Use the explicit or recursive formulas for the geometric sequence 45,135,140,1215,3645... To the sum of the first 9 terms of the sequence
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
A phone is made in five different colours with three different storage capacities. How many combinations are there?
Answer:
15 possible combinations
Step-by-step explanation:
In order to find the total number of combinations possible, we need to multiply the total number of different colors by the total number of storage capacities that each phone can have. Using the values provided we would get the following arithmetic expression...
5 colors * 3 capacities = 15
Therefore, we can see that there are a total of 15 possible combinations with these variations.
Which number produces a rational number when added to 1/5?
Answer:
1/5 is a rational number
Step-by-step explanation:
"In mathematics, a rational number is a number such as -3/7 that can be expressed as the quotient or fraction p/q of two integers, a numerator p and a non-zero denominator q. Every integer is a rational number: for example, 5 = 5/1."
The temperature on Wednesday was −5 degrees Celsius. By Friday the temperature fell to −10 degrees Celsius. Write and solve an equation that shows the change in temperature.
Answer: -5 + (10) = 5
Step-by-step explanation:
keep change flip -5 - (-10) you get -5 + (10) = 5
Use the tables to help you compare the two ratios.
2 tables. One table has 2 rows. The first row has entries 3, 6, 9. The second row has entries 10, 20, 30. The second table has 2 rows. The first row has entries 1, 2, 3. The second row has entries 5, 10, 15.
Compare the ratios 1:5 and 3:10.
The ratio 1:5 is less than 3:10
The ratio 1:5 is greater than 3:10
The ratio 1:5 is equal to 3:10
The ratios cannot be compared
Answer: A. The ratio 1:5 is less than 3:10
Step-by-step explanation:
In ΔXYZ, x = 1.4 cm, z = 2 cm and ∠Z=37°. Find all possible values of ∠X,
Answer: 24.9
Step-by-step explanation:
A pink crayon is mad with 12 ml of red wax for every 5 ml of white wax.
Which of the following wax mixtures will create the same shade of pink?
Choose 2 answers
Answer: Multiply 12 and 5 (by the same number) and add them to get whatever total ml of crayon wax is specified.
Ex: Total ml divided by 17, then find how many parts are red(12ml) and white(5ml)
Step-by-step explanation:
PLS HELP I WILL GIVE BRAINLIEST
The graph represents Jason’s trip on the bus, showing his distance from home as a function of time. Select all statements that are true based on the graph.
A. The bus is traveling at a decreasing speed.
B. The bus traveled a total distance of 310 miles.
C. The bus traveled at a faster speed during the first 4 hours of the trip.
D.After traveling 200 miles, the bus trip has more than 3 hours remaining.
E. The bus traveled a total distance of 130 miles in the first 4 hours of the trip.
F. During the first part of the trip, the bus traveled at a constant speed of 45 miles per hour.
Answer:
A , E, F
Step-by-step explanation:
Three statements are true based on the graph the correct options are D, E,F
How to find the speed of an object?If the object is going linearly, and at a constant speed, then the speed of that object is given by the distance it traveled to the time it took to travel that distance.
If the object traveled D distance in T units of time, then that object's speed is
[tex]Speed = S = \dfrac{\: Distance \: traveled}{\: Time \: taken} = \dfrac{D}{T} \: \rm unit \: length/unit \: time[/tex]
For option D, we can see in the graph the bus has completed 200 miles of distance between the 2nd and 3rd hour. So, there are more than 3hours remaining, and option D is correct
For option E, it is clear from the graph that after 4 hours the distance traveled by the bus is 130miles
For option F; the distance traveled in first 4 hours= total distance from home - remaining distance after 4 hours
310-130=180miles
time= 4hours
speed=distance/time
speed= 180/4= 45miles per hour
hence, D, E,F are true
Learn more about average speed here:
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The equation was y = 18x + 300.
What is the slope in the equation, and what does it
represent?
Answer:
slope is 18 and it represents the change in x or in your case, whatever x represents such as miles per hour or bananas eaten per minute
Step-by-step explanation:
Please help me I am its in the pic
Evaluate each expression for g = -7 and h = 3 and match it to its value.
