If the sum of first 7 terms of an A.P is 49 and the sum of first 17 terms is 289 find the sum of first 30 term
Answers
Sum of first 7 terms of an AP = 49.
Sum of first 17 terms = 289
Find:the sum of first 30 term
Solution:We know that,
Sum of first n terms of an AP – S(n) = n/2 * [ 2a + (n - 1)d ]
Hence,
→ 7/2 * [ 2a + (7 - 1)d ] = 49
→ 2a + 6d = 49 * 2/7
→ 2( a + 3d ) = 14
→ a + 3d = 14/2
→ a + 3d = 7 -- equation (1)
Similarly,
→ 17/2 * [ 2a + 16d ] = 289
→ 17/2 * 2 * (a + 8d) = 289
→ a + 8d = 289 * 2/17 * 1/2
→ a + 8d = 17 -- equation (2)
Subtract equation (1) from (2).
→ a + 8d - (a + 3d) = 17 - 7
→ a + 8d - a - 3d = 10
→ 5d = 10
→ d = 10/5
→ d = 2
Substitute the value of d in equation (1).
→ a + 3 * 2 = 7
→ a = 7 - 6
→ a = 1
Now,
Sum of first 30 terms = 30/2 * [ 2(1) + (30 - 1)(2) ]
→ S(30) = 15 (2 + 58)
→ S(30) = 15 * 60
→ S(30) = 900
Therefore, the sum of first 30 terms of the given AP is 900.
I hope it will help you.
Regards.
answer refer in pic siso
Related Questions
6(2x+4) plzzzzzzz I need help
Answers
Answer:
12x+24
Step-by-step explanation:
Answer:
-2
Step-by-step explanation:
Simplifying
6(2x + 4) = 0
Reorder the terms:
6(4 + 2x) = 0
(4 * 6 + 2x * 6) = 0
(24 + 12x) = 0
Solving
24 + 12x = 0
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '-24' to each side of the equation.
24 + -24 + 12x = 0 + -24
Combine like terms: 24 + -24 = 0
0 + 12x = 0 + -24
12x = 0 + -24
Combine like terms: 0 + -24 = -24
12x = -24
Divide each side by '12'.
x = -2
Simplifying
x = -2
yall i need this answerd asap plz help
Answers
Answer:
B
Hope this helped ;)
A realtor makes a 3% commission on every house they sell. If they just sold a house for $314 000, how much did the realtor make?
Answers
Answer: $9420
Step-by-step explanation: 314000x0.03 is 9420
Answer: 314,000 x 0.03 = $9,420
Rewrite the expression (z^1)^2 in the form z^n
Answers
Z^2
Explanation:
Any expression raised to the power of 1 equals itself.
Does anyone know this?
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Answer:The awnser Is this
Positive Roots: 2 or 0
Negative Roots: 1
if 12x+8 is less than 6,what is the value of 8x
Answers
25 POINTS what is the domain of the quadratic function graphed below?
a. all real numbers
b. x>=2
c. x>3
d. y=(0,8)
Answers
Answer:
A or D i tink
Step-by-step explanation:
becuz i tink b and c is not to me
Answer: (a) all real numbers
Step-by-step explanation:
The arrows mean that the line continues for infinity, so the x continues to change for infinity.
What is the opposite of negative 21 or -21
Answers
Answer:
21
Step-by-step explanation:
thats the opposite of negative 21
Answer:
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Step-by-step explanation:
Find the unit rate: $23.96 for 4 pounds
Answers
Answer:
5.99 dollars per pound
Step-by-step explanation:
Convert to a decimal by dividing the numerator by the denominator.
18 Which expression uses the greatest common factor and distributive property to write 18 + 24 as a product?
Answers
Answer:
48
Step-by-step explanation:
8
6. Complete la tabla con el número 4.956: Dígito Valor posicional Notación estándar Notación en potencia De esta forma el número 4.956 puede escribirse como: 7. Fernando tiene 12 cuadrados de cartulina y Catalina tiene 16. Si ambos disponen sus cuadrados uno aliado del otro, ¿cuál de los dos niños puede formar un cuadrado? 8. Escriba las siguientes cifras como notación científica. Número: Notación científica: 45000000 0,000000000000056 0,000000000034
Answers
Answer:
6. Miles [tex]{}[/tex] cientos decenas unidades
4 [tex]{}[/tex] 9 5 6
7. Catalina podrá hacer un cuadrado con longitud lateral de 4 cartones
8. 45000000 = 4.5 × 10⁶
0.000000000000056 = 5.6 × 10¹⁴
0.000000000034 = 3.4 × 10¹¹
Step-by-step explanation:
6. Los valores posicionales de dígitos son;
Miles [tex]{}[/tex] cientos decenas unidades
4 [tex]{}[/tex] 9 5 6
7. El número de cuadrados que tiene Fernando = 12
El número de cuadrados que tiene Catalina = 16
El largo y el ancho de un cuadrado son iguales, por lo tanto tenemos;
largo × ancho = Área del cuadrado
largo = ancho = lado del cuadrado
Lado del cuadrado × Lado del cuadrado = Área del cuadrado
(Lado del cuadrado) ² = Área del cuadrado
Lado del cuadrado = √ (Área del cuadrado)
Para Fernando, Área del cuadrado = 12
Lado del cuadrado para Fernando = √12 = 2 · √3 cartones
Para Catalina, Área del cuadrado = 16
Lado del cuadrado para Catalina = √16 = 4 cartones
Por tanto, Catalina podrá realizar un cuadrado con longitud lateral de 4 cartones
8. 45000000 = 4.5 × 10⁶
0.000000000000056 = 5.6 × 10¹⁴
0.000000000034 = 3.4 × 10¹¹
What is the square of 20
Answers
First you need to know that square means multiplicatin by itself to itself so square of 20 means 20×20=400
The square root of 20 is 4.472
The square or 20^2 is 20•20=400
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Answers
Answer:
26 notches would be made.
