[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]
12 cm
14 cm
1
-
Find volume
Answer:
Volume of cylinder = 6,330.24 cmSolution:
Volume of cylinder = area of base × altitude
Volume = πr² × altitude
V= 3.14 × 12² × 14
V = 3.14 × 144 × 14
V = 6,330.24 cm
A line passes through point (-2, 5) and has a slope of 3. Points A(x 3) and B(-2, y lie on the line.
The value of xis
and the value of yis
Answer:
x = -8/3
y = 5
Step-by-step explanation:
Finding the equation of the line:
y = 3x +c
Substituting (-2,5) into 'y=3x+c':
5 = -6 + c
c = 11
Hence,
y = 3x + 11
For finding x:
Substituting (x, 3) into 'y = 3x +11':
3 = 3x + 11
3x = -8
x = -8/3
For finding y:
Substituting (-2, y) into 'y = 3x + 11':
y = -6 + 11
y = 5
Hope this helps and be sure to have a wonderful time at Brainly! :D
please help! i reward brainliest
plz no silly answers
Answer:
With 4 times the number of machines, it would take 8 hours
Step-by-step explanation:
60 POINTS HELPP!!
The value of y varies directly with x. if x=3, then y=18. What is the value of x when y=84?
Answer:
it is 14
Step-by-step explanation:
if X=14 then Y=84
1 1/3 of 15
[tex]\frac{x}{y}[/tex]
Answer:
[tex]11 \div 3 \times 15 \\ 11 \div 1 \times 5 \\ 11 \times 5 \\ = 55[/tex]
Which pairs of rectangles are similar polygons?
Select Similar or Not Similar for each pair of rectangles
Answer:
Second and fourth pairs of rectangle are similar.
B is the midpoint of AC. AB = 5x-7, BC = 3x - 5. Find the value of x.
А
B
C
Answer:
the value of x is 1......
as we know B is the midpoint....
then,
5x-7=3x-5
5x-3x=-5+7
2x=2
x=2/2
x=1
Find the missing side of each triangle. Leave your answer in simplest radical form.
(Please show ur work)
Answer:
should be, must be, gotta be it
Step-by-step explanation:
13² = 7² + x²
169 = 49 + x
x² = 169 - 49
x² = 120
x = [tex]\sqrt{120}[/tex] (do this stpd calculus)
x = 2[tex]\sqrt{30}[/tex]
________
[tex] \: [/tex]
x² = 13² - 7²
x² = 169 - 149
x² = 120
x = √120
x ≈ 2√30m
Identify the 16th term of a geometric sequence where a1 = 4 and a8 = −8,748.
Step-by-step explanation:
The formula used to determine the terms is
an = a1 × rn - 1
It is given that
a1 = 4
a8 = -8,748
Substituting the values in the formula
-8748 = 4 × r8 - 1
r7 = -8748/4
r7 = -2187
r = -3
So the 16th term is
a16 = 4 × 316-1
a16 = -57395628
Therefore, the 16th term is -57395628.
What is the Prime factorization of 321411?
Answer:
The determined equation for number 321411 factorisation is 3 * 107137.
x-7= -3(x+1) over 5
What is x?
1 (a) (i) Yasmin and Zak share an amount of money in the ratio 21 : 19.
Yasmin receives $6 more than Zak.
Calculate the total amount of money shared by Yasmin and Zak.
(ii) In a sale, all prices are reduced by 15%.
(a) Yasmin buys a blouse with an original price of $40.
Calculate the sale price of the blouse.
Answer: 1(a) $120
(ii a) $34
Step-by-step explanation:
21-19 = 2
$6/2=3
21x 3( one ratio =$3) =63
19x3 = 57
63+57=120 - (1 A ans)
(ii a) 40x0.15 (percentage decrease)= 6
40-6 = $34
The total amount of money shared by Yasmin and Zak is $120.
