![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
help please! no links!
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Answers
Answer:
A
2,3 3,4.5 5,7.5
B
every 1:1.5
C
3,4.5 4,6 5,7.5
Step-by-step explanation:
because this is eqauling to all of the numbers
112°
?
find the measure of each angle indicated. the angle is supplementary.
Answers
Answer:
68
Step-by-step explanation:
Scooter rental company A charges an initial fee of $3 plus $1.15 for every hour. Scooter rental company B charges $1.75 for every hour. A customer finds that after h hours, the scooter rental companies will cost the same.
Which equation represents this situation?
1.75h+1.15h=3
1.75h=3−1.15h
1.15h=3+1.75h
1.15h+3=1.75h
Answers
Answer:
This is a little late but it's D. 1.15h+3=1.75h
Step-by-step explanation:
I took this test
to write
algebraically
following expressions:
the
1. Double an X number.
2. Triple an X number.
3. Double a number x plus 5.
4. The square of the triple of a
number x.
5. Three-quarters of a
number x.
Answers
Answer:
1. 2x
2. 3x
3. 2x+5
4. (3x)^2
5. 3\4(x)
I hope it makes sense
have a great day
if any questions pls ask
can anybody give me solving steps?
Answers
Answer:
angle relationship: same-side interior
value of x: 40
Step-by-step explanation:
the horizontal lines are parallel and the vertical line is the transversal, so 3x+x+20=180. combine the x's and subtract 20 from both sides to get 4x=160. then divide both sides by 4 to get x=40.
ASAP NEED HELP PLEASE 70 points ?!!!!
Answers
Answer:
f(1) = 5Step-by-step explanation:
Use the given formula and substitute the value of x:
f(x) = 4 + xf(1) = 4 + 1 = 5f(1)
4+15Done
14/25, 29/50, 53/100, 13/20, 3/5. Convert them into decimals
Answers
Answer:
14/25=0.56
29/50=0.58
53/100=0.53
13/20=0.65
3/5=0.60
Find m Give explanation please
Answers
Answer:
m < FGN = 88°
Step-by-step explanation:
The exterior angle theorem states that the measure of each exterior angle of a triangle is equal to the sum of the opposite and non-adjacent interior angles (also known as remote interior angles).
Given the exterior angle, m <FGN = (7x + 18)°, and the two remote interior angles, m < E = 38° and m < F = (6x - 10)°:
The following equality statement can be established according to the exterior angle theorem:
m < E + m < F = m <FGN
38 + 6x - 10 = 7x + 18
Combine like terms:
28 + 6x = 7x + 18
Subtract 6x from both sides:
28 + 6x - 6x = 7x - 6x + 18
28 = x + 18
Subtract 18 from both sides:
28 - 18 = x + 18 - 18
10 = x
Next, substitute the value of x = 10 into the equality statement to determine whether it is the correct value of x, and to find the measures of < FGE and < F.
m < E + m < F = m <FGN
38° + (6x - 10)° = (7x + 18)°
38 + 6(10) - 10 = 7(10) + 18
38 + 60 - 10 = 70 + 18
88 = 88 (True statement).
Therefore, m < FGN = 88°
A 56-inch board is cut into two pieces. One piece is three times the length of the other. Find the length of the shorter piece.
Answers
Answer:
14-inch
Step-by-step explanation:
let the length of shorter piece be x
x+3x=56
4x=56
x=56/4
x=14
PLSSSS HELPPP ILL MARK BRAINLIEST SOMEONE PLSSSSSS!!!!!!!!!
Answers
Answer:
B
Step-by-step explanation:
because if you multiply the denominators
find the value of 7x+5 given that -2x+7=5. simplify your answer as much as possible
Answers
Answer:
12
Step-by-step explanation:
-2x + 7=5
or, 7-5=2x
or, 2=2x
or, 2/2=x
or, 1=x
Then,
7x+5
=7×1+5
=7+5
=12
Answer:
x=1
Step-by-step explanation:
-7 both sides that will give you -2
-2x=-1 divide by -2 and u will get on i think that what you were asking
Hey!
Need help please...
[tex]\sf{Simplify~ 6x[/tex] ÷ [tex]\sf{23 = 0.[/tex]
answers/w explanation ✅ Nonsense answers, that's not the question I ask for will be reported.
Answers
Hey there!
6x ÷ 23 = 0
6x = 23 × 0
6x = 0
x = 0/6
x = 0
Hope it helps ya!
Note :- There's a latex error so I think this was the question you meant ~~.
Answer:
[tex] \frac{6x}{23} = 0[/tex]
[tex]6x = 0 \times 23[/tex]
[tex]6x = 0[/tex]
[tex]x = \frac{0}{6} [/tex]
[tex]x = 0[/tex]
What is the surface area of a cube if it has one side that is 40 cm
Answers
3x - 2y = -14
Standard Form
Slope- Intercept Form
Help????
Answers
Please help me with this geometry
Answers
Answer:
no
Step-by-step explanation:
!! Fake answers will be reported
Find angle 5& 6 too
Answers
Answer:
x = 10
y = 5
Angle 1: 80 degrees
Angle 2: 45 degrees
Angle 3: 100 degrees
Angle 4: 35 degrees
Angle 5: 35 degrees
Angle 6: 45 degrees
Angle 7: 100 degrees
Step-by-step explanation:
Since we know angle 1 is equal to 80, we can say that angle 7 is 100, since a line makes 180 degrees. Because of the congruence statements, we can assume angle 3 is also 100 degrees. That means, that out of the 360 degrees that make up a 4 sided shape, we are left with 160. Those 160 are shared with angles 2,4,5 and 6.