Answer:
c) 26
Step-by-step explanation:
If I am understanding the question correctly it's just asking how many notches there will be on a certain length of metal and so in order to find it, you would just divide 6 1/2 by 1/4, also written as 6.5 divided by 0.25, to get 26.
You can ignore a and b but can someone help me with c and d plz :)
Answers
Answer:
(below)
Step-by-step explanation:
c) the angles are in the interior on the same side of the transversal, making them supplementary
equation: 2x + 20 + 120=180 and then when solved you would get x =20
d) the angles are corresponding, which makes them congruent
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Answers
Answer:
sdf
Step-by-step explanation:
sdff
For the first one, 132 and 4 + x make a straight line, and a straight line is 180 degrees, so:
132 + 4 + x = 180
Add 132 and 4.
136 + x = 180
Subtract 136.
x = 44
You are right!
For the second one, 68 + x + 9 form a right angle, and a right angle is 90 degrees, so:
68 + x + 9 = 90
Combine 68 and 9.
77 + x = 90
Subtract 77.
x = 13
Hope this helps
What is the name of the lake located at letter B on the map above? Answer is C :)
Answers
Answer:
the answer is C. lake Texoma
hope this helps
Find the area of the rectangle contained within the following four lines
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Answers
Answer:
should be 15 hope I helped you out.
Step-by-step explanation:
Answer:
15 sq unit
Step-by-step explanation:
Easiest way to understand this question is to plot the lines on the graph which will give you a rectangle with four sides at given points.
the length of the said rectangle will be l = 1 + (-2)
and the breath b = 2 + (-3)
Area= lxb = 15 sq.unit
What is the maximum number of student tickets that can
be sold if the drama club meets its sales goal?
40
The members of the drama club have 100 tickets to sell
to the school play. Students pay $5 per ticket, and
nonstudents pay $10 per ticket. The drama club needs
to collect at least $800 in total ticket sales. The system
of inequalities represents the number of student tickets,
s, and the number of nonstudent tickets, n, the members
must sell.
60
80
100
Suns 100
5s + 10n 2 800
Answers
Answer:
The Drama Club scan sell all 100 student tickets at max if they reach their goal of $800.
Step-by-step explanation:
Answer:
40
Step-by-step explanation:
E2020
On a coordinate plane, a line goes through (1, negative 1) and (4, 2). A point is at (2, 5). What is the equation, in point-slope form, of the line that is perpendicular to the given line and passes through the point (2, 5)? y + 5 = x + 2 y − 2 = x − 5 y − 5 = −(x − 2) y + 2 = −(x + 5)
Answers
The equation is C. y − 5 = −(x − 2)
The line equation is y − 5 = −(x − 2), and the correct option is C.
What is the equation of a Straight Line?The equation of a straight line is given by
y = mx +c
where m is the slope and c is the y-intercept.
The line goes through the points (1, -1) and (4, 2),
The slope of the line will be
m = (y'-y)/(x'-x)
m = ( 2+1)/(4-1) = 1
The product of the slope of the line and the line perpendicular to it is -1
So, the slope of the line perpendicular to the given line is -1.
The line passes through the point (2,5)
The point-slope form is
(y-y') = m(x-x')
so, the equation will be
y − 5 = −(x − 2)
Therefore, the line equation is y − 5 = −(x − 2), and the correct option is C.
To know more about the Equation of Straight line
https://brainly.com/question/21627259
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The admission fee to an amusement park is $18. It costs an additional c dollars to rent a locker to hold your belongings. The total cost for 2 people to enter the amusement park and each rent a locker is $46. How much does it cost for one person to rent a locker?
Answers
Answer:
$5 for one person to rent a locker
Step-by-step explanation:
Assuming the $18 is for one person, then two people it would be $36, since $18 + $18 = $36 and it's stated there's two people. If you subtract $36 from $46 you get $10, and since it's for two people you split it in half (so basically divide by 2) you get $5 for a locker.
Hope this helps!
Best representation of 5 7/3
Answers
Answer:what it is
Step-by-step explanation:
22/3
Suppose scores on exams in statistics are normally distributed with an unknown population mean. A sample of 26 scores is given below. Use Excel to find a 90% confidence interval for the true mean of statistics exam scores. Round your answers to one decimal place and use increasing order.
