After simplifying logarithm equation is : [tex]log_{10} \frac{(a-5)^\frac{1}{2} }{a^\frac{1}{2}-5 } \\[/tex]
What is logarithmic equation ?In, mathematics a logarithmic equation is inverse of exponential equation. That means, we can easily convert the logarithmic equation into exponential equation and vice versa. The basic form of the logarithm function can be written as .
[tex]log_ax=N[/tex]
where, a is the base of function or equation
x define expression
Mathematically, if [tex]a^N=x[/tex] is an exponential function then, this can be converted to logarithmic function as [tex]log_ax=N[/tex].
There are many formulas that are given to us for solving several simple and complex problems based on logarithmic functions and logarithmic equations.
Some important formulas of logarithms are :
log a × b = log a + log blog a/b = log a - log blog a^x = x log alog a^a = 1log (√x) = 1/2 log (x)The given expression can be written as,
[tex]log_{10}(a^2-10a+25) + \frac{1}{2} log_{10}\frac{1}{(a-5)^3} - log_{10}(\sqrt{a} -5)\\\\[/tex]
apply formulas for log a + log b and log a - log b
[tex]log_{10}(a^2-10a+25) + log_{10}(\frac{1}{(a-5)^3})^\frac{1}{2} - log_{10}(\sqrt{a} -5)\\\\= > log_{10}(a^2-10a+25).(\frac{1}{(a-5)^3})^\frac{1}{2} - log_{10}(\sqrt{a} -5)\\\\= > log_{10}\frac{(a^2-10a+25). (\frac{1}{(a-5)^3})}{(\sqrt{a} -5) } \\\\= > log_{10} \frac{(a-5)^\frac{1}{2} }{a^\frac{1}{2}-5 } \\[/tex]
Thus, after solving the logarithm equation is : [tex]log_{10} \frac{(a-5)^\frac{1}{2} }{a^\frac{1}{2}-5 } \\[/tex]
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Brandi jogged for 2/1:2 mikes in 30 minutes sharana jogged 3/1:2 miles in 3:4hours who jogged at a slower rate
Based on the information provided, neither Brandi nor Sharana jogged at a slower rate.
What is rate?Rate can be defined as the speed at which an event happens or an object moves over a particular period of time.
It is also known as the ratio at which two or more term, quantities or objects with different units are compared.
The formula for rate is expressed as;
Rate = distance/ time
From the information given, we have that;
Brandi jogged a distance = 2/1 : 2 = 2 × 1/ 2 = 1 mile in 30 minutesSharana jogged a distance = 3/1 : 2 = 3/ 2 = 1. 5 miles in 3/ 4 × 60 minutes = 45 minutesSubstitute the values
Brandi's rate = 1/ 30 = 0. 03
Sharana's rate = 1. 5/ 45 = 0. 33
From the values gotten, we can see that neither Brandi nor Sharana jogged at a slower rate.
Thus, neither Brandi nor Sharana jogged at a slower rate.
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Simplify the expression. Write the answer in scientific notation.(6 x 10^-4)(6 x 10^-6)
An expression is a set of numbers or variables combined using the operations + , – , × or ÷ . The simplified expression of (6 x 10⁻⁴)(6 x10⁻⁶) is 36 x10⁻¹⁰.
What is Expression?An expression is a set of numbers or variables combined using the operations + , – , × or ÷ . Arithmetic expression that contains only numbers and mathematical operators and algebraic expression that contains variables, numbers and mathematical operators.
(6 x 10⁻⁴)(6 x10⁻⁶) is the given expression
Now multiply 6 with 6 and 10⁻⁴ with 10⁻⁶
36 x 10⁻⁴x 10⁻⁶
We need to add the powers of same base.
36 x10⁻⁴⁻⁶
36 x10⁻¹⁰
Therefore the simplified expression of (6 x 10⁻⁴)(6 x 10⁻⁶) is 36 x10⁻¹⁰.
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*Depressed 15 year old need helps* Brainliset to whoever responds i dont even care anymore if its right or wrong I wont judge ------decent points.....
