Expression as a single natural logarithm of 4 ln 3 is 4.39444915467
What is natural logarithm?
4 ln 3
=[tex]ln 3^{4}[/tex]
= ln 81
=4.39444915467
The inverse of an exponential function, the natural log is the logarithm to the base of the number e. Natural logarithms are unique varieties of logarithms that are employed in the treatment of time and growth-related issues.
The distinction between log and ln is that log is expressed in terms of base 10, while ln is expressed in terms of base e. As an illustration, log of base 2 is denoted by log2 and log of base e by loge = ln (natural log).
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Graph the piecewise-defined function. What are the domain and range? Over what intervals is the function increasing or decreasing?
2x + 5, -6 ≤ x ≤ -2 2x²-7, -2 < x < 1 1 ≤ x ≤ 3
a. f(x) = H - 4 - X, 1. -8 8 4 -4 O -4 H -8 4 X 1.00 8
Answer:
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I need help finding these, all of them not just one
One pair of vertical angles are ∠1 and ∠4.
One pair of angles that are congruent are ∠3 and ∠6.
One pair of angles that are congruent are ∠3 and ∠6.
What are vertical angles, linear pairs and congruency?Vertical angles are the angles opposite each other when two lines cross.
Vertical angles are congruent. This means vertical angles are equal to each other.
Therefore, one pair of vertical angles are ∠1 and ∠4.
Linear pair of angles are formed when two lines intersect each other at a single point.
Therefore, one pair of linear pair angles are ∠6 and ∠8.
Angles are congruent when they are the same. Congruent angles includes corresponding and alternate angles.
Therefore, one pair of angles that are congruent are ∠3 and ∠6.
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which is greater 5/2 or 7/4?
Answer:
Comparamos los dos números decimales anteriores, y podemos ver que 2.5 es mayor que 1.75. Por lo tanto, 5/2 es mayor que 7/4
Step-by-step explanation:
Answer:
7/4 because if you divide them both, 7/4's decimal will be greater
A baker has bags of flour that weigh three and 1/ 4 pounds each if the baker has a total of 1/2 bags of flour, what is the total weight of the bags of flour?
If the baker has a total of 1/2 bags of flour, the total weight of the bags of flour is 1.625
What is the weight of a bag of flour in pounds?
The fact that each bag of flour weighs 3 and 1/4 pounds means that each bag of flour is 3.25 pounds, in essence, the total weight of flour that the baker has can be determined as the weight of a bag of flour multiplied by the total of 1/2 bags of flour.
total weight of bags of flour=weight of a bag of flour*total weight of baker's flour
weight of a bag of flour=3.25 pounds
total weight of baker's flour=1/2 bag
total weight of bags of flour=3.25bags*1/2
total weight of bags of flour=1.625 pounds
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Let f(x)=x-4 and g(x)=x²-16 . Perform each function operation and then find the domain. f(x)+g(x)
The domain for g (x) + f (x) = x² + x - 20 will be all real numbers when f (x) = x - 4 and g (x) = x² - 16.
We are given the two functions as:
f (x) = x - 4
g (x) = x² - 16
Now, first, we need to add f (x) from g (x).
So, we get that:
g (x) + f (x) = x² - 16 + (x - 4)
g (x) + f (x) = x² - 16 + x - 4
g (x) + f (x) = x² + x - 20
Now, the domain of the function will be all real numbers as it will be defined for all the real numbers.
Therefore, we get that the domain for g (x) + f (x) = x² + x - 20 will be all real numbers when f (x) = x - 4 and g (x) = x² - 16.
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Open-Ended Write a problem that could be modeled with y=20(1.1) x
The problem that can be defined by the function is:
A cat breeding company has 20 cats initially. The number of cats increases by 10% each year. Write a function for the exponential growth of the number of cats over the years. How many cats will the company have after 10 years?
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 and x is the number of time periods.
Consider the modeled function y = 20(1.1)ˣ.
