adding all the tiles configuration together we will get,
[tex]x^2 - 8x + 16[/tex]
As we got the quadratic equation now, the roots of the quadratic equation can be written as,
[tex]x^2 - 8x + 16 = 0\\\\x^2-4x-4x+16=0\\\\x(x-4)-4(x-4)=0\\\\(x-4)(x-4)=0\\\\(x-4^2)=0[/tex]
Thus, the factors of the given tile configuration are (x-4).
Learn more about Quadratic Equations:
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