[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]
A radio station requires DJs to play 2 commercials for every 10 songs they play. What is the unit rate of songs to commercials.
Answer:
5 : 1 or 10 : 2
Step-by-step explanation:
How do i solve 2x=-3
i need answer ASAP
Answer:
[tex]x = \frac{-3}{2} \\or \\x = -\frac{3}{2}\\or\\-1.5[/tex]
Step-by-step explanation:
2x = -3
divide 2 from both sides
[tex]x = \frac{-3}{2} \\\\or \\x = -\frac{3}{2}[/tex]
Answer:
x=-1.5
Step-by-step explanation:
1. Divide on both sides to get the x alone; -3 divided by 2 is -.15 or -3/2
you recieve a pay raise of 5% then recieve a pay cut of 5%. after the two changes in pay your salary is unchanged
Answer:
true
Step-by-step explanation:
False, receive a pay raise of 5% then receive a pay cut of 5%. after the two changes in pay, your salary is changed.
Given that,
To justify the given statement is false or true.
The percentage is the ratio of the composition of matter to the overall composition of matter multiplied by 100.
here,
let the salary be x,
Salary after 5% raise = 1.05x
Salary after cut of 5% = [1 - 0.05] [1.05x]
Salary after a cut of 5% = 0.9975x
So the salary becomes 99.75% of the original salary x.
Thus, the given statement is false, receive a pay raise of 5% then receive a pay cut of 5%. after the two changes in pay, your salary is changed.
Learn more about percentages here:
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Does anyone know number 5?
Answer:
83 is the right answer.
Step-by-step explanation:
Answer:
10th term=83
Step-by-step explanation:
10th=11+(10-1)
=11+72
=83
use a double angle formula to rewrite the expression. 16sin (x) cos (x)
Answer:
8sin(2x).
Step-by-step explanation:
2sin(x)cos(x) = sin(2x)
So 16sin(x)cos(x)
= 8* 2sin(x)cos(x)
= 8sin(2x).
hedllloopp mee and u get brainlist!!!
Answer:
15 cm (make sure to not put value with answer (cm))
Step-by-step explanation:
9x9 = 81
12x12 = 144
81+144 = 225
[tex]\sqrt{225}[/tex] = 15
Answer:
15
Step-by-step explanation:
9^2 + 12^2 = C^2
81 + 144 = C^2
225 = C^2
15 = C
Hope this helps! Pls give brainliest!
can anybody help me with this?
Use this graph of f to find the solutions to f(x) = 0.
What is 268 divided by 6 with a remainder
Answer:
264 with a remainder of 4
Step-by-step explanation:
The solution is: 44 is 268 divided by 6 with a remainder 4.
Here, we have,
given that,
268 divided by 6
Given the following mathematical expression;
268 / 6
We would apply the law of division for fractions.
268 / 6
= 268 ÷ 6
= 44 + 4
the remainder is 4
Hence, The solution is: 44 is 268 divided by 6 with a remainder 4.
To learn more on division click:
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triangular field having the length of sides are 42m, 34m and 20m respectively. find the area of the field (need this answ with full explanation)
Answer:
[tex]A = 336[/tex] [tex]m^{2}[/tex]
Step-by-step explanation:
Using the formulas
[tex]A=\sqrt{s(s-a)(s-b)(s-c)}[/tex]
[tex]s=\frac{a+b+c}{2}[/tex]
Solving for [tex]A[/tex]
[tex]A=\frac{1}{4} \sqrt{-a^{4}+2(ab)^{2} +2(ac)^{2} -b^{4} +2(bc)^{2}-c^{4} }[/tex]
[tex]=\frac{1}{4} *\sqrt{-42^{4} +2*(42*34)^{2}+2*(42*20)^{2} -34^{4} +2*(34*20)^{2} -20^{4} }[/tex]
[tex]=336m^{2}[/tex]
Answer:
✌ just because that what the answer is I just know it cuz im right
Which of the following are solutions to the equation below?