Now, y = 20 × ( 1 + r)ˣ
f(x) = 20 × ( 1 + r)ˣ
Comparing the above equation with A(x) = a( 1 + r)ˣ
The initial amount is 20 and it increases 1 + r = 1.1.
Therefore, r = 0.1 = 10 %
Let's say we are starting a cat breeding company. Initially, we have 20 cats.
So, the problem for the function is:
A cat breeding company has 20 cats initially. The number of cats increases by 10% each year. Write a function for the exponential growth of the number of cats over the years. How many cats will the company have after 10 years?
So, a = 20, x = 10, and r = 10% = 0.1
Therefore,
A(x) = a( 1 + r)ˣ
y = a( 1 + r)ˣ
y = 20( 1 + 0.1 )ˣ
y = 20( 1.1)¹⁰
y = 20 × 2.594
y = 52
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4x + 5y = 6
6x - 7y = -20
Answer: x=-1, y=2
Step-by-step explanation:
4x + 5y = 6
6x - 7y = -20
(4x + 5y = 6)*1.5
6x + 7.5y = 9
6x - 7y = -20
7.5y-(-7y)=9-(-20)
7.5y+7y=9+20
14.5y=29
y=2
4x + 5y = 6
4x + 5(2) = 6
4x+10=6
4x=-4
x=-1
Will the answer to the subtraction problem below be odd or even?
5415-3556 = ?
O
A. Odd
B. Even
Answer:
Odd
Step-by-step explanation:
The answer to the equation is 1,859, making the answer odd.
Solve the system of equations using a matrix
-x+2 y+z=0
y=-2 x+3
z=3 x
The solution of x , y , z are 3 , -3 , 9 respectively using matrix.
Solving the system of linear equations using the inversion method consists of two new matrices . Matrix A: representing variables , matrix B: represents a constant The system of equations can be solved by matrix multiplication which is given by [tex]X=A^{-1}B[/tex] ..(1)We have given three equations -x+2 y+z=0 , y =-2 x+3 , z = 3 x
This can be written as AX=B
Where [tex]A=\left[\begin{array}{ccc}-1&2&1\\2&1&0\\-3&0&1\end{array}\right][/tex] and [tex]X=\left[\begin{array}{ccc}x\\y\\z\end{array}\right][/tex] [tex]B=\left[\begin{array}{ccc}0\\3\\0\end{array}\right][/tex]
A is the coefficient matrix, X the variable matrix and B the constant matrix.
[tex]|A|=-1(1)-2(2)+1(3)\\|A|=-1-4+3=-2[/tex]
Since , [tex]|A|\neq 0[/tex]
Hence, the system of equations is consistent and has a unique solution
A inverse is given by [tex]\frac{adjA}{|A|}[/tex] .....(2) and adj(A) is given by [tex]AdjA=C^T[/tex] ...(3)
Minor of matrix A will be
[tex]M_{11}=1\\M_{12}=2\\M_{13}=3\\M_{21}=2\\M_{22}=2\\M_{23}=6\\M_{31}=-1\\M_{32}=2\\M_{33}=-5[/tex]
Then Co - factor will be
[tex]C_{11}=1\\C_{12}=-2\\C_{13}=3\\C_{21}=-2\\C_{22}=2\\C_{23}=-6\\C_{31}=-1\\C_{32}=-2\\M_{33}=-5[/tex]
Matrix C will be represented by
[tex]C=\left[\begin{array}{ccc}1&-2&3\\-2&2&-6\\-1&-2&-5\end{array}\right][/tex]
Transpose of matrix C will be represented by
[tex]C^T=\left[\begin{array}{ccc}1&-2&-1\\-2&2&-2\\3&-6&-5\end{array}\right][/tex]
Then , putting this value in equation (3) , we get
[tex]adjA=C^T\\adjA=\left[\begin{array}{ccc}1&-2&-1\\-2&2&-2\\3&-6&-5\end{array}\right][/tex]
Putting the value of |A|=-2 and adjA in equation (2) , we get
[tex]A^{-1}=\frac{1}{-2}\left[\begin{array}{ccc}1&-2&-1\\-2&2&-2\\3&-6&-5\end{array}\right][/tex]
Putting the value of A inverse in equation (1) , we get
[tex]X=\frac{1}{-2}\left[\begin{array}{ccc}1&-2&-1\\-2&2&-2\\3&-6&-5\end{array}\right]\left[\begin{array}{ccc}0\\3\\0\end{array}\right]\\\\\\\left[\begin{array}{ccc}x\\y\\z\end{array}\right]=\frac{-1}{2} \left[\begin{array}{ccc}-6\\6\\-18\end{array}\right] \\\\\\\left[\begin{array}{ccc}x\\y\\z\end{array}\right]=\left[\begin{array}{ccc}3\\\ -3 \\9\end{array}\right][/tex]
On comparing , we get x = 3 , y = -3 , z = 9
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Corinna paid $3 for 12 eggs. What was the cost of 1 egg?
