Answer:
[tex]S_9 = 442845[/tex]
Step-by-step explanation:
Given
[tex]Sequence: 45,135,405,1215,3645[/tex]
Required:
The sum of the first 9 terms
We'll solve this question using the explicit formula:
Because it is a geometric sequence, we first calculate the common ratio (r).
[tex]r = \frac{T_n}{T_{n-1}}[/tex]
Let n = 2;
So, we have:
[tex]r = \frac{T_2}{T_{2-1}}[/tex]
[tex]r = \frac{T_2}{T_1}[/tex]
[tex]T_2 = 135; T_1 = 45[/tex]
So, we have:
[tex]r = \frac{135}{45}[/tex]
[tex]r = 3[/tex]
Explicitly, the sum of n terms of a geometric sequence is:
[tex]S_n = \frac{a(r^n - 1)}{r - 1}[/tex]
[tex]a = T_1 = 45[/tex]
[tex]r = 3[/tex]
[tex]n = 9[/tex]
The formula becomes:
[tex]S_n = \frac{a(r^n - 1)}{r - 1}[/tex]
[tex]S_9 = \frac{45* (3^9 - 1)}{3 - 1}[/tex]
[tex]S_9 = \frac{45* (3^9 - 1)}{2}[/tex]
[tex]S_9 = \frac{45* (19683 - 1)}{2}[/tex]
[tex]S_9 = \frac{45* (19682)}{2}[/tex]
[tex]S_9 = 45* 9841[/tex]
[tex]S_9 = 442845[/tex]
Hence, the sum of the first 9 terms is 442845
Hey sorry to bother you but what is (x+4)^2
Answer:
x^2 + 8x+ 16
Step-by-step explanation:
What is the distance between the following points:
A (5, 3) , B (13, 3)
Answer:
8
Step-by-step explanation:
Since the y for both points is 3 it is on the same line.... I have a screenshot attached. Next you would have to plot these points, I have another screenshot for that. Now, you would just have to count the distance between them. The easier way is to just subtract 5 from 13 (13-5) and you'll get 8.
Hope this helps :D
PLS HELP ME :) i’ll mark brainliest pls pls pls pls
Answer:
bam boom pow
Step-by-step explanation:
Answer please I need help it’s emergency I will mark you as brainlist ✨✨
Answer:
I think D
Step-by-step explanation:
I'm very very sorry if I'm wrong
Divide £143 in the ratio 2 : 11
Answer:
22 : 121
Step-by-step explanation:
2 + 11 = 13
143 / 13 = 11
2 × 11 = 22
11 × 11 = 121
The amount of £143 is divided into two sections that are £22 and £121.
What is the solution to the equation?The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.
Divide £143 in the ratio 2: 11.
Let the amount of £143 be divided into two sections that are 'x' and 'y'. Then the equations are given as,
x + y = £143 ...1
x / y = 2 / 11 ...2
From equations 1 and 2, then we have
(2/11)y + y = £143
(13/11)y = £143
y = £121
Then the value of 'y' is given as,
x + £121 = £143
x = £143 - £121
x = £22
The amount of £143 is divided into two sections that are £22 and £121.
More about the solution of the equation link is given below.
https://brainly.com/question/545403
#SPJ2
After the first four games of the 2019 professional football season, three players scored a total of 80 touchdowns. Ezekiel Elliot scored 1/4 of the touchdowns. Deshawn Watson scored 40% of the touchdowns. Patrick Mahoney scored the remaining touchdowns. How many touchdowns did Patrick Mahomes score?
28 touchdowns
52 touchdowns
32 touchdowns
20 touchdowns
Answer:
w
Step-by-step explanation:
Answer:
52
Step-by-step explanation:
which number line shows the solution to 2/3 x - 5>3 ? PLS I NEED IT FOR RIGHT NOW
Answer:
DStep-by-step explanation:
to understand thisyou need to know aboutinequalityalgebraPEMDASfirst note: it will be more easy if we solve the inequality first
so let's solve it together
[tex] \frac{2}{3} x - 5 > 3[/tex]
[tex] \frac{2}{3} x > 8[/tex]
[tex]2x > 24[/tex]
[tex]x > 12[/tex]
so what we get
we get that x is greater than 12
so the answer would be ddoes 2 feet and 1 inch add up too 3 feet
Answer:
No
Step-by-step explanation:
2 feet + 1 foot = 3 feet
1 foot = 12 inches, not 1 inch
If helpful, please give 5 star, thanks, and brainliest!
