Answer:
The common difference is -1.
The last term (the 14th term) is -11.5.
Step-by-step explanation:
In an arithmetic sequence, the second term is 0.5 and the sum of the first 14 terms is -70.
We want to determine the: (a) common difference and (b) the last term.
We can write an explicit formula to represent the sequence. An arithmetic sequence can be modeled by the formula:
[tex]\displaystyle x_n=a+d(n-1)[/tex]
Where a is the initial term, d is the common difference, and n represents the nth term.
Since the second term is 0.5:
[tex]x_2=0.5=a+d(2-1)[/tex]
Simplify:
[tex]x_2=0.5=a+d[/tex]
The sum of an arithmetic sequence is given by the formula:
[tex]\displaystyle S=\frac{k}{2}\left(a+x_k\right)[/tex]
Where k is the number of terms and x_k is the last term.
Since the sum of the first 14 terms is -70, S = -70 and k = 14:
Using our explicit formula, the last term is:
[tex]x_{14}=a+d(14-1)=a+13d[/tex]
Substitute:
[tex]\displaystyle -70=\frac{14}{2}(a+(a+13d))[/tex]
Simplifiy:
[tex]-10=2a+13d[/tex]
Rewrite the equation for the second term:
[tex]a=0.5-d[/tex]
Substitute:
[tex]-10=2(0.5-d)+13d[/tex]
Simplify:
[tex]-10=1-2d+13d[/tex]
Solve for d:
[tex]d=-1[/tex]
Hence, our common difference is -1.
Solve for a, the initial term:
[tex]a=0.5-(-1)=1.5[/tex]
So, our explicit formula is now:
[tex]x_n=1.5-1(n-1)=1.5-n+1=2.5-n[/tex]
So, the last term (which is 14) is:
[tex]x_{14}=2.5-(14)=-11.5[/tex]
If alex is visiting her moms house and eats a pizza that has 6 triangular pieces, how long would it take for alex’s mom to reach the moon?
Answer:
MY GuYYYY wHat Is ThIS qUeSTioN?!?!?
Step-by-step explanation: I think the answer is green btw
Which of the following is the simplified form of (3-5)3? A.-8. B.-1/64. C.8. D.-12
Answer:
Sorry keep trying buddy
Step-by-step
sorry
simplify this for me:
Answer:
3¹²
Step-by-step explanation:
First lets simplify:
(3⁵)² would be 3¹⁰
and 3⁻² would stay the same:
Now;
[tex]\frac{3^{10} }{3^{-2} }[/tex]
Now keep the base same and subtract exponents:
10 - (-2) = 12
=> Therefore the answer would be 3¹²
Hope this helps!
Answer:
3¹²
Step-by-step explanation:
This kinda Questions can be done using the Law of exponents as ,
[tex] a^m \div a^n = a^{m-n}[/tex][tex] (a^n)^m = a^{mn}[/tex]So using these properties we have ,
→ (3⁵)² / 3-²
→ 3¹⁰ / 3 -²
Now we will use the first formula stated above . That will Result the exponent into , 10 - (-2) = 10 + 2 = 12 . Hence ,→ 3¹²
• Hence the required answer is 3¹² .Given the function f(x) = -5+4x, then what is -f(x) as a simplified polynomial?
Answestf u
Step-by-step explanatio
ggggggggggggggggggggggggggggggggggg
Awnser this or ur gay
Answer:
The slope is 1
Step-by-step explanation:
One popular fast-food chain ordered (a) 2,400,000 slices of cheese last year. In December, the chain reached its goal of serving a total of (b) 40,000,000,000 cheeseburgers since opening. This was enough cheeseburgers to make a stack (c) 473,500 miles high. Also, the number of shakes served last year could have filled (d) 1,200 swimming pools.
Answer:
a. Two million, four hundred thousand
b. Forty billion
c. Four hundred seventy three thousand, five hundred
d. One thousand two hundred
Step-by-step explanation:
To Write the word names for each of the numerals
a. 2,400,000=Two million, four hundred thousand
b.40,000,000,000=Forty billion
c.473,500= Four hundred seventy three thousand, five hundred
d. 1,200=One thousand two hundred
Therefore the word names for each of the numerals will be:
a. Two million, four hundred thousand
b. Forty billion
c. Four hundred seventy three thousand, five hundred
d. One thousand two hundred
A training field is formed by joining a rectangle and two semircles, as shown below. The rectangle is 99 m long and 70 m wide. What is the length of a training
track running around the field? (Use the value 3.14 for and do not round your answer. Be sure to include the correct unit in your answer.)
