S = √2+√8+√18+√32+……………… n terms.
or, S = √2 + 2√2 +3√2 +4√2.+………………….+ n terms.
This is an A.P. in which a = √2. , d = √2.
Sn = n/2.[2.a +(n-1).d].
or, Sn = n/2.[ 2√2 +(n-1).√2].
or, Sn = (n/2).√2.[ 2 +n-1].
or, Sn = n.(n+1)/√2. Answer.
Given AP :√2,√8,√18,√32,...
First term = √2
Common difference = √8-√2
⇛ √(2×2×2)-√2
⇛ 2√2-√2
⇛√2
We know that
Sum of first n terms of an AP
⇛ Sn = (n/2)[2a+(n-1)d]
⇛ Sn = (n/2)[2√2+(n-1)(√2)]
⇛ Sn = (n/2)[2√2+√2 n -√2]
⇛ Sn = (n/2)[√2 n +√2)
⇛ Sn = (n/2)×(√2)(n+1)
⇛Sn = (n/√2)(n+1)
⇛ Sn = n(n+1)/√2
Additional comment:
nth term of an AP = a+(n-1)d
Sum of first n terms of an AP
Sn = (n/2)[2a+(n-1)d]
Sum of the first n terms = Sn =
(n/2)(a+an)
If a,b,c are the three consecutive terms in an AP then b = (a+c)/2
also read similar questions: Find the sum of last ten terms of the AP : 8, 10, 12,...., 126.
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The sum of the 8th & 4th of an Ap is 24 and sum of and sum of 6th & 10th term is 44 Find the Ap
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Write the first five terms of the geometric sequence whose first terns 6, and whose common ratio is 3.
The first five terms of the geometric sequence is 6, 18, 54, 162 and 486
Geometric progression is given by:
[tex]nth\ term=ar^{n-1}[/tex]
where a is the first term, r is the common ratio
Given that first term is 6, and common ratio is 3, Hence a = 6, r = 3
[tex]First\ term=6\\\\Second \ term=6(3)^{2-1}=18\\\\Third \ term=6(3)^{3-1}=54\\\\Fourth \ term=6(3)^{4-1}=162\\\\Fifth \ term=6(3)^{5-1}=486[/tex]
The first five terms of the geometric sequence is 6, 18, 54, 162 and 486
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Find the slope.
y = 3x – 11
m =[?]
you know that y=mx +c then in the place of m is 3 then answe is also three.
A jar contains 28 marbles. Half of the marbles are red. Half of the non-red marbles are white and the rest are blue. Todd chose a white marble at random and kept it. What is the probability that when Hosea now draws a marble it will also be white
Answer:
2/9
Step-by-step explanation:
28 marbles in all
"Half of the marbles are red."
28/2 = 14 red
"Half of the non-red marbles are white..."
14/2 = 7 white
"...and the rest are blue."
25 -14 -7 = 7 blue
"Todd chose a white marble at random... " -from the bag that has...
14 red 7 white 7 blue
"... and kept it."- so now the marbles left in the jar are...
14 red 6 white 7 blue
P (white) = Number of white marbles/ Total number of marbles = 6/27 = 2/9
Help plz no links will mark best answer
Answer:
20
Step-by-step explanation:
you know the ratio is 4:3 so you do 4+3=7 then you do 140÷7=20 so I bar represents 20
Half a number is subtracted from 7 results in 34
Answer:
[tex]-54[/tex]
Step-by-step explanation:
If the number being halved is x, we can write the expression
[tex]7-0.5x=34[/tex]
Now, bring like terms and solve!
[tex]-0.5x=27[/tex]
Multiple both sides by -2 and you get
[tex]x=-54[/tex]
Wanna check the answer? Well...
[tex]7-(-54*0.5)=7+27=34[/tex]
The kindergarten class at Stokes Elementary drinks about 210 pints of milk per week. About how many gallons of milk does the class drink in 10 weeks? Round your answer to the nearest tenth of a gallon if needed.
262.5 gallons of milk does the class drink in 10 weeks.