What is the ratio?The ratio is defined as the comparison of two quantities of the same units that indicates how much of one quantity is present in the other quantity.
(i) The given ratio is 21:19
Let Zak be having $x, the Yasmin will be having $(x+6).
Now, 21/19 = x+6/x
21x=19x+114
2x=114
x= $57
So, x+6= 57+6 = 63$
Total 63+57=$120
(ii) Given that, Yasmin buys a blouse with an original price of $40.
In a sale, all prices are reduced by 15%.
Now, 15% of 40
= 15/100 ×40
= 0.15×40
= 6
New cost =40-6
= $34
Therefore, the sale price of the Yasmin's blouse is $34.
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please help me find " What does the rate of change indicate about the context?"
Answer:
Rate of change is used to mathematically describe the percentage change in value over a defined period of time, and it represents the momentum of a variable. ... Subtract one and multiply the resulting number by 100 to give it a percentage representation.
The sum of 24 and 3 times a number y is equal to 56
Answer:
Step-by-step explanation:
24+3y=56 solve for y, subtract 24 from each side
3y=32 divide each side by 3
y=32/3
Answer:
y=32/3
Step-by-step explanation:
let the number be y, then
24+3y=56 solve for y, subtract 24 from each side
3y=32 divide each side by 3
y=32/3
Estimate each square root to the nearest hundredth of 32. Show your solution!
Answer:
[tex]{ \rm{ \sqrt{32} = \sqrt{2 \times 16} }} \\ \\ = { \rm{ \sqrt{2 \times 4 \times 4} }} \\ \\ = { \rm{ \sqrt{2} \times( \sqrt{4}) {}^{2} }} \\ \\ = { \rm{ \sqrt{2} \times 4 }} \\ \\ = { \rm{4 \sqrt{2} }} \\ \\ { \rm{ \sqrt{32} = 5.656854....}} \\ \\ { \boxed{ \rm{ \sqrt{32} = 5.66 \: }}}[/tex]
9514 1404 393
Answer:
5.66
Step-by-step explanation:
For an integer x = s² +r, where s and r are also integers, a first approximation of the square root of x will be ...
y = √x ≈ s +r/(2s+1)
An iterative improvement on the estimate can be had by ...
y' = s + r/(s +y)
Here, this means a first estimate can be obtained as ...
32 = 5² +7 ⇒ s = 5, r = 7
√32 ≈ y1 = s +r/(2s +1) = 5 7/11
Then an iterative improvement will be ...
y2 = s +r/(s +y1) = 5 +7/(10 7/11) = 5 77/117 ≈ 5.658 ≈ 5.66
_____
Additional comment
The above iterator will add about 1 decimal place for each iteration. The Babylonian method will roughly double the number of good decimal places with each iteration. For an approximate root of p/q, the next iteration using that method would be ...
p'/q' = (x·q² +p²)/(2pq)
Then our above estimate of 5 7/11 for the root of 32 would be refined to ...
p'/q' = (32·11² +62²)/(2·11·62) = 7716/1364 = 5 224/341 ≈ 5.65689.... This compares favorably to the first digits of the actual root: 5.65685....
A choir teacher is dividing 6 sopranos and 20 altos into singing groups. He wants each group to have the same combination of sopranos and altos, with no singers left over. What is the greatest number of groups he can make?
Given g(x)=x2-3x+8 evaluate
A) g(4). B) g(-5)
Answer:
g(4) = 12
g(-5) = 48
Step-by-step explanation:
I will assume that you meant g(x)=x^2 - 3x + 8,
A) To find g(4), substitute 4 for each instance of 'x' in this function:
g(4) = (4)^2 - 3(4) + 8, or
g(4) = 16 - 12 + 8, or
g(4) = 12
Similarly, g(-5) = (-5)^2 - 3(-5) + 8 = 25 + 15 + 8 = 48
g(-5) = 48
Answer:
A) 12
B) 18
Step-by-step explanation:
A) 4^2 - 3(4) + 8
16 - 12 + 8 = 12
B) -5^2 - 3(-5) + 8
25 + 15 + 8 = 48
&
b.