Answer:
no
Step-by-step explanation:
three feet equals 36 inches so two feet and one inch add up to 25 inches
At fuller elementary there are 4 bakers in the kitchen if each baker can make one cake every 20 minutes how many cakes will be baked in 3 hours
Answer: 36 cakes
Step-by-step explanation:
There are 4 bakers in this kitchen and they can each bake a cake in 20 minutes.
This means that the number of cakes baked in 20 minutes is 4 cakes.
3 hours in minutes is:
= 3 * 60
= 180 minutes
The number of 20 minute periods in 3 hours is therefore:
= 180/20.
= 9
If 4 cakes are baked in 20 minutes, the number of cakes in 180 is:
= 4 * 9
= 36 cakes
Answer:
36
Step-by-step explanation:
The sum of three consecutive integers is alway three times__?
Answer:The sum of three consecutive integers is alway three times the second integer.
I hope this is the answer your looking for
Step-by-step explanation:
The trampoline park has a policy that says "You must be 40 inches tall to
participate!" What percentage of this height is 34 inches?
Answer:
85%
Step-by-step explanation:
4. The senior class at High School A and High School B planned separate trips to New York City. The senior class at High School A rented and filled 1 van and 6 buses with 372 students. High School B rented and filled 4 vans and 12 buses with 780 students. Each van and each bus carried the same number of students. How many students can a van carry? How many students can a bus carry?
Answer:
van=18
bus=59
Step-by-step explanation:
Let v=van & b=bus
1v+6b=372
1v=372-6b
4v+12b=780
Lets divide by 4
1v+3b=195
then
1v=195-3b
substitute in first expression
372-6b=195-3b
simplify
177=3b
b=59
then substitute
1v=195-3(59)
1V=18
Answer:
van=18
bus=59
Step-by-step explanation:
Let v=van & b=bus
1v+6b=372
1v=372-6b
4v+12b=780
Lets divide by 4
1v+3b=195
then
1v=195-3b
substitute in first expression
372-6b=195-3b
simplify
177=3b
b=59
then substitute
1v=195-3(59)
1V=18
25 minutes after 6:50 what time would it be
Answer:
7:15
Step-by-step explanation:
6:50, take ten mins... now it is 7 o'clock and add the remaining fifteen minutes.
The time after 6:50 when 25 minutes is added so the actual time should be considered as the 7:15.
Calculation of the time:Since there is 25 minutes after 6:50
So,
After 10 minutes, it should be 7:00
And, after 15 minutes, it should be 7:15
Hence, The time after 6:50 when 25 minutes is added so the actual time should be considered as the 7:15.
Learn more about time here: https://brainly.com/question/17069398
Nila has r red peppers and 88 green peppers. Write an algebraic expression that tells how many total peppers she has.
Answer:
X= R +88
Step-by-step explanation:
X for total peppers
6.
True or False
ri
a.
A rectangle is a rhombus true
b. All squares are rectangles true
C. A rhombus is a parallelogram hrve
d. Opposite angles in all quadrilateral are congruent true
e. The Same-Side interior angles in a quadrilateral must equal 180
degrees
f. The diagonals of a rectangle are congruent
g.
A
square and a rhombus have diagonals that are perpendicular
h. If the opposite sides of a quadrilateral are congruent then it must be a
parallelogram
i. If one pair of opposite side of a quadrilateral are parallel and the other
opposite sides are congruent then it must be a parallelogram
NEED HELP ......
THANKS!!
Five children play a computer game and score 12, 15, 7, 8 and 10 points. What is the median score?
Problem 1: Convert 85° to radians. Use your keyboard and the keypad to enter your answer. Then click Done.
Answer:
17pi/72
Step-by-step explanation:
To convert degrees to radians, multiply by pi/360 degrees.
85 ° • pi/360 °
The degrees cancel out and it becomes
85pi/360
Simplify
17pi/72
Determine if the sequence below is arithmetic or geometric and determine the
common difference / ratio in simplest form.
2, 10, 50, ...
What is the slop of the line y-3=5(x-2)
Answer:
5
Step-by-step explanation:
The equation is written in point slope form [ y - y1 = m(x - x1) ] where m = slope. "m" in the given equation is 5 which is the slope.