[tex]y = \begin{cases}- 2x + 1& x > 1 \\- x + 2&x\leqslant1\end{cases}[/tex]
Step-by-step explanation:from the figure
(2,-3) (1,-1) => y = -2x + 1 (x > 1)(0,2) (1,1) => y = -x + 2 (x ≤ 1)[tex](x_1,y_1) \: (x_2,y_2) = >y = \frac{y_2 - y_1}{x_2 - x_1} \: x + a \\ a = y_1 - \frac{y_2 - y_1}{x_2 - x_1} \: x_1[/tex]
Does every function have an inverse which is a function? Does every relation have an inverse which is a relation?
No, all functions do not have an inverse functions. Those that do exists named invertible.
What is meant by inverse function?The inverse function of a function f in mathematics exists a function that reverses the operation of f. If the inverse of f exists, it is shown by the f⁻¹. The inverse of f exists if and only if f is bijective.
An inverse in mathematics is a function that "undoes" another function. In other words, if f(x) produces y, then y entered into the inverse of f produces x. An invertible function is one that has an inverse, and the inverse is represented by the symbol f ⁻¹.
In mathematics, an inverse function (or anti-function) exists as a function that "reverses" another function: if the function f used to an input x gives a result of y, then using its inverse function g to y gives the result x, i.e., g(y) = x if and only if f(x) = y.For a function f: X → Y to have an inverse, it must have the property that for every y in Y, there is exactly one x in X such that f(x) = y. This property ensures that a function g: Y → X exists with the necessary relationship with f.No, all functions do not have an inverse functions. Those that do are called invertible.
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find the distance between the points (7, 7) and (7, 4)
Answer:
the answer to that question is 3
need help i tried to do it on my own but ended up getting the wrong answer(attempting to try again to get a better score on it).
Answer:
25
Step-by-step explanation:
If youre going by 5's youd get 30 but then you gotta take away -5 so it comes out to 25
Answer:
25
Step-by-step explanation:
A Store-It-All storage facility requires users to enter a four digit code, using numbers 0-9, to get through the gate. You need to get a box of winter clothes from your storage container, but you forgot the code.
How many possible codes are there if the digits cannot be repeated?
There are 5040 possible codes.
What is the probability that you will guess the correct code on your first try?
P(correct code) = Answer
1/5040
If the digits can be repeated, how many possible codes are there?
There are_______ different codes. ( Need this one answered)
There are 10000 different possible codes to guess the correct code on the first try..
A percentage, or a figure between 0 and 100 percent, can also be used to express probability. The likelihood of an event occurring increases with its probability value or percentage. How many potential outcomes an event has will determine how likely it is to occur.
1)There are 5040 possible codes if the digits are not repeated.
2)Probability of guessing correct code on first try p = 1/5040.
3)There are 10000 different codes, if the digits are repeated.
Given,
Total digits = 10.
{0,1,2,3,4,5,6,7,8,9}
4 digit code must be formed.
1. Code without repeating digits
→ 4 digit code
Therefore possible ways = 10×9×8×7
= 5040
2. Probability of guessing correct code on first try.
n(A)→ event which has correct code=1
n(S)→total possible ways=5040.
P(A) = n(A)/n(S) = 1/5040
3. If the digits are repeated
→ 4 digit repeated
Therefore possible ways = 10×10×10×10
= 104
= 10000 ways
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For each annual rate of change, find the corresponding growth or decay factor. -0.1%
The decay factor for the annual rate of change of -0.1 % is 0.999.
A quantity must vary by a specific percentage each time period in order for growth or decay to be exponential.
With the function displayed to the right, you may represent exponential growth or decay.
A(x) = a( 1 + r)ˣ
Where A is the amount after x time periods, a is the initial amount, x is the number of time periods, and r is the rate of change.
Now, we have the annual rate of change as:
r = - 0.1 % = - 0.1 / 100 = - 0.001
From the function A(x) = a( 1 + r)ˣ , the corresponding factor is 1 + r.
So, let B = 1 + r
B = 1 + r
B = 1 + (- 0.001)
B = 1 - 0.001
B = 0.999
Now, the value of B is less than 1 therefore, the corresponding decay factor is 0.999.