What is Unitary Method?The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.
For example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.
12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.
As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.
This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.
Given:
The kindergarten class at Stokes Elementary drinks about 210 pints of milk per week.
as, we know that
1 pint= 0.125 Galloon
So, 210 pints milk = 210 x 0.125 = 26.25 Galloon
Then, In 10 weeks amount of milk drink
= 26.25 x 10
= 262.5 Gallon
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Two angles are complementary. The larger angle is 32° larger than the smaller angle. Find the measure of both angles, and separate your answers with a comma.
The angles are 29° and 61°.
Let the smaller angle be x
Let the larger angle be x+32.
The sum of the complimentary angles will be 90°.
Therefore, x + x + 32° = 90°
2x + 32° = 90°
2x = 90° - 32°
2x = 58°
x = 58/2
x = 29°
The larger angle = x + 32 = 29 + 32 = 61°
solve the system using substitution 5x+3y=-4 y-2x=6
Solving steps:-
5x+3y=−4
y−2x=6
-->To solve a pair of equations using substitution, first solve one of the equations for one of the variables. Then substitute the result for that variable in the other equation.
5x+3y=−4,−2x+y=6
-->Choose one of the equations and solve it for x by isolating x on the left hand side of the equal sign.
5x+3y=−4
-->Subtract 3y from both sides of the equation.
5x=−3y−4
--> Divide both sides by 5.
x = 1/5(-3y - 4)
--> Multiply 1/5 −3y−4.
x = -3/5y - 4/5
--> Substitute -3y - 4/ 5 for x n the other equation, −2x+y=6.
-2 (-3/5y - 4/5) + y = 6
--> Multiply −2 times -3y - 4/ 5
6/5y + 8/5 + y = 6
--> Add 6y/5 to y
11/5y + 8/5 = 6
--> Subtract 8/5 from both sides of the equation.
11/5y = 22/5
--> Divide both sides of the equation by 11/5, which is the same as multiplying both sides by the reciprocal of the fraction.
y = 2
--> Substitute 2 for y in x= -3/5y - 4/5. Because the resulting equation contains only one variable, you can solve for x directly.
x = -3/5 x 2 - 4/5
--> Multiply -3/5 times 2.
x = -6 - 4/ 5
--> Add -4/5 to -6/5 by finding a common denominator and adding the numerators. Then reduce the fraction to lowest terms if possible.
x = -2
--> The equation is now solved.
Answer : x = -2, y = 2
Explanation : If you think this answer is good, please give "Brainliest" or rate/heart my answer. Hope this helps you.
-5, 20, -80, 320, ... is a geometric
sequence.
What is the explicit rule
Answer:
Multiplied by -4
Step-by-step explanation:
-5 (-4) = 20
20 (-4) = -80
-80 (-4) = 320
A- CE=CD
B- CE = CA
C- BF=DF
D- DF=EF
please help!!
The perpendicular bisector theorem gives the statements that ensures
that [tex]\overleftrightarrow{FG}[/tex] and [tex]\overleftrightarrow{AB}[/tex] are perpendicular.
The two statements if true that guarantee [tex]\overleftrightarrow{FG}[/tex] is perpendicular to line [tex]\overleftrightarrow{AB}[/tex] are;
[tex]\overline{CE} = \overline{CD}[/tex] [tex]\overline{DF} = \overline{EF}[/tex]Reasons:
The given diagram is the construction of the line [tex]\mathbf{\overleftrightarrow{FG}}[/tex] perpendicular to line [tex]\mathbf{\overleftrightarrow{AB}}[/tex].
Required:
The two statements that guarantee that [tex]\overleftrightarrow{FG}[/tex] is perpendicular to line [tex]\overleftrightarrow{AB}[/tex].
Solution:
From the point C arcs E and D are drawn to cross line [tex]\overleftrightarrow{AB}[/tex], therefore;
[tex]\overline{CE} = \mathbf{\overline{CD}}[/tex] arcs drawn from the same radius.
