You can use the same technique I showed in another one of your questions (24467305).
Partial fractions:
[tex]\dfrac2{(2n-1)(2n+1)} = \dfrac a{2n-1} + \dfrac b{2n+1} \\\\ \implies 2 = a(2n+1) + b(2n-1) = (2a+2b)n + a- b \\\\ \implies \begin{cases}2a+2b=0 \\ a-b = 2\end{cases} \implies a = 1, b=-1[/tex]
Then we have a telescoping sum,
[tex]S = \displaystyle \sum_{k=1}^n \frac 2{(2k-1)(2k+1)} \\\\ S = \sum_{k=1}^n \left(\frac1{2k-1} - \frac1{2k+1}\right) \\\\ S = 1-\frac13 + \frac13 - \frac15 + \cdots +\frac1{2n-3}-\frac1{2n-1}+\frac1{2n-1}-\frac1{2n+1} \\\\ S = 1 - \frac1{2n+1} = \boxed{\frac{2n}{2n+1}}[/tex]
(And in case you were actually interested in an infinite sum, we can see that this converges to 1 as n goes to ∞.)
A car is traveling 90 miles per hour. How fast is it traveling in miles per minute?
Answer: 1.5 miles per minute
Step-by-step explanation:
The ratio for the hours is 90 Miles : 60 Minutes
Since 1 hour is 60 minutes, then 1 minute is 1/60 of a hour.
So, 1/60 will be the constant.
[tex]\frac{90}{1/60}[/tex]=1.5
One bulb of elephant garlic costs $2. How
many bulbs of elephant garlic can you buy for
$20?
Answer:
You can buy 10 bulbs of elephant garlic
Step-by-step explanation:
Since each bulb of elephant garlic is 2.
1 x 2 = $2
That is the cost of 1 elephant garlic.
10 x 2 = $20
That is the cost of 10 elephant garlic.
Find the area of the rectangle with the given base and height.
13 ft, 2 in
Answer:
Area of rectangle = 2.16 [tex]ft^{2}[/tex]
Step-by-step explanation:
Given ,
Base = 13 ft = 156 in
Height = 2 in
Area of rectangle = base * height
area = 156 * 2
area = 312 [tex]in^{2}[/tex]
area in square foot = [tex]\frac{312}{144}[/tex] = 2.16 [tex]ft^{2}[/tex] approx
pls answer this i need help
Answer:
Step-by-step explanation:
a) Number = x
Multiply it by 3 = 3*x = 3x
Now add 4 to it: 3x + 4
Equation:
3x +4 = 22
b)
3x + 4 = 22
Subtract 4 from both sides
3x + 4 -4 = 22 - 4
3x = 18
Divide both sides by 3
3x/3 = 18/3
x = 6
Answer:
Below in bold.
Step-by-step explanation:
The equation is
3x + 4 = 22
3x = 22 - 4 = 18
x = 18/3
x = 6.
Find the least number which must be subtracted from each of the following numbers
so as to get a perfect square. Also find the square root of the perfect square so
obtained.
(i) 402 (ii) 1989 (iii) 3250 (iv) 825
(v) 4000
Step-by-step explanation:
1 ) 402
402 - 2 = 400 which is a perfect sqrt ( 20)^2
so u must subtract 2
2) 1989
1989 - 53 = 1936 which is a perfect sqrt (44)^2
3) 3250
3250 -1 = 3249 which is a prefect sqrt (57)^2
4) 4000
4000 - 31 = 3969 which is a perfect sqrt (63)^2
anyone solve this maths questions from integers
Answer:
See THE IMAGE FOR SOLUTION
Answer:
3) Verify the following: (a) 48 = 48, TRUE (b) 230 = 230, TRUE
Step-by-step explanation:
3) Verify the following:
a. 16 [7 + (-4)] = [16 × 7] + [16 × (-4)]
= 16 [7 -4] = [112] + [16 × -4]
= 16 [3] = [112] + [-64]
= 48 = 112 - 64
= 48 = 48
This is true because both sides are equal.
b. -23 × [(-8) + (-2)] = [(-23) × (-8)] + [(-23) × (-2)]
= -23 × [-8 - 2] = [-23 × -8] + [-23 × -2]
= -23 × [-10] = [184] + [46]
= -23 × -10 = 184 + 46
= 230 = 230
This is true because both sides are equal.
how do you found the difference from -5 - (-3) = ?
Answer:
-2
Step-by-step explanation:
-5 - (-3)
-5 + 3
= -2
Solve the equation.
