[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]
Make a the subject of the formula where a is positive: a 6(a - 4b) = 2ac + 4d
Answer:
[tex]{ \tt{6(a - 4b) = 2ac + 4d}} \\ \\ { \tt{6a - 24b = 2ac + 4d}} \\ \\ { \tt{6a - 2ac = 4d + 24b}} \\ \\ { \tt{a(6 - 2c) = 4d + 24b}} \\ \\ { \boxed{ \tt{ \: a = \frac{4d + 24b}{6 - 2c} }}} \\ [/tex]
Use the division expression 8/12÷9/12.
Answer:
Step-by-step explanation:
please help on number 8!! it would be much appreciated
Answer:
a.) 135 degrees
b.) 45 degrees
c.) 45 degrees
Step-by-step explanation:
Use this link to see a visual representation on how to solve for these types of angles, it lets you click on any type of angle and see how it corresponds to other angles within the parallel line and traversal, give it a try!
https://www.mathsisfun.com/geometry/alternate-exterior-angles.html
help with this question
Answer:
option D is correct
x=O and x=-8
Juan cut StartFraction 5 Over 12 EndFraction of a yard of cloth into 5 pieces of equal length. What was the length of each piece of cloth?A. StartFraction 1 Over 60 EndFraction of a yardB. StartFraction 1 Over 25 EndFraction of a yardC. StartFraction 1 Over 12 EndFraction of a yardD. One-fifth of a yard
Answer:
It is c
Step-by-step explanation:
what is a set? describe the use of braces for listing the members of a set.
Answer:A set is a collection of objects that have something in common or follow a rule. The objects in the set are called its elements. Curly braces are used to indicate that the objects written between them belong to a set
Answer: A set is a collection of objects that have something in common or follow a rule. The objects in the set are called its elements.
Curly braces are used to indicate that the objects written between them belong to a set.
What is set?A set is a collection of objects that have something in common or follow a rule. The objects in the set are called its elements.
here, we have,
N={1,2,3,4,.......}
Determine the sets of natural number
Represent this set with letter N
From definition of natural numbers, they are integer numbers starting from 1;
In other words: 1,2,3,4,5, and so on.
To represent this as a set of N, we have
N={1,2,3,4,.......}
The ..... means that the counting still continues.
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please help! & please explain your answer!!
Answer:
9Step-by-step explanation:
Plan A remains with $450 stable charge and Plan B is:
200 + 30x, with x being the number of physical training sessionsIn order Plan B to be cheaper we set an inequality:
200 + 30x < 45030x < 250x < 250/30x = 8.33 < 9Hayami was riding her bike on a loop that is 15/16 mile long. she rode for 3/4 mile and then stopped to rest she rode another 1/8 mile and then has a flat tire. how far does Hayami have to walk her bike to complete the loop?
A.1/16 mile
b.1/32
c. 3/16
d. 1/8
1/16 mile
3/4 = 12/16
1/8 = 2/16
12/16 + 2/16 = 14/16
1/16 Mile left to walk
Hayami has to walk her bike Option A) 1/16 mile to complete the loop.
Hayami rode a total of 3/4 + 1/8 = 7/8 mile before getting a flat tire. To complete the loop, she needs to cover the remaining distance of the loop, which is
= 15/16 - 7/8
= 15/16 - 14/16
= 1/16 mile.
Thus, Hayami has to walk her bike 1/16 mile to complete the loop. Therefore, the correct answer is 1/16 mile.
To find out how far Hayami has to walk her bike to complete the loop, we need to calculate the remaining distance after she rode her bike before stopping for a rest and getting a flat tire.
1. First, we calculate the distance Hayami rode before stopping for a rest:
She rode 3/4 mile.
2. Then, we calculate the distance she rode after stopping for a rest but before getting a flat tire:
She rode 1/8 mile.
3. Now, let's find out the total distance she rode:
= 3/4 + 1/8
= 6/8 + 1/8
= 7/8 mile.
4. The length of the loop is \(15/16\) mile.
5. To find the remaining distance to complete the loop, subtract the distance she rode from the total loop length:
= 15/16 - 7/8
= 15/16 - 14/16
= 1/16 mile.
6. Therefore, Hayami has to walk her bike 1/16 mile to complete the loop.
In conclusion, the correct answer is 1/16 mile (Option A).
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Complete Question
Choose the correct answer from the given options:
Hayami was riding her bike on a loop that is 15/16 mile long. she rode for 3/4 mile and then stopped to rest she rode another 1/8 mile and then has a flat tire. how far does Hayami have to walk her bike to complete the loop?
A.1/16 mile
b.1/32 mile
c. 3/16 mile
d. 1/8 mile
Three consecutive integers add up to 51. The integers are *
16,17,18
15,16,17
17,18,19
18,19,20
Answer:
1st option
Step-by-step explanation:
let the three consecutive integers be n , n + 1 , n + 2 , then adding gives
n + n + 1 + n + 2 = 51, simplifying
3n + 3 = 51 ( subtract 3 from both sides )
3n = 48 ( divide both sides by 3 )
n = 16
n + 1 = 16 + 1 = 17
n + 2 = 16 + 2 = 18
The 3 consecutive integers are 16, 17, 18
person who answers this gets brainliest
If Manny the Martian's shadow is 17.5 ft. in length and the shadow of a yard stick sitting perpendicular to the ground is 7.5 ft., what is Manny's height?