[tex]\overleftrightarrow{FG}[/tex] is perpendicular to line [tex]\overleftrightarrow{AB}[/tex], given.
Therefore;
[tex]\overline{DF} = \overline{EF}[/tex] by perpendicular bisector theorem.
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An angle measures 26.9 degrees. What is its complement?
Answer:
63.1°
Step-by-step explanation:
Complementary angles sum 90°
90 - 26.9 = 63.1°
IF the domain is {0, 2, -6}, what is the range of y=-2x+3?
Answer:
Range is {3,-1, 15}
Step-by-step explanation:
Answer:
{3, -1, 15} is the range.
Step-by-step explanation:
Name.
Solve using
Substitution
L
y = 3x + 2
6x - 2y = 8
Answer:
No solution
Step-by-step explanation:
There is no solution to the system of equations y=3x+2 and 6x-2y=8, meaning that they are parallel to each other on a graph, with no points ever intersecting on each other's lines.
What are the roots of the equation x^2+18x+90=0x
2
+18x+90=0 in simplest a+bia+bi form?
[tex]x^2 +18x +90 = 0\\\\\text{Apply quadratic formula,}~~ x = \dfrac{-b \pm \sqrt{b^2 -4ac}}{2a} \\\\\text{In this case, a = 1 , b = 18 and c = 90.}\\\\\implies x = \dfrac{-18 \pm \sqrt{18^2 - 4 \cdot 1 \cdot 90}}{2(1)}\\\\\implies x = \dfrac{-18 \pm \sqrt{-36}}2\\\\\implies x = \dfrac{-18 \pm 6i}2\\\\\implies x= -\dfrac{18}2 \pm \dfrac{6i}2\\\\\implies x= -9 \pm 3i[/tex]
Which of the lines listed below is parallel to the line with the equation y = 3/2x + 5?
use desmos graphing calculator
Which value of y makes the equation y+4.2=21 true?
I NEED THE ANSWER ASAP I ONLY HAVE 20 MINS TO COMPLETE
A. y = 16.8
B.y=17.2
C.y=17.8
D=25.2
Answer:
A: 16.8
Step-by-step explanation:
4.2 and 16.8 both have decimal place values. If you line up the decimals when you add them, then you get 21.
Find radiuses of circles, if OO1=20cm and 3AK=2BK
Answer:
radius of smaller circle on the left = 8 centimetersradius of larger circle on the right = 12 centimeters=============================================================
Explanation:
The letter O looks very similar to the number zero, so I'm going to use other letters to avoid confusion. For the smaller circle on the left, it'll have center P. The circle on the right will have center Q. See the diagram below.
Based on that, we can say that PQ = 20 cm.
Let x = length of PK
PK + KQ = PQ
KQ = PQ - PK
KQ = 20 - x
We'll keep this in mind for later. I'll refer to this as "Fact 1" when it does come up later.
------------------------
We're given this equation
3AK=2BK
Let's get the numbers to one side and the letters to the other side like so:
3AK=2BK
3AK/BK = 2
AK/BK = 2/3
We'll use this later as well. I'll refer to this as "Fact 2" when it does come up later.
------------------------
Next, draw a segment from P to A to form triangle PAK (also shown in the diagram below). Do the same for points Q and B to form triangle QBK.
The segments PA and PK are radii of the smaller circle, so PA = PK which leads to triangle PAK being isosceles. Triangle QBK is also isosceles for similar reasoning.
The angles AKP and QKB are vertical angles, so they are congruent.
The facts mentioned so far boil down to the two triangles being similar triangles (use the angle angle method to prove).
------------------------
Now that we know the triangles are similar, we can use a proportion to solve for x.
PK/KQ = AK/KB
PK/KQ = 2/3 .... use fact 2
x/(20-x) = 2/3 .... use fact 1
3x = 2(20-x) .... cross multiply
3x = 40 - 2x
3x+2x = 40
5x = 40
x = 40/5
x = 8
So,
PK = x = 8KQ = 20-x = 20-8 = 12The radius of the smaller circle on the left is 8 cm.
The radius of the larger circle on the right is 12 cm.