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What is the surface area of a sphere with a radius of 2 inches? Round your answer to
the nearest tenth.
Please help, I'm super confused!!
You are solving a measurement problem where the numbers 5.2187 x 10^−3, 2.05 x 10^7, and 3.40 x 10^3 are multiplied. How many significant digits should the product have?
A. 5
B. 3
C. 2
D. 1
Using scientific notation, the number of significant digits that the product should have is:
B. 3.
What is scientific notation?A number in scientific notation is given by:
[tex]a \times 10^b[/tex]
With the base being [tex]a \in [1, 10)[/tex].
When two numbers in scientific notation are multiplied, we have that:
The bases are multiplied.The power of 10 is kept.The exponents are added.For this problem, the product is given by:
[tex]5.2187 \times 10^{-3} \times 2.05 \times 10^7 \times 3.4 \times 10^3[/tex]
Multiplying the bases and adding the exponents, we have that:
[tex]5.2187 \times 2.05 \times 3.4 \times 10^{-3 + 7 + 3} = 42.8 \times 10^{7}[/tex]
42.8 has to be divided by 10 to assume for the base have only one digit, hence:
[tex]42.8 \times 10^{7} = 4.28 \times 10^6[/tex]
Hence, considering the rounding, the number has 3 significant digits(4, 2 and 8), and option B is correct.
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The prime factorization of 6000
Answer:
3000 = 2*2*2*2*3*5*5*5
Step-by-step explanation:
6000/2 = 3000
3000/3 = 1000
1000/2 = 500
500/2 = 250
250/2 = 125
125/5 = 25
25/5 = 5
5/5 = 1
3000 = 2*2*2*2*3*5*5*5
i really dont know this
Answer:
y=x+6
Step-by-step explanation:
The gradient of the line is change in y/ change in x
Thus meaning the gradient is 1. (defined as x)
The line crosses through the y-axis on the point (0,6)
So your euqation will be y = (1 - the gradient) x + (interception of y-axis) 6
Answer:
y = x + 6
Step-by-step explanation:
The general form of an equation of a line is
y= mx+b
y = slope ·x + y-intercept
Find the slope of the line, m:
-Pick any 2 points on the line, for example lets pick the points (0, 6) and (3, 10)
-Start at any of the points and go towards the other while note the path
start at (0, 6) and to go to (4, 10) we have to
go up (rise) 4 units from 6 to 10 and
go to the right (run) 4 from 0 to 4.
Slope = m = rise/run = 4/4 = 1
m = 1
Find the y-intercept, b:
The y-intercept is where the line intersects the y-axis. By looking at the given graph we can see y-intercept is 6.
b = 6
The equation of our line is
y = x + 6
How do you write five hundred thousandths in number?
Answer: the answer is: 500,000
Simplify each expression.
ln e²
ln(e²) = 2, by properties of logarithm.
What is Logarithm?The opposite of exponentiation is the logarithm.This indicates that the exponent to which a fixed number, base b, must be raised in order to obtain a specific number x, is represented by the logarithm of that number.A number's natural logarithm is its logarithm to the base of the transcendental and irrational number e, which is roughly equivalent to 2.718281828459.
Now, as we know by properties of logarithm, [tex]log_b(a)^m = m(log_b(a))[/tex],
ln (e²) = 2 ( ln(e))
Also, as ln (e) = 1, ln (e²) = 2 (1) = 2.
Hence, ln(e²) = 2, by properties of logarithm.
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what is the greatest common factor of 20x6y 40x4y2−10x5y5? 10x4y 10 x begin power 4 end power y 5x2y5 5 x squared y begin power 5 end power 5x4y 5 begin power 4 end power y 20x6y
The greatest common factor of [tex]20x^{6} y+40x^{4} y^{2} -10x^{5} y^{5}[/tex] is [tex]10x^{4} y[/tex] .
The greatest common factor of a set of numbers is defined as the largest number that divides all the numbers in that given set and leaves 0 as remainder in each case.
