[tex]Simplify: \frac{ 5×(25)^{n+1} - 25 × (5)^{2n}}{5×(5)^{2n+3 }- (25)^{n+1}} \\ [/tex]
Need help please"....."
[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]
How do I solve for this?
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Answer:
angle L = 100 degrees
angle M = 110 degrees
angle N = 70 degrees
angle P = 80 degrees
Step-by-step explanation:
find value of 'x' then substitute into each of the four angle expressions
to find 'x', add all expressions and set them equal to 360 (there are 360 degrees in any four-sided polygon)
2x + 20 + 3x - 10 + 2x - 10 + 2x = 360
combine 'like' terms to get:
9x = 360
x = 40
angle L = 2(40) + 20 = 100 degrees
angle M = 3(40) - 10 = 110 degrees
angle N = 2(40) - 10 = 70 degrees
angle P = 2(40) = 80 degrees
Check:
100 + 110 + 70 + 80 = 360
May I please receive help?
Please help! Algebra question see picture...
Marking Brainliest!
Answer: G is -1/3
Step-by-step explanation:
the cost of a new laptop is $750 which genorates a sales tax of$37.50 what is the sales tax rate
Answer:
5%
Step-by-step explanation:
To find the sales tax rate, you would divide the tax by the cost to see the percentage of the tax.
$750 / $37.50= 0.05
The answer is 5%
Hope this helps
Given that in isosceles △ABC , base BC¯¯¯¯¯, BE¯¯¯¯¯⊥AC¯¯¯¯¯, and CF¯¯¯¯¯⊥AB¯¯¯¯¯, which of the following proves that BE¯¯¯¯¯≅CF¯¯¯¯¯?
1. Isosc. △ABC, base BC¯¯¯¯¯ (Given)
2. AB¯¯¯¯¯≅BC¯¯¯¯¯ (Def. of Isosc. △)
3. BE¯¯¯¯¯⊥AC¯¯¯¯¯, CF¯¯¯¯¯⊥AB¯¯¯¯¯ (Given)
4. ∠BEA and ∠CFA are Supplementary Angles (Def. of ⊥)
5. AB¯¯¯¯¯≅BC¯¯¯¯¯ (Supp. ∠s ≅ Thm.)
6. ∠A≅∠A (Reflex. Prop. of≅)
7. △ABE≅△ACF (SAS Steps 1, 6, 5)
8. BE¯¯¯¯¯≅CF¯¯¯¯¯ (CPCTC)
1. Isosc. △ABC, base BC¯¯¯¯¯ (Given)
2. AB¯¯¯¯¯≅BC¯¯¯¯¯ (Def. of Isosc. △)
3. BE¯¯¯¯¯⊥AC¯¯¯¯¯, CF¯¯¯¯¯⊥AB¯¯¯¯¯ (Given)
4. ∠BEC and ∠CFB are Supplementary Angles (Def. of ⊥)
5. AC¯¯¯¯¯≅BC¯¯¯¯¯ (Supp. ∠s ≅ Thm.)
6. ∠A≅∠B (Sym. Prop. of≅)
7. △ABE≅△ACF (SAS Steps 1, 6, 5)
8. BE¯¯¯¯¯≅CF¯¯¯¯¯ (CPCTC)
1. Isosc. △ABC, base BC¯¯¯¯¯ (Given)
2. AB¯¯¯¯¯≅AC¯¯¯¯¯ (Def. of Isosc. △)
3. BE¯¯¯¯¯⊥AC¯¯¯¯¯, CF¯¯¯¯¯⊥AB¯¯¯¯¯ (Given)
4. m∠BEA=m∠CFA=90∘ (Def. of ⊥)
5. ∠BEA≅∠CFA (Rt. ∠s ≅ Thm.)
6. ∠A≅∠A (Reflex. Prop. of≅)
7. △ABE≅△ACF (AAS Steps 5, 6, 1)
8. BE¯¯¯¯¯≅CF¯¯¯¯¯ (CPCTC)
1. Isosc. △ABC, base BC¯¯¯¯¯ (Given)
2. AB¯¯¯¯¯≅AC¯¯¯¯¯ (Def. of Isosc. △)
3. BE¯¯¯¯¯⊥AC¯¯¯¯¯, CF¯¯¯¯¯⊥AB¯¯¯¯¯ (Given)
4. m∠BEC=m∠CFB=90∘ (Def. of ⊥)
5. ∠BEC≅∠CFB (Rt. ∠s ≅ Thm.)