Answer:
0.25
Step-by-step explanation:
All i did was divided 3 by 12
Use natural logarithms to solve each equation. e x=18
2.89 is the value of x in equation [tex]e^x[/tex] = 18 solved by using natural logarithms.
We have been asked to find x in [tex]e^x[/tex] = 18 using natural logarithms
⇒ [tex]e^x[/tex] = 18
⇒ x = ㏑ (18)
⇒ x = 2.89
What is a natural logarithm?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.
Typically, the natural logarithm of x is denoted by the symbols ln x, loge x, or, if the base e is implicit, just log x. When adding parentheses for clarity, the values ln(x), loge(x), or log (x). In order to avoid ambiguity, this is notably done when the argument to the logarithm is not a single symbol.
The power to which e would need to be raised in order to equal x is the natural logarithm of x.
For instance, e2.0149... = 7.5, thus ln 7.5 equals 2.0149.
Since e1 = e, the natural logarithm of e itself, or ln e, is equal to 1, while the natural logarithm of 1 is 0, since e0 = 1.
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Correct questionUse natural logarithms to solve each equation.
[tex]e^x[/tex] = 18
3. Chris is 24. His age is two more than half his
father's age. How old is his father?
Define a variable and write an equation for each of the following and solve:
You use 130 feet of fencing to go around a rectangular pool and patio. The length of the area is 9 more than the width. What are the dimensions of the fence?
The dimensions of the fencing is 28 ft and 37 ft respectively.
How to find the dimension of the rectangular fence?He use 130 feet of fencing to go around a rectangular pool and patio.
The length of the area is 9 more than the width.
The dimension of the fence can be found as follows:
Therefore,
perimeter of the rectangular fence = 2(l + w)
where
l = lengthw = widthHence,
l = 9 + w
perimeter of the rectangular fence = 2(w + 9 + w)
perimeter of the rectangular fence = 2(2w + 9)
130 = 4w + 18
130 - 18 = 4w
112 = 4w
w = 112 / 4
w = 28 ft
l = 9 + 28 = 37 ft
Therefore, the width and length of the fencing is 28 ft and 37 ft respectively.
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How do you solve this equation
-1 = -1 + (p/8)
The solution to the given equation -1 = -1 + (p/8) is p = 0.
What is the solution to the given equation?Given the data in the question;
-1 = -1 + (p/8)p = ?Solve for p to determine the solution to the equation.
-1 = -1 + (p/8)
Rewrite the equation as;
-1 + (p/8) = -1
Next, move all terms containing p to the left side and all constants to the right side of the equation.
-1 + (p/8) = -1
(p/8) = -1 + 1
Add -1 and 1
p/8 = -1 + 1
p/8 = 0
p = 0 × 8
p = 0
The solution to the given equation -1 = -1 + (p/8) is p = 0.
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Use v=-0.0098 t+c ln R , where v is the velocity of the rocket, t is the firing time, c is the velocity of the exhaust, and R is the ratio of the mass of the rocket filled with fuel to the mass of the rocket without fuel. Find the velocity of a spacecraft whose booster rocket has a mass ratio of 20 , an exhaust velocity of 2.7km/s, and a firing time of 30 s . Can the spacecraft achieve a stable orbit 300km above Earth?
