If 1/3 log Vx + log x^3 = n log x for all value of x, then the value of n to the nearest tenth is:
Answers
The value of n, to the nearest tenth, is 1.5.
What is Logarithm?
A logarithm is a mathematical function that represents the exponent to which a base number must be raised to obtain a given number. In other words, it is the inverse operation of exponentiation. The logarithm of a number y to a given base b is denoted as log base b of y, or simply logby.
To solve the equation \(1/3 log(Vx) + log(x^3) = n log(x),\) we can use logarithmic properties to simplify it.
Let's start by applying the power rule of logarithms, which states that \(log(a^b) = b log(a\)). We can rewrite the equation as follows:
\(log(Vx)^(1/3) + log(x^3) = n log(x)\)
Next, we'll use the sum rule of logarithms, which states that log(a) + log(b) = log(a * b). Applying this rule, we get:
\(log((Vx)^(1/3) * x^3) = n log(x)\)
Using the property log(a * b) = log(a) + log(b), we can further simplify:
\(log((Vx * x^9)^(1/3)) = n log(x)\)
Now, applying the power rule again, we have:
\(log((Vx * x^9)^(1/3)) = log(x^n)\)
Since the logarithms on both sides are equal, we can equate their arguments:
\((Vx * x^9)^(1/3) = x^n\)
Now, we can remove the cube root by raising both sides to the power of 3:
\(Vx * x^9 = x^(3n)\)
Simplifying further:
\(V * x^(9/2) = x^(3n)\)
Now, we can equate the exponents:
9/2 = 3n
To solve for n, divide both sides by 3:
n = (9/2) / 3
n = 9/6
n = 1.5
Therefore, the value of n, to the nearest tenth, is 1.5.
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Related Questions
Solve for X due in the morning please help
Answers
84 degrees
Step-by-step explanation:
180=60+36+x
180=96+x
-96 -96
x=84
I need to figure the code out
Answers
The function with the greatest rate of change are:
1. C = 3
2. A = 5
3. A = 1
4. B = 3
What is the Rate of Change of a Linear Function?The rate of change of a linear function, also known as the slope of the line, represents the amount by which the output (y) changes for a given change in the input (x). In other words, it is the measure of how steep the line is.
The formula for the rate of change, or slope, of a linear function is:
slope = (change in y) / (change in x)
1. Rate of change for function A = change in y / change in x = 4/3
For B = 1/2
For C = 3/1 = 3
The function with the greatest rate of change is C = 3
2. Rate of change for function A = change in y / change in x = (10 - 5)/(1 - 0) = 5
For B = (12 - 8) / (3 - 1) = 2
For C = (6 - 3)/(1 - 0) = 3
The function with the greatest rate of change is A = 5
3. Rate of change for function A = change in y / change in x = 2/2 = 1
For B = (3 - 2)/(2 - 0) = 1/2
For C = 1/3
The function with the greatest rate of change is A = 1
4. Rate of change for function A = change in y / change in x = -1/3
For B = (10 - 1)/(4 - 1) = 3
For C = 2
The function with the greatest rate of change is B = 3
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help me i suck at this
Answers
Answer:
Area of ACEG is 100
10
Step-by-step explanation:
Pythagorean says CE = EG = AG = AC = 10
Answer:
I think the answer is 100
Step-by-step explanation:
Use the pythagorean theorem to find out the missing side
6^2 plus 8^2 equals 100
The square root of 100 is 10. The lengths of the sides are 10.
10 times 10 is 100.
I hope this helps :)
In the diagram, what is the measure of angle 1?
Answers
Answer:
C
Step-by-step explanation:
The adjacent angle to the left of 9x is 180 - 9x ( straight angle )
180 - 9x and 3x are corresponding angles and are congruent , then
3x = 180 - 9x ( add 9x to both sides )
12x = 180 ( divide both sides by 12 )
x = 15
Then
∠ 1 and 180 - 9x are vertically opposite angles and are congruent, so
∠ 1 = 180 - 9(15) = 180 - 135 = 45° → C
The null hypothesis claims that the proportion of community college students who work full-time is 0.45. the alternative hypothesis is that this proportion is greater than 0.45.which gives the most convincing evidence against this null hypothesis and in support of the alternative?
Answers
Yes , Who work full-time is 0.45 with full evidence.
What is null hypothesis ?
