ln(144) can be written in terms of ln(3) and ln(4) as:
ln(144) = 4 ln(2) + 2 ln(3) ≈ 4 ln(1.386) + 2 ln(3) ≈ 2.7726 + 2 ln(3)
We can use the logarithmic property that states that ln(a * b) = ln(a) + ln(b) to rewrite ln(144) in terms of ln(3) and ln(4).
First, we can find the prime factorization of 144:
[tex]144 = 2^4 * 3^2[/tex]
Using the property above, we can rewrite ln(144) as:
[tex]ln(144) = ln(2^4 * 3^2) = ln(2^4) + ln(3^2)[/tex]
Now, we can use another logarithmic property that states that ln(aᵇ) = b * ln(a) to simplify ln(2⁴) and ln(3²):
ln(144) = 4 ln(2) + 2 ln(3)
Therefore, ln(144) can be written in terms of ln(3) and ln(4) as:
ln(144) = 4 ln(2) + 2 ln(3) ≈ 4 ln(1.386) + 2 ln(3) ≈ 2.7726 + 2 ln(3)
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In the diagram, BC = 9. Find AB and AC by dragging the correct distance to its corresponding side?
Answer is: AC= 9[tex]\sqrt{3}[/tex] Units, AB = 18 units.
What is triangle?Triangles have three interior angles that add up to 180 degrees, and they can be classified based on the lengths of their sides and the measures of their angles.
In ΔABC, angle C is right angle,
so the triangle is right angle triangle;
tan30° = BC/AC
[tex]\frac{1}{\sqrt{3} }[/tex] = 9/AC
AC= 9[tex]\sqrt{3}[/tex] Units
and
Sin 30° = BC/AB
1/2 = 9/AB
AB = 18 units
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NEED HELP FAST! 20 POINTS!!
The value of x is 57 degrees. This was obtained by the use of the trigonometric ratios.
What is a right angle triangle?A right triangle, also known as a right-angled triangle, is one that we can say that an angle in this triangle would be 90 degrees.
The Pythagorean theorem can be used to obtain the lengths of the various sides that we have in the right angled triangle. This is one of the fundamental theories in the right angled triangle.
Let us now use the cosine to find the angle as shown below;
We know that;
Cos x = 11/20
x = Cos-1(11/20)
x = 57 degrees
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Write a formula for a linear function f(x) that models the situation, where x is the number of years after. In 2006 the average adult ate 56 pounds of chicken. This amount will increase by 0. 6 pounds per year until 2011
The required linear function is (f(x) = 0.6(x - 2006) + 56) and this can be determined by using the arithmetic operations.
Given :
In 2006 the average grownup ate fifty-six kilos of birds.
the amount will increase by means of zero.6 pounds in step with yr till 2011.
To determine the linear feature f(x) following steps can be used
Let 'x' be the number of years.
Then the total number of years since 2006 will be:
= x - 2006
The amount boom in kilos in line with 12 months could be:
= 0.6(x - 2006)
Now, add 56 to the above equation.
= 0.6(x - 2006) + 56
It is a type of function that has a constant rate of change between the independent variable (usually denoted as x) and the dependent variable (usually denoted as y). The general form of a linear function is y = mx + b, where m is the slope or the rate of change, and b is the y-intercept.
Linear functions are commonly used in mathematics, economics, physics, and engineering to model real-world phenomena that have a linear relationship between two variables. For example, the cost of producing a certain number of units of a product may be modeled by a linear function, where the slope represents the cost per unit and the y-intercept represents the fixed costs.
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explain and develop this
quote
Human suffering anywhere concerns men and women
everywhere.
Elie Wiesel, Night
Elie Wiesel's quote speaks to the idea that human suffering is a universal concern and that we all have a responsibility to respond to it. It is a call to action for all of us to be aware of the suffering of others and to do what we can to alleviate it.