The velocity of the spacecraft is 7.7025 km/s as calculated with the help of mass ratio.
What is mass ratio of a rocket?An indicator of a rocket's effectiveness is its mass ratio.It describes the ratio of the rocket's wet mass to its dry mass, or how much more massive the vehicle is with propellant than without.Given:
v = - 0.0098(t) + c (ln (R) ), where:v = maximum shuttle velocityt = firing timec = velocity of exhaustR = mass ratioTo find: Velocity of the spacecraft (v) = ?
Finding:
Here, c = 2.7 km/s, t = 30s, R = 20
On substituting the values of 'R', 't', 'v', we get:
v = -0.0098 ( 30) + 2.7 ( ln (20))
=> v = - 0.294 + 2.7 (2.995)
=> v = 7.7025 km/s
Hence, the velocity of the spacecraft is 7.7025 km/s as calculated with the help of mass ratio.
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question is in the picture
The solution to the system of equations using substitution is: x = 3 and y = -4.
How to Solve a System of Equations Using Substitution?Given the system of equations:
-7x - 2y = -13 -----> equation 1
x - 2y = 11 -----> equation 2
Rewrite equation 2
x - 2y = 11
x = 11 + 2y
Substitute x = (11 + 2y) into equation 1
-7(11 + 2y) - 2y = -13
-77 - 14y - 2y = -13
-77 - 16y = -13
-16y = -13 + 77
-16y = 64
y = -4
Substitute y = -4 into equation 2
x - 2(-4) = 11
x + 8 = 11
x = 11 - 8
x = 3
Therefore, the solution to the system of equations using substitution is: x = 3 and y = -4.
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whats the answer to −x2+6zy=
Answer:
- 2(x - 3zy)
Step-by-step explanation:
The midpoint of \overline{\text{AB}}
AB
is M(3, -4)M(3,−4). If the coordinates of AA are (8, -5)(8,−5), what are the coordinates of BB?
(-2, -3) represents the coordinate of point B from the given expression.
Midpoint of coordinatesThe formula for calculating the midpoint of coordinates is expressed as shown below:
Midpoint = {(x₁+x₂)/2, (y₁+y₂)/2}
Given the following parameters
Midpoint = (3, -4)
A = (8,-5)
Required
Coordinate point B
Substitute the given parameters
3 = (8+x₂)/2
3(2) = 8+x₂
6 = 8+x₂
x₂ = -2
Similarly
-4 = (-5+y₂)/2
-4(2) = -5+x₂
-8 = -5 +y₂
y₂ = -3
Hence the coordinate of point B from the given expression is (-2, -3)
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Evaluate each function at the specified value
f(x)=7x-5;x=6
If z=30 when x=3 and y=2 , write the function that models the relationship.
z varies jointly with x and y .
According to the question, to calculate the relationship model of the given equations which are as follows:
[tex]z=30[/tex] when [tex]x =3 ; y=2[/tex]
And the condition is z varies jointly with x and y which can be represented as: [tex]z = \frac{k}{xy}[/tex]
Substituting the values to get the final expression:
[tex]30 = \frac{k}{(3)(2)} =\frac{k}{6}[/tex]
[tex]k=180[/tex]
Substitute the value of 'k' in the original equation. And the final expression is: [tex]z = \frac{180}{xy}[/tex]
What is function?
In mathematics, function can be defined as an expression or the rule or the law. It defines the relationship between dependent variable and the independent variable.
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Does the horizontal line slope = 0?
Answer: Yes, all horizontal lines have slope of 0
Reason:
Recall that slope = rise/run
The rise tells us how far to go up or down. A horizontal line does neither. There's no change in y value.
So we have slope = rise/run = 0/run = 0, where "run" is any positive number you want. The run is how far to the right we go each time moving up or down.
