Generally speaking, arithmetic sequences have the form:
an=a1+(n-1)*d
Where:
an=the nth term in the sequence
a1=the 1st term in the sequence
n=the number of terms in the sequence
d=the difference between consecutive terms (i.e. d=an-an-1=a2-a1=a3-a2, etc.)
The SUM of the terms of an arithmetic sequence, notated Sn, is given by:
Sn=[n/2]*[2a1+(n-1)*d]
So if n=8 then:
a8=a1+7d=63
And if there are 94 terms in the sequence then:
S94=[94/2]*[2a1+93d]=47*(2a1+93d)=94a1+4371d=1000
So this is a system of equations where:
{ a1 + 7d = 63 (Multiply this first equation by -94 on both sides and add to second equation)
{ 94a1 + 4371d = 1000
-94a1 - 658d = -5922 (Add this new equation to second equation)
Therefore:
3713d = -4922
So:
d = -4922/3713
Answer: arithmetic / -30
Step-by-step explanation: This is an arithmetic sequence.
The reason I know that is because the same number is being
added each time to get the next term in the sequence.
In this case, we are adding -30 each time to reach the next term.
So the common difference is -30.
0.88 as a fraction in simplest form
Answer:
22/25
Step-by-step explanation:
0.88×100/1×100=88/100
88÷4/100÷4=22/25
Answer: 22/25
Step-by-step explanation:
i took the test
Which problem can be solved using the expression 1/4÷3?
A gardener bought 3 bags of soil and used 1/4 of the soil to plant rose bushes. How much soil did she use to plant the bushes?
A chef used 1/4 cup of cheese to make 3 of her specialty dishes. How much cheese did she use in each dish?
A driver made 3 trips, each using 1/4 tank of gas. How much gas did he use to make the trips?
Three liters of water were poured into a container and 1/4 liter leaked out. How much water is in the container now?
Answer: A chef used 1/4 cup of cheese to make 3 of her specialty dishes. How much cheese did she use in each dish?
Step-by-step explanation:
Hope it helped you!!
Answer:
a.
Step-by-step explanation:
3 bags of soil divided by 1/4 used = how much used soul out of the 3 bags.
1\4÷3=amount of used soil
Find the radius of the dartboard with a circumference of 333 in.
106 in
53 in
106.1 in
55 in
Answer:
55,278
Step-by-step explanation:
the radius is half of the diameter- 166.5
circumfrence-3.14(d)
3.14x333=55,278
pls help me!! DUE TODAYY!!
Write an equation for the following problems and then solve:
1. Five times a number added to twelve is nine times the number.
2. Twice the difference of a number and six is the sum of that number and two.
3. Four times a number is three times the difference of that number and one.
I think i only have 1 and 2.
1) 5x+12=9x
2) 2x=6
x=3
lol i’m not sure abt this tho
What postulate or theroem prove these triangles are congruent?
Answer:
The Answer To Your To Your Question Is SAS (Side-Angle-Side) Theroem
Answer:
Side angle side Theorem
Step-by-step explanation:
You are making a new type of deodorant from two different mixtures the first mixture is 30% smell proof and the second mixture is 80% smell proof to make a safe make sure it needs to be 50% smell proof how much of each makes you need if you want 1000 L total
Answer:
600 L of 30% proof and 400 L of 80% proof is needed
Step-by-step explanation:
Let the amount of 30% smell proof be x while that of 80% smell proof is y
Then;
x + y = 1000 •••••(i)
Also;
30% of x + 80% of y = 50% of 1000
0.3x + 0.8y = 500 •••••(ii)
From i, x = 1000 - y
Put this into ii
0.3(1000-y) + 0.8y = 500
300 - 0.3y + 0.8y = 500
0.5y = 500-300
0.5y = 200
y = 200/0.5
y = 400 L
But x = 1000 - y
x = 1000 - 400 = 600 L
Write an expression to match the words: Mr. Ortiz’s age is the sum of 8 and 7, doubled.
Answer:
(8+7)x2
Step-by-step explanation:
Help asappp!!!!!!!!!!
Answer:
2.5*15 is 37.5 miles so he has run more than 30 miles in 15 days.
Answer:
More than 30 milesStep-by-step explanation:
Estimated distance run everyday : 2.5 miles → rounding down = 2 miles
Time = 15 daysTotal = 2*15 = 30 milesSince we rounded down, the total distance in reality is more than 30 miles
How was your guys' Thanksgiving??? It's the first day of December, so that means there's only 24 more days til Christmas!!!! What do you guys want????