The quote "Human suffering anywhere concerns men and women everywhere" by Elie Wiesel in his book Night speaks to the idea that suffering is not an isolated event. Rather, it is something that affects all of humanity, regardless of where it occurs. This quote highlights the interconnectedness of humanity and the responsibility we all have to care for one another.
Wiesel, a Holocaust survivor, experienced unimaginable suffering during his time in concentration camps. Through his writing, he is able to convey the importance of recognizing and responding to the suffering of others. This quote serves as a reminder that we cannot turn a blind eye to the suffering of others, even if it is happening in a different part of the world.
In conclusion, Elie Wiesel's quote speaks to the idea that human suffering is a universal concern and that we all have a responsibility to respond to it. It is a call to action for all of us to be aware of the suffering of others and to do what we can to alleviate it.
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Solve 6 cos(4x) = 2 for the smallest three positive solutions. Give your answers accurate to at least two decimal places, as a list separated by commas.
The smallest three positive solutions are 0.31, 1.88, and 3.45, accurate to at least two decimal places.
To solve 6 cos(4x) = 2 for the smallest three positive solutions, we need to first isolate the cosine function:
6 cos(4x) = 2
cos(4x) = 2/6
cos(4x) = 1/3
Next, we can use the inverse cosine function to find the angle:
4x = 1.23 (rounded to two decimal places)
Now we can solve for x:
x = 1.23/4
x = 0.31 (rounded to two decimal places)
Since cosine is a periodic function, we can find the next two positive solutions by adding the period of the function (2π) to the previous solution:
x = 0.31 + (2π/4)
x = 1.88 (rounded to two decimal places)
x = 1.88 + (2π/4)
x = 3.45 (rounded to two decimal places)
The final answer is: 0.31, 1.88, 3.45
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Jim gives the cashier $20 bill at the pharmacy
Answer: bro hear me out rq in the explanation
Step-by-step explanation: Jim hands the cashier the $20 bill and, if necessary, provides his identification to purchase the item. The cashier will then record the purchase, give Jim his change, and thank him for his business.
A rectangle is
a trapezoid.
Answer: True
Step-by-step explanation:
Answer: No
Step-by-step explanation:
Definitely not.
Nathan's orchestra has 18 string
musicians, 9 percussion musicians,
15 brass musicians, and 12 woodwind
musicians. Six of the musicians cannot
play in the next performance. If the
remaining musicians plan to sit in rows
of 6 chairs, how many rows of chairs
are needed?
Rows of chairs that are needed to make 48 musicians sit is 8 rows.
What is division?The division is the process of repetitive subtraction. It is the inverse of the multiplication operation. It is defined as the act of forming equal groups. While dividing numbers, we break down a larger number into smaller numbers.
Given,
Number of musicians in orchestra
18 string musicians, 9 percussion musicians,
15 brass musicians, and 12 woodwind musicians
Total number of musicians
= 18 + 9 + 15 + 12
= 54
Six of the musicians cannot play in the next performance
Number of musicians playing in next performance
= 54 - 6
= 48
48 musicians will sit on 48 chairs
Number of chairs in one row = 6
Number of rows for 48 chairs = 48/6 = 8
Hence, 8 rows of chairs are needed to make 48 musicians sit.
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The right rectangular prism is made up of 48 cubes. Each cube has an edge length of 14 inch. Image_30414 What is the volume of this prism? Responses 14 cubic inch 1 fourth, cubic inch 12 cubic inch 1 half, cubic inch 34 cubic inch 3 fourths, cubic inch 1 cubic inch
The right rectangle prism contains 48 cubes, which results in a volume of 131,712 cubic inches.
what is prism ?A prism is a solid geometric form with two parallel bases that are congruent and typically shaped like polygons, as well as parallelogram-shaped sides that connect the bases. Prisms come in different shapes, such as hexagonal, triangular, and rectangle.
given
The 48 blocks that make up the right rectangular prism each have an edge length of 14 inches. By dividing the quantity of cubes by the sum of their individual volumes, one can determine the volume of the prism.
Each cube has a volume of (14 in.)3 = 2744 cubic inches.
Cube count is 48.
