Answers
Answer:
(b)
[tex]\displaystyle \frac{2005}{2006}[/tex]
Step-by-step explanation:
(a)
First, we have to prove that:
[tex]\displaystyle \frac{1}{x}-\frac{1}{x+1}=\frac{1}{x(x+1)}[/tex]
Operate:
[tex]\displaystyle \frac{1}{x}-\frac{1}{x+1}=\frac{x+1-x}{x(x+1)}[/tex]
Simplifying:
[tex]\displaystyle \frac{1}{x}-\frac{1}{x+1}=\frac{1}{x(x+1)} [1][/tex]
(b)
Now we use the above expression to find the sum:
[tex]\displaystyle S=\frac{1}{1\times 2}+\frac{1}{2\times 3}+\frac{1}{3\times 4}+...+\frac{1}{2005\times 2006}[/tex]
Let's use [1] for each term of the sum:
[tex]\displaystyle \frac{1}{1\times 2}=\frac{1}{1}-\frac{1}{2}[/tex]
[tex]\displaystyle \frac{1}{2\times 2}=\frac{1}{2}-\frac{1}{3}[/tex]
[tex]\displaystyle \frac{1}{3\times 4}=\frac{1}{3}-\frac{1}{4}[/tex]
[tex]\displaystyle \frac{1}{2005\times 2006}=\frac{1}{2005}-\frac{1}{2006}[/tex]
Substituting:
[tex]\displaystyle S=\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+....+\frac{1}{2005}-\frac{1}{2006}[/tex]
Note the terms 1/2 and -1/2, 1/3 and -1/3, etc. are canceled out, leaving only the first and last terms:
[tex]\displaystyle S=\frac{1}{1}-\frac{1}{2006}=\frac{2006-1}{2006}[/tex]
[tex]\boxed{\displaystyle S=\frac{2005}{2006}}[/tex]
Related Questions
Pls help will give Brainiest
Answers
Answer:
-5
Step-by-step explanation:
Hey there I really need help with this it’s due tonight and I haven’t got a chance to do it may you please help me?
Answers
Answer:
1. Second Option, 2. Second Option, 3. Second Option, 4. First Option, 5. Sonia, 6. 1/2 a mile (.5), 7. $0.25, 8. $21, 9. Stan, Tran, Fran.
Step-by-step explanation:
For all of them, just divide the top number by the bottom number and compare all the numbers.
The equation `2x - 3 = 4x + 3` is modeled above. What value of `x` makes the equation true?
Answers
2x=4x+6
-2x=6
Divide by -2
X=-3
If W + 6 = 3 and v-4 = 2, what is the value of w + v?
Answers
Answer:
w = - 3 and v = - 2
Step-by-step explanation:
Because w + 6 = 3 you would subtract 6 and whatever you do to one side you would do to the other.
w= - 3
Answer:
[tex]w + v = 3[/tex]
Step-by-step explanation:
Solve for w
[tex]w + 6 = 3[/tex]
Move 6 to subtract 3.
[tex]w = 3 - 6 \\ w = - 3[/tex]
Solve for v
[tex]v - 4 = 2[/tex]
Move 4 to add 2
[tex]v = 4 + 2 \\ v = 6[/tex]
Solve for w+v
Substitute w = -3 and v = 6
[tex]w + v = - 3 + 6 \\ w + v = 3[/tex]
Jolene and Samantha begin a trip from the same place at the same time. If Jolene's speed is 40 mph and
Samantha's speed is 50 mph, how many hours will it take for Samantha to get 25 miles ahead
Answers
Answer:
Step-by-step explanation:
Jolene speed =40 mph
Samantha speed=50mph
let x be the time Samantha needs to be ahead of Jolene
40x+25=50x
25=50x-40x
25=10x
x=2.5 hours
lin paid $94 for 6 meals. How much would 9 meals cost?
Answers
Answer:
140.4
Step-by-step explanation:
Answer:
$141.01 and if it is the nearest whole number it would be $141
Step-by-step explanation:
first you have to do 94 divided by 6. you do this to see how much 1 meal cost.
then you get: 15.67
now you take 15.67x3=47.01
cuz we need 3 more meals. we know this cuz we have 6 and want 9 so 6-9 is 3.
now we take 47.01+94=141.01
we just need to add 3 to the 6 we have to make 9 meals.
so your answer would be $141.01
plz give brainliest!
