A quotient of a number and 6
Explanation: Quotient means that you divide something by another. Let's let n be the "number". Therefore, "a quotient of a number and 6" refers to n6 or n÷6 .
Question: -3x+2c=-3 for x
What is the ratio of 86 and 113.5
9514 1404 393
Answer:
172 : 227
Step-by-step explanation:
The ratio can be turned to an integer ratio by multiplying both values by 2.
86 : 113.5= 2·86 : 2·113.5 = 172 : 227
"Write an equivalent expression by distributing the "-−" sign outside the parentheses:"
"-2.7u-(3v+8)"
i have no idea how to do any of this and the answer made no sense cause it didnt combine like terms
Activity No. 4
Find the indicated sum of the geometric sequence having the following characteristics:
1. 3, 6, 12, ... ; find S5
2. a1 = 14, r = 3, find the sum of the first five terms of this sequence.
3. a1 = 318, r =
1
2
, find Sn
4. S7 = 547, r = −3, find a1
5. Sn, if the sequence is 3, Answer the following. Solve the unknown.
1. The first term of the geometric sequence is 2 and its common ratio is 2. Find the 7th term of
the geometric sequence.
2. What is the second term of the geometric sequence if the first term is 3 and its last term is
1125?
3. Determine the sum of the geometric sequence 2, 6, 18, 54, 162.
4. If the sum of the first five terms of the sequence is 341 and has a common ratio of 4. Find
a1
.
5. What is the sum of an infinite geometric sequence whose first term is 192 and has common
ratio of 1
4
?
Geometric sequence is characterized by a common ratio
(1) Sum of first 5 terms
The first term of the sequence is:
[tex]\mathbf{a = 3}[/tex]
The common ratio (r) is:
[tex]\mathbf{r = 6 \div 3 = 2}[/tex]
The sum of n terms is calculated using:
[tex]\mathbf{S_n = \frac{a(r^n - 1)}{r - 1}}[/tex]
So, we have:
[tex]\mathbf{S_5 = \frac{3 \times (2^5 - 1)}{2 - 1}}[/tex]
[tex]\mathbf{S_5 = \frac{93}{1}}[/tex]
[tex]\mathbf{S_5 = 93}[/tex]
Hence, the sum of the first five terms is 93
(2) Sum of first 5 terms
The first term of the sequence is:
[tex]\mathbf{a = 14}[/tex]
The common ratio (r) is:
[tex]\mathbf{r = 3}[/tex]
The sum of n terms is calculated using:
[tex]\mathbf{S_n = \frac{a(r^n - 1)}{r - 1}}[/tex]
So, we have:
[tex]\mathbf{S_5 = \frac{14 \times (3^5 - 1)}{3 - 1}}[/tex]
[tex]\mathbf{S_5 = \frac{3388}{2}}[/tex]
[tex]\mathbf{S_5 = 1694}[/tex]
Hence, the sum of the first five terms is 1694
(3) Sum of first n terms
The first term of the sequence is:
[tex]\mathbf{a = 318}[/tex]
The common ratio (r) is:
[tex]\mathbf{r = \frac12}[/tex]
The sum of n terms is calculated using:
[tex]\mathbf{S_n = \frac{a(1 - r^n)}{1 - r}}[/tex]
So, we have:
[tex]\mathbf{S_n = \frac{318 \times (1 - \frac 12^n)}{1 - \frac 12}}[/tex]
[tex]\mathbf{S_n = \frac{318 \times (1 - \frac 12^n)}{\frac 12}}[/tex]
[tex]\mathbf{S_n = 636 (1 - \frac 12^n)}[/tex]
Hence, the sum of the first n terms is [tex]\mathbf{ 636 (1 - \frac 12^n)}[/tex]
(4) The first term
The sum of the first 7th term of the sequence is:
[tex]\mathbf{S_7 = 547}[/tex]
The common ratio (r) is:
[tex]\mathbf{r = -3}[/tex]
The sum of n terms is calculated using:
[tex]\mathbf{S_n = \frac{a(1 - r^n)}{1 - r}}[/tex]