48 squares at 2744 cubic inches each equals 131,712 cubic inches of volume for the prism.
The right rectangle prism contains 48 cubes, which results in a volume of 131,712 cubic inches.
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Given that p and q are 2 distinct real roots
[tex] \frac{7 + 2 \sqrt{10} }{3} [/tex]
m is 7, n is 2
Which answer choice correctly represents the quotient of 28,134 divided by 71?
A.
B.
C.
D.
Answer:
please give brainliest
Step-by-step explanation:
396.253521127
For 1-4, find each product. Use the arrays drawn on grids to help.
1. 26 x 18
2. 23 x 23
3. 19 x 27
4. 11 x 16
Answer:
1. 468
2. 529
3. 513
4. 176
Step-by-step explanation:
A 2-gallon container of window cleaner costs $34.24. What is the price per quart?
Answer: $4.28 per quart
Step-by-step explanation:
So there is 4 quarts in one gallon. Since there is 2 gallons that means there is 8 quarts total. now you want to take $34.24 and divide it by 8 and you will get $4.28
Write an equation for the graph that passes through (1,7) and (3,3).
We can use the two-point form to find the equation of the line passing through the two given points:
y - y1 = ((y2 - y1)/(x2 - x1))(x - x1)
where (x1, y1) = (1, 7) and (x2, y2) = (3, 3).
Substituting the values, we get:
y - 7 = ((3 - 7)/(3 - 1))(x - 1)
Simplifying the equation, we get:
y - 7 = (-2/2)(x - 1)
y - 7 = -x + 1
Adding 7 to both sides, we get:
y = -x + 8
Therefore, the equation of the line passing through the points (1, 7) and (3, 3) is y = -x + 8.
Hope this helps <3
Please give me Brainliest :)
Harvey asked some of his friends how old they
were. His results are shown in the table below.
What was the median age?
Age (years)
11
12
13
14
15
16
Frequency
2
5
4
3
2
4
Answer 13
Step-by-step explanation:Place all numbers in order from youngest to oldest. and the one in the middle is the median
Answer:13
Step-by-step explanation:
At the point where the cost is the same, how much will it cost to bowl at both bowling centers?
Part A: The cost of bowling will be the same at both centers if 4 games are bowled. Part B: It will cost $10 to bowl at both Fannin Lanes and Fun Time Lanes for 4 games.
Describe Bowling Games Cost?The cost of bowling games can vary depending on a number of factors, including the location, time of day, and day of the week. Generally, bowling alleys charge per game or per hour, with additional fees for shoe rentals and any other amenities or services.
The cost per game can range from a few dollars to upwards of $10 or more, depending on the location and other factors. Some bowling alleys also offer discounted rates for children, seniors, or members of certain groups.
Part A:
Let's assume that the number of games to be bowled is 'x'. The total cost of bowling at Fannin Lanes is 2.5x + 2, and at Fun Time Lanes it is 2x + 4. We need to find the number of games where the cost of bowling at both centers is the same.
2.5x + 2 = 2x + 4
0.5x = 2
x = 4
Therefore, the cost of bowling will be the same at both centers if 4 games are bowled.
Part B:
Using the value of 'x' found in Part A, we can find the cost of bowling at both centers.
At Fannin Lanes: 2.5(4) + 2 = 10
At Fun Time Lanes: 2(4) + 4 = 12
Therefore, it will cost $10 to bowl at both Fannin Lanes and Fun Time Lanes for 4 games.
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The complete question is:
Math part 3 question 7
We can start by first finding the value of 8°F, where F represents the function f(x) = x² - 8.
So, we have:
8°F = 8(f(x)) = 8(x² - 8) = 8x² - 64
Now, substituting x = -3, we get:
8°F(-3) = 8(-3)² - 64 = 8(9) - 64 = 8
Finally, substituting this value into the given expression, we have:
8°F(-3) - 4 = 8 - 4 = 4
Therefore, the statement "True" is correct.
ind all of the solutions of the polynomial equation: 4x^(4)-13x^(3)-21x^(2)+78x-18=0
The solutions of the polynomial equation are x = 0, x = 4.09, and x = -1.59.