Answer:
417.8 m
Step-by-step explanation:
99 * 2 + 2 * 3.14 * (70/2) = 417.8
Alex paid $20,448 for a new car. He will make equal payments each month or 4 years. What will be Alex's monthly car payment
Answer:
$426
Step-by-step explanation:
According to the question,
New car cost = $20,448
Time to repay = 4 years or 48 months
So, we can calculate the monthly car payment by using following formula,
Monthly car payment = New car cost ÷ Time to repay
By putting the value, we get
Monthly car payment = $20,448 ÷ 48
= $426
Hence, Alex monthly car payment is $426.
What is the equation
in slope-intercept
form of the line that
passes through the
points (-4, 20) and
(2,-34)?
Antoine works in a restaurant and he is paid his regular hourly rate of 40 hours a week and time and a half for all hours over 40 in that week. If the rate is $14/h and he works 47 hours calculate the total pay.
Ari thinks the perfect milkshake has 333 spoonfuls of caramel for every 555 scoops of ice cream. Freeze Zone makes batches of milkshakes with 666 spoonfuls of caramel and 888 scoops of ice cream.
What will Ari think about Freeze Zone's milkshakes?
Answer:
She wont think it is perfect
Step-by-step explanation:
The ratio of Ari's perfect ice cream is
333 caramel : 555 scoops
Freeze zone ratio is
666:888
Not proportional because you multiply 333 x 2 to get 666, but when you multiply 555 x 2 you wont get 888.
And tell her to cut down on the sugar.
If my answer is incorrect, pls correct me!
If you like my answer and explanation, mark me as brainliest!
-Chetan K
Answer:
A
Step-by-step explanation:
can someone please pls help me
3/11 - 2.12
ANSWER PLEASE
Answer:
-1.84727272727
Step-by-step explanation:
calculator
Answer:
The answer is, 3/11 - 2.12.=1.847
Step-by-step explanation:
Definition of fraction:In mathematics, a fraction is used to represent a portion of something larger. It represents the whole's equal pieces. The numerator and denominator are the two elements of a fraction. The numerator is the number at the top, and the denominator is the number at the bottom. The numerator specifies the number of equal parts taken, whereas the denominator specifies the total number of equal parts in the total.
5/10, for example, is a fraction.
The numerator is 5 and the denominator is 10.
According to the question:
3/11 - 2.12.
= [tex]3/11-212/100\\300-2332/1100\\2032/1100\\1.847[/tex]
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in how many ways can 4 books be arranged on a shelf if there are 8 books to choose from?
Answer:
1680 ways
Step-by-step explanation:
By using the formula for permutation, which is nPr=n!/(n-r)!,
8P4=8!/(8-4)!
=8!/4!
=8×7×6×5
=1680
Or if you just want to use the multiplication rule (which is simpler).
8×7×6×5=1680
Answer:
im pretty sure its
1680
Step-by-step explanation:
find 2 numbers if their sum is 3/5 and their difference is 7 and 1/5
Answer:
3,and, 7
Step-by-step explanation:
this question is asked to you find that 2 Number 3 upon 5 different 7 and 1 upon 5 means 1 3 upon 5 is equal to 1 and one number is remain 3 and two number are find is 3 and 7, that is answer 3 and 7
A cyclist rides his bike at 12 miles per hour. What is this speed per minute? How many miles will the cyclist travel in 20 minutes? Do not round you answers. Help thx
Answer:
In order to find the distance traveled in one minute, you have to divide the distance he can ride his bike in an hour by the number of minutes in a hour. 6/60= .1 mile per minute. If he rides his bike for five minutes, then you would multiply the number of minutes biked by the distance traveled in a minute. .1*5=.5 mile, or [tex]\frac{1}{2}[/tex] mile.
Step-by-step explanation:
The cyclist will travel 4 miles in 20 minutes.
What is Speed?Speed is the time rate at which an object is moving along a path,
To find the speed per minute, we can use the fact that there are 60 minutes in an hour. Therefore:
12 miles per hour = 12/60 miles per minute = 0.2 miles per minute
So the cyclist's speed is 0.2 miles per minute.
