The simplified form of the given logarithmic expression ln (x+1)+ln (x-1)= 4 is x = 0.67 (to the nearest thousandth).
What precisely are logarithms?A logarithmic term represents a number in log form. A log term is another name for it.
A quantity can also be the sum of two or so more quantities. As a result, a term can be the product of 2 or more quantities, one of which must be in logarithmic form. In those kind of instances, the terms are recognized as log terms.
A quantity can also be defined as the quotient of two quantities. So, if a term includes a quotient of quantities, or at least each of the quantities could be expressed in log form, this same terms are known as log terms.
Quotient Rule: ㏒(A/B) = ㏒A - ㏒BProduct Rule : ㏒A + ㏒B = ㏒(AB)Power Rule: n㏒A = ㏒AⁿBase Rule = ㏒ₐb = ㏒ₓb/㏒ₓaExponent Rule = e∧lnx = xNow, according to the stated condition in question;
ln (x+1)+ln (x-1) = 4
Applying the Product Rule on the left side of the equation;
ln (x+1)/ (x-1) = 4
Convert the obtained expression in the exponent form.
Thus,
e∧[ln (x+1)/ (x-1)] = e⁴
Now, apply the exponent rule.
(x+1)/ (x-1) = 4
Now, simplifying the equation.
(x+1) = 4 (x-1)
x+1 = 4x - 1
4x - x = 1 + 1
3x = 2
x = 2/3
x = 0.666...
x = 0.67 (to the nearest thousandth).
Therefore, the solution for the stated logarithmic expression ln (x+1)+ln (x-1)= 4 is x = 0.67 (to the nearest thousandth).
To know more about the exponent rule, here
https://brainly.com/question/25776256
#SPJ4
given that x is a number that is not negative, kelvin conjectured that x2>x 1. which value is a counterexample to kelvin's conjecture? −12 negative one half −2 negative 2 0 0 5
0 is a counterexample to Kelvin's conjecture.
Firstly rewriting the expression -
x²>x + 1
Now, we will use hit and trial method to find the counterexample to Kelvin's conjecture.
We can not use first two options, because question mentions that x is not negative. So, starting our hit and trial method from 0.
We will keep the value in expression to find the result -
0²>0 + 1
0 > 1
This contradicts or opposes Kevin's statement, as 0 is not greater than 1.
Trying the second number -
5²>5 + 1
25 > 6
This is in accordance with Kevin's conjecture or conclusion, as 25 is greater than 6.
Hence, 0 is the value which is a counterexample to Kelvin's conjecture.
Learn more about expressions involving x -
https://brainly.com/question/1890080
#SPJ4
The complete question is -
Given that x is a number that is not negative, Kelvin conjectured that x^2>x+1 .
Which value is a counterexample to Kelvin's conjecture?
−12
−2
0
5
This year, a small business had a total revenue of $14,200. If this is 29% less than their total revenue the previous year, what was their total revenue the previous year?
The total revenue the previous year is $20,000
How to calculate the total revenue ?This year the total revenue of the small business is $14,200
This amount is 29% less than the total revenue in the previous year
Therefore the total revenue in the previous year can be calculated as follows
100 - 29
= 71
= 71/100
= 0.71
Total revenue= 14,200/0.71
= 20,000
Hence the total revenue the previous year is $20,000
Read more on revenue here
https://brainly.com/question/23896400
#SPJ1
If you can't help me with that answer then can you help me with this one please?
Answer:
73° & 107°
Step-by-step explanation:
1. Those angles are supplementary, so they add up to 180 degrees.
2. (8x - 20) + (8x + 8) = 180
3. You need to add both 8x's together to make 16x. Do the same with -20 & 8. That makes -18. This is binomial addition.
4. 16x - 18 = 180
5. Add 18 to both sides
6. 16x = 198
7. Divide both sides by 16
8. x = 12.375
9. Plug in your x for both angles.
Hello Please Help for Brainlist +20 points its a geometry Question !!! (Math)
20 degrees is your angle
PLEASE HELP ME ASAP!!!!
Which of these is NOT a good use for a frequency chart?
A) Finding out how many pieces of pizza everyone ate
B) Finding out a percentage of a whole
C) Asking people where they went on vacation
D) All of these are good uses of a frequency chart.
Answer:
All are good ideas for a frequency chart.
But not 100% sure on A and C
Solve for X
-1/2+6/7 x+9.7
The equation solved for x gives -0. 61
What are algebraic expression?