The solutions of the polynomial equation 4x^(4)-13x^(3)-21x^(2)+78x-18=0 can be found by factoring the equation and setting each factor equal to zero.
First, we can factor out a common factor of 4x^2 from the equation:
4x^2(x^2-3.25x-5.25)+78x-18=0
Next, we can use the quadratic formula to solve for x in the equation x^2-3.25x-5.25=0:
x = (-(-3.25) ± √((-3.25)^2-4(1)(-5.25)))/(2(1))
x = (3.25 ± √(29.3125))/2
This gives us two solutions for x:
x = (3.25 + √(29.3125))/2 ≈ 4.09
x = (3.25 - √(29.3125))/2 ≈ -1.59
Finally, we can set each factor equal to zero and solve for x:
4x^2 = 0 -> x = 0
x^2-3.25x-5.25 = 0 -> x = 4.09 or x = -1.59
So the solutions of the polynomial equation are x = 0, x = 4.09, and x = -1.59.
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Please help I tried to answer this problem 10 times but got it wrong.
Answer:
16-year-old horse is equivalent to a 48-year-old human. x = 48
Step-by-step explanation:
We can set up a proportion to solve this problem:
horse age / human age = k
where k is the constant of proportionality. We're told that a 5-year-old horse is equivalent to a 15-year-old human, so we can use this information to find k:
5 / 15 = k
k = 1/3
Now we can use this value of k to find the equivalent human age for a 16-year-old horse:
16 / x = 1/3
Multiplying both sides by x:
16 = x/3
Multiplying both sides by 3:
x = 48
So a 16-year-old horse is equivalent to a 48-year-old human.
PLEASE HELP ME
The first two steps in the derivation of the quadratic formula by completing the square are shown below.
Which answer choice shows the correct next step?
Answer:
The correct next step is the answer choice
x^2+b/a x=-c/a
Step-by-step explanation:
You borrow $10,000 at effective rate 2.1%. When will the amount that you owe reach $15,000? Give your answer in years, rounded to the nearest tenth (0.1). [Hint: When using effective rate, what is the number of compounds per year, n?]
The amount that you owe will reach $15,000 after approximately 21.5 years.
Here is a step-by-step explanation of how to calculate this:
1. First, determine the number of compounds per year (n). In this case, since we are using an effective rate, n = 1.
2. Next, use the compound interest formula to find the final amount (A): A = P(1 + r/n)^(nt)
3. Plug in the given values for P ($10,000), r (0.021), n (1), and A ($15,000) and solve for t:
$15,000 = $10,000(1 + 0.021/1)^(1*t)
4. Simplify the equation and isolate t on one side:
1.5 = (1.021)^t
5. Take the natural logarithm of both sides:
ln(1.5) = t*ln(1.021)
6. Solve for t:
t = ln(1.5)/ln(1.021)
7. Use a calculator to find the value of t:
t ≈ 21.5
Therefore, the amount that you owe will reach $15,000 after approximately 21.5 years, rounded to the nearest tenth (0.1).
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The matrix \[ A=\left[\begin{array}{cccc} -3 & 0 & -4 & 0 \\ 7.5 & 0 & 10 & 0 \\ 3 & 0 & 4 & 0 \end{array}\right] \] is a matrix of a linear transformation \( T: \mathbb{R}^{k} \rightarrow \mathbb{R}^
The matrix A represents the linear transformation T that maps vectors from a k-dimensional vector space to a 3-dimensional vector space and can be used to find the image of a vector under the linear transformation is:
[tex]T=\left[\begin{array}{c} -15 \\ 37.5 \\ 15 \end{array}\right][/tex]
What is linear transformation?A linear transformation is a function that maps vectors from one vector space to another and preserves the operations of vector addition and scalar multiplication. In this case, the matrix A represents the linear transformation T that maps vectors from a k-dimensional vector space to a 3-dimensional vector space.
