![Simplify: [5(25)^n+1 - 25 (5)^2n]/[5(5)^2n+3 - (25)^n+1]](https://brainimage.s3.us-east-005.backblazeb2.com/contents/attachments/tkKSFIAMVHsOjvxRLa4j2b5yXuBqOKjM.jpeg)
Answers
[tex] \green{\large\underline{\sf{Solution-}}}[/tex]
Given expression is
[tex]\rm :\longmapsto\:\dfrac{5 \times {25}^{n + 1} - 25 \times {5}^{2n} }{5 \times {5}^{2n + 3} - {25}^{n + 1} } [/tex]
can be rewritten as
[tex]\rm \: = \: \dfrac{5 \times { {(5}^{2} )}^{n + 1} - {5}^{2} \times {5}^{2n} }{5 \times {5}^{2n + 3} - {( {5}^{2} )}^{n + 1} } [/tex]
We know,
[tex] \purple{\rm :\longmapsto\:\boxed{\tt{ {( {x}^{m} )}^{n} \: = \: {x}^{mn}}}} \\ [/tex]
And
[tex] \purple{\rm :\longmapsto\:\boxed{\tt{ \: \: {x}^{m} \times {x}^{n} = {x}^{m + n} \: }}} \\ [/tex]
So, using this identity, we
[tex]\rm \: = \: \dfrac{5 \times {5}^{2n + 2} - {5}^{2n + 2} }{{5}^{2n + 3 + 1} - {5}^{2n + 2} } [/tex]
[tex]\rm \: = \: \dfrac{{5}^{2n + 2 + 1} - {5}^{2n + 2} }{{5}^{2n + 4} - {5}^{2n + 2} } [/tex]
can be further rewritten as
[tex]\rm \: = \: \dfrac{{5}^{2n + 2 + 1} - {5}^{2n + 2} }{{5}^{2n + 2 + 2} - {5}^{2n + 2} } [/tex]
[tex]\rm \: = \: \dfrac{ {5}^{2n + 2} (5 - 1)}{ {5}^{2n + 2} ( {5}^{2} - 1)} [/tex]
[tex]\rm \: = \: \dfrac{4}{25 - 1} [/tex]
[tex]\rm \: = \: \dfrac{4}{24} [/tex]
[tex]\rm \: = \: \dfrac{1}{6} [/tex]
Hence,
[tex]\rm :\longmapsto\:\boxed{\tt{ \dfrac{5 \times {25}^{n + 1} - 25 \times {5}^{2n} }{5 \times {5}^{2n + 3} - {25}^{n + 1} } = \frac{1}{6} }}[/tex]
Related Questions
The probability that a red block is selected from a bucket is
3/8, and the probability that a blue block is selected is 2/8.
What is the probability that a red block or a blue block is
selected?
a) 1
b) 1/2
c) 5/8
d) 6/8
Answers
Answer:
5/8
Step-by-step explanation:
Since we don't know what the other color (s) are, all we need to do to determine the probability is add the two fractions, and that is your probability.
Answer:
5/8
Step-by-step explanation:
The probability of a red block shows 3/8. This means there are 8 blocks total and only 3 of them are red.
The probability of a blue block shows 2/8. Again there are 8 total blocks and only 2 are blue.
So the total number of blocks remains the same....8
The total of red and blue blocks is 3 + 2 = 5
So the probability would be 5/8
What is the 40th term of the arithmetic sequence?
21, 18, 15, 12, 9,...
−96
6
138
−99
Answers
Answer:
We start off with 21 as the first term. So a1 = 21
The common difference is d = -3 because we subtract 3 each time to get from one term to the other (eg: 21 to 18 is minus 3)
The nth term of an arithmetic sequence is found by using this formula
an = a1 + d(n-1)
let's plug in the values we have so far to get
an = 21 + (-3)(n-1)
an = 21 - 3(n-1)
an = 21-3n+3
an = -3n+24
Why do this? Well it's helpful so we can find any term in the formula we want. In this case, we want the 40th term. So just plug in n = 40 from here and you're done
an = -3n+24
a40 = -3*40+24
a40 = -96
pointing you to the answer of choice B) -96
find the distance from the origin to
the point (7,4).
Answers
Answer:
8912
Step-by-step explanation:
don't use awnser plz
Can someone help me please ?
Answers
Answer:
-4[tex]y^{5}[/tex]
Step-by-step explanation:
-8[tex]y^{10}[/tex]/2[tex]y^{5}[/tex] = -8/2 * [tex]y^{10 - 5}[/tex]
= -4[tex]y^{5}[/tex]
it won't let me answer all the word's all i can give is: 8/2 = -8/2 *
= -4
3/4 of a number 120 What is three-eights of the number? please answer no point scamming i will give you brainiest
Answers
Answer:
60Step-by-step explanation:
Let the number is x.
