Answers
[tex]\textit{logarithm of factors} \\\\ \log_a(xy)\implies \log_a(x)+\log_a(y) \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \ln\left( r^2s^{10}\sqrt[4]{r^2s^{10}} \right)\qquad \qquad \stackrel{\textit{let's for a second make}}{z = r^2s^{10}} \\\\\\ \ln\left(z\cdot \sqrt[4]{z} \right)\implies \ln\left(z\cdot z^{\frac{1}{4}} \right)\implies \ln\left(z^{1+\frac{1}{4}} \right)\implies \ln\left(z^{\frac{5}{4}} \right)[/tex]
[tex]\stackrel{\textit{and substituting back}}{\ln\left( \left[ r^2s^{10} \right]^{\frac{5}{4}} \right)}\implies \ln\left( r^{2\cdot \frac{5}{4}} ~~ s^{10\cdot \frac{5}{4}} \right)\implies \ln\left( r^{\frac{5}{2}}~~s^{\frac{25}{2}} \right) \\\\\\ \ln\left( r^{\frac{5}{2}} \right)~~ + ~~\ln\left( s^{\frac{25}{2}} \right)\implies \stackrel{A}{\cfrac{5}{2}}\ln(r)~~ + ~~\stackrel{B}{\cfrac{25}{2}}\ln(s)[/tex]
Related Questions
help for 100 points !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answers
Answer:
In the PDF. All the answers should be there. Let me know if I'm missing any.
Answer:
Answers are below
Step-by-step explanation:
Ignore all of my extra work and the words my hand are "after each week (the very top one" and "represents the"
Answers
Answer:
Green nails
Step-by-step explanation:
Jimmy jogged for a total of 6.8 miles last week. How many feet did Jimmy jog last
week? (1 mile - 5,280 feet)
Answers
Answer:
35904 ft
Step-by-step explanation:
We can set up an unit converter to find how many feet Jimmy jogged...
[tex]6.8 mi(\frac{5280ft}{1mi})[/tex]
Note that in this case, the miles (units) cancel out leaving us with:
[tex]6.8*5280ft=35904\ ft[/tex]
Write 0.0045% as a decimal
Answers
Answer:
0.0045%
Step-by-step explanation:
0.0045 is not a fraction so it is a decimal already.
Answer:
0.000045
Step-by-step explanation:
good luck!
please i cannot slove it. can u
Answers
Answer:
Step-by-step explanation:
[tex]a^{-1}=\dfrac{1}{a} \ ; \ b^{-1}=\dfrac{1}{b} \ ; \ c^{-1}=\dfrac{1}{c}[/tex]
[tex]\dfrac{1}{1+a+b^{-1}}+\dfrac{1}{1+b+c^{-1}}+\dfrac{1}{1+c+a^{-1}}=\dfrac{1}{1+a+ \dfrac{1}{b}}+\dfrac{1}{1+b+\dfrac{1}{c}}+\dfrac{1}{1+c+\dfrac{1}{a}}[/tex]
[tex]= \dfrac{1}{\dfrac{1*b}{1*b}+\dfrac{a*b}{1*b}+\dfrac{1}{b}}+\dfrac{1}{\dfrac{1*c}{1*c}+\dfrac{b*c}{1*c}+\dfrac{1}{c}}+\dfrac{1}{\dfrac{1*a}{1*a}+\dfrac{c*a}{1*a}+\dfrac{1}{a}}\\\\\\=\dfrac{1}{\dfrac{b+ab+1}{b}}+\dfrac{1}{\dfrac{c+bc+1}{c}}+\dfrac{1}{\dfrac{a+ac+1}{a}}\\\\\\=\dfrac{b}{b+ab+1}+\dfrac{c}{c+bc+1}+\dfrac{a}{a+ac+1}[/tex]
abc = 1
c = 1/ab
[tex]=\dfrac{b}{b+ab+1}+\dfrac{\dfrac{1}{ab}}{\dfrac{1}{ab}+b*\dfrac{1}{ab}+1}+\dfrac{a}{a+a*\dfrac{1}{ab}+1}\\\\\\[/tex]
[tex]= \dfrac{b}{b+ab+1}+\dfrac{\dfrac{1}{ab}}{\dfrac{1+b+ab}{ab}}+\dfrac{a}{\dfrac{ab+1+b}{b}}\\\\\\=\dfrac{b}{b+ab+1}+\dfrac{\dfrac{1}{ab}*ab}{1+b+ab}+\dfrac{ab}{ab+1+b}[/tex]
[tex]=\dfrac{b}{b+ab+1}+\dfrac{1}{1+b+ab}+\dfrac{ab}{1+b+ab}\\\\\\=\dfrac{b+1+ab}{b+1+ab}\\\\\\=1[/tex]
A sleep study found that the number of hours each person slept was normally
distributed. The study found that the average person slept 8.2 hours with a standard deviation of 0.7 hours.