The matrix [tex]\[ A=\left[\begin{array}{cccc} -3 & 0 & -4 & 0 \\ 7.5 & 0 & 10 & 0 \\ 3 & 0 & 4 & 0 \end{array}\right] \][/tex]
is a matrix of a linear transformation [tex]\( T: \mathbb{R}^{k} \rightarrow \mathbb{R}^{3} \).[/tex]
The matrix A can be used to find the image of a vector under the linear transformation T. For a vector [tex]\( \mathbf{x} \in \mathbb{R}^{k} \)[/tex], the image of the vector under the linear transformation T is given by the matrix-vector product [tex]\( A\mathbf{x} \).[/tex]
For example, if [tex]\( \mathbf{x} = \left[\begin{array}{c} 1 \\ 2 \\ 3 \\ 4 \end{array}\right] \)[/tex]
Then the image of the vector under the linear transformation T is given by
[tex]\[ A\mathbf{x} = \left[\begin{array}{cccc} -3 & 0 & -4 & 0 \\ 7.5 & 0 & 10 & 0 \\ 3 & 0 & 4 & 0 \end{array}\right] \left[\begin{array}{c} 1 \\ 2 \\ 3 \\ 4 \end{array}\right] = \left[\begin{array}{c} -15 \\ 37.5 \\ 15 \end{array}\right] \][/tex]
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What’s the answer ?
if f(x) = 3*2ˣ + 2 is vertically stretched by a factor of 2, then the new function g(x) is 6*2ˣ + 4.
What is the new function g(x)?
To vertically stretch the function f(x) by a factor of 2, we need to multiply the entire function by 2.
This will stretch the function vertically, making it twice as tall as before.
Therefore, if f(x) = 3*2ˣ + 2 is vertically stretched by a factor of 2, then the new function g(x) is:
g(x) = 2*f(x)
g(x) = 2*(3*2ˣ + 2)
g(x) = 6*2ˣ + 4
So the new function g(x) is 6*2ˣ + 4.
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Consistent and Dependent Consistent and Independent Inconsistent y=-x+1 y=-x y=x+2 y=x y=x y=2x 00*30:03
The first system is inconsistent, the second system is consistent and dependent, and the third system is consistent and independent.
A system of equations can be classified as consistent, dependent, or inconsistent. A consistent system has at least one solution. A dependent system has infinitely many solutions, and an inconsistent system has no solution.
The first system of equations, y=-x+1 and y=-x, is inconsistent. This is because there is no value of x that can make both equations true at the same time. The graphs of these equations would be parallel lines that never intersect, meaning there is no solution.
The second system of equations, y=x+2 and y=x, is consistent and dependent. This is because there are infinitely many solutions that make both equations true. The graphs of these equations would be the same line, meaning every point on the line is a solution.
The third system of equations, y=x and y=2x, is consistent and independent. This is because there is only one solution that makes both equations true. The graphs of these equations would be two lines that intersect at one point, meaning there is only one solution.
In summary, the first system is inconsistent, the second system is consistent and dependent, and the third system is consistent and independent.
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Find the measure of angle A. 7x-2
80°
9x+6
On a bicycle, Lomasi rides for 10 hours and is 22 miles from her house. After riding for 12 hours, she is 26 miles away. What is Lomasi's rate?
Lomasi's rate is 2 miles per hour. She traveled 4 miles in 2 hours, so her rate is 2 miles per hour.
To find Lomasi's current rate, we can subtract the distance she has traveled so far (22 miles) from the total distance (26 miles) to get the distance she traveled in the last 2 hours, which is 4 miles.
Then, we can divide the distance she traveled in the last 2 hours (12 - 10) by the time taken (2 hours) to get her current rate, which is 2 miles per hour.
Therefore, Lomasi's current rate is 2 miles per hour.
Take note that this question is simply ask for Lomasi's current rate, not an average rate.