The hypothesis that the estimate is based solely on chance is called the null hypothesis. Thus, the null hypothesis is true if the observed data (in the sample) do not differ from what would be expected on the basis of chance alone. The complement of the null hypothesis is called the alternative hypothesis.Null hypothesis testing is a formal approach to deciding whether a statistical relationship in a sample reflects a real relationship in the population or is just due to chance.Generally, there are two types of hypothesis. One is a null hypothesis, and another is an alternative hypothesis. In probability and statistics, the null hypothesis is a comprehensive statement or default status that there is zero happening or nothing happening.
So, Who work full-time is 0.45 with full evidence.
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Whats 4/5 as a decimal?
Answers
hi <3
it would be 0.8
hope this helps :)
Solve the problem. Round as appropriate.
The gravitational attraction A between two masses varies inversely as the square of the distance between them.
The force of attraction is 9 lb when the masses are 2 ft apart, what is the attraction when the masses are 6 ft
apart?
A) 3 lb
B) 1 lb
0 2 lb
D) 4 lb
Answers
Answer:
i need the points
Step-by-step explanation:
i need hlp with this question offer I 50 points
Answers
We can start by multiplying both sides of the equation by the reciprocal of 2/3, which is 3/2, to get rid of the fraction:
```
2/3 ( ) = -5 + 4x
(3/2) * 2/3 ( ) = (3/2) * (-5 + 4x)
( ) = -15/2 + 6x
```
Now we can compare this expression to the possible answer choices to see which one makes the equation true:
A: -15/2 + 6X --> This is the same expression we just solved for, so it must be the correct answer.
B: 10/3 + 8/3X --> This expression does not match our solution.
C: 5 2/3+3 1/3X --> This expression does not match our solution.
D: -15+12X --> This expression does not match our solution.
Therefore, the answer is A: -15/2 + 6X.
pllllllllsssssss help 25 points
Answers
Answer:
just buy a phone with a screen protector
Step-by-step explanation:
How do I find the surface area of a cylinder?
Answers
Answer:
SA = 2πr² + 2πrh
Step-by-step explanation:
2πr² will provide the surface area of the top and bottom of the cylinder
2πrh will provide the surface area of the cylinder portion that connects the top and bottom
Solve the absolute value equation. Graph the solution. |x-3|=1
Answers
Answer:
4
Step-by-step explanation:
hihihihihihihihihihi
Marvin has read 8% of the novel he started reading last Saturday. Which decimal is equivalent to the percentage of the novel Marvin has read?
Answers
Answer:
0.8 or 0.08 i believe
Step-by-step explanation:
hope this helps!
A faraway planet is populated by creatures called Mizjigs. All Mizjigs are either black-footed or red-footed and either one-headed or two-headed.
Ragon, who lives on this planet, does a survey and finds that her colony of
650 contains 120 black-footed, one-headed Mizjigs; 200 red-footed, two-headed Mizjigs; and 300 one-headed Mizjigs.
Answers
Answer:
The correct awenser is 270 because when you fill out the chart the total black footed Mizjigs it is 270.
Step-by-step explanation:
(a) Write 7.97 x 10 ^-6 as an ordinary number.
Answers
Answer:
0.00000797
Step-by-step explanation:
Please tell me how to do this or what the answer is :((
Answers
Answer:
(2,-6)
Step-by-step explanation:
You have to go along the X axis then along the Y axis (across the landing, up/down the stairs).
Jake paints 13 birdhouses red. He wants 7 yellow. How many more does he paint red than yellow? Use the strategy Make 10 to subtract
Answers
As per unitary method, Jake painted 6 more birdhouses red than yellow.
The Unitary Method is a strategy used to simplify mathematical calculations. The idea is to make the calculation easier by breaking down the numbers into smaller parts and then recombining them to find the final answer.
In this problem, we want to find out how many more birdhouses Jake painted red than yellow. To do this, we'll use the Unitary Method to subtract 7 from 13.
Starting with the larger number, we'll break down 13 into 10 and 3. We can then subtract 7 from 10 and find that there is a difference of 3.
This means that we have 3 left over from the larger number, which we can add to the smaller number (3) to find the final answer.
Therefore, the final answer is 3 + 3 = 6.