In the given expression
[tex]20x^{6} y+40x^{4} y^{2} -10x^{5} y^{5}[/tex]
Applying Prime Factorization and Writing all the terms in the above expression as
[tex]20x^{6} y=10x^{4}y *2x^{2}[/tex]
[tex]40x^{4} y^{2} =10x^{4} y*4y[/tex]
[tex]10x^{5} y^{5} =10x^{4}y*xy^{4}[/tex]
As we can see that [tex]10x^{4} y[/tex] is common and greatest in all the terms .
Hence [tex]10x^{4} y[/tex] is the Greatest common factor.
Therefore , the greatest common factor of [tex]20x^{6} y+40x^{4} y^{2} -10x^{5} y^{5}[/tex] is [tex]10x^{4} y[/tex] , the correct option is (a)[tex]10x^{4} y[/tex].
The given question is incomplete , the complete question is
What is the greatest common factor of [tex]20x^{6} y+40x^{4} y^{2} -10x^{5} y^{5}[/tex]
(a)[tex]10x^{4} y[/tex]
(b)[tex]5x^{2} y^{5}[/tex]
(c)[tex]5x^{4} y[/tex]
(d)[tex]20x^{6} y[/tex]
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You deposit $500 in a savings account for 8 years. How much interest will you earn if the account earns 7% simple interest annually?
[tex]~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\\ P=\textit{original amount deposited}\dotfill & \$500\\ r=rate\to 7\%\to \frac{7}{100}\dotfill &0.07\\ t=years\dotfill &8 \end{cases} \\\\\\ I = (500)(0.07)(8) \implies I = 280[/tex]
Answer:
$280
Step-by-step explanation:
500x7%=35
35x8=280
kate and jean paint a house together in 6 days
Answer:
Okay? whats the question
Step-by-step explanation:
what are the best anime jobs that use math?
Answer:
Possibly Design and 3d printing
Step-by-step explanation:
3D printing and design requires precise measurements and angles. Maybe you can look into jobs with these requirements?
Hope this helped :)
Answer:
Careers that involve math
Step-by-step explanation:
A university's freshman class has 8600 students. 1634 of those students are majoring in Economics. What percentage of the freshman class are Economics majors?
Answer:
[tex]19\%[/tex]
PercentagesPercentages are evaluated values that say how much of a whole is occupied by that value. For example, if we were to say 75% of a strawberry pie remained, we could also see this as 3/4, or three-fourths.
To solve this particular problem, we will need to divide two values and convert a decimal to a percentage.
SolveFirst, set up the fraction of economics majors that are freshman students to the total number of freshman students.
[tex]\displaystyle \frac{1634}{8600}[/tex]
Then, divide the two using a calculator or long division.
[tex]\displaystyle \frac{19}{100}[/tex]
Finally, to convert this to a decimal, use a calculator.
[tex]0.19[/tex]
To convert a decimal to a percentage, multiply the decimal by 100.
[tex]0.19 \times 100 = 19\%[/tex]
The final answer is [tex]19\%[/tex].
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Answer:
19%
Key Points:
Freshman class size: 8,600 studentsEcon Major: 1,634 studentsIn order to find the percentage of freshman majoring in economics, we must divide the econ major students by the overall size of the freshman class.
[tex]\frac{1634}{8600}[/tex]
Our next step is to grab a calculator and input 1634 ÷ 8600. You can alternatively use the long division method but a calculator would work best. After calculating, your answer should come out to be 0.19
Now, you need to multiply it by 100 so that you can create a percentage.
0.19 × 100 = 19%
Therefore, 19% of the freshman class are economics majors.
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Mean: Use when there are no____
Ex: I, 3, 9, 5, 7, 8, 2, 3
data point that is very
______from the other data points.
Ex: 7, 10, 13, 6, 229, 9, 8
Median: Use when there are_____
Ex: 12, 108, 14, 15, 17, 13, 14,11
Mode: Use when your data can be put into_____
Ex: Students voting for their favorite flavor of Ice cream:
chocolate, vanilla, vanilla, strawberry, chocolate, chocolate
Answer:4
7
82
83
Step-by-step explanation:
REALLY EASY
tyrone likes to snack on his big bag of candy. he takes 888 pieces of candy from the bag each time he snacks. after he has snacked 181818 times, there are only 666 pieces of candy remaining in the bag. the number ccc of pieces of candy remaining in the bag is a function of sss, the number of snacks tyrone eats.