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questions to ask grade 12 students on a questionnaire about taking a gap year after school
Some of the questions to ask grade 12 students on a questionnaire about taking a gap year after school are:
Are you planning to take a gap year after completing high school?If yes, what are your reasons for taking a gap year?Have you already planned your gap year activities? If yes, what are they?Are you worried about losing academic momentum by taking a gap year?How do you plan to finance your gap year activities?Are you planning to work during your gap year? If yes, what type of job are you looking for?Have you discussed your gap year plans with your parents or guardians?How do you think a gap year will impact your personal growth and development?What are questionnaire used for in a study?A questionnaire refers to a set of questions or items used to collect information about respondents' attitudes, experiences, or opinions. Questionnaires can be used to collect both quantitative and qualitative data. Questionnaires are widely used in market research, as well as social and health sciences.
As the researcher's study focus on semester taken after high school and prior to post-secondary education, such questionnaire involve will focus on variables on the student gap year.
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can someone please answer these questions for me
The answers for each line are:
a) the slope is -2
b) The slope is 2/5 and the y-intercept is -2.
c) x = 10/4
d) y = -7x - 2
How to get the slope of the line?A linear equation can be written as:
y = a*x + b
Where a is the slope and b is the y-intercept.
We know that if the line passes through (x₁, y₁) and (x₂, y₂), then the slope is:
a = (y₂ - y₁)/(x₂ - x₁)
a) Then the slope of the line that passes through (2, -5) and (-2, 3) is:
a = (3 + 5)/(-2 - 2) = 8/-4 = -2
b) The line is 2x - 5y = 10
Isolating y we will get:
5y = 2x - 10
y = (2/5)*x - 2
The slope is 2/5 and the y-intercept is -2.
c) Here we need to solve:
-4 = (1 + 9)/(0 - x)
-4*-x = 10
x = 10/4
d) if the slope is -7, then we have:
y = -7x + b
And the line also passes through (-1, 5), then:
5 = -7*-1 + b
5 = 7 + b
5 - 7 =b
-2 = b
The line is:
y = -7x - 2
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The regular price of a laptop computer is $865. 0. This week, it is on sale for $812. 00 off. What is the sale price of the computer?
The sale price of the laptop computer is $53.00. We subtracted the discount amount from the original price.
Discount is a reduction in the price of a product or service that is offered to customers by a seller, usually as an incentive to increase sales or clear out inventory. It is typically expressed as a percentage of the original price.
To calculate the sale price of the laptop computer, we need to subtract the discount amount from the original price.
Discount amount = Regular price - Sale price
Discount amount = $865.00 - $812.00
Discount amount = $53.00
Therefore, the sale price of the laptop computer is $812.00.
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Problem4(10%)LetA,B∈Rn×n, and suppose that eitherAorBis non-singular. IfABis diagonalizable, show thatBAis also diagonalizable.
BA is also diagonalizable
Let A and B be two n x n matrices such that either A or B is non-singular. If AB is diagonalizable, then there exists an invertible matrix P and a diagonal matrix D such that:
AB = PDP-1.
Since P is invertible, we can also write:
BA = (PDP-1)-1PDP-1 = P-1D-1PDP-1
Since D-1 is also diagonalizable, it follows that BA is also diagonalizable.
Answer:Let A, B ∈ Rn×n and suppose that either A or B is non-singular. If AB is diagonalizable, then BA is also diagonalizable. Let AB be diagonalizable, then AB = CDC−1 where C is a diagonal matrix and D is a matrix with non-zero diagonals.Let B−1 and C be invertible matrices such that BA = B−1(AB)B = B−1(CDC−1)B = (B−1CB)(B−1DB−1)Since B is invertible, the matrix B−1CB is diagonal. The matrix B−1DB−1 is also diagonal because its inverse is a diagonal matrix. Thus, BA is diagonalizable. Therefore, if AB is diagonalizable, then BA is also diagonalizable, as required.To sum up:If A, B ∈ Rn×n and either A or B is non-singular, then AB is diagonalizable, which means that BA is also diagonalizable.
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