[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]
submarine titan descended 93 meters into the ocean to look for fish. Submarine Odyssey descended 3 times as deep. What is Odyssey's depth below sea level in meters?
Answer:
279 meters
Step-by-step explanation:
This is just some simple multiplication. 93*3=279
Submarine Odyssey's depth below sea level is 279 meters.
Given that two submarines titan and odyssey, titan descended 93 meters and odyssey descended 3 times as deep.
We need to find the depth of the submarine odyssey.
To find Odyssey's depth below sea level, we can start by determining the depth that Submarine Titan descended.
According to the given information, Submarine Titan descended 93 meters into the ocean to look for fish.
Now, we need to find the depth that Submarine Odyssey descended, which is three times as deep as Submarine Titan.
We can calculate this by multiplying the depth of Submarine Titan (93 meters) by 3:
Depth of Submarine Odyssey = 93 meters x 3 = 279 meters
Therefore, Submarine Odyssey's depth below sea level is 279 meters.
Learn more about multiplication click;
https://brainly.com/question/16334081
#SPJ2
F(x)=x2 -x and g(x)=12-x2
Answer are in pictures below
3. Solve the following questions.
(a) x +3 = 5
(b) 2x – 3 = 5
4. Solve the following questions.
(a) - 17 = -10
(b) x+7
___ =13
-2
Answer:
3a. x=8 3b. x=4 4a. 7 4b. -13.5
Use the following function rule to find f(81).
Answer:
1
Step-by-step explanation:
x/81
x=81
81÷81=1
--------------------
can someone please help me with this
Answer:
45.625cm²
Step-by-step explanation:
To solve this, we need to do the area of the circle - the area of the rectangle:
Area of the circle
a = πr² (r is the radius, half the diameter)
a = π × 4²
a = π × 16
a = 16π or 50.265cm²
Area of the rectangle
a = length × width
a = 5 × 1
a = 5cm²
50.265 - 5 = 45.265
Hope this helps!
A recent report found that a local creamery has a 35% market share in a certain region. Employees in the marketing
department of the creamery conduct a survey to confirm the results by randomly selecting 300 residents from the regon
The employees asked the question which brand of ice cream do you usually purchase to each resident Use a normal
approximation to calculate the probability that at most 80 of these people will choose the creamery's brand. Use a T1-83,
83 plus, or T-34 calculator to find the probability
- Round your answer to four decimal places
Using the normal approximation to the binomial, it is found that there is a 0.0015 = 0.15% probability that at most 80 of these people will choose the creamery's brand.
In a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
It measures how many standard deviations the measure is from the mean. After finding the z-score, we look at the z-score table and find the p-value associated with this z-score, which is the percentile of X.The binomial distribution is the probability of x successes on n trials, with p probability of a success on each trial. It can be approximated to the normal distribution with [tex]\mu = np, \sigma = \sqrt{np(1-p)}[/tex].In this problem:
35% market share, hence [tex]p = 0.35[/tex].300 residents are surveyed, hence [tex]n = 300[/tex].The mean and the standard deviation are given by:
[tex]\mu = np = 300(0.35) = 105[/tex]
[tex]\sigma = \sqrt{np(1-p)} = \sqrt{300(0.35)(0.65)} = 8.26[/tex]
Using continuity correction, the probability that at most 80 of these people will choose the creamery's brand is [tex]P(X \leq 80 + 0.5) = P(X \leq 80.5)[/tex], which is the p-value of Z when X = 80.5, thus:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{80.5 - 105}{8.26}[/tex]
[tex]Z = -2.97[/tex]
[tex]Z = -2.97[/tex] has a p-value of 0.0015.
0.0015 = 0.15% probability that at most 80 of these people will choose the creamery's brand.
A similar problem is given at https://brainly.com/question/25298431
what is 7.5% less than 120
Answer:
111Step-by-step explanation:
7.5% less than 120
120 - 7.5% of 120 = 120(1 - 7.5/100) = 120*0.925 =11142 divided by (-7) =
the answer is -6.
the negative 7 turns the answer negative.