6. ∠A≅∠B (Sym. Prop. of≅)
7. △ABE≅△ACF (AAS Steps 5, 6, 1)
8. BE¯¯¯¯¯≅CF¯¯¯¯¯ (CPCTC)
The correct proof that proves that BE ≅ CF is the proof in option C. (see attachment).
Recall the following:
An isosceles triangles has two sides that are congruent and a base.AAS Congruence Theorem proves that two triangles are congruent if they possess two pairs of congruent sides and a pair of non-included congruent sides.All corresponding parts of two congruent triangles are equal in measure to each other, based on the CPCTC Theorem.The isosceles triangle ABC given is shown in the image attached below.
To prove that, BE ≅ CF, establish the fact that △ABE ≅ △ACF by the AAS Congruence Theorem.
Since △ABE ≅ △ACF, therefore BE ≅ CF by the CPCTC Theorem.
Thus, the correct proof that proves that BE ≅ CF is the proof in option C. (see attachment).
Learn more about AAS Congruence Theorem on:
https://brainly.com/question/3168048
Which of the following numbers are rational, but NOT integers?
Select one or more:
a.√33
b.8.4
c.3/4
d.0
Answer:
0
Step-by-step explanation:
Zero is a rational number, and we know that the integer 0 can be written in any one of the following forms. ... Thus, 0 can be written as, where a/b = 0, where a = 0 and b is any non-zero integer. Hence, 0 is a rational number and not an integer.
You are selling tickets to your school musical. Student tickets cost $2 and general admission tickets are $3. You sell 17 tickets and collect $42 how many of each type of ticket did you sell?
Answer:
9 student tickets and 8 general admission ticketsStep-by-step explanation:
Let the number of student tickets is s and general admission tickets - g.
Set equations and solve:
s + g = 172s + 3g = 42Double the first equation and subtract from the second to eliminate s:
2s + 3g - 2s - 2g = 42 - 2*17g = 8Find s:
s = 17 - 8 = 9Let the student tickerts and general tickets be x and y respectively
x+y=17=>x=17-y2x+3y=42--(2)From (1) put in (2)
2(17-y)+3y=4234+y=42y=8And
x=17-8=9greatest common factor of 5, 6 and 15
Answer:
1
Step-by-step explanation:
As you can see when you list out the factors of each number, 1 is the greatest number that 5, 6, and 15 divides into.
Which of the following statements must be true based on the diagram below.please help
Answer:
A: ST is a segment bisector
Step-by-step explanation:
ST is a segment bisector. Point S cuts in between segment QP. While Point T cuts between segment PO.
State the reason for statement #5.
PLEASE ANSWER FAST
1. Given
2. Given
3. Alternate Interior Angles
4. Reflexive Property
5. SAS
Hope this helps!! :)
Please help with this math problem ASAP!! I will mark brainliest! :)
Answer:
y=4 x=6
Step-by-step explanation:
you said asap do i dont have time to explain
please please please help PLEASE PLEASE
Step-by-step explanation:
refer to the picture.. hope this helps :)
helpppppppppppppppppppppppppppppppppppppppppppppppppp plessssssssssss
screenshot
Answer:
2.511 square kilometers
PLEASE PROVIDE A PICTURE graph the solution to this system of inequalities in this coordinate plane. 3у > 2х + 12
2x +y < -5
Answer:
The double shaded region
BRAINLIEST!!! +10 POINTS!!! REAL ANSWERS ONLY PLEASE!!!
Answer:
plus ten points huh i only see five
Step-by-step explanation:
Answer:
|-x| + 3
Step-by-step explanation:
I say that because -x will be turned into positive x and then add the 3, and you will get the answer.
If AM = x + 8 and MB= 6x – 2, find MB.
Answer:
10
Step-by-step explanation:
Firstly, AM=x+8
or, A=x+8-M......eqn (i)
MB=6x-2
or, B=6x-2-M......eqn (ii)
Now,
from eqn (i) and (ii)
x+8-M=6x-2-M
or, 8+2=6x-x-M+M
or, 10=5x
or, 10÷5=x
therefore, x=2
Again,
MB=6x-2
=6×2-2
=12-2
=10
is it correct
please mark me as BRAINLIEST
Given the following function, find f(-2), f(0), and f(1).
f(x) = x2 + 3
=
Answer:
jjjjnnuiuhjiihhiihb
Step-by-step explanation:
tyuijiojnoo.