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Triangle CDE is similar to triangle FGH. Find the measure of side HF. Round your answer to the nearest to E H н 40 F G 21 D 53
Answers
According to the Pythagoras theorem, the measure of the side HF is 34.05
Pythagoras theorem in math is defines the statement that is in a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides
Here we have given the side values of the triangle, that is written as,
=> EH = 40
=> EF = 21
Here let us consider that EH refers the hypotenuse and EF refers the adjacent side,
Then according to the Pythagoras theorem, the opposite side HF is calculated as by apply the given values on the formula,
=> 40² = 21² + HF²
When we simplify this one then we get,
=> 1600 = 441 + HF²
Therefore, HF² = 1159
Now, we have to take the square root on both side then we get the value of HF as,
=> HF = 34.05
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Definition of a derivative (limit of the difference quotient)
Answers
The derivative of a function f(x) at a point x = a is defined as the limit of the difference quotient as h approaches zero:
f'(a) = lim (h → 0) [f(a + h) - f(a)] / h
What is derivative?
The derivative of a function in calculus measures the function's sensitivity to changes in its input variable. Specifically, at a particular point, it represents the function's rate of change with respect to its input variable at that moment.
The derivative of a function f(x) at a point x = a is defined as the limit of the difference quotient as h approaches zero:
f'(a) = lim (h → 0) [f(a + h) - f(a)] / h
This limit represents the instantaneous rate of change or slope of the function at the point x = a. The difference quotient is the change in the function value divided by the change in the input variable (or the distance between two points on the graph of the function).
The derivative is a fundamental concept in calculus, and it has many applications in various fields of science, engineering, and economics. It allows us to calculate important quantities such as velocity, acceleration, and marginal cost, and it is used to optimize functions and solve many real-world problems.
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The settlers who brought their Mennonite and Amish faiths with them were from which country?
* it's not Switzerland*
and it supposed to be in this article
I have two history classes and I forgot which one this one is for.
Answers
If area of the triangle formed by the points A(3, 0), B(0, 3) & P(a, b) is Click to zoom sq. units, then identify the correct statement(s)
Answers
When the area of the triangle formed by the points A(3,0), B(0, 3) & P(a, b) is 3/2 sq. units, the correct statement will be A. Locus of P will be a union of two parallel lines
How to calculate the valueArea = 1/2 * |x1*(y2-y3) + x2*(y3-y1) + x3*(y1-y2)|
where (x1,y1), (x2,y2), and (x3,y3) are the coordinates of the three vertices of the triangle, and |.| denotes the absolute value.
Substituting the given values, we get:
3/2 = 1/2 * |3b - 3a - 9|
3 = |3b - 3a - 9|
Now, 3b - 3a - 9 could be either positive or negative.
In this case, we can simplify the above equation as:
3b - 3a - 9 = 3b - 3(a + 3) > 0
which implies:
a < b - 3
or
b > a + 3
This represents the equation of two lines that are parallel to each other and pass through the points (3,-3) and (-3,3), respectively. Therefore, statement A is correct.
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If area of the triangle formed by the points A(3,0), B(0, 3) & P(a, b) is 3/2 sq. units, then identify the correct statement(s)
A. Locus of P will be a union of two parallel lines
B. Locus of P will be a union of two perpendicular lines
C. Locus of P is given by x^2 + y^2 + 2xy – 6(x + y) + 8 = 0
D. Locus of P is given by x^2 - y^2 + 2y - 6x + 8 = 0
15 Aiko records the time, in seconds, that it takes for the children in her class to swim a
16 8 9
202558
5 7
8
(a) Work out the median time.
0 2
2 4
4 6
7
3
4
5
6 1
Key: 1 | 6
= 16 seconds
seconds
16
Answers
The median time is given as follows:
22 seconds.
What is the median of a data-set?The median of a data-set is the middle value of a data-set, the value of which 50% of the measures are less than and 50% of the measures are greater than.
Considering the key format of the stem-and-leaf plot, the observations are given as follows:
16, 18, 19, 20, 22, 25, 25, 28, 57.
The data-set has an odd cardinality of 9, hence the median is the (9 + 1) = 5th element, which is of 22.
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Kate is going on a long distance car trip. She begins with 16 gallons of gas in her car and her car burns 3 gallons of gas each hour. If she ends her road trip with 1 gallon of gas left in the tank, how many hours was she driving
Answers
9514 1404 393
Answer:
5 hours
Step-by-step explanation:
Starting with 16 gallons and ending with 1 gallon means that Kate has used 15 gallons of gas. Burning 3 gallons per hour means her travel time was ...