Algebraic expressions are expressions that comprise variables, terms, factors, constants and coefficients.
They are also made up of certain arithmetic operations such as addition, subtraction, multiplication, division, bracket, parenthesis, etc.
Given the expression;
-1/2 + 6/7 = x + 9.7
Find the lowest common multiple
-7 + 12/14 = x + 9. 7
Add the numerators
5/ 14 = x + 9. 7
Find the quotient
0. 36 = x + 0. 97
collect like terms
x = 0. 36 - 0. 97
x = -0. 61
Thus, the equation solved for x gives -0. 61
Learn more about linear equations here:
https://brainly.com/question/2030026
#SPJ1
HELP ASAP!!! WILL MARK BRAINLIEST!!!
Line j: y = 2/3x + 1/2
Line k: y = 1/2x + 2/3
Line l: y = 2/3x + 3/2
Line m: y = 3/2x + 1/2
These four lines have been graphed on the same coordinate grid. Which lines are parallel to each other?
A. k & m
B. k & l
C. j & l
D. j & m
Answer:
line J and line L are parallel so C.
The parallel line are j and l.
Hence the correct answer is c.
Given are four lines that have been graphed on the same coordinate grid.
We need to check which of these are parallel to each other.
To determine which lines are parallel to each other, we need to compare their slopes. Parallel lines have the same slope.
The general form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept.
Let's identify the slopes of the given lines:
Line j: y = (2/3)x + 1/2
Slope of j: 2/3
Line k: y = (1/2)x + 2/3
Slope of k: 1/2
Line l: y = (2/3)x + 3/2
Slope of l: 2/3
Line m: y = (3/2)x + 1/2
Slope of m: 3/2
Now, let's see which lines have the same slope:
A. k & m - The slopes are different (1/2 and 3/2). These lines are not parallel.
B. k & l - The slopes are different (1/2 and 2/3). These lines are not parallel.
C. j & l - The slopes are the same (2/3). These lines are parallel.
D. j & m - The slopes are different (2/3 and 3/2). These lines are not parallel.
So, the correct answer is:
C. j & l
Learn more about Parallel lines click;
https://brainly.com/question/29762825
#SPJ7
PLEASE HELP ME ASAP!!!!!
What is the first step in making a frequency chart?
A) Doesn't matter
B) Write down numbers
C) Draw a box
D) Figure out what you are comparing
What is the solution set for the open sentence with the given replacement set?
13 x 7, {4, 5, 6, 7}
1.4
2.5
3.6
4.7
The solution set for the open sentence with the given replacement set is; 6
What is the solution set of the given equation?
We are given the equation as;
13 - x = 7
To solve this , let us use subtraction property of equality to subtract 13 from both sides to get;
13 - 13 - x = 7 - 13
-x = -6
Use division property of equality to divide both sides by -1 to get;
x = 6
Now, the set of possible solutions is {4, 5, 6, 7}. Thus, our solution falls within the set.
Read more about Equation solution at; https://brainly.com/question/2972832
#SPJ1
How do you write 4/25 as a percentage?
Answer: 16% :)
Step-by-step explanation: 25x4=100, and 4x4=16. so 16/100, which equals 16%
Answer:
[tex] \sf {\large{16 \: \%}}[/tex]
Step-by-step explanation:
We know that
4/25 is the same as 4÷25
Then using
Long Division for 4 divided by 25 gives us
0.16
Converting our number to a percentage:
0.16×100
=16%
20 customers are eating dinner at a local restaurant. The restaurant accepts cash or credit as forms of payment. Of the 20 customers, 4 have enough cash to pay for their meal, 16 have a credit card, and 3 have enough cash and a credit card. Using this information, answer the following questions. 1. What is P(A), the probability that a customer has enough cash? 2. What is A(B), the probability that a customer has a credit card? 3. What is P(A and B), the probability that a customer has enough cash and a credit card? 4. What is P(A or B), the probability that a customer has enough cash or a credit card?
P(A) = 4 / 20, this is the probability that a customer has enough cash
P (B) =16 / 20, this is the probability that a customer has a credit card.
P (A and B) = 3 / 20, this is the probability that a customer has enough cash and a credit card.
The probability that a customer has enough cash or a credit card is 0.85.
Probability is defined as the ratio of favorable outcomes to a total number of outcomes.
It is given that, 20 customers are eating dinner at a local restaurant.
The total number of customers = 20
Of the 20 customers,
4 have enough cash to pay for their meal
16 have a credit card and
3 have enough cash and a credit card.