3/4 of a number is 120:
3/4x = 120x = 120*4/3 = 160What is three-eights of the number:
160*3/8 = 60rewrite the equation in slope-intercept form 5x - 6y = 12
Answers
Answer:
M = [tex]\frac{5}{6}[/tex] Is correct answer
Step-by-step explanation:
Write in slope-intercept form, y = m x + b.
m = [tex]\frac{5}{6}[/tex]
Graph in pic
(Hope this helps can I pls have brainlist (crown)☺️
(x + 1) divided by 6y
pls show working out pls thx.
Answers
Natural logarithm (redirect from LN(1+X))including: ln ( 1 + x ) = x 1 1 − x 2 2 + x 3 3 − x 4 4 + x 5 5 − ⋯ = x 1 − 0 x + 1 2 x 2 − 1 x + 2 2 x 3 − 2 x + 3 2 x 4 − 3 x + 4 2 x 5 − 4 x + ⋱ {\displaystyle32 KB (5,254 words) - 16:48, 18 October 2021
PLSSS HLEPP ME OUTT ITS URGENTTTT!!
Answers
increase in x results in the decrease in y
Answer:
• Decrease in x results in the increase in y
• Increase in x results in the decrease in y
If someone answers this you getting 25 points and brainliest :D
Answers
the answer Is 0.24
Step-by-step explanation:
2.1 times 4.4 is
9.24
3.6 divided by 0.4 is
9
9.24 - 9
= 0.24
Remeber guys, we need to use pemdos. In this case we need to do 1. Multiplication
2. Division
3. Subtraction
We cannot do subtraction or division first. We need to go by order.
Will give brainliest to the correct answer
Write each function in slope-intercept form
:9.4y=−8x−10
10. −5x+ 2y=−10
Answers
Step-by-step explanation:
9) y= -2x - (5/2)
10) y = -5 + (5/2)
i need help with get more math
Answers
Answer:
I'm not sure I understand but if you want more math to do look up Quizlet and do some of those tests
State the domain and range of the following function.
Answers
Answer:
Answer C
Step-by-step explanation:
seeing as how the x coordinates of the points are 2,3,4,6,7, we know that the answer must have these numbers, and only these numbers, as the domain. The only answer that has that is answer C.
Simplify the expression to a + bi form:
(1 – 8i) + (8 + 6i)
Answers
-
3
How many
foot pieces of
8
wood can you cut from a
board that is 1 7/8 feet long?
Answers
Step-by-step explanation:
17×8=136
136×8=1088
sorry if it's wrong I actually have a flu and my brain ain't working sorry but please mark me the brainiest
Answer:
1 full piece
Step-by-step explanation:
there are 12 inches in a foot so there are 12/1 x 15/8 inches in 1 7/8 feet, which is:
22 1/2 inches
22.5 ÷ 12 = 1.875 pieces or 1 full piece
The total area of Russian is about 20,000,000
Answers
Answer: 19,990,000 times
Step-by-step explanation: Land area of Russia = 20000000
Land area of Puerto Rico = 10000
20000000 - 10000 = 19,990,000
[tex] \sqrt[5]{1150? } = [/tex]
please give me a answer please
Answers
If you only need 1 d.p then it’s 4.1
Match the reasons with the statements given.
Given:
Triangle ABR
Prove:
<1 = <2
(< means angle)
Pls help me
Answers
Answer:
Question about the triangle, what type of triangle is it?
Step-by-step explanation:
MARKING BRAINLIEST: Can someone create a online graph - More information in the screenshot below
Answers
Answer:
Step-by-step explanation:
make a graph of what we need more of an explanation
7x+3y=8
3x-4y=14
solve by elimination method
Answers
Answer:
{x,y} = {2,-2}
Step-by-step explanation:
System of Linear Equations entered :
[1] 7x + 3y = 8
[2] 3x - 4y = 14
Graphic Representation of the Equations :
3y + 7x = 8 -4y + 3x = 14
Solve by Substitution :
// Solve equation [2] for the variable x
[2] 3x = 4y + 14
[2] x = 4y/3 + 14/3
// Plug this in for variable x in equation [1]
[1] 7•(4y/3+14/3) + 3y = 8
[1] 37y/3 = -74/3
[1] 37y = -74
// Solve equation [1] for the variable y
[1] 37y = - 74
[1] y = - 2
// By now we know this much :
x = 4y/3+14/3
y = -2
// Use the y value to solve for x
x = (4/3)(-2)+14/3 = 2
Solution :
{x,y} = {2,-2}
g(x) = 3x-1
f(x) = x + 5.