yu8ijhiihj
What is the solution to the equation? square root -2x-5-4=x A. -7 and -3 B. 3 and 7 C. -3 D. 7
Answer:
3
Step-by-step explanation:
step1 Isolate the square root on the left hand side
Original equation
√2x-5-4 = -x
Isolate
√2x-5 = 4-x
step2 eliminate the radical on the left hand side
Raise both sides to the second power
(√2x-5)2 = (4-x)2
After squaring
2x-5 = x2-8x+16
step3 Solve the quadratic equation
Rearranged equation
x2 - 10x + 21 = 0
This equation has two rational roots:
{x1, x2}={7, 3}
step4 Check that the first solution is correct
Original equation, root isolated
√2x-5 = 4-x
Plug in 7 for x
√2•(7)-5 = 4-(7)
Simplify
√9 = -3
Solution does not check
3 ≠ -3
step5 Check that the second solution is correct
Original equation, root isolated
√2x-5 = 4-x
Plug in 3 for x
√2•(3)-5 = 4-(3)
Simplify
√1 = 1
Solution checks !!
Solution is:
x = 3
Answer:
-3
Step-by-step explanation: i got it right on my test
On a drawing of a model airplane, the scale used is 1 in.:3 ft. How many feet would 4.5 inches represent?
A. 13.5 feet
B. 6.5 feet
C. 1.5 feet
D. 4.5 feet
Answer:
13.5
Step-by-step explanation:
4.5*3=13.5
I NEED HELP ON 1 PLEASEEE
Answer:
C
Step-by-step explanation:
SA of a cylinder formula:
A=2πrh+2πr^2
A=2π(3)(15)+2π(3)^2
A=339.29in^2
Hope that helps
Answer:
Step-by-step explanation:
Hi there!
From the given figure;
Radius(r) = 3 inch
Height (h) = 15 inch
Now;
Total surface area (TSA) = 2πr(r+h)
TSA = 2*([tex]\frac{22}{7}[/tex])*3(3+15)
TSA = [tex]\frac{132}{7}[/tex]*18
TSA = 339.42in².
Therefore, the answer is option c (339.29in²).
Hope it helps!
967 times 24 equals?
Answer:
23,208 is the final answer.
Hope this helps!
Answer:
23,208
Hopefully this is correct
Look at the figure. How can you prove the triangles are congruent?
A) it is not possible to determine if the triangles are congruent
B) ABD = CBD by the SSS postulate
C) ABD = CBD by the SSS postulate
Answer:
Δ ABD ≅ Δ CBD SSS
Step-by-step explanation:
AB ≅ CB Given
AD ≅ DC Given
BD ≅ BD Reflexive property
Δ ABD ≅ Δ CBD SSS
What is the value of 6(9+2)/h when g = 6 and h = 4?
Answer: 12
Plug 6 and 4 into the problem-
6(6 + 2)/4
6(8)/4
48/4 = 12
Hey there!
6(g + 2) / h
= 6(6 + 2) / 4
= 6(8) / 4
= 8(6) / 4
= 8 + 8 + 8 + 8 + 8 + 8 / 4
= 16 + 16 + 16 / 4
= 32 + 16 / 4
= 48 / 4
= 48 ÷ 4 / 4 ÷ 4
= 12 / 1
= 12 ÷ 1
= 12
Therefore, your answer is: 12
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
Your mother bought 2 kilograms of chicken and 3 kilograms of pork to consume in week. How many kilograms of chicken and pork did your family consume in a month?
Answer:
20?.... seems right to me.
Step-by-step explanation:
9514 1404 393
Answer:
20 kg
Step-by-step explanation:
The mass of the chicken and pork for 1 week is (2 kg) +(3 kg) = 5 kg.
Normally, we think of a month as 4 weeks.
(4 wk)(5 kg/wk) = 20 kg
If pork and chicken are consumed at the same rate for 4 weeks, the family will consume 20 kg of pork and chicken.
_____
If we consider a year to be 52 weeks (it is actually 1 or 2 days longer), then the number of weeks in an average month is ...
52/12 = 4 1/3 weeks/month
Multiplying that value by 5 kg/week will give 21 2/3 kg per month.
__
The answer depends on the assumption you make about weeks in a month.
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
A family of 2 adults and 3 children goes to a play . admission costs $8per adults and $5 per child. what expression would show the total admission cost for the family
Answer:
8 + 8 + 16 5 * 3 is 15 16 + 15 is 31 that is the answer to the question
pls helpppppppppppppppppp meeeeeee marking BRAINLIEST!
Convert the mixed numbers to improper fractions:1. 5 6/72. 8 3/9
Convert 62 miles to hour to feet to second
62 Miles per Hour =
90.933333 Feet per Second
(rounded to 8 digits)