Event A is the probability that a customer has enough cash
Event B is the probability that a customer has a credit card.
P(A) = 4 / 20 = 1 / 5, this is the probability that a customer has enough cash
P (B) =16 / 20 = 4 / 5, this is the probability that a customer has a credit card.
P (A and B) = 3 / 20, this is the probability that a customer has enough cash and a credit card.
To find the probability that a customer has enough cash or a credit card :
The formula used is P(A or B) = P(A) + P(B) - P(A∪B)
P (A or B) = P(A) + P(B) - P (A and B)
= 4 / 20 + 16 /20 - 3 / 20
= 17 / 20
= 0.85
Therefore, The probability that a customer has enough cash or a credit card is 0.85.
Learn more about probability here:
https://brainly.com/question/12226830
#SPJ9
Solve the equation.
1/3 (
(9x + 3) = 3x + 1
Answer: x=0
Step by step explanation:
1/3 (9x+3) =3x+1
=3x+1=3x+1
=3x-3x=1-1
=0x=0
So x=0
I hope this helps you! Have a nice day!!!!
Seven-tenths of half a century is please help me
The meaning and equivalent of the word phrase; seven-tenths of half a century as given in the task content is; 35 years.
What is the meaning and equivalent the word phrase; seven-tenths of half a century as given in the task content?According to the task content, it follows that the meaning and equivalent of seven-tenths of half of a century is to be determined.
On this note, since it follows from place value that seven-tenths means; 7 × (1/10) = 7/10.
Also, since half a century means; (1/2) × 100 years = 50 years.
Ultimately, the word phrase given in the task content is equivalent to;
= (7/10) × 50 years.
= 35 years.
Ultimately, the meaning and equivalent of the word phrase; seven-tenths of half a century as given in the task content is; 35 years.
Read more on word phrase;
https://brainly.com/question/28428605
#SPJ1
Which graph represents the inequality 3y - 5x≤-6?
Answer: Graph A represents the given inequality 3y−5x>−6. Option A is correct.
From the graphs, the graph is to choose which best describes the inequality 3y−5x>−6
Step-by-step explanation: hope this helps
Graph A represents the inequality 3y - 5x≤-6. Correct option is A. The inequality 3y - 5x ≤ -6 represents a linear inequality in two variables, y and x.
To graph this inequality, we can rearrange it into slope-intercept form (y = mx + b), where m is the slope, and b is the y-intercept.
Let's rearrange the given inequality:
3y - 5x ≤ -6
First, add 5x to both sides of the inequality:
3y ≤ 5x - 6
Now, divide both sides by 3 to isolate y:
y ≤ (5/3)x - 2
Now, you have the inequality in slope-intercept form:
y ≤ (5/3)x - 2
To know more about Graph:
https://brainly.com/question/5561502
#SPJ2
Explain why the expansion at the right of log₄√t/s is incorrect. Then do the expansion correctly.
The correct expansion of log₄√t/s is 1/2 log₄(t/s).
Logarithms is another way of writing exponents. Logarithm is nothing but another way of expressing exponents and can be used to solve problems that cannot be solved using the concept of exponents only. Understanding logs is not so difficult. To understand logarithms, it is sufficient to know that a logarithmic equation is just another way of writing an exponential equation.
Logarithm and exponent are inverse forms of each other. One can understand this from the section below. Initially, a mathematician named John Napier introduced logarithms for making calculations in a simple way and this concept is quickly adopted by other scientists, engineers, etc.
Given that, log₄√t/s and we have to expand this logarithmic function having base 4 accordingly. So, let's proceed to solve this logarithmic expansion.
log₄√t/s = log₄((t/s)^(1/2))
= log₄((t/s)^(1/2))
Apply log rule, logₐ(xᵇ) = b.logₐ(x), assuming x ≥ 0
= 1/2 log₄(t/s)
Hence, log₄√t/s = 1/2 log₄(t/s) is the correct expansion.
Therefore, 1/2 log₄(t/s) is the required answer.
Learn more in depth about logarithmic function at https://brainly.com/question/13473114
#SPJ4
What is 0.00784 rounded to 2 significant figures? Pls I need this quick
The answer would be 0.0078
The decimal number 0.00784 rounded off to 2 decimal places is 0.
What is rounding off of numbers?We round off numbers to make them easier to remember and it also keeps its value approximately to the place it has been rounded off.
To round off any number to any place we'll look for the digit next to that place and if it is equal to or greater than 5 we'll add one to the previous digit and make all the digits after it zeroes and if the digit is less than 5 we do not add one to the preceding digit and simply make all the digit after it to zeroes.