Writing in Slope-Intercept Form, 4 Ways (3, 2) & (-3, -4)
help plz:)
Answers
Answer:
[tex]let \: slope \: be \: s \\ s = \frac{( {y}^{1} - {y}^{o} ) }{( {x}^{1} - {x}^{o} ) } \\ s = \frac{( - 4 - 2)}{( - 3 - 3)} \\ s = \frac{ - 6}{ - 6} \\ s = 1[/tex]
I need this math problem done as soon as possible!
Answers
Answer:
See below
Step-by-step explanation:
Parent function:
y = 3ˣTransformed function:
y = 4(3)⁻²ˣ⁺⁸ + 6, (note. I see this as 8, sorry if different but it doesn't make any change to transformation method)Transformations to be applied:
f(x) → f(-x) reflection over y-axisf(-x) → f(-2x) stretch horizontally by a factor of 2f(-2x) → f(-2x + 8) translate 8 units rightf(-2x + 8) → 4f(-2x + 8) stretch vertically by a factor of 44f(-2x + 8) → 4f(-2x + 8) + 6 translate 6 units upRewrite the following expression using one or more properties of logarithms and evaluate? Plz help :)
Answers
Answer:
[tex]log( \frac{1}{ {10}^{ - 5} } ) = log( {10}^{5} ) = 5 log(10) = 5[/tex]
5 is the right answer.Find the equation in slope intercept form
(-8,-2) and (-4,6
Answers
Answer:
y = 2x + 14
Step-by-step explanation:
Answer:
y = 2x + 14
Step-by-step explanation:
Use the slope equation:
[tex]m = \frac{y2-y1}{x2-x1}[/tex]
[tex]m = \frac{6-(-2)}{-4-(-8)}\\m = \frac{8}{4}\\m = 2[/tex]
Next, find the y-intercept by subbing in one of the points and the slope into what you have so far in the equation:
(-8, -2)
y = mx + b
-2 = 2(-8) + b
-2 = -16 + b
-2 + 16 = b
b = 14
Now you have your final equation:
y = 2x + 14
The amount of Interest a store charges a customer for buying on the installment plan is a?
A) annual percentage rate
B sales tax
C unpaid balance
D) finance charge
Answers
annual percentage rate
  Can someone pleaseeee help if you’re correct I’ll give u brainlist
Answers
Answer:
Just about 3.6
Step-by-step explanation:
a² + b² = c²
√(a² + b²) = c
√(2² + 3²) = c
√(4 + 9) = c
√(13) = c
3.605551275 = c
c ≈ 3.6
Answer:
p = 3 as angle C and angle D are equal which means they are isoceles triangle and their base sides are equal i.e DB=CB so p. = 3
through: (-3,-5), parallel to y = 2x + 2
Answers
Answer:
y = 2x + 1
Step-by-step explanation:
Since you have an equation and a point, all you need to do is substitute the coordinates into the equation and then solve for the y-intercept (or "b"):
y = mx + b
y = 2x + 2
(-3, -5)
-5 = 2(-3) + b
-5 = -6 + b
-5 + 6 = b
b = 1
Now you have your final equation:
y = 2x + 1
*Remember that parallel lines have the same slope, so finding a new slope is not needed!
The ratio of the sides of two similar polygons is 3:2. The area of the smaller polygon is 24cm squared. What is the area of larger polygon
Answers
Answer: 36cm
Step-by-step explanation:
From the question, we are informed that the ratio of the sides of two similar polygons is 3:2 and that the area of the smaller polygon is 24cm squared.
Therefore, the area of the larger polygon would be calculated as:
= 24cm ÷ 2/3
= 24cm × 3/2
= 36cm
The sum of the measures of angles for a triangle is 180°. Find the value of x and then the measures of the 3 angles
Answers
Answer:
The value of x is 50
The measures of the 3 angles are 50°, 100°, 30°
Step-by-step explanation:
Let us solve the question
∵ The sum of the measures of the angles of a triangle is 180°
∵ The measures of the 3 angles of the given Δ are x°, 2x°, (x - 20)°
→ Add them and equate the sum by 180
∴ x° + 2x° + (x - 20)° = 180°
→ Add the like terms
∵ (x + 2x + x) + (-20) = 180
∴ 4x - 20 = 180
→ Add 20 to both sides
∵ 4x - 20 + 20 = 180 + 20
∴ 4x = 200
→ Divide both sides by 4 to find x
∴ x = 50
∴ The value of x is 50
To find the measures of the 3 angles substitute x by 50 in their expressions
∵ The measure of one angle is x
∴ The measure of the 1st angle is 50°
∵ The measure of the 2nd angle is 2x
∴ The measure of the 2nd angle = 2(50)
∴ The measure of the 2nd angle is 100°
∵ The measure of the 3rd angle is (x - 20)
∴ The measure of the 3rd angle = (50 - 20)
∴ The measure of the 3rd angle is 30°
∴ The measures of the 3 angles are 50°, 100°, 30°
Given the following diagram, find the missing measure. m 4 = 2x°, m 2 = (4/3)x°, m 3 = 20°, find x. 10 30 20 60
Answers
Answer:
B. 30 degrees
Step-by-step explanation:
Find the diagram attached
From the diagram:
Interior angles are m<3 and m<2
Exterior angle = <4
using the rule that says that the sum of interior angles is equal to the exterior angle we have:
m<2+m<3 = m<4
(4/3)x°+20 = 2x°
multiply through by 3:
4x° + 60 = 6x°
4x°-6x° = -60
-2x° = -60
x°= -60/-2
x° = 30°
Hence the value of x is 30 degrees
Julie’s Great Dane weighs 45 kg and Anne’s cat weighs 7 kg. How much bigger, as a percentage, is Julie’s dog?