Answer: I want corona to end
Step-by-step explanation:
Answer:
Heres what I want
Step-by-step explanation:
A GOOD 2021
please help me i’ll mark brainliest
Answer:
It is a function because it doesn't have 2 inputs (do vertical line test)
Step-by-step explanation:
A function only has one input.
TIP: make sure no points connect. If they do, it's not a function.
Help please, need to show work.
9514 1404 393
Answer:
3. m∠A < 80°
Step-by-step explanation:
The exterior angle NGS, marked as 80°, has a measure that is the sum of the measures of the remote interior angles: GAN, GNA.
If we assume that angle measures cannot be zero, then we must have ...
m∠A +m∠N = 80°
m∠A = 80° -m∠N
Since m∠N > 0, the measure of angle A must be less than 80°.
This conclusion matches choice 3.
2x² – 5x-3
Quadratics all work has to be shown
Answer:
(2x+1)(x-1)
Step-by-step explanation:
2x² – 5x-3
2x²+x-6x-3
x(2x+1)-3(2x+1)
(2x+1)(x-1)
Manny is buying new clothes for school. He buys three shirts for $14.95 each and a tie for $12. Everything in the store is on sale for 15% off. What is Manny's total cost?
Given:
Cost of each shirt = $14.95
Cost of a tie = $12
Discount on Sale = 15% off
Manny buys three shirts and a tie.
To find:
The Manny's total cost.
Solution:
We have,
Cost of 1 shirt = $14.95
Cost of 3 shirt = 3 × $14.95
= $44.85
Cost of a tie = $12
Total cost before discount = Cost of 3 shirt + Cost of a tie
= $44.85 + $12
= $56.85
Everything in the store is on sale for 15% off. So,
[tex]\text{Manny's total cost}=56.85-\dfrac{15}{100}\times 56.85[/tex]
[tex]\text{Manny's total cost}=56.85-0.15\times 56.85[/tex]
[tex]\text{Manny's total cost}=56.85-8.5275[/tex]
[tex]\text{Manny's total cost}=48.3225[/tex]
Therefore, the Manny's total cost is $48.3225.
Sara has opened her own bakery, where customers can buy three chocolate chip cookies for $2.49. a. What is the unit price? b. What is the constant of proportionality, or k? c. In a complete sentence, explain what k means in the context of this problem.
Answer:
a) $0.83
b) k = 1.205
c) In the context of this problem, k means
The number of chocolate chip cookies increases as the price increases because number of chocolate chip cookie is directly proportional to its price
Step-by-step explanation:
Sara has opened her own bakery, where customers can buy three chocolate chip cookies for $2.49.
a. What is the unit price?
The unit price means the cost of 1 cookie
Hence:
3 chocolate chip cookies = $2.49
1 chocolate chip cookies = x
3x = $2.49 × 1
x = $2.49 × 1/3
x = $0.83
Hence, the unit price = $0.83
b. What is the constant of proportionality, or k?
Chocolate chip cookie ∝ Price
Chocolate chip cookie is directly proportional to the Price
C = kP
Where k is constant of proportionality
k = Chocolate chip cookie/Price
k = C/P
Hence,
k = 3/2.49
k = 1.2048192771
k = 1.205
c. In a complete sentence, explain what k means in the context of this problem.
In the context of this problem, k means
The number of chocolate chip cookies increases as the price increases because number of chocolate chip cookie is directly proportional to its price
16. BD is an altitude in AABC find the value of x'if MZADB -
(3x + 15)°
Answer:
x = 25°Step-by-step explanation:
Since BD is altitude, BD ⊥ AC
Therefore ∠ ADB = 90°
3x + 15° = 90°3x = 90° -15°3x = 75°x = 75°/3x = 25°what is the final step in the inequality -2(5-4x)<6x-4
Answer:
x < 3
Step-by-step explanation:
-2(5-4x)<6x-4
In this inequality, we are to solve for x using the steps below;
-2(5-4x)<6x-4
Expand the parentheses on the left hand side of the expression;
-10 + 8x < 6x - 4
Collect like terms to both sides;
-10 + 4 < 6x - 8x
-6 < -2x
Divide both sides by - 2; Note the sign of the inequality changes;
3 > x or x < 3
A cashier contains 53 coins worth $4.40 they are all nickels and dimes right to equations that would be used to solve the system and solve
Answer:
(n+d=53) (.05n+.10d=4.40) :)
HELP PLEASEEEE ON THIS
Answer:
I am so sorry bro but the question literally makes no sense. If the people are selling 320 per night bc the price is $9.00, and rise it up to 0.15, one that would not help lower the selling per night and also there is no other way by solving to problem... :(
Step-by-step explanation:
You spend $40 on 5 pounds of concrete. How much is 1 pound?