In the diagram, transversal tcuts across the parallel lines a and b. Match the pairs of angles with the relationship that shows they are
congruent.
alternate exterior angles
22, 23 and 25, 28
alternate interior angles
21, 28 and 22, 27
corresponding angles
23, 26 and 24, 25
vertical angles
21, 25 and 22, 26
Answer:
we know that
case a) alternate exterior angles
m∠2=m∠7 --------> by alternate exterior angles
m∠1=m∠8 --------> by alternate exterior angles
case b) alternate interior angles
m∠3=m∠6 --------> by alternate interior angles
m∠5=m∠4 --------> by alternate interior angles
case c) corresponding angles
m∠1=m∠5 --------> by corresponding angles
m∠3=m∠7 --------> by corresponding angles
m∠2=m∠6 --------> by corresponding angles
m∠4=m∠8 --------> by corresponding angles
case d) vertical angles
m∠1=m∠4 --------> by vertical angles
m∠2=m∠3 --------> by vertical angles
m∠5=m∠8 --------> by vertical angles
m∠6=m∠7 --------> by vertical angles
therefore
the answer in the attached figurewe know that
case a) alternate exterior angles
m∠2=m∠7 --------> by alternate exterior angles
m∠1=m∠8 --------> by alternate exterior angles
case b) alternate interior angles
m∠3=m∠6 --------> by alternate interior angles
m∠5=m∠4 --------> by alternate interior angles
case c) corresponding angles
m∠1=m∠5 --------> by corresponding angles
m∠3=m∠7 --------> by corresponding angles
m∠2=m∠6 --------> by corresponding angles
m∠4=m∠8 --------> by corresponding angles
case d) vertical angles
m∠1=m∠4 --------> by vertical angles
m∠2=m∠3 --------> by vertical angles
m∠5=m∠8 --------> by vertical angles
m∠6=m∠7 --------> by vertical angles
therefore
the answer in the attached figure
Step-by-step explanation:
THIS IS NOT MY ANSWER
Congruent angles are angles with equal measures
How to match the pair of angles with their relationships?Angles between parallel lines and transversals are congruent by any of the following relationships
Alternate exterior anglesAlternate interior anglesCorresponding anglesVertical anglesUsing the above angle relationships, the classifications of the angles are:
Alternate exterior angles
m∠2=m∠7
m∠1=m∠8
Alternate interior angles
m∠3=m∠6
m∠5=m∠4
Corresponding angles
m∠1=m∠5
m∠3=m∠7
m∠2=m∠6
m∠4=m∠8
Vertical angles
m∠1=m∠4
m∠2=m∠3
m∠5=m∠8
m∠6=m∠7
Read more about congruent angles at:
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larger two degit number is --------
Answer:
99
Explanation:
The largest 2-digit number is 99 as the next number is 100 which is a 3-digit number
Translate the following phrase into an algebraic expression. Use the variable b to represent the unknown quantity.
The number of soda bottles split 5 ways
Answer:
s/5=b
Step-by-step explanation:
The required expression is n/5 = b
What is an expression?One mathematical expression makes up a term. It might be a single variable (a letter), a single number (positive or negative), or a number of variables multiplied but never added or subtracted. Variables in certain words have a number in front of them. A coefficient is the number used before a phrase.
Given:
We have the variable b to represent the unknown quantity.
The expression,
the number of soda bottles split 5 ways.
That means,
Let n be the number of soda bottles.
So,
using division operation,
n / 5 = b
Therefore, the expression is n/5 = b.
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please help, been stuck on this
A vehicle has a speed with the formula v=(90+20t)m/min. The distance covered every minute is s=1/2vt km. If this vehicle has been moving for 1/2 hours, then the distance that has been traveled is .... km
Answer:
around 7
Step-by-step explanation:
7 is my lucky number
Natasha is making curtains. Each set of curtains uses 8 yards of fabric. She has 61 yards of fabric. How much fabric will be left over after she makes as many sets of curtains as she can?