Given, 0.00784 and we have to round off to two significant figures means
the number will have 2 digits after the decimal place.
Now, 0.00784
= 0.00780.
= 0.0078.
= 0.0080.
= 0.008.
= 0.010.
= 0.01.
= 0.00.
= 0.
So, 0.00784 rounded off to 2 decimal places is 0.
learn more about rounding off of numbers here :
https://brainly.com/question/17353491
#SPJ2
So basically what you have to do is subtract the above ground level (1) with ground level (4) and you’ll get 3 which is negative bc it counts as below ground level . Now that the car rises 13 meters subtract 13-3= 10 and add it with the other ground level 6 meters . 10-6=4
Rollercoaster Car is at 4 m above the ground by using integer concept.
As per the question statement, Rollercoaster Car that goes above and below the ground.
Before solving the question, we need to know the concept of integer operations on a number line.
Here the car is [tex]1 meter[/tex] above the ground level and then goes 4 meter down.
So the position is [tex]1-4=-3 meter[/tex] or 3 meter below the ground level.
Now it rises 13 meter above the ground. So now the position is [tex]-3+13 = 10 meter[/tex] or 10 meter above the ground.
Now it again falls by 6 meter so position is [tex]10-6 = +4 meters[/tex] or 4 meters above the ground.
Therefore the final position is 4 meters above the ground level.
Integers: a number without a fraction (no decimals). Includes the digits 1, 2, 3, etc., in counting, zero {0}, and the antithesis of the numerals "-1, -2, -3,... " We can classify them all in the following order: {..., -3, -2, -1, 0, 1, 2, 3, ...}To learn more about integers and its operations, click on the link given below:
https://brainly.com/question/15276410
#SPJ9
A square ABCD (shown below) is rotated 90° clockwise of the origin match the corresponding coordinates after rotation
The square is rotated 90° clockwise about the origin to new points A'(2, 2), B'(4, 2), C'(4, 4) and D'(2, 4)
What is transformation?Transformation is the movement of a point around the coordinate plane. Types of transformations are rotation, translation, reflection and dilation.
Rotation is the flipping of a figure about a fixed point.
Square ABCD have vertices at A(-2, 2), B(-2, 4), C(-4, 4) and D(-4, 2). The square is rotated 90° clockwise about the origin to new points A'(2, 2), B'(4, 2), C'(4, 4) and D'(2, 4)
Find out more on transformation at: brainly.com/question/13763238
#SPJ1
The midpoint of BC is M(5, 2). One endpoint is B(8, 0). Find the coordinates of the other endpoint C. Write the coordinates as decimals or integers. C = (, ) Submit
The coordinate of point C from the given expression is (2, 4)
Midpoint of coordinatesThe formula for calculating the midpoint of coordinates is given by the equation shown below:
Midpoint = {(x₁+x₂)/2, (y₁+y₂)/2}
Given the following parameters
Midpoint = M(5, 2)
B(8, 0)
Required
Coordinate point C
Substitute the given parameters
5 = (8+x₂)/2
5(2) = 8+x₂
10 = 8+x₂
x₂ = 2
Similarly
2 = (0+y₂)/2
2(2) = 0+x₂
4 = 0 +y₂
y₂ = 4
Hence the coordinate of point C from the given expression is (2, 4)
Learn more on midpoint here: https://brainly.com/question/5566419
#SPJ1
-5x^2-2x^3-4x write the polynomial in standard form then identify the polynomial by the number of terms
Answer: - 2x³ - 5x² - 4x, trinomial
Step-by-step explanation:
When writing a polynomial, the standard form is to have the terms ordered from highest power to lowest power. 3 > 2, so we will reorder them as so;
- 5x² - 2x³ - 4x ➜ - 2x³ - 5x² - 4x
To identify the polynomial, we will look at the number of terms. This polynomial has three terms, so it is a trinomial.
- 2x³ - 5x² - 4x
[1] - 2x³
[2] - 5x²
[3] - 4x
You owe $1,032.56 on a credit card with an 11.25% APR. The minimum due is $67.00
and you pay it at the beginning of the month. How much interest is accrued by the end of the month?
Interest accrued at the end of the month is $1.41.
What is the interest on credit card?Credit cards impose interest on any sums that you don't pay by the due date each month. Interest accrues everyday when you hold a balance from month to month based on the so-called Daily Periodic Rate (DPR). DPR is only another term for your daily interest charge.