A 8 ft
B 5.5 ft
C 6 ft
D 7 ft
Answer:
letter B.
Step-by-step explanation:
5.5ft
hope it helps you
f) create a residual plot for your data.
g) does your residual plot show that the linear model from the regression calculator is a good model?
h) using your equation estimate the gpa of a student who studies for 15 hours a week.
PLSSSSS NEED HELP
Answer: Consider the plot created from the residuals of a line of best fit for a set of data. Does the residual plot show that the line of best fit is appropriate for the data? Yes, the points have no pattern.
Step-by-step explanation:
theres 6 bags and 185 rasins how many are in each bag
Answer:
1110
Step-by-step explanation: If it was multiplication it would 1110 but you cat divide 185 by 6 so if it was 186, not 185 and you divided by 6 you would get 31 hope this helps
What is 29 divided by 0174620
0.0001660749
29÷0174620= 0.0001660749
hope this helped you- have a good day bro cya)
Answer:166.0749055091055
PlEaSe HeLp.
i'M VeRy CoNfUsEd.
Answer:
For first page I belive both of the answer are b. The second page I believe b and c
Step-by-step explanation:
Answer:
answers are a,b,a,d
Step-by-step explanation:
Can anyone help me ?
Answer:
x=7.5
Step-by-step explanation:
15÷2=7.5
A different store needs to make at least $20,000 to make a profit in March. They average $685 a day for the month. James used rounding and estimation to say, “$685 is almost $700. $700 × 30 days is $21,000. I think it is going to be a close call!” What do you think?
what is 53 + x = x + 53
- BRAINLIEST answerer
4/5 - 3/8
plz help me might give brainlist
Answer:
17/40
Step-by-step explanation:
4/5-3/8=32/40-15/40
=17/40
Answer:
Solution:
17/40 Alternative form 0.425
Step-by-step explanation:
Explanation how:
Write all numerators above the least common denominator 40
32-15/40
hope to help
Identify the center and radius of the circle with equation x2 + y2 - 8x - 4y - 5=0.
center:
radius:
Instructions: Evaluate f(x) = 2x + 5 for the following and enter
your answer in the space provided. Do not include any spaces in
your answer.
f(-1) =
f(2)=
f(0) =
f(z)=
Answer:
f(1) = 3
f(2) = 9
f(0) = 5
f(z) =2z + 5
Step-by-step explanation:
f(x) = 2x +5 let x = -1; 2, 0, z and simplify if you can.
f(-1) = 2(-1) +5 ; -2 +5
f(2) = 2(2) + 5; 4 + 5
f(0) = 2(0) + 5; 0 + 5
f(z) = 2z +5; 2z + 5
Write the equation of the line in point-slope form.
Answer:
y= 4/3x+2
Step-by-step explanation:
the y intercept is at 2 and you do rise over run for m
Change 32/6 to a mixed number in lowest terms .
Answer:
5 1/3
Step-by-step explanation:
( I’ll give you brainliest!!!) Find the length of the third side. If necessary, write in simplest radical form.
Answer:
The Pythagorean Theorem, a2+b2=c2, a 2 + b 2 = c 2
I dont know the exact positions to put the lengths, but tell me if this helps!
The price of a car that was bought for $20,000 has depreciated 8% yearly.
Write a model to describe the value of the car.
A.f(t)=20,000(0.92)t
B.f(t)=20,000(1.92)t
C.f(t)=20,000(0.08)t
D.f(t)=20,000(1.08)t
Step-by-step explanation:
[tex] \sf{ \longmapsto \: D.f(t)=20,000(1.08)t}[/tex]
the angles of a triangle measure 4 degrees,86 degrees, and 90 degrees.
Answer:
It is a right angled triangle.
Step-by-step explanation:
Because it has 90° angle in it.
Hope it helps..!!<3
(Type an ordered pair, using integers or decimals)
Answer:
(0,-3) is the correct answer because e-3 is on the y axis
Answer:
-5,0
Step-by-step explanation:
The x-intercept is where the line intercepts the x-axis
Please answer number 5 only
Answer:
y=3
x=2
Step-by-step explanation:
3 x 18 =54
2 x 12 = 24
54+24=78
Answer:
x = 2; y = 3
Step-by-step explanation:
x + y = 5
12x + 18y = 78
Do system of equation
-> x = 2; y = 3
Maizes grandmother open the second account with $75 for her when she was born the account is 4% simple interest each year when Maize is 10 years old how much will she have in the savings account?
Answer:
She'd have $45
Step-by-step explanation:
4% of 75 is 3 dollars.
So 3 dollars per year and after 10 years the account lost $30 to the simple interest.
3*10(AmountOfYears)=30
So 75-30=45
$45 would be left in the savings account.
A count went from 605 to 203. What was the approximate percent decrease? Round the numbers to find an estimate of the percent decrease.
A. The percent decrease was approximately 25%.
B. The percent decrease was approximately 33%.
C. The percent decrease was approximately 50%.
D. The percent decrease was approximately 66%.
IT'S D
HOPE THIS HELP MARK ME BRAINLIST
What is the difference between 4 and -5?
Answer:
l-5l+l4l=9
l . l means total value from zero.