1 divided by 3/8
5 divided by 7/8
Answer:
2.66666666667
1.14285714286
Step-by-step explanation:
Answer:
1 divided by 3/8=2 2/3 and 5 divided by 7/8=5 5/7
Step-by-step explanation:
first you have to divided the 1 and 3/8 you will get 8/3 then you divided that and you will get 2 2/3
After you do that one you go to 5 divided by 7/8 you will get 40/7 then you divided that and you will get 5 5/7
Samuel drives 144 miles in 24 hours. If he continues at the same rate, he will have driven
miles in 6 hours.
Answer:
36
Step-by-step explanation:
Find the unit rate for each hour
144/24=6
6 hrs every hour
6*6=36 miles in 6 hours
A 230 inch pipe is cut into two pieces. One piece is 4 times length of the other. find the length of the shorter piece
Answer: 46 x 4 = 184
184 + 46 is 230
Step-by-step explanation:
6 times 10 to the 8th power divided by 2 times 10 to the negative 4th power
Answer:
30
Step-by-step explanation:
I think but if is wrong i'm sory
4. Andrew likes to solve puzzles.
It took him 4.5 minutes to complete one puzzle with 18 numbers.
It took him 6 minutes and 24 seconds to complete a different puzzle with 32 numbers.
a
For each puzzle work out how many seconds it took Andrew to complete one number.
b
Use your answer to part a to decide which puzzle Andrew completed faster.
Answer:
Step-by-step explanation:
Andrew likes to solve puzzles.
It took him 4.5 minutes to complete one puzzle with 18 numbers.
It took him 6 minutes and 24 seconds to complete a different puzzle with 32 numbers.
a For each puzzle work out how many seconds it took Andrew to complete one number.
b Use your answer to part a to decide which puzzle Andrew completed faster.
Please Help Me. Put the following equation of a line into slope-intercept form, simplifying all fractions.
6x+4y=4
-108y^4 - 4y
I just need the steps, screw the answer if you want.
Answer:
-4y(3y + 1) (9y^2 - 3y + 1)
Step-by-step explanation:
-108y^4 - 4y
= -4y(27y^3 + 1)
= -4y(3y + 1) (3^2y^2 - 3y + 1)
= -4y(3y + 1) (9y^2 - 3y + 1)
Answer:
-4y(3y + 1) (9y^2 - 3y + 1)
Question 6 of 25
What is sin 45°?
Answer:
B.
[tex] \frac{1}{ \sqrt{2} } [/tex]
Identify the segment bisector of XY.
n
5x + 8
9x + 12
Х
M
1
ОХМ
Ο Χ
O line n
O YM
The length of XY is
Given the image attached, the segment bisector that divides XY into two and the length of XY are as follows:
Segment bisector of XY = line nLength of XY = 6Recall:
A line that divides a segment into two equal parts is referred to as segment bisector.In the diagram attached below, line n divides XY into XM and MY.
Thus, the segment bisector of XY is: line n.
Find the value of x:
XM = MY (congruent segments)
Substitute[tex]5x + 8 = 9x + 12[/tex]
Collect like terms and solve for x[tex]5x + 8 = 9x + 12\\5x - 9x = -8 + 12\\\\-4x = 4\\\\x = -1[/tex]
XY = XM + MY
[tex]XY = 5x + 8 + 9x + 12[/tex]
Plug in the value of x[tex]XY = 5(-1) + 8 + 9(-1) + 12\\\\XY = -5 + 8 -9 + 12\\\\\mathbf{XY = 6}[/tex]
Therefore, given the image attached, the segment bisector that divides XY into two and the length of XY are as follows:
Segment bisector of XY = line nLength of XY = 6Learn more here:
https://brainly.com/question/19497953
Help pls the photo is up
Answer:
here it is plz mark me as brainliest
Write an
exponential function in the form y = ab^x
that goes through points (0,13) and (3,832).
Answer:
y = 13 × [tex]4^{x}[/tex]
Step-by-step explanation:
Substitute the given values into the exponential
Using (0, 13 ) , then
13 = a[tex]b^{0}[/tex] ( [tex]b^{0}[/tex] = 1 ) , so
a = 13
y = 13 [tex]b^{x}[/tex]
Using (3, 832 )
832 = 13 b³ ( divide both sides by 13 )
64 = b³ ( take cube root of both sides )
b = [tex]\sqrt[3]{64}[/tex] = 4
The exponential function is
y = 13 [tex](4)^{x}[/tex]
What is the solution to the system of linear equations? Show your work using either substitution or elimination.