Step 1: Make the initial payment of $882 ($1,032 - $150).
Step 2: $882 times 1.00938 is $890.27
Step 3: Pay $1,032 multiplied by 1.00938 ($1,041.68) at the conclusion.
Step 4. $1,041.68 - $150= $891.68
The interest for the first month is $1.41.
To learn more about interest on credit card from given link
https://brainly.com/question/24267737
#SPJ9
A box of cereal can be purchased in the large size, which is 15 ounces for $3.14, or the family size, which is 24 ounces for $5.34. Which size box of cereal has the lowest price per ounce, and what is the amount?
a -Large size at $0.21 per ounce
b-Large size at $0.22 per ounce
c-Family size at $0.21 per ounce
d-Family size at $0.22 per ounce
Given the values that we have here for the large sizes and the family size of cereal the one that has the lowest price per ounce is that of the Large size at $0.21 per ounce
How to solve for the sizes of the cerealsFor the family size
We would first have to divide 5.34 by 24
= 5.34 / 24
= 0.22 per dollar
For the large size we have
15 ounces for $3.14
= 3.14 / 15
= 0.21 dollars
Hence we can see that the size of the cereal that is the lowest price per ounce is given as Large size at $0.21 per ounce
Read more on quantities here:
https://brainly.com/question/28293787
#SPJ1
?(21)+?(4)=300 what is the answer
[tex]21x + 4y = 300[/tex]
We have infinitely many numbers that make this equation hold. For example:
[tex](x,y)=(69,-287.25) \\ (x,y)=(1,69.75) \\ (x,y)=(7,38.25)[/tex]
This could go on forever, so your question does not have a right answer.
Which statement explains the relationship between terms in the table? XOSO5 10 15 20 Each term in Pattern X is of the corresponding term in Pattern Y. Each term in Pattern X is of the corresponding term in Pattern Y. Y O 15 30 45 60 Each term in Pattern X is 3 times the corresponding term in Pattern Y. Each term in Pattern X is 5 times the corresponding term in Pattern Y.
Could someone please solve and explain this to me?
2ab^-2 • (b^2)^-2
(*if a number has ‘^’ before it, that means it’s an exponent).
Answer:
[tex]2ab^{(-6)}[/tex]
Step-by-step explanation:
Multiply exponents/group exponents
[tex]2ab^{(-2)} \times b^{(-4)}\\2ab^{-2 + -4}\\2ab^{-6}[/tex]
What is the greatest common factor of 24 and 4?
Answer: 2
UvU This might help might not
(1/5) to the power of 2 X (1/5) to the power of 2
Answer: 0.0016
Step by step explanation:
Answer:
=1/5⁴ = 1/625
Step-by-step explanation:
(1/5)² (1/5)² = (1/5)⁴
= 1⁴ / 5⁴
= 1 / 625
What is the solution of the system?
4 x+2 y=4
6 x+2 y=8
(F) (-2,2)
(G) (2,-2)
(H) (1,2)
(I) (-1,2)
For the system of equations 4 x+2 y = 4 and 6 x+2 y = 8, the solution is (2, - 2).
We are given the system of equations as:
4 x+2 y = 4 … (1)
6 x+2 y = 8 … (2)
We need to solve it to find the value of x and y.
Subtracting equation (1) form equation (2), we get that:
6 x - 4 x + 2 y - 2 y = 8 - 4
Combining the like terms, we get that:
2 x = 4
x = 4 / 2
x = 2
Now put it in equation (1) to get the value of y
4 (2) + 2 y = 4
8 + 2 y = 4
2 y = - 4
y = - 2
(x, y) = (2, - 2)
Therefore, we get that, for the system of equations 4 x+2 y = 4 and 6 x+2 y = 8, the solution is (2, - 2).
Learn more about equation here:
https://brainly.com/question/1214333
#SPJ4
work out the mean for this data set: 9.1, 1, 3.7, 6.1, 9.8
Answer: 5.94
Step-by-step explanation: In order to find the mean, you first add up all the values in the data set and then divide this number by the number of values!
Hope it helps ^^
A triangle has two sides of lengths 4 and 7. What value could the length of the third side be? Check all that apply
A.7
B.17
C.11
D.5
E.9
F.3
Answer: E
Step-by-step explanation:
4 x 4 = 16
7 x 7 = 49
16 + 49 = 65
8.062 is the square root of 65.
Round 8.062 I guess you could round it to 9 but I believe the actual answer should be 8.