The function's formula is given by c=150-8s .
It is given in the question that
number of candies taken by tyrone in each snack = 8
number of times tyrone snacks = 18
Total candies= (number of times tyrone snacks)x(number of candies taken in each snack )
Total candies=18x8=144.
There are 6 candies left in the bag .
So total candies = 144+6=150.
It is also given that "s" is the number of snacks tyrone eats .
and "c" is the number of candies remaining.
number of candies tyrone eats in each snack = 8
number of candies tyrone eats in s each snack =8s
the number of candies remaining = (total candies) - (number of candies tyrone eats in s each snack ).
Substituting the values we get
c=150-8s.
Therefore , the function's formula is given by c=150-8s .
The given question is incomplete , the complete question is
Tyrone likes to snack on his big bag of candy. he takes 8 pieces of candy from the bag each time he snacks. after he has snacked 18 times, there are only 6 pieces of candy remaining in the bag. the number "c" of pieces of candy remaining in the bag is a function of s, the number of snacks Tyrone eats. Write the function's formula.
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Which equation below is graphed? Question 6 options: y = 3x+2 y =-3x +2 y = 3x - 2 y = -3x - 2
The linear function that contains the points (0,3) and (-1,5) is given by:
y = -2x + 3.
What is the missing information?
The graph is not given and I couldn't find the problem on a search engine, hence I am going to suppose that two points on the graph are (0,3) and (-1,5).
You can select the value of y when the function crosses the y-axes(y-intercept) and another point and follow the same procedure I am going to do here.
What is a linear function?A linear function is modeled in slope-intercept form by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.For this problem, we have that when x = 0, y = 3, hence the slope is of b = 3. When x = -1, y = 5, hence the slope(change in y divided by change in x) is given by:
(3 - 5)/(0 - (-1)) = -2.
Hence the function is:
y = -2x + 3.
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Landscaping A homeowner is planting hedges and begins to dig a 3 -ft-deep trench around the perimeter of his property. After the first weekend, the homeowner recruits a friend to help. After every succeeding weekend, each digger recruits another friend. One person can dig 405 ft³ of dirt per weekend. The figure at the right shows the dimensions of the property and the width of the trench.
a. Geometry Determine the volume of dirt that must be removed for the trench.
The trench will require 9168 cubic feet of dirt to be removed.
Here, we are given that a homeowner is digging a 3 -ft-deep trench around the perimeter of his property.
Length of the property = 210 feet
Breadth of the property = 180 feet
Let us now consider one side of the 180-foot-long trench.
There are two such trenches, each with a width of 4 feet and a height of 3 feet.
Thus the volume of the trench = 2(length × breadth × height)
Volume = 180 × 4 × 3 × 2
= 4320 cubic feet
Now we are left with two other sides of the trench with the following dimensions-
Height = 3ft
Breadth = 4ft
Length = 210 - 8 = 202ft
Thus, volume = 202 × 4 × 3 × 2
= 4848 cubic feet
Thus, the total volume of the trench = 4848 + 4320 = 9168 cubic feet.
Hence, The removal of 9168 cubic feet of earth is necessary.
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Your question was incomplete. Check for the missing figure below.
AB is bisected by midpoint M. Given A( 3 , 7) and the midpoint M( -2 , 9), find the other endpoint B.
The coordinates of endpoint B are (-7, 11)
Midpoint of a lineFrom the question, we are to determine the coordinates of the endpoint B
If the coordinates of the endpoints of a line, AB, are A(x₁, y₁) and B(x₂, y₂), then the coordinates of the midpoint is given by
((x₁+x₂)/2, (y₁+y₂)/2)
From the given information,
The coordinates of A are (3, 7) and the coordinates of the midpoint are (-2, 9)
Let the coordinates of endpoint B be (x, y)
Then,
(3+x)/2 = -2
3 +x =-4
x = -4 -3
x = -7
and
(7 + y)/2 = 9
7 + y = 18
y = 18 - 7
y = 11
Hence, the coordinates are (-7, 11)
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help would be appreciated <3
The coordinates of K' are (-2, 3) and the coordinates of M' are (-4, 1)
How to determine the coordinates of K' and M'?What are the coordinates of K'?
The graph represents the given parameter
On the graph, we have the following coordinates for point K
K = (4, 1)
The transformation vector is given as
[-6]
[2]
The transformation vector implies that
(x, y) = (x - 6, y + 2)
So, we have
K' = (4 - 6, 1 + 2)
Evaluate
K' = (-2, 3)
Hence, the coordinates of K' are (-2, 3)
What are the coordinates of M'?
The graph represents the given parameter
On the graph, we have the following coordinates for point M
M = (2, -1)
The transformation vector is given as
[-6]
[2]
The transformation vector implies that
(x, y) = (x - 6, y + 2)
So, we have
M' = (2 - 6, -1 + 2)
Evaluate
M' = (-4, 1)
Hence, the coordinates of M' are (-4, 1)
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identify the prime factorization for each number 10 x 4 or 2 x 5 2 x 5
Prime factorization of 10 x 4 is 2 x 5 x 2 x 2.
Finding the prime numbers that are multiplied together to produce the original number is the process of prime factorization. The prime factors of 16, for instance, are 2 x 2 x 2 x 2.
Any number can be represented as a sum of prime numbers by prime factorization. A number with exactly two factors, 1 and the number itself, is said to be a prime number. As an illustration, the prime factorization of 18 is 2 x 3 x 3. Here, the two main factors of 18 are 2 and 3. For instance, 72 = 2 x 3 x 3 x 2 can be written as a product of prime factors. The prime factorization of 72 is said to be the expression 2 x 3 x 3 x 2.
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Six hundred residents of a city are polled to obtain information on voting intentions in an upcoming city election. the 600 residents in this study is an example of a(n) _____
Six hundred residents of a city are polled to obtain information on voting intentions in an upcoming city election. The 600 residents in this study is an example of a sample.
Those people who make up a sample are taken from a broader population. Sampling is the process of deciding which group you will use to gather data for your study.
In order for a sample to be representative of the population we are interested in investigating, each participant must have an equal chance of being randomly chosen for the study.
For example, you could interview a sample of 100 students if you were examining the attitudes of students at your university.
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Round to the nearest ten, then estimate the product. 35 x 99 = ___
a. 2,700
b. 3,000
c. 3,600
d. 4,000
Answer:
The answer is 4,000.
Step-by-step explanation:
The closest to 35xn= 3,465
Answer:
Step-by-step explanation:
35 to the nearest 10 is 40 and 99 to the nearest 10 is 100 so 4 times 100 is 4,000 so your answer should be d. 4,000
The sum of two numbers is 14. One number is two less than three times the other. Write an equation to represent the situation
using as a variable.
Answer:
Number 1 is 4
Number 2 is 10
Step-by-step explanation:
Number 1 is x
Number 2 is 3x - 2
so x + (3x - 2) = 14
x + 3x - 2 = 14
4x = 14 + 2
4x = 16
x = 4
so
Number 1 is 4
Number 2 is 3(4) - 2 = 10
all of them please i need help with it its hw
The correct algebra properties are listed below:
EDHAIFCBGWhat properties are used in each case of algebraic operations?
In this problem we find nine cases of mathematical operations with real numbers, each case has to be defined by defining the appropriate property according to real algebra. Now we proceed to define each case:
11 + 0 = 11 Modulative property of addition (Correct choice: E)x · (y · z) = (x · y) · z Associative property of multiplication (Correct choice: D)8 + (- 8) = 0 Existence of additive inverse (Correct choice: H)14 + 20 = 20 + 14 Commutative property of addition (Correct choice: A)2 × (1 / 2) = 1 Existence of multiplicative inverse (Correct choice: I)22 × 1 = 22 Modulative property of multiplication (Correct choice: F)(19 + 12) + 8 = 19 + (12 + 8) Associative property of addition (Correct choice: C)a × 9 = 9 × a Commutative property of multiplication (Correct choice: B)7 · (4 + 11) = 7 · 4 + 7 · 11 Distributive property (Correct choice: G)To learn more on algebra properties: https://brainly.com/question/1448147
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