Answers
Answer:
Step-by-step explanation:
Using the formula for calculating confidence interval
CI = xbar±z×S/√n
xbar is the mean of the sample
z is the z score at 90% = 1.645
S is the standard deviation of the score
n is the sample size = 26
Since we are not given the scores, we can assume the values of our mean and standard Deviation
Let xbar = 38
S = 3.0
Substitute the given values into the formula
CI = 38±(1.645×3.0/√26)
CI = 38±(1.645×3.0/5.099)
CI = 38±(1.645×0.5884)
CI = 38±0.9678
CI = (38-0.9678, 38+0.9678)
CI = (38.0322, 38.9678)
CI = (38.0, 38.9)
Hence the 90% confidence interval for the true mean of statistics exam scores is 38.0≤p≤38.9
Note that the we will need to generate the mean and standard deviation from the data but since we are not given the required data, we had to assume the value we used in calculation.
Simply the expression below .
8+ ( 15 - 3 ) + 4
help please .
Answers
8 + 12 + 4
20 + 4
24
your answer is 24
Answer:
24
Step-by-step explanation:
8+ ( 15 - 3 ) + 4
8+12+4
20+4
24
Picture provided
Please solve.
Answers
Step-by-step explanation:
hope this helps, good night!!!!
If ∠1 and ∠2 are complementary, m∠1 = (8x-6)°, and m∠2 = (14x+8)°
URGENT PLEASE HELP
Answers
Answer:
D
Step-by-step explanation:
Sydney and Tom each count the number of steps it takes for them to walk to school. Sydney counts a 4-digit number of steps. The total of Sydney's steps and Tom's steps in also a 4-digit number of steps. What is the greatest possible digit in the thousands place for Sydney's steps or for Tom's steps? Explain.
Answers
Answer:
8
Step-by-step explanation:
Using the information provided we can say that the largest number of steps for either Sydney or Tom would be 8999 making the digit in the thousands place an 8. This is because both Sydney and Tom counted 4 digits meaning the lowest number for either of them is 1000 steps. Since the question also states that the combination/total of both their steps is still a 4 digit number, this means that the total must not exceed 9,999 steps. Therefore if the minimum is 1000 the maximum can only be 8,999 before going into the 5 digit number of steps.
Write an expression that is equivalent to three over five (3y + 15). (4 points)
A three over five y + 9
B three over five y + 15
C nine over five y + 9
D nine over five y + 15
HELP ASAP
Answers
Answer:
The equivalent to three over five (3y + 15) is nine over five y + 9 ⇒ C
Step-by-step explanation:
Let us solve the question
∵ Three over five means [tex]\frac{3}{5}[/tex]
∴ Three over five (3y + 15) = [tex]\frac{3}{5}[/tex] (3y + 15)
→ By using the distributive property, multiply each term inside the
bracket by three over 5
∴ [tex]\frac{3}{5}[/tex] (3y + 15) = [tex]\frac{3}{5}[/tex] (3y) + [tex]\frac{3}{5}[/tex] (15)
→ Multiply three over five by 3y
∵ [tex]\frac{3}{5}[/tex] (3y) = [tex]\frac{3(3)}{5}[/tex] (y) = [tex]\frac{9}{5}[/tex] y
→ Multiply three over five by 15
∵ [tex]\frac{3}{5}[/tex] (15) = [tex]\frac{3(15)}{5}[/tex] = [tex]\frac{45}{5}[/tex] = 9
∴ [tex]\frac{3}{5}[/tex] (3y) + [tex]\frac{3}{5}[/tex] (15) = [tex]\frac{9}{5}[/tex] y + 9
∴ [tex]\frac{3}{5}[/tex] (3y + 15) = [tex]\frac{9}{5}[/tex] y + 9
∴ The equivalent to three over five (3y + 15) is [tex]\frac{9}{5}[/tex] y + 9
c please give 4 stars :)
A taxi service charges $1.00 for the first mile then $0.10 for each additional mile after that. How much would you pay for having the taxi drive you 2 MILES?
Answers
Answer:
$1.10
Step-by-step explanation:
In an equation, this would be written as follows (where y equals the total price and x is the number of miles driven):
[tex]y = 0.10(x-1) + 1.00[/tex]
Therefore:
[tex]y=0.10(2-1)+1.00[/tex]
[tex]y= 0.10(1)+1.00[/tex]
[tex]y=0.10+1.00[/tex]
[tex]y=1.10[/tex]
y = $1.10
what is the domain of the function represented by the graph?
Answers
Answer: x is equal to or bigger than -3
Step-by-step explanation:
Which shows a set of three equivalent decimals?
1.9, 1.90, 1.900
1.9, 1.90, 1.090
1.9, 0.19 0.190
O 1.9, 1.09, 1.009
Answers
The best choice is A)
when you add a zero, it does not count on a decimal, so,
1.9, 1.90, 1.900.
Answer:
the answer is a
Step-by-step explanation: