Answer:
Step-by-step explanation:
wow, this is kinda complicated math for HS.. :? we have to know what type of series this is, and that means knowing all the different kinds.. unless maybe in the instructions it tells you you are working with arithmetic series? It is one of those so we can use those formulas... other series can have much more complex formulas.. series comes up in Calc II in college.. but .. unless you're going to be an engineer you probably don't need it.. soooooo anyway..
we can use Sn = n/2(2a1 + d(n-1) )
where d is the difference of a2 -a1 ( this will be the same for all terms)
since we're given Sn = 209 set the problem to 209 and solve for n :/
sounds hard huh.. :? let's see
209 = n/2( 2(4) + 3(n-1))
209 = n/2(8 + 3n-3)
209 = n/2(5+3n)
2*209 = n(5+3n)
418 = 3[tex]n^{2}[/tex] + 5n
0 = 3[tex]n^{2}[/tex] + 5n-418 ( use quadratic formula to find n )
( -5 ± [tex]\sqrt{5^{2}-4*3*(-418) }[/tex] ) / 2(3)
( -5 ±[tex]\sqrt{25+5016}[/tex] ) / 6
( -5 ±[tex]\sqrt{5041}[/tex] ) / 6
( -5 ± 71 ) / 6 ( they were nice to us and make it work out perfectly :) )
positive route = 71-5 /6 = 66/6 =11
negative route = 71-(-5) /6 = 71+5/6 = 76/6 = 12[tex]\frac{2}{3}[/tex]
since 12[tex]\frac{2}{3}[/tex] isn't going to really work for us... let's try 11
an= a1 + d(n-1)
an = 4 + 3(11-1)
an = 4 + 30
an = 34
now let's see if we can get 209 for our 11 terms of the series
Sn = 11/2(2(4) + 3(11-1))
Sn = 11/2(8 + 30)
Sn = 418 /2
Sn = 209 yay.. we got it.. it's the 11th term.. and thank you quadratic formula. You get a Christmas present this year :P
n = 11
The number of the terms of the sequence will be equal to 11.
What is an arithmetic progression?The sequence in which every next number is the addition of the constant quantity in the series is termed the arithmetic progression.
Given series is 4+7+10+..... and the sum of the terms of the series is 209.
The summation of the n terms of the series is written by the formula below,
Sn = n / 2 [( 2a+(n-1)d]
Substitute the values in the equation above,
209 = n / 2 [(2 x 4 + ( n -1)3]
418 = n(5+3n)
3n² + 5n - 418 = 0
The above quadratic equation will give two values of n. The values of n are,
n = 11
n = -12.55
The terms can not be equal to a negative number.
Therefore, the number of the terms of the sequence will be equal to 11.
To know more about arithmetic progression follow
https://brainly.com/question/24205483
#SPJ2
Find the 6th term 9 18 36
Answer:
I think the answer is 288.
Step-by-step explanation:
The rule seems to be multiplying the past number by 2. So, 9*2=18 and 18*2=36. If we continued that rule we would then get 72, 144, and the sixth term is then 288.
hope this helps :D
Answer:
Step-by-step explanation:
This is a geometric sequence because any term divided by the previous term is a constant called the common ratio. r=36/18=18/9=2 A geometric sequence is expressed as
[tex]a_n=ar^{n-1},\text{ where a=initial term, r=common ratio, n=term number}\\ \\ a_n=9(2^{n-1})\\ \\ a_6=9(2^5)\\ \\ a_6=288[/tex]
HELP ASAP! What is the slope of the line???
Answer: the slope is 1
Step-by-step explanation:
Slope is basically rise over run. Looking at the graph you see it rises one unit and then goes over to the left by one unit. 1÷1 equals 1 so That is your slope.
this is a quiz on special right triangles. please help me i cannot fail this. i will mark brainliest
Answer:
x=4
Step-by-step explanation:
Consider ΔKLJ:
sinθ=opposite/hypotenuse
sin30=LJ/8√2
LJ=0.5*8√2=4√2
Consider ΔMLJ:
sinθ=opp/hyp
sin45=x/4√2
1/√2=x/4√2
4√2/√2=x
x=4
please help me answer
Find the value of X, Z, and Y in the graph below?