1. What range of hours of sleep are the 99.7% closest to the mean?
2. The 2.5% of the people who slept the most got more than how many hours
of sleep?
3. The 16% of the people who slept the least got less than how many hours sleep?
Answers
Answer:
1. 6.1-10.3
Thats all i know.. hope it helps
numbers or variables that form a product are _____
Answers
Answer:
it is called a monomial
Step-by-step explanation:
kuz I said
A rhombus is
a parallelogram.
always
sometimes
never
Answers
A rhombus is ALWAYS a parallelogram but NOT all parallelograms are a rhombus.
Answer:
Always
Step-by-step explanation:
Rhombi hold all the characteristics of parallelograms and have their own too added on.
Hope that helps!!
4c divided by 6 + 2a for c= 4 for a =5
Answers
Given expression:
[tex] \sf4c \div 6 + 2a[/tex]
Given values:
a = 5c = 4Rule we are going to use:
BODMAS
B = BracketsO = Of OrderD = DivisionM = Multiplication A = AdditionS = SubtractionSolution:
Substitute the variables with their given values and solve using the BODMAS rule[tex] \tt4 \times 4 \div 6 + 2 \times 5[/tex]
[tex] \tt \: \frac{ \cancel4 \times 4}{ \cancel6} + 10[/tex]
[tex] \tt \: \frac{2 \times 4}{3} + 10[/tex]
[tex] \tt \frac{8}{3} + 10[/tex]
[tex] \boxed{ \bf \: \frac{38}{3} }[/tex]
2.4 as a mixed number
Answers
Answer:
2 2/5
Step-by-step explanation:
18x + 27 divided by 9
Answers
18x + 3
1. We are combining like terms / using PEMDAS order by dividing before adding
18x + 3 is the most simplified equation you could get as you can’t add 18x and 3 as they aren’t like terms and there’s no possible answer that it gives us to solve it as a two-step equation.
18x + 3
Answer:
that is the answer
Step-by-step explanation:
I hope it's help
The rule T⟨4, −1⟩ is used on the preimage point (2, −7). What is the image point?
Answers
The image point for the given rule and preimage is (6 - 8)
What is the image point?When we apply a rule T<a, b> to a preimage point (x, y) we get the image (x + a, y + b), so this is like a translation.
So if we apply the rule T<4, -1> to the preimage point (2, -7), the image will be:
(2 + 4, - 7 + (-1)) = (6 - 8)
Concluding, the image point is (6 - 8)
If you want to learn more about translations, you can read:
https://brainly.com/question/2972832
Which of the following is a quadratic function?
A)f(x)=2-7x^2
B)f(x)=4^x
C)f(x)=0x^2+7x-4
D)f(x)=3x+8
Answers
Answer:
A.
Step-by-step explanation:
A quadratic equation is raised to a degree of 2. Because there is an [tex]x^{2}[/tex] term, it is considered a quadratic equation.
Answer:
The curve will touch the x-axis at x = 2, but not pass through it.
Step-by-step explanation:
I got it right on my test.