Answers
Answer:
0.3%
Step-by-step explanation:
45kg-15kg=30kg
Percentage: 30kg = 0.3%
so 0.3%
hope it helps!
If 2a+4b=5 and a is equal to three times b, what is 3a?
Answers
Answer:
3A = 3(1 1/2) = 4 1/2
Step-by-step explanation:
2A + 4B = 5
A = 3B
2(3B) + 4B = 5 [substitute the A for the 3B]
10B = 5 so B = 1/2 [now plug the info in]
2A + 4(1/2) = 5
2A + 2 = 5 [subtract 2 from both sides of the equation]
2A = 3 [divide by 2 to isolate A]
A = 3/2 [now plug in the answers to check your work]
2(3/2) + 4(1/2) = 5
6/2 + 4/2 = 3 + 2 = 5
Divya wants to rent a car to drive for the weekend. The rental company has a special that allows her to rent it for $200 for the weekend, plus $0.07 per mile. Divya only has $230. Write an inequality, solve, and determine her limitations when renting.
Answers
Answer:
[tex]200 + 0.07m \leq 230[/tex]
A maximum of [tex]\approx[/tex] 428 miles is the distance what Divya can travel.
Step-by-step explanation:
Given that:
Rent to be paid for the car in the weekend = $200
Charges to be paid per mile = $0.07
Total money available with Divya = $230
To find:
The inequality as per her limitations and solution to the problem.
Solution:
Let the number of miles for which Divya can drive = [tex]m[/tex] miles
Charges for one mile = $0.07
Charges for [tex]m[/tex] miles = $0.07[tex]m[/tex]
Total charges for renting and [tex]m[/tex] miles = Rental charges + Operational charges
Total charges for renting and [tex]m[/tex] miles = $200 + $0.07[tex]m[/tex]
These are charges must be lesser than equal to the amount of money available with Divya.
Therefore, we can write:
[tex]200 + 0.07m \leq 230[/tex]
Subtracting 200 from both the sides:
[tex]0.07m \leq 30[/tex]
Dividing both sides with 0.07:
[tex]m \leq \dfrac{30}{0.07}\\m\leq 428.6[/tex]
Therefore, a maximum of [tex]\approx[/tex] 428 miles is the distance what Divya can travel.
By what number must be 566 be divided so as to give a quotient 15 and reminder 11?
Answers
Step-by-step explanation:
566 - 11 = 555
555 / 15 = 37.
The number is 37.
Answer:
[tex]\boxed{\pink{\sf \leadsto The \ required \ number \ is \ 37 . }}[/tex]
Step-by-step explanation:
We need to find the number By what number must be 566 be divided so as to give a quotient 15 and reminder 11.
So , let us take the number be x .
Now , we know that ,
[tex]\boxed{\red{\bf Dividend = Quotient\times Divisor + Remainder }}[/tex]
Here , 566 will be Dividend , 11 is remainder and 15 quotient . x will be the Divisor .
[tex]\implies Dividend = Quotient\times Divisor + Remainder \\\\\implies 566 = 15 \times x + 11 \\\\\implies 566 = 15x + 11 \\\\\implies 15x = 566 - 11 \\\\\implies 15x = 555 \\\\\implies x =\dfrac{555}{15}\\\\\underline{\boxed{\orange{ \tt \implies x = 37}}}[/tex]
Hence the required number is 37 .0.75x - y = - 2.1
0.6y 2.4x +9
Answers
Answer:
4x-3
Step-by-step explanation:
Yea
The third and fourth number in an exponential sequence 100 and 500. what are the first and second numbers in this sequence?
