14 A formula for determining the finite sum, S, of an arithmetic sequence of numbers is
S=n/2(a+b)
where n is the number of terms, a is the first term, and b is the last term.
Express b in terms of a, S, and n.
Answer:
b = 2S/n - a.
Step-by-step explanation:
S=n/2(a + b)
a + b = S / n/2
a + b = 2S/n
b = 2S/n - a.
If the formula for determining the sum of the given arithmetic sequence is S = n/2(a + b), then 'b' can be expressed as b = [(2S/n) - a].
What is an arithmetic sequence ?An arithmetic sequence is a sequence where the difference between any to consecutive terms are always equal.
Here, a and b are the first and the last terms respectively and n is the number of terms.
Therefore, the sum of the arithmetic sequence is:
S = n/2(a + b)
⇒ 2S/n = (a + b)
⇒ b = (2S/n) - a
Learn more about an arithmetic sequence here: https://brainly.com/question/25715593
#Tag #SPJ2
find the postive value of x when y = 25
A rectangle has dimensions x and x + 5. Determine the value of x that gives the rectangle an area of 36 cm^2.
a) 9
b) 4
c) 6
d) none of these
none of these i guess
14/25, 29/50, 53/100, 13/20, 3/5. Convert them into decimals
Answer:
14/25=0.56
29/50=0.58
53/100=0.53
13/20=0.65
3/5=0.60
help me please i need an equation and solution
Answer:
3x - 2 = 4
x = 2
Step-by-step explanation:
3x - 2 = 4 ---> plus 2 on both sides
3x = 6 --> divide by 3 on both sides
x = 2
i need help please with this
Answer:
Thus, width is 6 and length is 25.
Step-by-step explanation:
Let us assume the width is x, then, the length is (4x+1).
Therefore, 2x + 2(4x+1) = 62
Or, 2x + 8x + 2 =62
Or, 10x = 60
Or, x = 6
Answer:
27 units.
Step-by-step explanation:
The perimeter is equal to 2 x length + 2 x width.
If the width is 4 then:
62 = 2 x length + 2 x 4
62 = 2 x length + 8
Then, we can subtract 8 from both sides.
54 = 2 x length
Next, divide both sides by 2
27 = length
so,
The length is 27 units.
Please help me as soon as you can.I will give you 30points and who answers the quickest will be the brainiliest
help fast pleaseee
NO RANDOMS
Answer:
a)-30
b)-60
c)98
d)-54
Step-by-step explanation:
320/-4
-180/3
-14X-7
6X-9
find 3 values of x and y that satisfy the equation y = 3x - 2
Answer:
x = 1, y = 1
x = -2, y = -8
x = 3, y = 7
Step-by-step explanation:
[tex]\sf 3x+44=50[/tex]
Answer:
2
Step-by-step explanation:
1) Subtract 44 from both sides of the equation
3x + 44 - 44 = 50 - 44
2) Simplify
a. Subtract the numbers
3x = 50 - 44
b. Subtract the numbers
3x = 6
3) Divide both sides of the equation by the same term
3x/3 = 6/3
4) Simplify
a. Cancel terms that are in both the numerator and denominator
x = 6/3
b. Divide the numbers
x = 2
Which tenths is 8.275 between
Answer:
8.3
Step-by-step explanation:
what is the answer?
8^-3
Answer:
-72
Step-by-step explanation:
Answer:
Step-by-step explanation:
[tex]a^{-m}=\dfrac{1}{a^{m}}\\\\8^{-3}=\dfrac{1}{8^{3}}=\dfrac{1}{8*8*8}=\dfrac{1}{512}[/tex]
Please answer the question for brainliest!