Zoe invested $5,500 in an account paying an interest rate of 8 1/2% compounded continuously. Aubrey invested $5,500 in an account paying an interest rate of 8 1/4% compounded annually. To the nearest dollar, how much money would Aubrey have in her account when Zoe's money has doubled in value?
Answers
Answer:
Audrey will have $10,498.10 when Zoe's money has doubled in value.
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
BracketsParenthesisExponentsMultiplicationDivisionAdditionSubtractionLeft to RightAlgebra I
Equality Properties
Multiplication Property of EqualityDivision Property of EqualityAddition Property of EqualitySubtraction Property of EqualityAlgebra II
Natural Logs and Exponentials
Compounded Continuously Interest Rate Formula: [tex]\displaystyle A = Pe^{rt}[/tex]
P is the principle amountr is the interest ratet is timeCompounded Annually Interest Rate Formula: [tex]\displaystyle A = P(1 + r)^t[/tex]
P is the principle amountr is the interest ratet is timeStep-by-step explanation:
Step 1: Define
Identify.
Zoe:
P = $5,500
r = 0.085
A = 2P
Aubrey:
P = $5,500
r = 0.0825
Step 2: Find Time
Find time elapsed by using Zoe.
Substitute in variables [Compounded Continuously Interest Rate]: [tex]\displaystyle 2P = 5500e^\big{0.085t}[/tex]Substitute in P: [tex]\displaystyle 2(5500) = 5500e^\big{0.085t}[/tex]Simplify: [tex]\displaystyle 2 = e^\big{0.085t}[/tex]Isolate t term: [tex]\displaystyle \ln 2 = 0.085t[/tex]Isolate t: [tex]\displaystyle t = \frac{\ln 2}{0.085}[/tex]So the time it takes for Zoe to get double her money is approximately 8.15467 years.
Step 3: Find Audrey's Money
Substitute in variables [Compounded Annually Interest Rate]: [tex]\displaystyle A = 5500(1 + 0.0825)^\big{\frac{\ln 2}{0.085}}[/tex]Evaluate: [tex]\displaystyle A = 10498.10[/tex]∴ after the elapsed time of approximately 8.15467 years, Zoe would have made double her money valued at $11,000 and Audrey would have made $10,498.10.
---
Topic: Algebra II
Unit: Logarithmic Functions
help pls its attached as a file
Answers
1(6r + 7) + 1(13 + 7r)
6r + 7 + 13 + 7r
13r + 20
2. (13 - 3/2r) - (1 - r )
1(13 - 3/2r) - 1(1 - r )
13 - 3/2r - 1 + r
12 - (3/2r - 2/2r)
12 - 1/2r
3. (-8 - r) + (2r - 4)
1(-8 - r) + 1(2r - 4)
-8 - r + 2r - 4
-12 + r
4. (7r - 3/2) - (2/3 + 6r)
1(7r - 3/2) - 1(2/3 + 6r)
7r - 3/2 - 2/3 - 6r
r + (- 3/2 - 2/3)
r +(- 9 - 4 / 6)
r + -13/6
r - 13/6
Hope this helps!
Tri scored a total of 31 points in the basketball game, and he scored p points in the second half of the game. Write an expression to determine the number of points he scored in the first half of the game. Then, find the number of points he scored in the first half of the game if he scored 7 points in the second half of the game
Please No Fake Answers this QUESTION IS ALOT OF POINTS ON A TEST
Answers
Answer:
If he scored x points in the first half, then x + p = 31
Answer:
expression: y = 31 - pHe scored 24 points in the first half.expression:
first half points + second half points = total points obtained
Let first half points be y
y + p = 31
y = 31 - p ......this is the expression.
solve:
y = 31 - p
y = 31 - 7
y = 24 points
Find the values of x and y. Write your answers in simplest form
Answers
Answer:
x = 12√3
y = 12
Step-by-step explanation:
=>> x/24 = perpendicular/hypotenuse
=>> x/24 = sin 60°
=>> x/24 = √3/2
=>> x = 24√3/2
=>> x = 12√3
now the value of y
=>> y/24 = cos 60°
=>> y/24 = 1/2
=>> y = 12
The weight of an object is affected by gravity. Something that weighs 1 pound on earth will weigh 1.08 times that weight on Saturn. If a rock weighs 2 1/2
pounds on Earth, what will the object weigh on Saturn?