find g (f (4)
Answers
Answer:
g(x)=3
Step-by-step explanation:
Answer:
26
Step-by-step explanation:
g(x) = 3x-1
f(x)= x+5
g(f(4)
plug 4 into f
f(4)
now apply x+5
f(4)=4+5=9
plug 9 into g
g(9)
now apply 3x-1
g(9)=3(9)-1
3 ×9= 27
27-1=26
hence the answer is 26
(sorry if I'm wrong I just finished this topic myself)
If you can help please do! Thank you!
Answers
Answer:
see explanation
Step-by-step explanation:
The diagonals of a parallelogram bisect each other , then
CO = OA = b
DO = OB = a
(a)
CA = CO + OA = b + b = 2b
(b)
DC = DO + OC = a - b
(c)
CB = CO + OB = b + a = a + b
Write the equation of a line, in slope intercept form,
that has a slope of 5 and an intercept of (0,-3).
Answers
Answer:
y = 5x -3
Step-by-step explanation:
Slope intercept form is y = mx + b
m = slope
b = the y intercept
The problem gives you a slope of 5, and it gives you the y interecept of -3.
Plug those into slope intercept form:
y = 5x -3
please help I will make Brainliest if correct (show working)
Answers
Answer:
I beleive X=2
Area is 24
Step-by-step explanation:
X=2 because the side with B has 4cm and on the other it has 6 but the 4 can be put into 6 and 6-4 is 2 if that made any sense
The area is 4 times 2= 8 and then 8 times 2 is 16
16+8=24
write the equation
it passes through (0,-2) and is perpendicular to the graph of y=5x+7
Answers
Step-by-step explanation:
the line passes through (0,-2) and perpendicular to the graph of y=5x+7.
solution :
the slope = -1/5
the equation :
y+2 = -1/5 (x-0)
y = -1/5x - 2
A company orders 28 box lunches from a deli for 204 $.40 if each box lunch cost the same amount what is the unit cost of each box lunch
Answers
The total price is 204.40 for 28 boxes. So we need to divide the total price of how many were bought.
$204.40 / 28 = $7.8 for each box
a recreational club charges a one time $20 membership fee and $3 for use of the pool
i just need an answer and step by step work of it someone help me please.
Answers
Answer:
what is the question asking?
can someone pls help me with number 5 pls show your work so i can understand thanks
Answers
Step-by-step explanation:
Let's represent Aaron's age with x and
Charlene's age with x+8
x+x+8=44
2x+8=44
2x=44-8
2x=36
x=36÷2
x=18
Aaron is 18 years old.
While Charlene is 18+8=26 years old.
Hope this helps!
is 5x - 4y = 3 linear?
Answers
Answer:
Yes
Step-by-step explanation:
The highest exponent is 1.
Answer:
Yes 5x -4y= 3 is a linear
Step-by-step explanation:
It is a linear because it makes a straight line when it's on a graphed.
Hope this was helpful :)
HELP ASAP SHOW YOUR WORK AND EXPLAIN HOW YOU GOT YOUR ANSWER-NO LINKS OR JOKING AROUND
4. The steps for solving 7x + 3 = 52 are shown. Explain how each step helps solve the equation. Include the phrases, "Isolate the variable by _____," "Simplify," and "Isolate the variable term by _____" in your answers.
Answers
Answer:
x = 7
Step-by-step explanation:
Rearrange the equation to make x the subject.
Original:
7x + 3 = 52
subtract 3 from both sides
7x = 52 -3
7x = 49
Divide both sides by 7
x = 49/7
x = 7
!
Darren is training for a triathlon. Each week, he goes to the gym for a maximum of 20 hours. He spends at least 8 of those hours weightlifting (x). He wants to spend no more than 15 hours doing cardio exercises (y). Write a system of linear inequalities that represents the restrictions of this scenario.
Answers
The graph of the equations was plotted using geogebra graphing and attached.
Let x represent the hours weightlifting and y represent the hours doing cardio exercises.
Since he spend a maximum of 20 hours, hence:
x + y ≤ 20 (1)
Also, he spends at least 8 of those hours weightlifting, hence:
x ≥ 8 (2)
He wants to spend no more than 15 hours doing cardio exercises, this is:
y ≤ 15 (3)
The graph of the equations was plotted using geogebra graphing and attached.
Find out more at: https://brainly.com/question/17178834