X-6= 8
A x=-2
B x=2
C x=-14
D x= 14
Answer:
Option D is correct
Step-by-step explanation:
[tex]x - 6 = 8 \\ x = 8 + 6 \\ x = 14[/tex]
Hope it is helpful....Answer:
Option D is correct
Step-by-step explanation:
[tex]x - 6 = 8 \\ x = 8 + 6 \\ x = 14[/tex]
Hope it is helpful.....i need help with numbers 15 and 18!!! what does x equal? help asap!!
Answer:
15. x = 112 degrees
18. x = 120 degrees
Step-by-step explanation:
15.
A triangle's angles always equal 180 degrees so we can find the two unknown angles by subtracting 44 from 180 and then dividing it by 2.
2a + 44 = 180
2a = 136
a = 68
Each unknown angle equals 68 degrees. The line from 44 degrees to x degrees segments a line that has a 180 degree angle so we can subtract 68 from 180 to get x.
x + 68 = 180
x = 112
18.
We can use the same concept here but now every angle equals each other so we can divide 180 by 3 to get the measure of those angles.
3a = 180
a = 60
Now we do the same thing as last time to find x.
x + 60 = 180
x = 120
Riley's monthly bank statement showed the following deposits and withdrawals:
-−$105.11, -−$33.75, $113.62, $119.42, $29.64
If Riley's balance in the account was $35.27 at the beginning of the month, what was the account balance at the end of the month?
Answer:
$159.09
Step-by-step explanation:
Math
Select the point that is a solution to the system of inequalities.
ys-X+3
ys x2-3x
Answer:
B (-1 , 0)
Step-by-step explanation:
0 <= -(-1) +3
0 <= 4
0 <= (-1)^2 - 3 (-1)
0<= 4
I need Ans Fast !!!!!!!
Step-by-step explanation:
A={6,9,11},B=ϕ
Here, B is empty set.
Therefore,
A∪B
=A∪ϕ
={6,9,11}
A intersection ϕ is ϕ I guess
If you’re willing to help, that’d be nice.
Answer:
tw ni oe haso layo esma question sodnww aokos
What is the next fraction in this sequence? Simplify your answer.
1/5. 7/20. 1/2. 13/20
..
Answer:[tex]a^5=\frac{4}{5}[/tex]
Step-by-step explanation:
The 5th term of the arithmetic sequence is 4/5
What is Arithmetic Progression?
An arithmetic progression is a sequence of numbers in which each term is derived from the preceding term by adding or subtracting a fixed number called the common difference "d"
The general form of an Arithmetic Progression is a, a + d, a + 2d, a + 3d and so on. Thus nth term of an AP series is Tn = a + (n - 1) d, where Tₙ = nth term and a = first term. Here d = common difference = Tₙ - Tₙ₋₁
Sum of first n terms of an AP: Sₙ = ( n/2 ) [ 2a + ( n- 1 ) d ]
Given data ,
Let the arithmetic progression be represented as A
Now , the value of A is
A = 1/5 , 7/20 , 1/2 , 13/20 ....
Now , the first term of the arithmetic sequence is a₁ = 1/5
The second term a₂ = 7/20
The common difference d = second term - first term
So , the common difference d = 7/20 - 1/5
The value of d = 3/20
Now , the nth term of the AP is given by
Tn = a + (n - 1) d, where Tₙ = nth term
Substituting the values in the equation , we get
T₅ = ( 1/5 ) + ( 5 - 1 ) ( 3/20 )
On simplifying the equation , we get
T₅ = ( 1/5 ) + ( 4 x 3 ) / 20
T₅ = 1/5 + 12/20
T₅ = 16/20
T₅ = 4/5
Therefore , the value of T₅ is 4/5
Hence , the 5th term of the arithmetic sequence is 4/5
To learn more about arithmetic progression click :
https://brainly.com/question/1522572
#SPJ2
Solve the equation 5 - (4x + 7) - 4 = 7. Explain each step of your process using a verbal
description.
I need help :/
Answer:
x = -13/4
Step-by-step explanation:
5 - (4x + 7) - 4 = 7
Distribute the minus sign
5 - 4x -7 - 4 = 7
Combine like terms
-4x-6 = 7
Add 6 to each side
-4x-6+6 = 7+6
-4x= 13
Divide by -4
-4x/-4 = 13/-4
x = -13/4
Answer: -13/4 or -3.25 or - 3 1/4
Step-by-step explanation:
How many terms are in the expression shown?
2n+5-3p+4p
Answer:
4 terms
Step-by-step explanation:
The terms in the expression are unique in that they cannot be combined.
The 4 terms are
2n
+ 5
- 3p
+ 4p
4-3x=8-4x please help
Answer : #1= Answer:x=−4
#2=Answer:x=7
The circumference of a circle is 6 inches. What is the area of the circle?
r
Α= πr2
O
А Зп іn. 2 2
0 B 97 in 2
O
C. 12 in 2
O
D. 361 in 2
Review progress
Question 35
of 36
+ Back
Back
Next-
Answer:
Step-by-step explanation:
A store has a sale with 30% off every item. When you enter the store, you receive a coupon that states that you receive an additional 30% off. Is this equal to a
60% discount? Explain your answer.