9514 1404 393
Answer:
(x, y, z) = (49, 58, 122)
Step-by-step explanation:
The same-side exterior angles have a sum of 180°.
(x +9) +(3x -25) = 180
4x -16 = 180
x -4 = 45
x = 49
Vertical angles are congruent:
y = 49 +9 = 58
z = 180 -y = 122 = 3(49) -25
The values of x, y, and z are ...
X = 49Z = 122Y = 58the graph of y = 4x^2 - 4x - 1 is shown use the graph to find estimates for the solutions of a and b
Answer:
a) -0.25 and 1.25
b) -0.5 and 1.5
Step-by-step explanation:
a) For 4x^2-4x -1 = 0
What we have to do here is to simply find he points on the x-axis in which the graph crosses it
we have this as;
approximately-0.5 and 1.5
what we are saying is that the plot crosses the x-axis at x = -0.25 and x = 1.25
ii) what we have to do here is to find the point at which y = 2
After finding this point, we trace it to the plot sideways, before we trace to the x-axis
By tracing, we have the crossing on the x-axis at these points at -0.5 and 1.5
Joe pays $4.20 per carton for fresh eggs from the farmers’ market.
If x represents the number of egg cartons and y is the total cost, which of the following representations contains an error?
4.20 -$+$+"$8(#83+78$88873888#9
How do I graph this?
A used book store also started selling used CDs and videos. In the first week, the store sold a combin
ation of 40 CDs and videos. They charged $4 per CD and $6 per video
and the total sales were $180. Determine the total number of CDs and videos sold
Set up two equations, one for number of CD's and videos sold and one for amount of money
made. Then solve for each variable by graphing in Desmos. Clearly state your answers in a
sentence.
Answer:
300 cds
Step-by-step explanation:
because 60x3=180 and 40 divied by 4 is 10.
SOMEONE HELP ME IS DUE TODAY PLZ
Answer:
good luck
Step-by-step explanation:
good luck
How do you solve this (for x) and what is the answer for x?
Answer:
Area for a rectangle-
l x b
(x + 5)+ (2x) =110
3x=110-5
x=105/3
x=35
Thus the answers are-
2 x 35
=70
35 + 5
=40
Please help, I’ll give brainliest
Answer:
2 more hours
Step-by-step explanation:
1 1/2 + 2 1/6 = 1 3/6 + 2 1/6 = 3 4/6 = 3 2/4
3 2/3 - 1 2/3 = 2
What is the measure of the arc in the
picture above?
I will make BRAINLIEST !
Answer:
9.42 km
Step-by-step explanation:
Measure of the arc
[tex] = \frac{ \theta}{360 \degree} \times 2\pi r \\ \\ = \frac{45 \degree}{360 \degree} \times 2 \times 3.14 \times 12 \\ \\ = \frac{1}{8} \times 75.36 \\ \\ = 9.42 \: km[/tex]
AL
2
In a high school stadium there are 750 seats. There are twice as many seats in the home
section as there are in the visitor section. Which system of equations could be used to
determine the number of seats in the home section, h, and the number of seats in the
visitor section, v, in the stadium?
PLEASE HELP HURRY PLEASEEE
Answer:
There are 250 home section and 2(250) = 500 visitor section.
Step-by-step explanation:
Let there are h number of seats in the home section and v is the number of seats in the visitor section.
h+v = 750 ...(1)
There are twice as many seats in the home section as there are in the visitor section.
v = 2h ...(2)
From equations (1) and (2).
h+2h = 750
3h = 750
h = 250
Hence, there are 250 home section and 2(250) = 500 visitor section.