1. gh
10
2. g2 - h
2
3. g + h2
-21
4. g + h
-10
5. h - g
46
6. g - h
-4
Answers:
1. gh = -21
2. g^2 - h = 46
3. g + h^2 = 2
4. g + h = -4
5. h - g = 10
6. g - h = -10
Step-by-step explanation:
1. -7 x 3 = -21
2. -7^2 = - 49
-49 + 3 = -46
3. 3^2 = 9
-7 + 9 = 2
4. -7 + 3 = -4
5. 3 - -7 = 3 + 7 = 10
6. -7 - 3 = -10
Please please please help me I do not understand this
X
Complete the table
Graph
Vertical
change
horizontal
change
slope
А
B
B
С
(30,75)
(10.3.5)
(10.35)
/(1,3)
|(2.1.5)
Answer:
The complete table is shown below:
Graph Vertical Change Horizontal Change Slope
A 6 3 2
B 2 8 1/4
C 40 20 2
Step-by-step explanation:
Graph A
From graph A, it is clear that
(x₁, y₁) = (1, 3)
(x₂, y₂) = (4, 9)
Vertical change = y₂ - y₁ = 9 - 3 = 6
Horizontal change = x₂ - x₁ = 4 - 1 = 3
Using the formula
Slope = m = Vertical Change / Horizontal Change
= [y₂ - y₁] / [x₂ - x₁]
= [9 - 3] / [4 - 1 ]
= 6 / 3
= 2
Thus, the slope of the line = m = 2
Graph B
From graph B, it is clear that
(x₁, y₁) = (2, 1.5)
(x₂, y₂) = (10, 3.5)
Vertical change = y₂ - y₁ = 3.5 - 1.5 = 2
Horizontal change = x₂ - x₁ = 10 - 2 = 8
Using the formula
Slope = m = Vertical Change / Horizontal Change
= [y₂ - y₁] / [x₂ - x₁]
= [3.5 - 1.5] / [10 - 2 ]
= 2 / 8
= 1/4
Thus, the slope of the line = m = 1/4
Graph C
From graph C, it is clear that
(x₁, y₁) = (10, 35)
(x₂, y₂) = (30, 75)
Vertical change = y₂ - y₁ = 75 - 35 = 40
Horizontal change = x₂ - x₁ = 30 - 10 = 20
Using the formula
Slope = m = Vertical Change / Horizontal Change
= [y₂ - y₁] / [x₂ - x₁]
= [75 - 35] / [30 - 10 ]
= 40 / 20
= 2
Thus, the slope of the line = m = 1/4
Therefore,
The complete table is shown below:
Graph Vertical Change Horizontal Change Slope
A 6 3 2
B 2 8 1/4
C 40 20 2
Explain what the inequality means in relation to the positions of these numbers on the number line.
Answer:
City M is colder then city L because city L is closer to the midle/the 0
Step-by-step explanation:
Greg took a test. Out of 12 questions, he answered only nine correctly. What percent of the questions did he score correctly?
Answer:
9/12×100
0.75×100
=75%
Divide number he got correct by total questions, then multiply by 100.
9/12 = 0.75
0.75 x 100 = 75%
The answer is 75%
Pls help due ASAP
Show workings
Answer:
JP = 18
PS = 9
Step-by-step explanation:
ps being the shorter side is one third of the line JS and 1/3 of 27 is 9
jp being the longer side is 2/3 the length of js and 2/3s of 27 is 18
Answer:
JP=18
PS=9
Step-by-step explanation:
centroid divides median in the ratio 2:1
so,
JP:PS=2:1
Now take PS be x
then JP=2x
now, given JS=27
JP+PS=27
2x+x=27
3x=27
x=9
so,
PS=9
AND JP=18
Find the distance between the points ( -9, -2 ) and ( -1, 4 )
Answer:
the distance between the two points is 10
It costs $5 to buy a pen and $3 to buy a rulers If you have $50 to spend, write an inequality representing all the possible combinations of pens and rulers you could buy, then graph it.