So, we have:
[tex]\mathbf{547 = \frac{a(1 - (-3)^7)}{1 - -3}}[/tex]
[tex]\mathbf{547 = \frac{a(2188)}{4}}[/tex]
Multiply both sides by 4
[tex]\mathbf{2188= a(2188)}[/tex]
Divide both sides by 2188
[tex]\mathbf{1= a}[/tex]
Rewrite as:
[tex]\mathbf{a = 1}[/tex]
Hence, the first term is 1
(5) Find the 7th term
The first term of the sequence is:
[tex]\mathbf{a=2}[/tex]
The common ratio (r) is:
[tex]\mathbf{r=3}[/tex]
The nth term of a geometric sequence is:
[tex]\mathbf{T_n = ar^{n -1}}[/tex]
So, we have:
[tex]\mathbf{T_7 = 2 \times 3^{7 -1}}[/tex]
[tex]\mathbf{T_7 = 1458}[/tex]
Hence, the seventh term is 1458
(6) Sum of geometric sequence
The first term of the sequence is:
[tex]\mathbf{a=2}[/tex]
The common ratio of the sequence is:
[tex]\mathbf{r = 6 \div 2 = 3}[/tex]
The number of terms is:
[tex]\mathbf{n = 5}[/tex]
The sum of n terms is calculated using:
[tex]\mathbf{S_n = \frac{a(r^n - 1)}{r - 1}}[/tex]
So, we have:
[tex]\mathbf{S_5 = \frac{2 \times (3^5 - 1)}{3 - 1}}[/tex]
[tex]\mathbf{S_5 = \frac{484}{2}}[/tex]
[tex]\mathbf{S_5 = 242}[/tex]
Hence, the sum of the first five terms is 242
(7) The first term
The sum of the first five terms is given as:
[tex]\mathbf{S_5 = 341}[/tex]
The common ratio is:
[tex]\mathbf{r = 4}[/tex]
The sum of n terms is calculated using:
[tex]\mathbf{S_n = \frac{a(r^n - 1)}{r - 1}}[/tex]
So, we have:
[tex]\mathbf{341 = \frac{a \times (4^5 - 1)}{4 - 1}}[/tex]
[tex]\mathbf{341 = \frac{a \times 1023}{3}}[/tex]
Solve for a
[tex]\mathbf{a = \frac{3 \times 341}{1023}}[/tex]
[tex]\mathbf{a = 1}[/tex]
Hence, the first terms is 1
(8) Sum to infinite
The first term of the sequence is:
[tex]\mathbf{a = 192}[/tex]
The common ratio (r) is:
[tex]\mathbf{r = \frac 14}[/tex]
The sum to infinite is:
[tex]\mathbf{S_{\infty} = \frac{a}{1 - r}}[/tex]
So, we have:
[tex]\mathbf{S_{\infty} = \frac{192}{1 - 1/4}}[/tex]
[tex]\mathbf{S_{\infty} = \frac{192}{3/4}}[/tex]
[tex]\mathbf{S_{\infty} = 256}[/tex]
Hence, the sum to infinite is 256
Read more about geometric sequence at:
https://brainly.com/question/18109692
how many ounces are in 2.5 pounds?
40 , 32, 4.4, 6.4 ?
Answer:
40 ounces
Step-by-step explanation:
Which decimal is equivalent to 7.44343434...?
7.443
7.443
7.4434
7.4434
The last two have a line on the top, above the 4434 and the other is above 34
I need help with these two problems.
Write in slope intercept form.
Through (2,2) and parallel to y=x+4.
Through (3,4) and perpend to y=-2x-4
Answer:
the equation is - [tex]y=x[/tex]
Explanation:
Given -
[tex]y=x+4[/tex]
We have to find a line passing through the point [tex](2,2)[/tex] nd parallel to the given line.
Find the slope of the given line.
It is the coefficeint of [tex]x[/tex]
m₁ = 1
The two lines are parallel. Hence
m₂=m₁=1 Where m₂is the slope of the second line.
You have slope and the points [tex](2,2)[/tex]
Find the Y intercept
[tex]y=mx+c\\2=(1)(2)+C\\2=2+C\\C=2-2=0[/tex]
Y-Intercept [tex]C=0[/tex] and slope m₂=1
Fix the equation
[tex]y=x[/tex]
21. Ronit is buying storage boxes for her CDs. She has
456 CDs. Each box holds 36 CDs. How many boxes
will she need?