Check all that apply.
x2 + 6x + 9 = 20
A. x= 13 + 20
B. X = -2.75 +3
C. X = 2.5+ 3
D. X = -1/5 + 20
E. X = 2.5 - 3
F. x = -24/5-3
Calculate the area of the shaded part to 1dp
Answer:
To find the area of the shaded region
A = Area of circle - Area of square
12cm is the diagonal of the square and diameter of the circle.
To find the side of the square,
d = √2 * s
12cm = √2 * s
s = 8.49cm
Area of square = L²
As = (8.49)²
As = 72.1cm²
Area of circle = πr²
r = 6cm
Ac = (π*36)cm²
Ac = 113.1cm²
A = Ac - As
A = 113.1cm² - 72.1cm²
A = 41cm²
The area of the shaded region is 41cm².
Answer: I can't tell from the photo which is the shaded part. I'll answer on the assumption it is either the square in the circle, or the 4 areas defined by the semicircles outside the square, but inside the circle.
Step-by-step explanation: Note the caveat above.
Circle Area = pi*r^2 or (3.14)*(6cm)^2 = 113.1 cm^2
Area of the square: The 12cm line forms an hypotenuse with either side. The sides are all equal, so if x is 1 side, we can say the area is x^2. We also know tha x^2 + x^2 = 12
x^2 = 6 cm^2 (the area of the square)
The two possible answers:
1) Shaded portion is the square: 6 cm^2
2) Shaded area means the 4 semicircles outside the square but within the circle: 113.1 cm^2 - 6 cm^2 = 107.1 cm^2
*HELP*
Which of the following is the definition of a weighted average?
Group of answer choices
The ratio of the width to the height of a television screen.
a computing error caused by switching two adjacent digits.
an indicator, sign or measure of something.
An average resulting from the multiplication of each component by a factor reflecting its importance.
Answer: an average resulting from the multiplication of each component by a factor reflecting its importance.
Step-by-step explanation:
Answer:
An average resulting from the multiplication of each component by a factor reflecting it's importance.
Step-by-step explanation:
Assuming only one is selectable. Only possible answer doesn't need much explanation I believe.
A square has a area of 121 square centimeters. what is the length of each side
There are 5 chaperones for every 14 kids on a field trip. If there are 152 people on the trip, how many of them are adults?
Answer:
there are 40 chaperones and 112 kids.
Step-by-step explanation:
5 chaps. plus 14 kids -- 19 people
152 people divided by 19 -- 8
chaperones = 5 x 8 kids = 14 x 8
Need help with this ‘
Someone please help it’s due soon..
Wilde River Highschool and Oakview Mills High Schol played each other in a football game for the country Championship. Going into the 4th quarter, the teams were tied 21-21. Based on the following statistics in the 4th quarter, make an argument for which team you predict to win. Be sure to include mathematical reasoning in your argument.
Gains- Closer to scoring
Loses- Farther from scoring
SOMEONE PLEASE HELPPOOO
Answer: Oakview Mills will win
Step-by-step explanation:
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
Find the sin, cod, tan, sec, and cot of the following triangle with the given information.
Answer:
cos o sin
Step-by-step explanation:
Your bank account has in it. You deposit $5 per day.
(a) How much money is in your account after 5 days? Show your work
(b) After you have made all of your deposits, you withdraw $2 a day until your account balance is 0
many days will you withdraw $2? Show your work
What is the slope of line
Answer:
4
Step-by-step explanation:
(y1-y2)/(x1-x2) = (2-10)/(1-3) = -8/-2 = 4
G.
G
7 cm
8 cm
-
Find volume
Step-by-step explanation:
The volume = [tex](\frac{22}{7} )(7^{2} )(8)[/tex]
= 1232
please give me a brainliest answer
Please help.
Point M is the mid-point of PQ. The coordinates of P and M are given below.