Answer:
x = 14
Step-by-step explanation:
10x-30+5x = 180
Combine like terms
* 15x-30 = 180
Add 30 from both sides
* 15x 30+-30 = 180+30
Divide 15 both sides
* 15x/15x = 210/15x
x = 14
Hope this helps :)
Option is
AA
SAS
Not enough information to prove similarity
SSS
Answer:
AA as the angles are similar the sides are not similar so AA is the answer
Step-by-step explanation:
PLZ HELP MEEEEEE
Kaltin will rent a car for the weekend. She can choose one of two plans. The first plan has an initial fee of $75 and costs an additional $0.70 per mile driven. The second plan has no initial fee but costs $0.90 per mile driven. How many mlles would Kaltlin need to drive for the two plans to cost the same?
Answer:
x equals 375
Step-by-step explanation:
75+0.70x=0.90x
For babysitting, Nicole charges a flat fee of $3, plus $5 per hour. Write an equation for the
cost, C, after h, hours of babysitting. How much will Nicole make after babysitting for 10
hours?
For FHG find the measure of the smallest angle ∠HFG, if m∠GHF = 92° and m∠HGF =72°
will give brailist to correct answer and if you show the work
The sum of the measure of angle of a triangle = 180° .
Given two angles = 92° and 72°
_________________________92° + 72° = 164°
180° - 164° = 16° (Ans)
Answer:
the answer is 16!
42 divided by (-7) =
the answer is -6.
the negative 7 turns the answer negative.
please help me thank you
Answer:
2.4 cm
Step-by-step explanation:
1.2/3 = 0.96/x
x = (3 *0.96) / 1.2
x = 2.4 cm
8 and 10 in independent practice please
Answer:
8.) Rational
10.) Irrational
Step-by-step explanation:
8.) This is rational because although it is a decimal, it is terminating, meaning it has an end.
10.) This is irrational because it is a repeating decimal with seemingly no pattern.
what is
m(x)=4x+15; m(x)=7
Answer:
x = -2
Step-by-step explanation:
m(x) = 4x+15; m(x) = 7
7= 4x+15
7-4x=15
-4x=15-7
-4x=8 / :(-4)
x= -2
discrete or continuous function
Answer:
continuous becasue the arrows point out meaning the go on forever
Step-by-step explanation:
Find the distance between points (1, 3) and (9, 18) on the coordinate plane.
Convert a mark of 72 out of 120 to a mark out of 300
Answer:
180 out of 300
Step-by-step explanation:
Basically,
300÷120=2.5
Thereof,
72×2.5=180.
Hope this helps!
tag brainliest please...
please help me. i dont know how to do it.
Answer:
[tex]A = 48.815[/tex]
Step-by-step explanation:
[tex] \frac{a}{ \sin(A) } = \frac{b}{ \sin(B) } [/tex]
[tex] \frac{12.5}{ \sin(A) } = \frac{15.4}{ \sin(68) } [/tex]
[tex]12.5 \sin(68) = 15.4 \sin(A) [/tex]
[tex] \frac{12.5 \sin(68) }{15.4} = \frac{15.4 \sin(A) }{15.4} [/tex]
[tex] \sin(A) = \frac{12.5 \sin(68) }{15.4} [/tex]
[tex] A=\sin ^{ - 1} ( \frac{12.5 \sin(68) }{15.4} ) [/tex]
[tex]A = 48.815[/tex]
help please, please anybody
Answer:
the answer is the third one 3
PLEASE HELP ASAP MY HANDS E GETTING TIRED AND I NEED TO SLEEP e>e
Answer:
[tex] \sf k = 1 \\\\ \sf y = x [/tex]
Step-by-step explanation:
A graph between the amount of time that backpacker hikes to the distance travelled is given .
We need to find the constant of proportionality and the equation of the relationship .According to the Question ,
[tex]\sf \implies y \propto x \\\\\sf \implies y = kx [/tex]
Where k is a constant . Now from the graph , when y is 5 x is also 5 . On substituting the numbers ,[tex]\sf\implies 5 = k(5) \\\\\sf \implies k =\dfrac{5}{5}\\\\\sf \implies \boxed{\frak{\pink{ k = 1 }}}[/tex]
Again the constant of proportionality is the slope of the line.