HELP ASAP
Answer:
Step-by-step explanation:
Bbdbbdbs
what is the probability that someone in chicago is stung by a bee
Step-by-step explanation:
0.075 % is the probability of that
For the next two questions, use the following coordinates to answer: (1, 3), (5, 2), (1, 5), (2, 3).
Answer:
Use the coordinate plane below to answer the following questions. a. Use a straightedge to construct a line that goes.
Step-by-step explanation:
f(x)=−x+2, find f(0)
Answer:
[tex]find \: f(0) \\ \\ f(x) = - x + 2 \\ f(0) = - (0) + 2 \\ f(0) = - 0 + 2 \\ f(0) = 2[/tex]
AB is parallel to CD. CD is rotated 180° Which statement describes the relationship between ('D' and the transformed AB? How can
you prove it?
Answer:
Answer :- Statement (B) ,C'D' ll AB
Given AB is parallel to CD. CD rotated.
Consider a transversal line l intersecting AB and CD at angle x.
therefore By slope formula,
slope of AB and CD = m =tanx
Now after rotation of 180 CD become C'D'
therefore, slope of C'D' = =tanx=m
Hence C'D' ll AB.
17 + (-3x)
x= -12
evaluate the expression
7+(-3x)
7+(-36)
-29
I hope this helps!
what is the answer to this question!!! −8−10×(−1)+7×(−1)
Answer:
[tex]-5[/tex]
Step-by-step explanation:
**Follow PEMDAS order of operations**:
ParenthesesExponentsMultiplicationDivisionAdditionSubtraction__________________________
[tex]-8-10\times \left(-1\right)+7\times \left(-1\right)[/tex]
1) Multiplication/Division:
[tex]10\times \left(-1\right)[/tex]
[tex]-10[/tex]
[tex]-8-\left(-10\right)+7\times \left(-1\right)[/tex]
[tex]7\times \left(-1\right)[/tex]
[tex]-7[/tex]
2) Addition/ Subtraction:
[tex]-8-\left(-10\right)-7[/tex]
[tex]-\left(-10\right)=+10[/tex]
[tex]-8+10-7[/tex]
[tex]-8+10=2[/tex]
[tex]2-7[/tex]
[tex]=-5[/tex]
______________________________
Helpp me plsss!!!!!!!!!!!!!
answer for y = x^{2} – 10x
Answer:
Direction: Opens Up
Vertex: ( 5 , − 25 )
Axis of Symmetry: x = 5
I'm not sure if this was a graphing question however that is how you solve it.
I need help with question 26 please.
Answer:
it is not balanced because of sulphur on left side 2 sulphur
on the right side 3 sulphur
Answer another question I found online. Or your not big brain.
Answer:
You returned 5 shirt.
Step-by-step explanation:
$30.60 ÷ $6.12 = 5
Answer:
5 shirts
Equation:
-$30.60 / -$6.12 = 5
So 5 would be your answer! :)
Bob and John are saving money. Bob starts with $15 and saves $4 each week. John starts with $3 and
saves $7 each week. At what week will they have the same amount of money?
Answer:
week 4 each will have $31
Step-by-step explanation:
Answer:
Week 4
Step-by-step explanation:
Bob's savings over the course of 4 weeks
15 + 4 = 19(W1) + 4 = 23(W2) + 4 = 27(W3) + 4 = 31(W4)
John's savings over the course of 4 weeks
3 + 7 = 10(W1) + 7 = 17(W2) + 7 = 24(W3) + 7 = 31 (W4)
Brian invests £8200 into his bank account.
He receives 6.0% per year simple interest.
How much will Brian have after 2 years?
Give your answer to the nearest penny where appropriate.
Answer:
£9184
Step-by-step explanation:
Interest = PRT/100
P = Price
R = Rate
T = time
First Let's find the interest for 2 years
[tex]interest = \frac{8200 \times 6 \times 2}{100} \\ = 984[/tex]
So, the interest is £984
Now let's find the full amount he received after two years ,
[tex]8200 + 984 = 9184[/tex]
Total Amount = £9184
Hope this helps you
Let me know if you have any other questions :-):-)
SOLViNg Equations
You are an electrician for the city where you live. You get a
call about a parking lot at baseball field where the lamp posts
keep shutting off, due to the circuit breaker. A circuit
breaker is a switch that automatically stops the flow of
electricity due to a current being too strong or some other
dangerous situation. You've been called in to figure out why
the circuit is breaking
8
One of the most common formulas dealing with electricity is
called Watt's Law. This algebraic equation states that "pi
(power measured in watts) is equal to "V" (the voltage
measured in volts ) times "T" (the current measured in amps).