The distance between point Q and point P is 6 1/2 units .Which number could represent point Q?please help me
Answer:
[tex]Q =2\frac{1}{2}[/tex] or [tex]Q =- 10\frac{1}{2}[/tex]
Step-by-step explanation:
Given
[tex]P = -4[/tex] --- missing from the question
[tex]Distance = 6\frac{1}{2}[/tex]
Required
Determine the possible value of Q
The distance can be calculated using absolute function as:
[tex]Distance = |Q - P|[/tex]
Substitute values for distance and P
[tex]6\frac{1}{2} = |Q - (-4)|[/tex]
[tex]6\frac{1}{2} = |Q +4|[/tex]
The absolute function can then be split as:
[tex]6\frac{1}{2} = Q + 4[/tex] or [tex]-6\frac{1}{2} = Q + 4[/tex]
Make Q the subject in both cases:
[tex]Q = 6\frac{1}{2} - 4[/tex] or [tex]Q = -4 - 6\frac{1}{2}[/tex]
[tex]Q =2\frac{1}{2}[/tex] or [tex]Q =- 10\frac{1}{2}[/tex]
WILL GIVE BRAINLIST AND LOST OF PIONTS!!!!!!!!!!!PLEASE HELP!!!
The community library charges a late fee of $0.25 per day for every book that is overdue. The charge for a video is shown in the table. Soren checks out one book and one video and returns them 5 days late. What is the total he will pay in late fees?
5 day video late fee: $
5 day book late fee: $
Total 5 day late fee: $
Answer:
5 day book fee would be $1.25 and 5 day video is $2.25 + 1.25= $3.50
Step-by-step explanation:
Answer:
$10.00
Step-by-step explanation:
Fee for book: $0.25 * 5 = $1.25
Fee for day: $1.75 * 5 = $8.75
Total fee: $1.25 + $8.75 = $10.00
pls answer guys if you do you get something good
Answer:
10 pounds of barley
Step-by-step explanation:
Answer:
10
Step-by-step explanation:
7*5=35
therefore, 2*5=10
Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.
An event organizer is reserving rooms for two company-wide events. For the quarterly meeting this month, she reserved 3 conference rooms and 5 ballrooms, which can seat a total of 399 attendees. For safety training next month, she reserved 1 conference room and 5 ballrooms, which can seat 363 attendees. How many attendees can each room accommodate?
Answer:
x=18 y=69
Step-by-step explanation:
3x+5y=399
x+5y=363
2x=36
x=18
18+5y=363
5y=345
y=69
Find the area of a triangle with a base of 3 cm and height of 8 cm
Answer: The area of a triangle is 12cm²
Answer:
8 x 3 = 24cm
Step-by-step explanation:
8 + 8 + 8 = 24cm
or
3 + 3 + 3 + 3 + 3 + 3 + 3 + 3 = 24cm
Solve for x: -30 - 5x = 120
A. X = -18
B. X = -30
C. X = 30
D. X = 18
Answer:
B. X = -30
Step-by-step explanation:
Answer:
b. -30
Step-by-step explanation:
-30 - 5x = 120
+30 +30
-5x = 150
150 / - 5 = -30
i answered first can i have brainliest?
what is the slope of the line that passes through the points (3,-2) and (9,-2)? 0 3 -3 undefined
Answer:
[tex]\boxed{\textsf{ The slope of the line is $\bf{\dfrac{3}{2}}$.}}[/tex]
Step-by-step explanation:
Two points are given to us and we need to find the slope of the line that passes through these two points . The two points are (3,-2) and (9,-2) .As we know that the slope of the line is given by [tex]\tan\theta[/tex]
Slope of a line is :-
[tex]\qquad\boxed{\boxed{ \sf Slope =\dfrac{ y_2-y_1}{x_2-x_1}=\tan\theta }}[/tex]
On using this formula we can find the slope of the line .
Putting the respective values :-
[tex]\sf\implies Slope = \dfrac{y_2-y_1}{x_2-x_1}\\\\\sf\implies Slope = \dfrac{ 9-3}{2+2} \\\\\sf\implies Slope =\dfrac{6}{4}\\\\\sf\implies\boxed{\pink{\sf Slope = \dfrac{3}{2} }}[/tex]
Answer:
Its zero -w-
Step-by-step explanation:
The measures of the legs of a right triangle both measure 7 yards. What is the length of the hypotenuse? Round your answer to the nearest tenth.
[tex] {a}^{2} + {b}^{2} = {c}^{2} [/tex]
[tex] {7}^{2} + {7}^{2} = {98}^{2} [/tex]
[tex] \sqrt{98} = 9.9 \: yards[/tex]
A French restaurant used 555,580 ounces of cream last year. This year, due to a menu update, it used 45% less. How much cream did the restaurant use this year?