To find these, we need to find 5 and 6. But we need to find x before we can solve for those. So take the equations from 5 and 6 to solve for x.
(3x+5)+(5x-5)+100=180
(3x+5)+(5x-5)=80
8x=80
x=10
Now plug x in to solve for angle 5 and 6
3(10)+5 = 35. Angle 5
5(10)-5 = 45. Angle 6
Now, because we know that there are only 160 degrees left to share between angles 2,4,5,6 we can say that angles 2+5=80 and 4+6=80. We already figures out what angle 5 and 6 are, so just substitute and solve.
(angle 2)+35 = 80
(angle 2) = 45 degrees
(angle 4)+45 = 80
(angle 4) = 35 degrees
To solve for y, set angle 7 equal to 100 degrees:
100 = y^2 + 15y
100 = y(y+15)
y = 5
The oldest elephant at a zoo eats 162 pounds of hay per day. This elephant eats 3 times as much hay as the youngest elephant. How much hay does the youngest elephant eat per day?
A 54 pounds
B 59 pounds
C 53 pounds
D 64 pounds
Answers
Answer:
A.54
Step-by-step explanation:
because 162 divided by 3 equal 54.3
a girl that is 5ft tall casts a shadow 4ft long. at the same time, a tree casts a shadow 24 ft long. how long is the tree?
Answers
Answer:
25 Feet
Step-by-step explanation:
Im sorry if i am wrong, but it is 25 because the girl is 5 feet, and one feet less of a shadow. So it is obvious to me that the tree is 1 foot larger.
Let f(x) = 3x + 7.
Find f '(x).
Answers
The inverse of f(x) is when you switch the position of the x's and y's (or f(x))
x=3y+7, and then isolate the y so you get a normal function
(x-7)/3
Izzati, Ai Ling, Rina and Susan share some stamps. Izzati and Ai ling take 1/4 and 1/8 of the total number of stamps respectively. After that, Rina takes 7/10 of the remaining stamps. Eventually, all the remaining stamps are taken by Susan. If Susan gets 42 stamps, find the total number of stamps originally.
Answers
Step-by-step explanation:
Assuming that the total stamp is x
According to the question
Izzati's stamps is 1/4
Ailing's number of stamps is 1/8
X= 1/4 x 1/8 = 5/8 - the remaining stamps.
Rina’s number of stamps is 7/10 x 5/8 = 35/80 x
5/8 x 35/80 = 15/80 - (Susan's stamps)
According to the question
15/80 = 42
X: 224
the total number of stamps originally is 224.
Eric has 240 coins in his collection 11/20 are pennies and 4/40 are nickels
Answers
Answer:
There would be 36 coins left
Step-by-step explanation:
I don't know if that was the question but you would do:
11/20x2=22/40
22/40+4/40=26/40
26/40=13/20
One twentieth of 240 is 12
12x3=36
Hope this helped
Which of the following is not a perfect cube?125729225512
Answers
Answer: if you meant: 125, 729, 225, 512.
The answer is 225
Step-by-step explanation:
[tex]\sqrt[3]{125}[/tex] = 5
[tex]\sqrt[3]{729}[/tex] = 9
[tex]\sqrt[3]{512}[/tex] = 8
[tex]\sqrt[3]{225}[/tex] = 6.08220199557
the temperature of an enclosure for a pet snake should be about 80f, give or take 5. find the maximum and minimum temperatures
Answers
Answer:
The max is 85F
The min is 75F
Step-by-step explanation:
Happy To Help :)
May I please receive help?
Answers
Answer:
what u will recieve
Step-by-step explanation:
please telle
What is the surface area in square inches of a cube with a side 7
inches long?
10
Answers
Answer:
28
Step-by-step explanation:
7x4
Answer:
249 inches
Step-by-step explanation:
a cube is equal on all sides so if one side is 7 all sides are 7, if you multiply 7 by 7 you get 49 but that's just one face of the cube, there are 6 faces on a cube so 49 x 6 is 249
Find the slope of the line satisfying the following conditions.
vertical through (6, -7)
Answers
Explanation:
The slope of any vertical line is always undefined. This is because [tex]\text{slope} = \frac{\text{rise}}{\text{run}}[/tex], and the "run" portion is 0. The run represents the change in x, but we don't have a change in x for vertical lines. The x value is always some constant.
So this is why the run is 0, and it leads to a division by zero error, causing an undefined slope.
(Inscribed Angles)
Find m∠N.
Answers
Answer:
x=9 y=3
Step-by-step explanation:
because 5x+9=6x and 6y-1=3y+8
x=9 y=3
branlist please
32 is 4 times as much as what number
Answers
Answer: 8
Step-by-step explanation:
The 4 times of the number 8 results to 32.
What is Algebra?A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.
Variables are the name given to these symbols because they lack set values. In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.
Given:
32 is 4 times as much as what number
let the number be x.
So, 4 times of x = 32
4x = 32
Divide both side by 4.
4x/4 = 32/4
x= 8
Hence, the 4 times of the number 8 results to 32.
Learn more about algebra here:
https://brainly.com/question/24875240
#SPJ3
What is the slope of a line that is parallel to the given line
Answers
the slope of the parallel line would also be: -3/2
Hope this helps!!
Answer:
The slope of the parallel line is -3/2
Step-by-step explanation:
Calculate the slope using rise over run then simplify.
-6/4 , -3/2
Will give 30 points, please don't answer just for them
Wilson bought fruit that weighs 2 and 1 over 2 pounds. How many ounces does the fruit weigh? Show your work.
Answers
Answer:
1 that weighs 2pounds and 3 pounds,
Step-by-step explanation:
16 ounces in a pound
16x2 and 16x3
32
48