How much is 1/9 of 3/8 (in lowest terms)?
A)4/17
B)03/17
C)1/36
D)1/24
Answer:
1/24
Step-by-step explanation:
multiply 1/9 and 3/8. The product of the two factors is 3/ 72. Seeing the two factors on the other hand, we can cancel out 3. Hence the final answer to this problem in lowest terms becomes 1/24.
Evaluate the integral:
Substitute x = √7 sin(t) and dx = √7 cos(t) dt. Then
∫ √(7 - x²) dx = ∫ √(7 - (√7 sin(t))²) • √7 cos(t) dt
… = √7 ∫ √(7 - 7 sin²(t)) cos(t) dt
… = 7 ∫ √(1 - sin²(t)) cos(t) dt
… = 7 ∫ √(cos²(t)) cos(t) dt
We require that -π/2 ≤ t ≤ π/2 in order for the substitution we made to be reversible. Over this domain, cos(t) ≥ 0, so
√(cos²(t)) = |cos(t)| = cos(t)
and the integral reduces to
… = 7 ∫ cos²(t) dt
Recall the half-angle identity for cosine:
cos²(t) = (1 + cos(2t))/2
Then the integral is
… = 7/2 ∫ (1 + cos(2t)) dt
… = 7/2 (t + 1/2 sin(2t)) + C
… = 7t/2 + 7/4 sin(2t) + C
Get the antiderivative back in terms of x. Recall the double angle identity for sine:
sin(2t) = 2 sin(t) cos(t)
We have t = arcsin(x/√7), which gives
sin(t) = sin(arcsin(x/√7)) = x/√7
cos(t) = cos(arcsin(x/√7)) = √(7 - x²)/√7
Then
∫ √(7 - x²) dx = 7/2 arcsin(x/√7) + 7/4 • 2 sin(arcsin(x/√7)) cos(arcsin(x/√7)) + C
… = 7/2 arcsin(x/√7) + x/2 √(7 - x²) + C
Which expression is equivalent to f+f-5f
The mean temperature for the first 7 days in January was 4 °C.
The temperature on the 8th day was 6 °C.
What is the mean temperature for the first 8 days in January?
A bolt has 16 1/2 turns per inch. How many turns would be in 2 1/2 inches of threads?
Answer:
41 1/4 turns
Step-by-step explanation:
create a proportion:
turns / inches = turns / inches
't' = turns
16.5 / 1 = t / 2.5
cross-multiply to get:
t = 41.25 or 41 1/4
Need help asap! Pls
Answer:
Step-by-step explanation:
The upper right angle is supplement to 130° and a corresponding angle to (3x + 5)
130 + (3x + 5) = 180
3x + 5 = 50
3x = 45
x = 15
subtract the sum of h and 6 from 4
please help ill mark brainliest
Answer:
it's 11
Step-by-step explanation:
help please use picture
Answer:
y= -1x+4
Step-by-step explanation:
-1/1 is simplified to -1
The next number in the sequence shown below is 156.
1, 15, 155,
The next number of the sequence 1, 15, 155, ...... will be 1555.
What are sequence and series?A sequence is a list of elements that have been ordered in a sequential manner, such that members come either before or after.
A sequence in arithmetic is an enumerated collection of items in which duplicates are permitted and order is important. It has members, just like a set. The distance of the order is defined as the number of items.
The sequence is given below.
1, 15, 155, ......
The next number of the sequence will be given by adding the digit 5 in the one's place. Then the sequence is given as,
1, 15, 155, 1,555, 15,555, 155,555,......
Then the number will be 1555.
More about the sequence link is given below.
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graph the function
f (x) = |x + 2| - 5
Answer:
View the link for the answer
What is the equation for the line in slope-intercept form?
Enter your answer in the box.
Answer:
y= -4/2x+ -4
Step-by-step explanation:
looked at the graph
I need help
With this one question
Answer:
$88
Step-by-step explanation:
442.70 rounded to the nearest 10 dollars is 440.
20%= .2.
440 times .2 =
88