Answers
Answer:
4 and 20
Step-by-step explanation:
100 times 5 is 500. If we go backwards 500 ÷ 5 = 100.
100 ÷ 5 = 20. 20 ÷ 5 = 4.
An exponential sequence is a sequence that grows more every time. It would get really big really quickly.
The first and second numbers in this sequence is 4 and 20
Given that,
The third and fourth number in an exponential sequence 100 and 500.Based on the above information, the calculation is as follows:
[tex]= 500 \div 100[/tex]
= 5
And,
[tex]= 100 \div 5 = 20, \\\\20 \div 5 = 4[/tex]
Learn more: https://brainly.com/question/834969?referrer=searchResults
Select all ordered pairs that satisfy the function
y = 4x +3.
O (-1-1)
(211)
(4,7)
(71)
Answers
Answer:
(-1,-1 )
and (2,11)
Step-by-step explanation:
put first value to x and second value to y and see if y satisfy the equation
the real square root of -16
Answers
Answer:
ur answer is 4 hope it helps
Emily makes $24 per hour. She worked 80 hours of regular time for the last pay
period and 5 hours of overtime at $36 per hour.
a. What was her gross pay?
b. How much money in deductions was taken off her cheque if her net pay was
$1719.50?
C. What percent was taken off as deductions? (to one decimal place)
Answers
Answer:
A. The gross pay is $2100 (24×80)+(5×36)
B. 2100-1719.50 = $380.5
C. (1719.50/2100) × 100 = 81.9%
When the ? method , interest is charged only on the balance remaining in your account ?
A) annual percentage rate
B) unpaid balance
C) sales tax
D) finance charge
Answers
pls help i have to find the mistake they made when he solved the equation
2(x + 3) = 6
2x + 3 = 6
- 3 - 3
2x = 3
+2 +2
x = 1.5
Answers
Answer:
Mistake is 2x + 3 = 6. It should be 2x + 6 = 6. Therefore x = 0
Step-by-step explanation:
2(x + 3) = 6
Expand the bracket:
2x + 6 = 6
Subtract 6 from both sides:
2x = 0
Divide both sides by 2
x = 0
Una caixa plena de raim pesa 21 kilos. Si el raim que hi ha pesa 19 quilo, quant pesa la caixa buida
Answers
Aquesta pregunta és incompleta
Pregunta completa
Una caixa plena de raïm pesa 21 quilos. Si el raïm d’allà pesa 1.9 quilos, quant pesa la caixa buida
Answer:
7.6 quilograms
Step-by-step explanation:
Pas 1
Convertim el pes de la caixa completa de raïm a quilograms
1 lliura = 0.454 quilograms
21 lliures = x
Creu Multiplicar
x = 21 × 0.454 quilograms
x = 9.52544 quilograms
Aproximadament 9.5 quilograms
Ens van dir que el raïm d’allà pesava 1.9 quilos,
Per tant, el pes de la caixa buida és
= 9.5 - 1.9
= 7.6 quilograms
El pes de la caixa buida és de 7.6 quilograms
Qustion 21
Ranjan walks a distance of 5 km towards East,
then turns to his right and walks for 4 km. He
then turns left and walks for 4 km. At this
point he turns to his right and walks for 2 km.
He turns right and walks 1 km. How many
kilometers is he from the starting point?
A 10 km
Answers
Answer:
8km
Step-by-step explanation:
Going by the sketch attached in the picture, the distance between starting point and present position is 8 km.
The sketch is crucial to determine the answer to the question, Hence, kindly check the picture attached for reasoning being the choice of result.
Which facts could be applied to simplify this expression? Select three options.
(Negative 5 x minus 3 y) minus (negative x minus 3 z)
To subtract like terms, subtract the coefficients, not the variables.
Like terms are terms that contain the same variable, raised to the same power.
The simplified expression is Negative 6 x minus 3 y + 3 z.
The simplified expression is Negative 4 x minus 3 y + 3 z.
Negative (negative x) is equivalent to Negative x, so Negative 5 x minus x = negative 6 x
Answers
Answer:
Negative 4 x minus 3 y + 3 z.
Step-by-step explanation:
We need to simplify the given expression : (-5x-3y)-(-x-3z)
Here, x,y and z are variables.
Combining like terms, we get :
(-5x-3y)-(-x-3z) = (-5x-3y)+x+3z
= (-5x+x)-3y+3z
= -4x-3y+3z
Hence, the equivalent expression is -4x-3y+3z. Hence, the correct option is (b) "The simplified expression is Negative 4 x minus 3 y + 3 z".
Answer:
a,b,d
Step-by-step explanation: