[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]
Help please!! Geometry
Applying angle pair relationships
Answer:
m∠2 = 75°
m∠1 = 105°
Step-by-step explanation:
1. First, we should recognize that the angle that's 75° and ∠2 are alternate interior angles, formed on the interior of the opposite sides of the transversal. Alternate interior angles are congruent, so m∠2 = 75°.
2. Next, ∠2 and ∠1 are a linear pair, meaning their angle measures add up to 180°. Considering that m∠2 is 75 degrees, we just have to subtract 75 from 180, and we get the measure of ∠1.
[tex]180-75[/tex] [tex]105[/tex]Therefore, m∠1 = 105°.
i need an explanation what....wajfasjf
Solve the equation. Prove that it makes the equation true.
3b-8=d-6
Answer:
um just one question are you sure it's supposed to be d-6 instead of b-6
Step-by-step explanation:
if it's b-6 instead of d then the answer is 1
2x+10=12
so x=??
[tex]\huge \dag \sf{Help \: me}[/tex]
Answer:
[tex]\sf\longmapsto\sf\boxed {x = 1}[/tex]
Step-by-step explanation:
[tex]\sf\longmapsto \: 2x + 10 = 12[/tex]
[tex]\sf\longmapsto \: \: 2x + 10 - 10 = 12 - 10[/tex]
[tex]\sf\longmapsto \: 2x = 2[/tex]
[tex]\sf\longmapsto \: \frac{2x}{2} = \frac{2}{2} [/tex]
[tex]\sf\longmapsto \: x = 1[/tex]
Answer:
[tex]\boxed {\sf x=1}[/tex]
Step-by-step explanation:
[tex]\sf 2x+10=12[/tex]
[tex]\boxed{\mathrm{Subtract\:}10\mathrm{\:from\:both\:sides}}[/tex]
[tex]\sf 2x+10-10=12-10[/tex][tex]\sf 2x=2[/tex][tex]\boxed{\mathrm{Divide\:both\:sides\:by\:}2}[/tex]
[tex]\sf \cfrac{2x}{2}=\cfrac{2}{2}[/tex][tex]\sf x=1[/tex][tex]\boxed{\sf Hope\: it\:helps!}[/tex]
2/3 = 4/x+3 what is x?
Answer:
-12/7
Step-by-step explanation:
2/3=4/x+3
2/3-3=4/x Subtract 3 from both sides
2/3-9/3=4/x Make them have a common denominator
-7/3=4/x
-7/3x=4
x=(4)/(-7/3)
x=[tex]\frac{-12}{7}[/tex]
evaluate: 5/6 + 4/9 =___?
Answer:
23/18 or 1 5/18
Step-by-step explanation:
In mathematics, adding and subtracting fraction required that all fractions are in similar, in converting dissimilar fraction into set of similar fraction requires finding its Least Common Denominator (LCD) or Least Common Multiple (LCM).
Equation Given
5/6 + 4/9
Finding LCM
- List down their multiples
The multiples of 6 = 6 12 18 24
The multiples of 9 = 9 18 27 36
Thus, their Least Common Multiple (LCM) is 18
Converting Dissimilar Fraction into Similar Fraction
The LCM is already the denominator
Divide the LCM by its original denominator then multiply by numerator to get the new numerator
5/6
(18 ÷ 6) × 5 = 15/18, new fraction
4/9
(18 ÷ 9) × 4 = 8/18, new fraction
Evaluate
15/18 + 8/18
= 23/18, or
= 1 5/18
Answer:
23/18 or 1 5/18
Step-by-step explanation:
In mathematics, adding and subtracting fraction required that all fractions are in similar, in converting dissimilar fraction into set of similar fraction requires finding its Least Common Denominator (LCD) or Least Common Multiple (LCM).
Equation Given
5/6 + 4/9
Finding LCM
List down their multiples
The multiple of 6
6 12 18 24
The multiple of 9
9 18 27 36
Thus, their Least Common Multiple (LCM) is 18
- Converting Dissimilar Fraction into Similar Fraction
The LCM is already the denominator
Divide the LCM by its original denominator then multiply by numerator to get the new numerator
5/6
(18 ÷ 6) × 5 = 15/18, new fraction
4/9
(18 ÷ 9) × 4 = 8/18, new fraction
- Evaluate
15/18 + 8/18
= 23/18, or
= 1 5/18
The graph shown below expresses a radical function that can be written in the for f(x)=a(x+6)
Answer:
Step-by-step explanation:
MY SISTER HAVE DIS EQUETION I TELL YOU
evaluate 2/6 + 1/3 + 1/2 = ?
Answer:
2/6 + ⅓ + ½
= (2+2+3)/6
= 7 / 6
= 1⅙
Step-by-step explanation:
brainliest plz
Answer:
1 1/6
Step-by-step explanation:
Find the common denominator for 6, 3, 2
6 is divisible evenly by all three of those numbers so 6 is the lowest common denominator.
Convert all the fractions into sixths.
The first fraction is already done.
1/3..... the denominator needs to be multiplied by 2 so you have to multiply the numerator by the same amount.
1/3 x 2/2 = 2/6
1/2.... the denominator needs to be multiplied by 3 so you do the same thing to the numerator.
1/2 x 3/3 = 3/6
Now you have
2/6 + 2/6 + 3/6 = 7/6
Simplify the answer
6/6 = 1 so remove 6/6 from 7/6 and you are left with just 1/6
So your answer will be 1 and 1/6 or 1 1/6
Sarah and Maya must split the $15 they earned, from scorekeeping a volleyball game. Sarah says, “ there’s only one way to split this money, we both get $7.50.” Maya argued that there were an infinite number of ways to divide the money. Who is correct? Prove their argument.
(Please help!)
Answer:
sarah is correct
Step-by-step explanation:
there are not multiple ways to divide you can only use division and the equation is 15/2
Today, both the soccer team and the basketball team had games. The soccer team plays every 4 days and the basketball team plays every 5 days.
Answer:
20
Step-by-step explanation:
Assuming you are referring to the day that both teams would play on the same day, it would be the 20th.
There are two ways you can do it.
1. List out the multiples of each number
2. multiply the two days together
If you want to do it the first way it would look like this...
5 10 15 20
4 8 12 16 20
When you do it like this it shows you that the 20th day is the day they would both play together
If you want to do it the second way it would look like this...
4th day X 5th day = 20th day
Either way you solve the problem you get the same answer, this may not work for every problem like this, but it works for this particular one
If (a + b)^2 = a^2 +n + b^2 , what is n?
Answer:
[tex] {(a + b)}^{2} = {a}^{2} + 2ab + {b}^{2} \\ n = 2ab[/tex]
8.
(a) Rowena buys and sells clothes.
(1)
She buys a jacket for $40 and sells it for $45.40.
Calculate the percentage profit.
Work Shown:
45.40 - 40 = 5.40
She made $5.40 in profit. Divide this over the original price to find the percentage profit
(5.40)/(40) = 0.135 = 13.5%
guys pls help me!!!!!!
Answer: 100
Step-by-step explanation:
A line equals 180 so subtract 180-80 to get your answer.
HELP
Convert log xy = 1/2 to exponential form
a. x^y=1/2
b. y^x=1/2
c. square root of x=y
d. square root of y=x
Answer:
Logxy =1/2
Step-by-step explanation:
what is the equation of the line that is perpendicular to y = −2x + 5 through the point (-4, -5)
Step-by-step explanation:
m1=-2
m1m2=-1
-2m2=-1
m2=1/2
y+5/x+4=1/2
so 2y+10=x+4
2y-x=-6
Answer:
[tex]y=\frac{1}{2}x-3[/tex]
Step-by-step explanation:
Hi there!
We are given the equation y=-2x+5 and we want to find the equation of the line that is perpendicular to that line, and pass through the point (-4, -5)
Perpendicular lines have slopes that multiply to get -1.
So to find the slope of the perpendicular line: use the formula [tex]m_1*m_2=-1[/tex], where [tex]m_1=-2[/tex]
Substitute:
-2m=-1
Divide both sides by -2
m=[tex]\frac{1}{2}[/tex]
Here's the equation of the line so far, as we know it, written in slope-intercept form (y=mx+b, where m is the slope and b is the y intercept):
[tex]y=\frac{1}{2}x+b[/tex]
We need to find b.
Because we know the line passes through the point (-4, -5), we can use it to help solve for b.
Substitute -4 as x and -5 as y
[tex]-5=\frac{1}{2}(-4)+b[/tex]
Multiply:
-5=-2+b
Add 2 to both sides
-3=b
Substitute -3 as b:
y=[tex]\frac{1}{2}x-3[/tex]
Hope this helps!
12 can someone please explain this
Answer:
B = x = 44 degrees
Step-by-step explanation:
Interior angles of a triangle = 180 degrees.
There are 2 congruent sides so the angle to the right of 67 degrees is also 67 degrees
180 - 2(67) = 46 degrees (the third angle of the triangle)
x + 46 degrees = 90 degrees ( complementary angles)
x = 44 degrees
In Triangle ABC with vertices A(-5,-4), B(3,-2), and C(-1,6), M is the midpoint of AB and N is the midpoint of BC. Show that MN = 1/2 AC. Provide your complete solutions and proofs in your paper homework and enter the numeric answers online
The midpoint of a line divides the line into equal segments.
See below for the proof of [tex]\mathbf{MN = \frac{1}{2}AC}[/tex]
The given parameters are:
[tex]\mathbf{A = (-5,-4)}[/tex]
[tex]\mathbf{B = (3,-2)}[/tex]
[tex]\mathbf{C = (-1,6)}[/tex]
The coordinates of M (midpoint of AB) are calculated as follows:
[tex]\mathbf{M = \frac{1}{2}(x_1 + x_2, y_1+y_2)}[/tex]
So, we have:
[tex]\mathbf{M = \frac{1}{2}(-5 + 3, -4-2)}[/tex]
[tex]\mathbf{M = \frac{1}{2}(-2, -6)}[/tex]
[tex]\mathbf{M = (-1, -3)}[/tex]
The coordinates of N (midpoint of BC) are calculated as follows:
[tex]\mathbf{N = \frac{1}{2}(x_1 + x_2, y_1+y_2)}[/tex]
So, we have:
[tex]\mathbf{N = \frac{1}{2}(3 - 1, -2 +6)}[/tex]
[tex]\mathbf{N = \frac{1}{2}(2, 4)}[/tex]
[tex]\mathbf{N = (1, 2)}[/tex]
Distance MN is:
[tex]\mathbf{MN = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}}[/tex]
So, we have:
[tex]\mathbf{MN = \sqrt{(-1 - 1)^2 + (-3 - 2)^2}}[/tex]
[tex]\mathbf{MN = \sqrt{29}}[/tex]
Distance AC is calculated as follows:
[tex]\mathbf{AC= \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}}[/tex]
So, we have:
[tex]\mathbf{AC= \sqrt{(-5 - -1)^2 + (-4 - 6)^2}}[/tex]
[tex]\mathbf{AC= \sqrt{116}}[/tex]
Split
[tex]\mathbf{AC= \sqrt{4 \times 29}}[/tex]
Take positive square root of 4
[tex]\mathbf{AC= 2\sqrt{29}}[/tex]
To prove that:
[tex]\mathbf{MN = \frac{1}{2}AC}[/tex]
We have:
[tex]\mathbf{\sqrt{29} = \frac{1}{2} \times 2\sqrt{29}}[/tex]
[tex]\mathbf{\sqrt{29} = \sqrt{29}}[/tex]
The above equation is true.
Hence. [tex]\mathbf{MN = \frac{1}{2}AC}[/tex]
Read more about midpoints and distance at:
https://brainly.com/question/11231122
Can anyone help with this equation? PLS
I need this for right now!
Answer: [tex]5^{3}[/tex]
Step-by-step explanation:
find the missing number so that the equation has no solutions. _x-18=-3(x+4)
Answer:X=5
Step-by-step explanation:took the test
01.01 LC)Look at the following numbers: −4, −5, 0, 5 Which pair of numbers has a sum of zero? 5, −5 −5, 0 −4, 5 −4, 0
Answer:
5, -5
hope this helps
Answer:
Train to BaDussy
Step-by-step explanation:
explain step by step please and thanks
Answer:
B
Step-by-step explanation:
5(h)=w+8. get rid of 5 by multiply
5h=w+8
w=5h-8
calculate the range of the following numbers: 11,13,15,9,19,12,21,14,10,15,16,8,11,11,10
Answer:
it should be 13
Step-by-step explanation:
Answer:
The Range is 13
Step-by-step explanation:
Mean (Average): 13
Median: 12
Range:13
Largest: 21
Smallest: 8
Sum: 195
Count: 15
(Hope this helps can I pls have brainlist (crown)☺️
May I please receive help?
Answer:
81+71+x=180
152+x=180
x=180-152
x=28°
Step-by-step explanation:
Hope that this is helpful.
Have a great Day.
In February, 1985, the cost of a gallon of milk was $2.26. In November of 2007, how much would that gallon of milk cost?
Answer:
is this the full question?
ryan has a balance of $75 in his savings account and deposits $25 each week. He needs at least $300 to buy the gift he wants for his birthday. Which inequality can be used to find W, the number of weeks when Ryan will have more than $300
Answer:
25x + 75 ≥ 30
Hope this helps!
MNPQRSTU est le parallélépipède rectangle représente ci-dessous
Answer:mie is
Step-by-step explanation: hehe
A cube has a volume of 73 cubic centimeters. What is its surface area in
square centimeters?
Just type the number of the answer.
Answer:
104.80 cm²
Step-by-step explanation:
Formula to know: Volume = e³ ; SA = 6e²
V = e³ Substitute what you know V = e³ and solve
73 = e³
[tex]\sqrt[3]{73}[/tex] = e one edge of the cube
Find the SA
SA = 6e² Substitute the value for e
SA = 6([tex]\sqrt[3]{73}[/tex])²
SA = 6([tex]\sqrt[3]{73} \sqrt[3]{73}[/tex] )
Sa = 104.80
Help help help help
Answer:
17 - 2= 15
so if you do
15 ÷ 3 = 5
so x= 5
Solve the equation x2-81 = 0.
Answer:
40.5
Step-by-step explanation:
x2 - 81 = 0 --> + 81 to both sides
2x = 81 --> divide by 2 on both sides
x = 40.5
Answer:
2x-81=0
2x=0+81
2x=81
x=81
2
x=40.5 ANSWER.
MARK ME AS A BRAINLIST PLZ.
Evaluate -5x+8 when x=3 The value of the expression is
Answer:
-7
Step-by-step explanation:
replace x by 3
-5^3+8
-15+8
=-7