Answer:
No, It is not equal to a 60% discount.
Step-by-step explanation:
Think of this. I go into a store and everything is 50% off and I have a coupon myself that is a 50% off discount for a specific item. It may seem like the item is now free, but it isn't. Imagine the item was $1 before any discount. Then the store took 50% off of the $1, leaving it at $0.50. So now with my discount of 50% off the item I will be taking this 50% off of $0.50 = my final discounted cost of $0.25.
Hope I helped you understand :)
Write the equation of the line perpendicular to 2x-5y=-12 that passes through the point (10,-1) in slope-intercept form.
Answer:
[tex]y=-\frac{5}{2}x-24[/tex]
Step-by-step explanation:
[tex]2x-5y=-12\\5y=2x+12\\y=\frac{2}{5}x+\frac{12}{5}\\[/tex]
if two lines perpendicular,
[tex]m_{1} .m_{2}=-1\\ \frac{2}{5} .m_{2}=-1\\m_{2}=-\frac{5}{2}[/tex]
the line perpendicular to this line is
[tex]y=-\frac{5}{2}x+k[/tex] ; k ∈ R
the line passes through the point (10,-1)
so,
[tex]-1=-\frac{5}{2} (10)+k\\-1=-25+k\\k=-24[/tex]
∴the equation of the line perpendicular to 2x-5y=-12 that passes through the point (10,-1) is
[tex]y=-\frac{5}{2}x-24[/tex]
Help.. Suppose Q is the midpoint of PR
Answer:
[tex]3x+41[/tex] or 38
Step-by-step explanation:
If Q is the midpoint of Line PR, then lines PQ and QR add up to equal Line PR. We then get
[tex]PQ=6x+25\\QR=16-3x\\PQ+QR=PR\\6x+25+16-3x=PR\\3x+41=PR\\[/tex]
If you want to know the exact number that PR is, we can do additional steps where PQ = QR.
[tex]PQ=6x+25\\QR=16-3x\\PQ=QR\\6x+25=16-3x\\9x+25=16\\9x=-9\\x=-1\\\\3x+41=PR\\3(-1)+41=PR\\-3+41=PR\\38=PR\\PR=38[/tex]
g(x)=2/3x-1
find g(-3)
Answer:
g(-3) = -3
Step-by-step explanation:
Plug in -3 everywhere that x is.
g(-3) = (2/3)(-3) - 1
g(-3) = (-6/3) - 1
g(-3) = -2 - 1
g(-3) = -3
Is 122/48 in its simplest form or is it’s simplest form 61/24?
Answer:
61/24 is its simplest form! :)
Step-by-step explanation:
Aliyana spent half of her weekly allowance on Takis. To earn more money her parents let her mow the lawn for $6. What is her weekly allowance is she ended the week with $13?
Which is larger?
1) 7/11 or 5/8
2) 5/12 or 7/9
Answer:
7/11
7/9
Step-by-step explanation:
7/11 = 35/55
5/8 = 35/56
Take the fraction eith smaller denominator
5/12 = 35/84
7/9 = 35/45
take the fraction eith the smaller denominator
write a rule in the box below that shows how to simplify a power raised to another power use A as the base and M and N as the exponents
Answer:
A is the answer of the power
Jaxon swam 100 meters in 2 minutes 30 seconds. If each lap is 25 meters long which is most likely to be her time in seconds per lap
37.5 sec/lap
Step-by-step explanation:
2 m and 30 sec to sec equals 150 sec
each lap is 25 m
100 ÷ 25 = 4 laps
150 ÷ 4 = 37.5 sec per lap
please help me solve this
Answer:
x>-1.5
Step-by-step explanation:
8k - 3 - 10 ( I have to simplify it)
8k - 3 - 10
Solution,
= 8k - 3 - 10
= 8k - 13.
Answer:
8k - 13
Step-by-step explanation:
8k - 3 - 10
-(3 - 10) = -13
= 8k - 13
Angle PRS is 98 degree. It is made of two smaller angles. One smaller angle is 3x-8 and the other one is 2x+6. What is the measure of the smaller angle?
Answer:
46
Step-by-step explanation:
The sum of the two smaller angle measures is 98.
(2x + 6) + (3x - 8) = 98
Combine like terms.
5x - 2 = 98
5x = 100
x = 20
Plug this into the expressions for the two smaller angle measures.
2x + 6 = 2(20) + 6 = 46
3x - 8 = 3(20) - 8 = 52
The smaller of the two angles measures 46.