(Show your work) Factor out the GCF: 6x3y2z4 - 7x2y5z
Answer:
x²y²z is the Greatest Common Factor
Therefore,
6x³y²z⁴ - 7x²y⁵z = x²y²z (6xz³ - 7y³)
Step-by-step explanation:
Given the expression
6x³y²z⁴ - 7x²y⁵z
The first step is to factor out the greatest common factor from each term
6x³y²z⁴ = 2 · 3 · 6 · x · x · x· y · y · z · z · z · z
7x²y⁵z = 7 · x · x · y · y · y· y · y · z
So
G.C.F = x · x . y · y . z
G.C.F = x²y²z
Thus, x²y²z is the Greatest Common Factor
Therefore,
6x³y²z⁴ - 7x²y⁵z = x²y²z (6xz³ - 7y³)
all states have a minimum wage. true or false
Answer:
OF course it's False
Step-by-step explanation:
As many places like US itself have high wages
f (4) = 20x -10
help
Answer:
70
Step-by-step explanation:
20(4)-10
80-10
=70
Answer:
f(4)=70
Step-by-step explanation:
f(4)=20x-10
f(4)=20(4)-10
f(4)=80-10
f(4)=70
Please answer!!!!! I will give brainliest!
Answer: answered :)
Step-by-step explanation:
45+5t=45
solving for t
Answer:
t=0
Step-by-step explanation:
The first thing you want to do is isolate the varible t. So you going to subrtact the 45 from both sides, which leaves you with, 5t=0. Next you are going to divide 5 from both sides, which leaves you with t=0. To make sure its right, plug it in. 45+5(0)=45. 45=45.
Find the length of side x in simplest radical form with rational denominator. the short leg is root 2 and the long leg is x we don't know the hypotenuse.
Answer:
√2 + x
Step-by-step explanation:
To obtain the hypotenus, h:
Using Pythagoras rule :
h² = opposite² + Adjacent²
Opposite = √2
Adjacent= x
h² = (√2)² + x²
Take the square root of both sides
h = √2 + x
Hence, the hypotenus is √2 + x
10 points
Question 6. A bakery offers a sale price of $2.50 for 4 muffins. What is
the price for 12 muffins? *
A $5.00
B $7.00
C$7.50
O D $10.00
Answer:
2.50 : 4
x : 12
2.50 x 12=4x
4x= 30
x=30/4
x= $7.50
C
Could someone help? Thanks
Answer:
x = -3, y = -0.512
x = -1, y = -3.2
x = 0, y = -8
x = 2, y = -50
Step-by-step explanation:
what is the value of 4x 2 +7x−10 if x=4 pleaseeee help lol
I'll give away 60 points to the first 10 people who gets this answer right
Answer:
The 15?
Step-by-step explanation:
Answer:
balance
i
Step-by-step explanation:
mark as brainleast and fo-ll-ow me
The exponential function is graphed below.( ) y=3 3 1 xWhat is the value of the x-intercept for the function?
Answer: 2^(3) equals to 8.
So the x value is 3.
Step-by-step explanation: Hope this Helps!
Calculate the value of 3x + 4y when x = -6 and y = 5.
Answer:
x = -6
-18+4y=0 => 4y=18 =>y=18/4=9/2
Y=5
3x+20=0 => x=3x= -20=> x= -20/3
Step-by-step explanation:
The value of the given expression is -38.
Simplify fractions by cancelling all the common factors from both the numerator and the denominator and writing the fraction in its lowest/simplest form.
Given an expression, 3x + 4y
Putting x = -6 and y = -5, we get,
3x(-6) + 4x(-5)
= -18-20
= -38
Hence, The value of the given expression is -38.
For more references on simplification, click;
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[tex]solve \: this[/tex]
............ ..
Answer:
9Step-by-step explanation:
it's the answerhope it helpsA coin is flipped 20 times. The coin lands on HEADS 12 times. Write the ratio for landing on heads in fraction and percent form.
Answer:
12/20
60%
Step-by-step explanation:
A fraction has a numerator and denominator
The numerator is the total number of heads
The denominator is the total number of times the coin was flipped
[tex]\frac{12}{20}[/tex]
To express in percent form, multiply by 100
[tex]\frac{12}{20}[/tex] x 100 = 60%