Here the slope of the line is 1 and its y intercept is 0 . On using slope intercept form ,[tex]\sf\implies y = mx + c \\\\\sf \implies y = 1(x) + 0 \\\\\sf \implies \boxed{\pink{\frak{ y = x }}}[/tex]
[tex] \sf \: please \: answer \: and \: do \: not \: spam[/tex]
¢αяσυѕєℓ :)
It's based on integrals....
Hello Carousel!
[tex] \huge \boxed{\mathbb{QUESTION} \downarrow}[/tex]
Solve the integral.[tex] \large \boxed{\mathfrak{Answer \: with \: Explanation} \downarrow}[/tex]
[tex] \tt \:\int \: \frac{ x + 2 }{( {x}^{2} + 3x + 3) \sqrt{x + 1}} \: dx \\ [/tex]
First, let's take I as ⇨ [tex]\tt \:\int \: \frac{ x + 2 }{( {x}^{2} + 3x + 3) \sqrt{x + 1}} \: dx \\ [/tex].
[tex]\tt \:I = \int \: \frac{ x + 2 }{( {x}^{2} + 3x + 3) \sqrt{x +1}} \: dx \\\tt \: I =\int \: \frac{ x + 2 }{( {x}^{2} + 2x + 1 + x + 2) \sqrt{x + 1}} \: dx \\ \tt \:I =\int \: \frac{ x + 2 }{( ({x + 1}^{2}) + x + 2) \sqrt{x + 1}}[/tex]
Let, x + 1 = m² => dx = 2mdm.
[tex]\tt \:I =\int \: \frac{ {m}^{2} + 1}{ {m}^{4} + {m}^{2} + 1 \cdot \: m} 2mdm \\ \tt \:I =\int \: \frac{ {m}^{2} + 1}{ {m}^{4} + {m}^{2} + 1 \cdot \: \bcancel{ m}} 2 \bcancel{m}dm \\ \tt \: I = \: \int \: \frac{ {m}^{2} + 1}{ {m}^{4} + {m}^{2} + 1 } 2dm[/tex]
Now, divide the numerator & denominator by m²....we'll get it as...
[tex]\tt \:I =2\int \: \frac{ 1 + \frac{1}{ {m}^{2} } }{ {m}^{2} + 1 + \frac{1}{ {m}^{2} } } \: dm \\\tt \: I =2\int \: \frac{ 1 + \frac{1}{ {m}^{2} } }{( {m}^{2} + \frac{1}{ {m}^{2} } - 2) + 3} \: dm \\\tt \: I =2\int \: \frac{ (1 + \frac{1}{ {m}^{2} }) \: dm }{ ({m} - \frac{1}{ m } ) ^{2} + 3} [/tex]
Now, let m - 1/m be t => (1 + 1/m²) dm = dt
[tex]\tt \:I =2\int \: \frac{ dt}{ {t}^{2} + 3 } \\ \tt \:I = 2\int \: \frac{ dt}{ {t}^{2} + ( \sqrt{3}) ^{2} }[/tex]
We know, [tex]\tt \:\int \: \frac{dx}{ {x}^{2} + a ^{2} } = \frac{1}{a} tan ^{ - 1} (\frac{x}{a} ) + c[/tex]...therefore...
[tex]\tt \:I = \frac{2}{ \sqrt{3} } {tan}^{ - 1} ( \frac{t}{ \sqrt{3} } ) + c \: \rightarrow \boxed{ \tt \: eq. \: 1}[/tex]
Now, substitute the value of 't' in eq. 1..we'll get..
[tex]\tt \:I = \frac{2}{ \sqrt{3} } {tan}^{ - 1} ( \frac{m - \frac{1}{m} }{ \sqrt{3} } ) + c \: \rightarrow \boxed{ \tt \: eq. \: 2}[/tex]
Now, substitute the value of 'm' in eq. 2...we'll get...