Answers
Answer:
2.7 lb
Step-by-step explanation:
2x1.08=2.16
1/2x1.08=0.54
2.16
+ 0.54
2.70
2.70 = 2.7
PLEASE HELP!!!
41. A bag contains 13 red marbles, 12 green marbles and 5 blue marbles. If you mix up the
marbles and pull one out at random, what is the probability that it will be blue? (Answer,
of course, as a fraction in lowest terms.)
Answers
Answer:
Number of red marbles = 13
Number of green marbles = 12
Number of blue marbles = 5
Total Number of marbles = 13+12+5
Total Number of Marbles = 30 marbles
[tex] \bf \: probability \: of \: blue \: marbles \: = \frac{number \: of \: blue \: marbles}{total \: number \: of \: marbles} [/tex]
[tex]\sf \dashrightarrow \: probability \: of \: blue \: marble = \frac{5}{30} \\ \\ \sf \dashrightarrow \: probability \: of \: blue \: marble = \cancel \frac{5}{30} \\ \\ \sf \dashrightarrow \: probability \: of \: blue \: marble = \frac{1}{6} [/tex]
So, the probability of blue marbles would be ⅙ .
Answer:
1/6 chance of getting blue
Step-by-step explanation:
find your total (30) that will be your denominator
the number of blue marbles will be your numerator (5)
then simplify 5/30 to 1/6
6. It takes one hour longer to fill the empty pool when only the input pipe is open than it takes to empty the filled pool when only the drain pipe is open. It takes 72 hours to empty the filled pool when both pipes are open. How many hours does it take to fill the empty pool when only the input pipe is open
Answers
Using the together rate, it is found that it takes 144.5 hours to fill the empty pool when only the input pipe is open.
What is the together rate?It is the sum of each separate rate.
In this problem:
The input's pipe rate is 1/x.The drain's pipe rate is of 1/(x-1).The together rate is of 1/72.Hence:
[tex]\frac{1}{x} + \frac{1}{x - 1} = \frac{1}{72}[/tex]
[tex]\frac{x - 1 + x}{x(x - 1)} = \frac{1}{72}[/tex]
[tex]x^2 - x = 144x - 72[/tex]
[tex]x^2 - 145x + 72 = 0[/tex]
Which is a quadratic equation with coefficients a = 1, b = -145, c = 72, hence:
[tex]\Delta = b^2 - 4ac = (-145)^2 - 4(1)(72) = 20737[/tex]
[tex]x_1 = \frac{145 + \sqrt{20737}}{2} = 144.5[/tex]
[tex]x_2 = \frac{145 - \sqrt{20737}}{2} = -0.5[/tex]
Time is a positive measure, hence, it takes 144.5 hours to fill the empty pool when only the input pipe is open.
More can be learned about the together rate at https://brainly.com/question/25159431
1,5,9,13 generalize the pattern by finding the nth term
Answers
Answer:
an= a1 +(n-1)*4
Step-by-step explanation:
a1 = 1, a2 =5, a3 = 9, a4= 13,... an= ?
we see that each term is getting bigger so usually that will happen because of addition or multiplication-in our case add 4 to previous term
a1 = 1,
a2 = a1+(2-1) 4 = 1+4 = 5,
a3 = a1 + (3-1)*4 = a1+8 = 1 + 8 = 9,
a4= a1 + (4-1)*4 = a1 + 12 = 1+12= 13,
...
an= a1 +(n-1)*4
please hurry A side of the triangle below has been extended to form an exterior angle of 133°. Find the value of xx.
Answers
Solution:
Note that:
x + 108 + (180 - 133) = 180Simplify the equation to find x.