P= VI
Here is what you know about the baseball field parking lot situation.
There are 9 lamp posts connected to this circuit.
Each lamp post has a 400 watt lamp installed.
The circuit is 120-volt and 20-amp.
Here is what you don't know, but can figure out:
How much power can
the circuit handle?
(Use Wate's Law)
How many watts does 9
lampposts require?
How many lampposts
could this circuit actually
handle?
Answer: 2400
Step-by-step explanation:
120*20
The power consumed by circuit is 2400 watt
What is Power?The quantity of energy transferred or transformed per unit of time is known as power. The watt, or one joule per second, is the unit of power in the International System of Units.
Electrical power is the product of voltage and current. P = V X I .
Given:
Potential Difference= 120 vatt
Current = 20 Ampere
Now, using
Power = V x I
Power= 120 x 20
Power = 2400 Watt
Hence, the power consumed by circuit is 2400 watt
Learn more about power here:
https://brainly.com/question/22103646
#SPJ5
In the following equation, a and b represent integers.
2x + a = 5 – bax
What values of a & b would result in infinitely many solutions?
Write your answers in this form: a=#, b=#
I don’t understand how to use this app :(
Step-by-step explanation:
write this equation on a pice of paper then go to the camera button select which one you want and then take a pic of it. i am in a math class a year above me and this is what we are learning these types of problems confuse me I wish I could help
Does anyone know this answer?
Nine friends vote on their favorite fruit. Only one person in the group votes for kiwi.
Choose the decimal that is equivalent to this fraction.
0.1
0.11
0.111111…
0.212121…
Answer:
0.111111…
Step-by-step explanation:
In the problem described, we understand that 1 in 9 friends prefer kiwi.
That's the equivalent of [tex]x = \frac{1}{9}[/tex] which is equal to [tex]0.1111111...[/tex]
Please let me know if you have any questions in the comments.
Have fun studying! :)
Find the value of x.
Answer:
135
Step-by-step explanation:
720 degrees in a 6 sided shape. already have 2 right angles so its 720- 180 = 540
540÷4 is 135
Which of these numbers is prime? Choose 1 answer: 3 30 63 77 E 91
Answer:
3
Step-by-step explanation:
3 is the only number here with factors of itself (3) and 1
Answer:
3
Step-by-step explanation:
pls help
Use quadratic regression to find
the equation of the parabola
going through these 3 points.
(-1,-23), (-3,-67), (2,13)
y = [ ? ]x2 + [ ]x + [ ]
Answer:
y = 4x² -19x -5
Step-by-step explanation:
When you graph it (or use an appropriate tool), it can help us to figure out that the equation is:
y = 4x² -19x -5
(Quadratic regression = the process of determining the equation of a parabola that best fits a set of data)
Hope this helps, have a nice day :D
Answer:
y=-2x^2+14x+(-7)
Step-by-step explanation:
using the 3 points of (-1, -23) (-3, -67) (2, 13)
How can i multiply 25.00 by 4.19?
PLEASE ANSWER THIS QUESTION. I DON'T KNOW WHAT I'M DOING WRONG!
Answer:
Step-by-step explanation:
1. BOC and 90 degrees and complemetary angles
2. BOC and 30 degrees
3. 30 degrees
4. 60 degrees
What's the answer to problem 19 Geometry?
please help ill mark brilliant
Answer:
(-4,0)
Step-by-step explanation:
1. First, let's graph f(x) = |x + 4|.
(The image is below the explanation).
2. As you can see, the line at first starts going down, but then the turning point occurs at (-4,0). The graph then continues to go upwards.
Therefore, the answer is (-4, 0).
the outside temperature decreases by 7 in 3.5 hours how much did the temperature change each hour
Answer:
24.5
Step-by-step explanation:
24.5 is the temperature change each hour