Answer:
8
Step-by-step explanation:
40 divided by 5 is 8
40/5=8
PLEASE HELP ASAP ILL MARK BRAINLEST
Answer: B. 7•1/8
Step By Step Explanation:
bc it's the best answer choice:)
Carl and Tim start a yard cleaning business. During the first week they
purchased 2 shovels and 2 brooms for $45. They also purchased garbage bags
for $13. Carl cleaned the Kingston's Front and Backyard and Tim cleaned the
Murphy's Driveway.
Answer:
50 you welcome
Step-by-step explanation:
jgjgkgjggkgkgjgjvjckggpggkgkck
Complete the equation of the line through (1,4) and (2,2).
y=
Answer:
[tex]y=-2x+6[/tex]
Step-by-step explanation:
ILL GIVE BRAINLIST
Lydia is deciding between two different movie streaming sites to subscribe to. Plan A costs $5 per month plus $2.50 per movie watched. Plan B costs $24 per month plus $1.50 per movie watched. Let A represent the monthly cost of Plan A if Lydia watches & per month, and let B represent the monthly cost of Plan B if Lydia watches x movies per month. Write an equation for each situation, in terms of x, and determine which plan would be cheaper if Lydia plans on watching 21 movies each month.
Answer:
A= 2.50x+52.50x+5
B= 1.50x+241.50x+24
Step-by-step explanation:
Plan B is $2 cheaper than Plan A when watching 21 movies.
Lydia Plan B would be 2 dollars cheaper than plan A.
Equation on each plan are:
A = 2.50x + 5
B = 1.50x + 24
Lydia deciding between two different movie streaming site to subscribe to.
Lydia have two plan, Plan A and Plan B.
What is Linear equation in one variable?
The linear equation in one variable is an equation which is represent in the form of ax + b = c, where a and b are two integers and x is a variable and has only one solution.
Here, Plan A costs $5 per month plus $2.50 per movie watched.
A = 5 + 2.50 x
here, x is movies per month.
And Plan B costs $24 per month plus $1.50 per movie watched.
B = 24 + 1.50 x
When Lydia plans on watching 21 movies each month.
x = 21
⇒ A = 5 + 2.50 (21) = 57.50
⇒ B = 24 + 1.50 (21) = 55.50
So, Lydia Plan B would be 2 dollars cheaper than plan A.
Learn more about Linear equation visit:
https://brainly.in/question/2123544
#SPJ2
F
E
B
D
a. Identify at least two pairs of congruent angles in the figure and explain how you know they are
congruent.
Answer:
A,B,C,D,E,F
Step-by-step explanation:
So it's A,D
Consider the following graph of an exponential function.
Part A: Define the domain.
Part B: Define the range.
Part C: Where is the graph increasing?
Part D: Where is the graph decreasing?
Part E: Identify any relative maximums.
Part F: identify any relative minimums.
Answer: welcome
Step-by-step explanation:
A= All are real numbers
B=y>-2
c= the graph is not increasing
d= the graph is decreasing for all real numbers of x
none for both
Aditya has $120 in his savings account and Sarah has $180 in her account. Each week Aditya adds $14 to his account and Sarah adds $10 to hers. How many weeks will it be before Aditya and Sarah have the same amount of money saved up? Write an equation and solve.
A swimming pool was filling with water at a constant rate of 200 gallons per hour . The pool had 50 gallons before the timer started. write an equation in standard form to model the situation.
Answer:
200x+y=50
Step-by-step explanation:
ax+by=c
In slope intercept form it would be y=200x+50
what's 3 3/4 - 7/8? (please help i’m too lazy to do it)
9. the learning modalityyou prefer this new normal a.modular learning b.online learning c.digital learning
Answer: A module learning
Step-by-step explanation:
Answer:
Modular education partitions degrees into smaller, Lego-like building blocks of learning, each with their own credentials, learning and skills outcomes. ... Modular learning also enables lifelong learning because working professionals are able to learn new skills in shorter amounts of time, even while they work. So why I like it
Step-by-step explanation:
Part A
View the graph of f(x) =- 2x2 - 4x + 3 in Desmos. Can the graph of f(x) be
the equation that matches this graph above? Explain your reasoning using
complete sentences.
What the answer ?