Answer:
305,569 ounces of cream.
Step-by-step explanation:
Take 45% and turn it into a decimal, which is 0.45.Multiply 555,580 by 0.45. This is 250,011Since the keyword is less, we want to subtract 555,580 by 250,011. This is 305,569. This is your answer.1/2 divided by 4 what does that =
Answer:
1/8
Step-by-step explanation:
Answer:
The answer is 0.125
Step-by-step explanation:
Hope this helps
Find the area plzzzzzzxxxzzxxxzzzzzzz
Step-by-step explanation:
step 1. break up the shape into 2 triangles and one rectangle
step 2. A = area of triangle 1 (t1) + area of triangle 2 (t2) + area of the rectangle (r)
step 3. t1 = (1/2)bh where b is the base and h is the height. definition of the area of a triangle.
step 4. t1 = (1/2)(3)(2) = 3ft^2.
step 5. t2 = (1/2)(3)(3) = 4.5ft^2.
step 6. r = bh where b is the base and h is the height. definition of the area of a rectangle.
step 7. r = bh = (8)(4) = 32ft^2.
step 8. A = t1 + t2 + r = 3 + 4.5 + 32 = 39.5ft^2.
Lin's sister has a checking account. If the account balance ever falls below zero, the bank charges her a fee of $5.95 per day. Today, the balance in Lin's sister's account is -$2.67. In 14 days, Lin's sister will be paid $430 and will deposit it into her checking account. If there are no other transactions besides this deposit and the daily fee, will Lin continue to be charged $5.95 each day after this deposit is made? Explain or show your reasoning.
Answer: No, the bank will not keep charging her the $5.95 after the deposit is made.
Step-by-step explanation:
Today, Lin's sister's balance is -$2.67
She gets charged $5.95 per day.
There are 14 days until she can charge some money in the bank account, so the bank will charge $5.92 14 times
So her balance after 14 days will be:
Balance = -$2.67 - $5.95*14 = -$85.97
When she charges the $430 in the account, her balance will be:
Balance = -$85.97 + $430 = $344.03
So now she has a positive balance, which means that the bank does not charge her anymore.
Sally cycle 14 miles north and 13 miles east. To return to her starting points she took the shortest distance shown in the diagram by the dotted line
Answer:
Step-by-step explanation:
There's no diagram and no question, but I assume it shows a right triangle.
distance = √(14²+13²) = √365 ≅ 19.1 miles
The length of an object, f(x), in yards, is a linear function of the length of the object, x, in feet. What units should be used to describe the rate of change in f(x) with respect to x?
A.
Inches per foot
B.
Feet per yard
C.
Yards per foot
D.
Yards per inch
Answer:
DADDY CHILL
Step-by-step explanation:
Llam is setting up folding chairs for a meeting. If he arranges the chairs In 7 rows of the same length, he has 5 chairs left over. If he arranges the chairs in 5 rows of that same length, he has 23 left over. How many chalrs does Llam have?
Liam has total 40 chairs with him
POPULATION In 2000, the world population was calculated to be 6,071,675,206. The world population increases at a rate of about 1.2% annually.
Write a function that represents the world population y after x years.
A) y = 6,071,675,205(1.012)^x
B) y = 6,071,675,206(1.012)^x
C) y = 6,071,605,205(1.012)^x
D) y = 6,071,675,215(1.012)^x
PLEASE HELP!!
Answer:
B) y = 6,071,675,206(1.012)^x
Step-by-step explanation:
It appears that this question asks for an exponential model that represents the population growth. I believe you could view the equation in the form y = (initial population)(rate)^x
Since the initial population is 6,071,675,206, you could substitute that in to get y = 6,071,675,206(rate)^x
Since your rate is increasing by 1.2% (0.012 in decimal form), just convert that to decimal form (knowing that 100% = 1.0, add 0.012 to get 1.012). Substitute that in to get y = 6,071,675,206(1.012)^x
Hope that helps. Feel free to let me know if it made sense.