[tex] \tt \: I = \frac{2}{ \sqrt{3} } {tan}^{ - 1} ( \frac{ \sqrt{x + 1} - \frac{1}{ \sqrt{x - 1} } }{ \sqrt{3} } ) + c \\ \tt \:I = \frac{2}{ \sqrt{3} } {tan}^{ - 1} ( \frac{x + 1 - 1}{ \sqrt{3} \sqrt{x - 1} } ) + c \\ \boxed{\boxed{ \bf \: I = \frac{2}{ \sqrt{3} } {tan}^{ - 1} ( \frac{x }{ \sqrt{3 (x - 1} )} ) + c }}[/tex]
The correct answer is Option B.__________________
The question is really long & tricky but once you get the hang of it you'll be good. Good luck!__________________
Hope it'll help you!
ℓu¢αzz ッ
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Answer:
m<b=107º
Step-by-step explanation:
180-41-32=107
D and B are congruent
Divided: x³-2x²-x+2 by x+1. Using long division method.
[tex]\large\underline{\sf{Solution-}}[/tex]
Given that
[tex] \purple{\rm :\longmapsto\:Dividend = {x}^{3} - {2x}^{2} - x + 2}[/tex]
and
[tex] \purple{\rm :\longmapsto\:Divisor = x + 1}[/tex]
So, By using Long Division Method, we have
[tex]\begin{gathered}\begin{gathered}\begin{gathered} \:\: \begin{array}{c|c} {\underline{\sf{}}}&{\underline{\sf{\:\: {x}^{2} - 3x + 2\:\:}}}\\ {\underline{\sf{x + 1}}}& {\sf{\: {x}^{3} - {2x}^{2} - x + 2 \:\:}} \\{\sf{}}& \underline{\sf{- {x}^{3} - {x}^{2} \: \: \: \: \: \: \: \: \: \: \:\:}} \\ {{\sf{}}}& {\sf{\: \: \: \: \: \: \: \: \: \: \: \: \: \: - 3{x}^{2} - x +2 \: \: \: \: \: \: \: \:\:}} \\{\sf{}}& \underline{\sf{\:\: \: \: \: \: \: \: \: \: \: \: 3{x}^{2} + 3x \: \: \: \: \: \: \:\:}} \\ {\underline{\sf{}}}& {\sf{\:\: \: \: \: \: \: \: \: \: \: \: \: \: 2x + 2 \:\:}} \\{\sf{}}& \underline{\sf{\: \: \: \: \: \: \: \: \: \: \: \: - 2x - 2\:\:}} \\ {\underline{\sf{}}}& {\sf{\:\: \: \: \: \: \: \: \: \: \: \: \: \: \: 0\:\:}} \end{array}\end{gathered}\end{gathered}\end{gathered}[/tex]
So,
[tex]\bf\implies \:Remainder = 0[/tex]
Verification
[tex] \purple{\rm :\longmapsto\:Dividend = {x}^{3} - {2x}^{2} - x + 2}[/tex]
[tex] \purple{\rm :\longmapsto\:Divisor = x + 1}[/tex]
[tex] \purple{\rm :\longmapsto\:Remainder = 0}[/tex]
[tex] \purple{\rm :\longmapsto\:Quotient = {x}^{2} - 3x + 2}[/tex]
Now, Consider
[tex]\rm :\longmapsto\:Divisor \times Quotient + Remainder[/tex]
[tex]\rm \: = \: (x + 1)( {x}^{2} - 3x + 2) + 0[/tex]
[tex]\rm \: = \: {x}^{3} - {3x}^{2} + 2x + {x}^{2} - 3x + 2[/tex]
[tex]\rm \: = \: {x}^{3} - {2x}^{2} - x + 2[/tex]
[tex]\rm \: = \: Dividend[/tex]
Hence, Verified
CARRY ON LEARNING
CAN YOU BRAINLEST ME PLEASE