Need help rlly soon! Also please show work!
Answer:
x = 11 ; y =13
Step-by-step explanation:
3x - 2 y = 7 -------------(I)
y = x + 2 -----------(II)
Substitute y = x + 2 in equation (I)
3x - 2(x + 2) = 7
3x - 2*x + 2*(-2) = 7
3x - 2x - 4 = 7
x - 4 = 7
x = 7 + 4
x = 11
Plugin x = 11 in equation(II)
y = 11 + 2
y = 13
factor the following equation
1263 + 14b2 + 30b + 35
Answer:
Step-by-step explanation:
2 ( 7 b 2 + 15 b + 649 )
Answer:
1298+28b+30b
1298+58b
2(649+29b)
Can you use mechanical pencils on the PSAT?
Answer:
no
Step-by-step explanation:
only number 2 pencils im pretty sure
Line m passes through
points X and Y. Line n passes through points x
and Z. If m and n have equal slope, what can
you conclude about points X, Y, and Z? Explain.
Answer:
X, Y, Z are collinear
Step-by-step explanation:
X,Y,Z lie on the same straight line
The slope of the lines are the same thus line m and n both passes through X, Y, and Z points and thus all three points will be colinear.
What is the slope?A slope is a tangent or angle at a point and a slope is the intensity of inclination of any geometrical lines.
Slope = Tanx where x will be the angle from the positive x-axis at that point.
Given that line m is passing →
Points X and Y
Line n passing →
Points X, Z
The slope of m = slope of n
If the slope same then the line will be parallel and since both lines are passing through the same point X thus they will be a colinear line.
All points that lie on the colinear line are colinear points.
Hence "X, Y, and Z all three points will be colinear".
To learn more about slopes,
https://brainly.com/question/3605446
#SPJ2
Shaheer takes 4 1/2 minutes to run ONE
PROPER LAP around the School
How many laps can he do in each time
a) 30 minutes
b) 20 minutes
c) 15 minutes
Answer:
Im not
sure but i think its (B) i really hope its right
Step-by-step explanation:
[tex]\sf HELP![/tex]
[tex]\sf 17=2x-9[/tex]
Answer:
x=13
Step-by-step explanation:
Switch sides:
2x−9=17
Add 9 to both sides:
2x−9+9=17+9
Simplify
2x=26
Divide both sides by 2:
2x/2 =26/2
Simplify to get the result.
x=13
Answer:
x=13
Step-by-step explanation:
[tex]\sf 2x-9=17[/tex]
[tex]\sf 2x-9+9=17+9[/tex]
[tex]\sf 2x=26[/tex]
[tex]\sf \cfrac{2x}{2}=\cfrac{26}{2}[/tex]
[tex]\sf x=13[/tex]
A mineral's density is 5g/cm and its volume is 2cm. What is the mass?
Answer:
10kg//
Step-by-step explanation:
density=5g/cm
volume=2cm
mass=?
we know,
density=m/v
d×v=m
m=5×2
hence,10kg//
Answer:
10g/cm
Step-by-step explanation:
If [tex]Distance= \frac{Mass}{Volume}[/tex]
Then
Mass = Density x Volume
Without using a calulator, find A and B, A^B - B^A = 1.
Answer:
A = 1
B = 0
Step-by-step explanation:
Find the unit rate: 6 children from 2 families.
Answer: For every 1 family there is 3 children.
Step-by-step explanation:
Find the slope of the line that passes through each pair of points A. (-3,4) and (2,-3)
Answer:
slope = (4-(-3))/(-3-2)=7/-5=-[tex]\frac{7}{5}[/tex]
Step-by-step explanation:
Answer: m=-7/5
Step-by-step explanation:
[tex](-3,4) (2-^-3) \\\\\frac{-3-4}{2-^-3} \\m=-\frac{7}{5}[/tex]
I will brainlist who can answer this 4 Questions!!
III. Answer each of the follow
Answer:
25. 7 months
26. Php 12500
27. a. 3x-4y=8
b. 4x+2y=0
c. _ graph yourself
d. Yes it does
28. A. Yes
B. Yes
C. No