Answer: Yes
Step-by-step explanation:
When you have a horizontal line it is flat and has no slope at all
____________________________________
So the slope = 0
a bag contains 6 blue marbles 4 red marbles and 2 yellow marbles.
what is the probability of selecting a blue marble replacing it then selecting another blue marble?
Answer:
1/4
Step-by-step explanation:
Blue/total x blue/total
6/12 x 6/12 Which is the same as
1/2 x /12 = 1/4
What is the length of the diagonal shown in the rectangular prism? Round your answer to the nearest tenth. Rectangular prism is shown with length labeled 7 feet on top. Right, width labeled 4 feet. Middle right, height labeled 5 feet. A diagonal is drawn between bottom left vertex of front face and top right vertex of back face. ft
The length of the diagonal (D) of this rectangular prism is equal to 9.5 feet.
What is Pythagorean theorem?Pythagorean theorem can be defined as a mathematical expression in Euclidean geometry that can be used to solve for any of the three (3) side lengths of a right triangle.
How to determine the diagonal (D) of this rectangular prism?In order to determine the length of the diagonal (D) of this rectangular prism, we would first of all determine the diagonal of the base by applying Pythagorean theorem:
d² = l² + b²
d² = 4² + 7²
d² = 16 + 49
d² = 65
d = √65
Now, we can determine the length of the diagonal (D) of this rectangular prism:
D² = d² + h²
D² = √65² + 5²
D² = 65 + 25
D² = 90
D = √90
Diagonal, D = 9.5 feet.
Therefore, the length of the diagonal (D) of this rectangular prism is equal to 9.5 feet.
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i cant find this pramplme Which word in the sentence gives a clue about the meaning of the word livid?
father
driver
upset
new
upset is right
Answer:
Step-by-step explanation:
upset
there are 500 students and 325 say they have too much homework what percent said they have too much homework
Answer:
65%
Step-by-step explanation:
To find percentage, we take the fraction of the total and multiply it by 100.
[tex]\frac{325}{500} \times=\frac{325}{5}=65[/tex]
Answer:
[tex]153.84\%[/tex]
Step-by-step explanation:
[tex] 1. \: \frac{500}{3.25} \\ 2. \: 153.84\%[/tex]
Simplify each expression.
36¹/₂
The problem is on indices. Write 36 in form of its prime factors. Apply the power rule (a^m)^(1/n)=a^(m/n).
36^(1/2)
(6^2)^(1/2) = 6^(2×1/2) = 6
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Help me pls!! 4 math questions
Which value, 12 or 3, is an extraneous solution of x-6=√3 x ? Explain your reasoning
Both 3 is an extraneous solution.
We have the equation x - 6 = [tex]\sqrt{3x}[/tex]
To find the value of x we need to square on both side of the equation
[tex](x-6)^{2}[/tex] = [tex](\sqrt3{x} )^{2}[/tex]
[tex]x^{2}[/tex] - 12x + 36 = 3x
[tex]x^{2}[/tex] -15x + 36 = 0
[tex]x^{2}[/tex] - 12x - 3x + 36 = 0
x ( x- 12 ) - 3( x - 12) = 0
(x -12 ) ( x - 3) = 0
Therefore we get x = 12 , 3
Now we will put both the value of x in the equation
x - 6 = [tex]\sqrt{3x}[/tex]
Let put 12 first
12 - 6 = [tex]\sqrt{3 * 12}[/tex]
6 = 6
Now put 3
3 - 6 =[tex]\sqrt{3 * 3}[/tex]
- 3 [tex]\neq[/tex] 3
Therefore 3 is an extraneous solution .
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The position of a submarine relative to sea level, changes by - 7 miles each hour. How many hours did it take
submarine to reach 43.75 miles below sea level?PLEASE HELP
43.75 divided by 7 is 6.25, thus your answer is 6.25 hours
d.
Rule: Output =
Input
-2
0
3
4
8
er
Process
Ox
3x
4x
8+
Output
-15
-5
10
15
35
Answer:
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