Answer: 5 yards will be left over.
Step-by-step explanation:
8 * 7 = 56
so then you would minus 56 from 61 which equals 5. Sorry if that's a weird way to get it but...
A real root of X3 – 3x2 + x + 7 = 0 lies between two consecutive integers.
Find these two integers.
Answer:
B. between -2 and -1
Step-by-step explanation:
Brainlyist please
Obasi earns 150% of his regular hourly wage while working overtime.
What fraction of his regular hourly wage does Obasi earn while working overtime?
Answer:
35/100
Step-by-step explanation:
percents go buy hundreds, so 35 percent in fraction form would be 35/100
Answer:
1/2 extra with overtime
Step-by-step explanation:
150%=150/100
150/100=15/10
15/10=3/2
1 and 1/2
Question 1 (Essay Worth 10 points)
(03.03 MC)
A marine biologist is studying the growth of a particular species of fish. She writes the following equation to show the length of the fish, f(m), in cm, after m months:
f(m) = 4(1.08)m
Part A: When the marine biologist concluded her study, the length of the fish was approximately 6.86 cm. What is a reasonable domain to plot the growth function? (4 points)
Part B: What does the y-intercept of the graph of the function f(m) represent? (2 points)
Part C: What is the average rate of change of the function f(m) from m = 3 to m = 7, and what does it represent? (4 points)
Answer: HEre finnaly this is right..
Part A: When the marine biologist concluded her study, the length of the fish was approximately 6.86 cm. What is a reasonable domain to plot the growth function?
0≤x≤8
Part B: What does the y-intercept of the graph of the function f(m) represent?
the length at the start of the study
Part C: What is the average rate of change of the function f(m) from m = 3 to m = 7, and what does it represent?
6.86−5.047−3=1.82
it represents the average growth in length of the fish from the 3rd month to the 7th month of the study
Step-by-step explanation:
PLEASE HELP!!!
5. Which combination of segment lengths
can be used to construct a triangle?
A. 8 cm, 12 cm, 24 cm
B. 15 cm, 38 cm, 49 cm
C. 34 cm, 63 cm, 97 cm
D. 50 cm, 55 cm, 136 cm
Answer:
c
Step-by-step explanation:
Which equation in standard form has a graph that passes through the point (-2, 6) and has a slope of !.A. 3x — 2y = 12 B. 3x — 2y = 6 C. 3x — 2y = -18 D. 3x — 2y = 18
Answer:
Your answer should be C
Step-by-step explanation:
Answer:
3x - 2y = -18
Step-by-step explanation:
3x - 2y = -18 and (-2, 6)
(3)(-2) - (2)(6) = -6 - 12 = -18
Tanya who's worked out a budget that allows her to pay her mortgage and save for her three young children's college funds
Answer: fixed rate mortgage
Step-by-step explanation:
Its correct
Fixed rate mortgage will be for Tanya who's worked out a budget that allows her to pay her mortgage and save for her three young children's college funds.
What is Fixed rate mortgage?A fixed rate mortgage is one in which the interest rate remains constant for the duration of the loan.
This means that the monthly payment amount remains constant, making budgeting and planning easier for borrowers.
Tanya should look for a mortgage with a low interest rate and a manageable monthly payment that fits into her budget.
A shorter loan term means a higher monthly payment but less overall interest paid over the life of the loan.
Tanya has worked out a budget that allows her to pay her mortgage while also saving for her three young children's college funds.
Thus, the answer is Fixed rate mortgage.
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Your question seems incomplete, the probable complete question is:
Tanya who's worked out a budget that allows her to pay her mortgage and save for her three young children's college funds Which Mortgage is Right?
I need help fast please
Answer:
point H is in quadrant II