(15 gal)/(3 gal/h) = 5 h
Kate was driving for 5 hours.
Which of the following are possible side lengths of a triangle? (select all that apply) a. 1, 1, 2 b. 3, 4, 5 c. 5, 5, 11 d. 7, 8, 12 e. 4, 4, 4 f. 4, 8 ,13
Answers
Choice B
Choice D
Choice E
=================================================
Explanation:
Use the triangle inequality theorem. This is the idea where adding any two sides must lead to a result larger than the third side; otherwise, a triangle is not possible. I recommend cutting out strings of paper of these lengths to confirm that you can make a triangle or not.
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For choice A, a triangle is not possible since the first two sides add to 1+1 = 2, but this isn't larger than the third side of 2 units. All we can do really is just form a straight line and not a triangle. We can rule choice A out.
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Choice B is a triangle. Specifically it is a 3-4-5 right triangle that is famous with the pythagorean theorem. Note how...
3+4 = 7 is larger than 54+5 = 9 is larger than 33+5 = 8 is larger than 4so adding any two sides of this triangle leads to the sum being larger than the third remaining side. Choice B is one of the answers.
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Choice C is not a triangle. We have 5+5 = 10 but that isn't larger than 11. We can rule this out.
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Choice D is a triangle since
7+8 = 15 is larger than 127+12 = 19 is larger than 88+12 = 20 is larger than 7any two sides sum to a value larger than the third side
----------------------------------
Choice E is a triangle. We have an equilateral triangle with all sides the same length, and all angles the same value (60 degrees). This is another answer.
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Choice F is similar to choice C. We have the first two sides add to something smaller than the third side (4+8 = 12 is smaller than 13). We can rule this out.
Order the numbers 11/20, 49, 0.5 from least to greatest.
Answers
Please like
HELP PLEASE CAN SOMEONE SOLVE THE QUESTIONS IN THE SCREENSHOT PROVIDED THIS IS URGENT
Answers
Answer:
T = 0.7(220 – a)
Step-by-step explantion:
Hope it helped
help me i’ll give extra points
Answers
Answer:
y=400x
Step-by-step explanation:
This is because the graph rate is up 400 each time. Ex. (1,400) (2,800) (3,1200) etc
Hope this helped
p(x)=x⁴-2x³+2x²-3x+6 to (x-1)
Answers
Answer:
x⁴-2x³+2x²-3x+6 to (x-1) is
(x^3-x^2+x-2)*(x-1)+4
For the following system of inequalities, show the shaded region solution (upload a picture of what you have), and also show the corner points 8x+16y≥20060x+40y≥9602x+2y≥40x≥0;y≥0
Answers
The shaded region is the area that satisfies all the given inequalities. It is the region where all the lines and axes overlap.
To find the shaded region, we need to graph the system of inequalities on a coordinate plane.
The first inequality, 8x + 16y ≥ 200, represents a line.
To graph it, we can find two points on the line by setting x = 0 and y = 0, and then connecting the points.
The second inequality, 60x + 40y ≥ 960, also represents a line. Similarly, we can find two points on this line and connect them.
The third inequality, 2x + 2y ≥ 40, represents another line. Again, find two points and connect them.
Finally, the last two inequalities x ≥ 0 and y ≥ 0 represent the x-axis and y-axis, respectively.
The shaded region is the area that satisfies all the given inequalities. It is the region where all the lines and axes overlap.
To find the corner points, we need to identify the intersection points of the lines. These points are the corners of the shaded region.
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Pls find side x which is opposite
Answers
Answer:
9.1 =x
Step-by-step explanation:
Since this is a right triangle, we can use trig functions.
We want to find x, which is opposite the angle and we know the hypotenuse.
We can use sin theta, which is the opposite side over hypotenuse.
sin theta = opp /hyp
sin 49 = x/12
12 sin 49 =x
9.05651=x
To 1 decimal place
9.1 =x
Given that a is a positive integer, show that
√3a(√12a + a√3a)
is always a multiple of 3.
Input note: write the expression in the form 3(...)
Answers
Answer:
\(3(a^2+2a)\)
Step-by-step explanation:
\(\sqrt{3a}(\sqrt{12a}+a\sqrt{3a}) \\ \\ =\sqrt{36a^2}+a\sqrt{9a^2} \\ \\ =6a+a(3a) \\ \\ =3a^2+6a \\ \\ =3(a^2+2a)\)