M (5, -2) and P (11, -10)
Based on the information, what is the coordinates of Q?
Answer:
(-1,-6)
Step-by-step explanation:
(-1,-6)
Multiply coordinates of mid point by 2
take away from point P
please help me or I'm gonna fail math
Answer:
Step-by-step explanation:
as said in my comment
A: (3x-2)X(x+1)
B: substitute 3 in(if m=meters),
(3x3-2)
9-2
7X(x+1)
3+1
4
7X4
28
Answer:
a) 3x^2 + x - 2
b) 28m
Step-by-step explanation:
a) Since the Area for a normal square is b*l (base x length)
Do the same with this (Using FOIL ig)
(3x - 2) * (x + 1)
3x^2 + 3x - 2x - 2
3x^2 + x - 2
b) Since it's asking us to find out what the number will be while x = 3m, just substitute 3 for every "x" in the answer we got for a
3(3)^2 + (3) - 2
3(9) + (3) - 2
27 + 3 - 2
30 - 2
28m
Therefore the actual area of this rectangle is 28m
PLEASE HELP DUE IN 10 MINUTES NOBODY WILL HELP IM DESPERATE SO I WILL GIVE BRAINLIEST 5 STARS AND A THANKS JUST QUESTION 2 PLEASE :C IM REALLY SORRY THERE ARE NOT A LOT OF POINTS
Answer:
(6,16)
Step-by-step explanation:
Solve for the first variable in one of the equations, then substitute the result into the other equation.
x=6, y=16
Solution is (3,10).
Sorry if I'm late
Need help ASAP plz help
x ft
x ft
Bedroom
5 ft
Closet
5 ft
6 ft
Bathroom
Answer:
bedroom is 12ft which is equal to 6ft on left of bathroom if we add 6 +6=12 because it is rectangle and bathroom is square and square have 4 equal sides so both sides are 12ft
HELP PLEASE HELP MEMEEE
Answer:
its 35 feet less
Step-by-step explanation:
but can u take another angled photo
1. Determine the lowest common multiple of 4, 9 and 12
A. 30
B. 36
C. 48
D. 54
2. Simplify 80g : 16kg
A. 4 : 5
B. 3 : 4
C. 2 : 7
D. 1 : 20
3. How many square-shaped tiles with sides of y cm that are required to cover 15y × 4y floor?
A. 60
B. 64
C. 72
D. 86
4. Puan Anis bought 8kg of beef which cost RMx per kilogram. She paid with 2 pieces of RM50 note and received a balance of RM4. Find the value of x
A. 12
B. 14
C. 16
D. 18
5. Find the circumference of a circle with radius of 21 cm
A. 66
B. 44
C. 63
D. 132
6. Anita has RMb. She spent RM(2a + 1) per day for a week. Given the balance of her money is RM45, find a formula for b
A. 2a + 46
B. 14a - 38
C. 14a + 45
D. 14a + 52
7. Given 9x²/y² - 3x = 5w, express y in terms of w and x
A. y = x/5w+x
B. y = 3x/5w+3x
C. y = 3x²/5w+3x
D. y = 3x/5w+x
I NEED ANSWERS FOR THESE QUESTIONS TQ :)
Answer:
a,b,d,d,c,a,a
Step-by-step explanation:
According to the following equation, what happened to the carbon and oxygen?
they combined chemically to form a new compound
they combined physically to form a new element
they combined physically to form a new mixture
they combined chemically to form carbon and oxygen
Answer:
b
Step-by-step explanation:
Given that f ( x ) = 3 x − 7 and g ( x ) = 3 x + 9 , evaluate f ( g ( 2 ) )
Answer:
38
Step-by-step explanation:
f ( x ) = 3 x − 7
g ( x ) = 3 x + 9
f(g(2))
First find g(2)
g(2) = 3(2)+9 = 6+9 = 15
Then find f(15)
f(15) = 3*15 -7 = 45 -7 =38