To find how many miles the cyclist will travel in 20 minutes, we can use the formula:
distance = rate x time
Plugging in the given values, we get:
distance = 0.2 miles per minute x 20 minutes
distance = 4 miles
Therefore, the cyclist will travel 4 miles in 20 minutes.
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can someone please help me on this question? 30 points
Answer:
Equation: 3x-20+x=180
4x-20=180
4x=200
x=50
Step-by-step explanation:
seven less than the quotient of nineteen and 2
Answer:
19x2-7
mark me brainliestt :))
Carson invested $3,900 in an account paying an interest rate of 2.1% compounded
monthly. Assuming no deposits or withdrawals are made, how much money, to the
nearest ten dollars, would be in the account after 14 years?
Answer:
Try using an interest calculator
Step-by-step explanation:
It's a life saver!
Susan's balance in her checking account was $155.75.
She spent $89.43 at the grocery store, and $128.04 at
the mall. What is Susan's new checking account
balance after the purchases? Type in your answer
without the '$' sign.
last assignment due in math 4 me..
i forgot how to solve these, could anyone explain/solve one or both of these
Answer:
First one is 204 the second one is 207
Step-by-step explanation:
Mutliply width* length
Who could help me with this please and thank you
Answer:
Step-by-step explanation:
let the number be x
so according to the question ur equation is
4x=5<x^2
4x-5=x^2
4-5=x^2/x
-1=x
Find the volume and surface area of the composite figure. Give four answer in terms of π. HELP NEEDED NOW!!! THE RED IS THE ONE I GOT WRONG!!
Answer:
Divide the figure above into a cylinder and a dome
+) the volume of the dome is
[tex]v1 = \frac{1}{12} \pi6 {}^{3} = 18\pi[/tex]
the surface area is
[tex]s1 = \pi3 {}^{2} = 9\pi[/tex]
+) the volume of the cylinder is
[tex]v2 = \pi.3 {}^{2} .13 = 117\pi[/tex]
the surface area is
[tex]s2 = 2\pi.3.13 + 2\pi.3 {}^{2} = 96\pi[/tex]
so the volume of this figure is
[tex]v = v1 + v2 = 18\pi + 117\pi = 135\pi[/tex]
the surface area of this figure is
[tex]s = 9\pi + 96\pi = 105\pi[/tex]
HELP...........................................................................................................ALGEBRA 1
Answer:
-10
Step-by-step explanation:
Answer:
-9 & 5
Step-by-step explanation:
the domain #s are the #s that have the white and black dot
Samantha saves at least 10% of the money she earns each month. She earns $120 each month for a year. Which inequality describes the total amount Samantha saves?
Step-by-step explanation:
10 % each month is $12.00 12 months in a year 12 x 12.00 = $144.00
The inequality to describe the total amount Samantha saves is s > 15.
The correct option is (A).
What is Inequality?Inequalities are mathematical formulas in which neither side is equal. We compare two values in inequality.
As per the given data:
We are given that Samantha saves at least 10% of her monthly salary.
Samantha is earning $150 each month for a year.
To find the amount Samantha at least saves in a month:
= 10% of her monthly salary
= 10% × 150
= 10/100 × 150
= 15 dollars
As she is saving, at least 15 dollars, then the inequality to describe her savings is as follows:
savings > 15
The inequality to describe the total amount Samantha saves is s > 15.
Hence, The inequality to describe the total amount Samantha saves is
s > 15.
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(The given question is incomplete, the complete question is given below)
The circumference of a circle is 24 PI IN. What is the area, in square inches. Express your answer in terms of pi.
Answer:
45.84
Step-by-step explanation:
split 75 in the ratio 7:8
Answer:
35 and 40
Step-by-step explanation:
total ratio= 15
7/15×75=35
8/15× 75= 40
equivalent fractions, please help
The answer is 7/10. I hope this helps you, have a good day!
Answer:
Step-by-step explanation:
49/70 = 7/10
Help with math please
Rewrite the formula for the circumference
of a circle, C = 2πr in terms of its
diameter d.
Answer:
C = (pi)d
Step-by-step explanation:
hope this helps!! BAD BUNNY IS COMING
have a nice day:)
Answer:
diameter of circle=2radius
circumference of a circle =2πr
=(2r)(π)
=dπ unit