=> x + 108 + (180 - 133) = 180=> x + 108 + (47) = 180=> x + 155 = 180=> x = 180 - 155 = 25°→ x + 108 + (180 - 133) = 180°
→ x + 108 + (47) = 180°
→ x + 155 = 180°
→ x = 180 - 155 = 25°
Instructions for a craft project say that the length of a piece of red ribbon should be 7 inches less than the length of a piece of blue ribbon. How long is the blue ribbon if the red ribbon is 12 inches?
Answers
Answer:
12 inches of red ribbon + 7 inches
therefore the length of a blue ribbon is = 19 inches
Answer:he right
Step-by-step explanation:
Please Help!
Determine the solution to the system of equations graphed below and explain your reasoning in complete sentences. g(x) = -2x - 3 and f(x) = Ix+1I - 4
Answers
Answer:
(0,3)
Step-by-step explanation:
It is where the lines intersect
The value of the g(x) is equal to the value of f(x). Then the solution of the equation is at (0, -3).
What is the linear system?A Linear system is a system in which the degree of the variable in the equation is one. It may contain one, two, or more than two variables.
The given expression are as follows
g(x) = -2x - 3 and f(x) = Ix+1I - 4
For the solution of the system, the value of the g(x) is equal to the value of f(x). Then we have
[tex]\begin{aligned} \rm g(x) &= \rm f(x)\\\\\rm -2x - 3 &= \rm x + 1 - 4\\\\-\rm 2x - 3 &= \rm x - 3\\\\\rm 3x &= 0\\\\\rm x &= 0 \end{aligned}[/tex]
Then the g(x) will be
g(x) = -2(0) - 3
g(x) = - 3
Then the solution of the equation is at (0, -3).
More about the linear system link is given below.
https://brainly.com/question/20379472
please help
i reallly need it
Answers
Answer:
300 in³Step-by-step explanation:
The volume is:
V = Bh, where B- area of base, h - heightFind the area of base, which is the trapezoid:
B = 1/2*(5 + 7.5)*6 = 37.5 in²Find the volume:
V = 37.5*8 = 300 in³Girl Scouts are selling cookies for $5 a box. Mark buys four boxes and donated $10 extra. What equation represents this situation?
If anyone can help me with this problem that will be amazing, thank you!!!
Answers
Answer:
y= 4x + 10
Step-by-step explanation:
It would equal this because mark buys 4 boxes x and he donated 10 dollars. So it would be that. You could also plug in 5 for x so it could be
y= 4(5) +10
But, either one should work.
Find the perimeter of this semi-circle with radius, r = 31cm. Give your answer rounded to 1 DP
Answers
Answer:
97.4cm
Step-by-step explanation:
The radius is 31cm so π x 31= 97.3893 rounded to 1DP is 97.4cm
What is the correct justification for the first step in solving this equation? 3(x - 4) + 1 = 12x
Answers
Answer:
x = -11/9
Step-by-step explanation:
3(x-4) + 1 = 12x
Step 1: Use distributive property
3*x - 3*4 + 1 = 12x
3x - 12 + 1 = 12x
Step 2: Combine like terms
3x - 11 = 12x
Step 3: Subtract '3x' from both sides
-11 = 12x - 3x
-11 = 9x
Step 4: Divide both sides by 9
-11/9 = x
Answer:
Solve the first part in Parenthese
Step-by-step explanation:
3(X-4)
3x-12+1=12x
-1 -1
3x-11-12=12x
-12 -12
3x-11=0x
-11 -11
3x= -11x
/3 /3
x= -11/9
Ben had $40.00..he gave his brother 2/5 of the amount.how much money did Ben's brother receive?
Answers
Answer:
16
Step-by-step explanation:
The recipe uses 5/8 oz of simple syrup for 1/4 pint of tea. Find the unit rate in oz per pint
Answers
Answer:
The recipe uses 5/8 oz of simple syrup for 1/4 pint of tea. Find the unit rate in oz per pint
Step-by-step explanation:
The recipe uses 5/8 oz of simple syrup for 1/4 pint of tea. Find the unit rate in oz per pint