Best of Luck!
Answer:
y-3=5(x-2)
y-3=5x-10
10-3=5x-y
5x-y=7
slope=-(coefficient of x/coefficient of y)=-(5/-1)=5
Gap is having a sale where you can buy one shirt and get two other shirts at a sale price of 40%off before tax. Sales tax on all items is 5%. If you buy three shirts that were originally 28$ each before tax, how much do you pay in total.
Answer:
$64.68 total
Step-by-step explanation:
Answer:
58.34
Step-by-step explanation:
28+28+28−40%+5%+5%+5%
3 x 10^-3 as an ordinary number
===============================================
Explanation:
Think of the first 3 as 3.0
The exponent -3 tells us to move the decimal point three spaces to the left
So the 3.0 turns into 0.003
We can say [tex]3.0 \times 10^{-3} = 0.003[/tex]
--------------
Other examples:
[tex]7.2 \times 10^{-2} = 0.072\\\\5.18 \times 10^{-1} = 0.518\\\\6.4 \times 10^{3} = 6400\\\\[/tex]
The negative exponent means "move that many spaces to the left", while the positive exponent has us move the decimal point that many spaces to the right.
A book company charges a shipping fee of $3 for the first item in a package, $2 for the second item and $1 for each additional item in the package. For example, the shipping fee charged for one package of four items is $3 + $2 + $1 + $1 = $7. How many dollars are saved by shipping 10 items in two packages of five items each, rather than five packages of two items each?
Answer:
$9
Step-by-step explanation:
3+2+1+1+1=8
8x2=16
3+2=5
5x5=25
25-16=9
Year 10
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Overview
Question Progress
Homework Progress
14/38 Marks
+
Expand and simplify (x + 3)(x - 3)(3x + 2)
Answer:
=3x³+2x²−27x−18
Step-by-step explanation:
(x+3)(x−3)(3x+2)
=((x+3)(x−3))(3x+2)
=((x+3)(x−3))(3x)+((x+3)(x−3))(2)
=3x³−27x+2x²−18
=3x³+2x²−27x−18
The diameter of a bike wheel is 21 inches. If the wheel makes 13 complete rotations , how far does the bike travel?
Answer:
πd = c
π21 = 65.9734457
c = 66 inches
66 X 13 = 858 inches
If using the method of completing the square to solve the quadratic equation x^2+20x+28=0x which number would have to be added to "complete the square"?
Answer:
100 will have to be added to both sides to complete the square
Step-by-step explanation:
Given:
x^2+20x+28=0
x² + 20x + 28 = 0
x² + 20x = -28
Using completing the square method of solving quadratic equation
Find the square of half of the coefficient of x
Coefficient of x = 20
Half of the coefficient of x = 20/2
= 10
Square of the half of the coefficient of x = 10²
= 100
Add the square of the half of the coefficient of x to both sides of the equation
x² + 20x = -28
x² + 20x + 100 = -28 + 100
(x + 10)² = 72
Answer:
(x + 3/2)^2 = 121/4
Step-by-step explanation:
khan academy gave me the answer. trust me bro.
Carlos told t-shirts and had to the festival. he made a $3 profit for each t-shirt he sold. he also made a profit of $45 from selling hats. if he made a total profit of $93 how many t-shirts did he sell?
Answer:
jnjcasicnwew
Step-by-step explanation:
Write 1 2/5 as a percent.
Answer: 140%
Step-by-step explanation:
1 can be written as 100%
2/5 can be written as 40/100 which can be written as 40%
100%+40%=140%
Alexander invested $240 in an account paying an interest rate of 2.3% compounded annually. Assuming no deposits or withdrawals are made, how much money, to the nearest dollar, would be in the account after 9 years?
Answer:
295
Step-by-step explanation:
To find this we use the following equation
AV=PV(1+i)^n
Where AV= accumulated value
PV= present value
i= interest rate
so we have
AV=240(1+.023)^9
This is pretty easy to solve and we get
240*1.227
294.50
Which rounds to 295
Answer:
i believe its 295
:)
HELP ME pls
moe is 8 years older than zach if 20 years ago moe was three times as old as zach what are there present ages
Answer:
34 and 30
Step-by-step explanation:
8 times 3 = 34
and 34-4=30
divide 8 by 2 and you'll get 4
so, 34-4=30
