When the value of f(x) = log4x as x approaches +∞ Both have an asymptote of x = 0 and Both have a domain of all real numbers. Hence, option B and D are correct.
The graphs of f(x) = log2x and g(x) = log10x are similar in shape, both being increasing and concave down. As x approaches +∞, the value of f(x) = log4x approaches +∞ as well, since log4x grows without bound as x gets larger and larger.
The correct options are B and D. The graphs of f(x) = log2x and g(x) = log10x are similar in that both increase from left to right and have a domain of all real numbers. Both have an asymptote of x = 0. As x approaches +∞, the value of f(x) = log4x approaches +∞ as well.
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Complete question - In the problems below, f(x) = log2x and
g(x) = log10x.
How are the graphs of f and g similar? Check all that apply. What happens to the value of f(x) = log4x as x approaches +∞?
A. Both have a y-intercept of 1.
B. Both increase from left to right.
C. Both have an asymptote of x = 0.
D. Both have a domain of all real numbers.
Which ordered pairs represent points on the graph of this equation? Select all that apply. 2x = -1/2y a) 4,6 b) -6,-1 c) 0,-4 d) -1,4 e) 0,0 f) 4,-2
The ordered pairs that represent points on the graph of the equation 2x = -1/2y are d) (-1,4) and e) (0,0).
What is equation?An equation is a mathematical statement that shows the equality of two expressions. It consists of two sides, a left-hand side and a right-hand side, separated by an equal sign. An equation can contain variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division.
According to given information:The equation 2x = -1/2y can be rewritten as y = -4x. This is a linear equation in slope-intercept form, with a slope of -4 and y-intercept of 0.
To determine which ordered pairs represent points on the graph of this equation, we can substitute the x and y values into the equation and check if it satisfies the equation.
a) (4,6):
y = -4x
6 = -4(4)
6 = -16
This ordered pair does not satisfy the equation.
b) (-6,-1):
y = -4x
-1 = -4(-6)
-1 = 24
This ordered pair does not satisfy the equation.
c) (0,-4):
y = -4x
-4 = -4(0)
-4 = 0
This ordered pair does not satisfy the equation.
d) (-1,4):
y = -4x
4 = -4(-1)
4 = 4
This ordered pair satisfies the equation.
e) (0,0):
y = -4x
0 = -4(0)
0 = 0
This ordered pair satisfies the equation.
f) (4,-2):
y = -4x
-2 = -4(4)
-2 = -16
This ordered pair does not satisfy the equation.
Therefore, the ordered pairs that represent points on the graph of the equation 2x = -1/2y are d) (-1,4) and e) (0,0).
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La suma de las edades de 3 hermanos es de 36. La edad del mayor es igual a la suma de los dos hermanos menores, dentro de 8 años el menor doblará la edad del mayor¿cuál es la edad de los hermanos?
The age of oldest is 44 and age of youngest is 18.
We have,
Sum of age of 3 brother = 36
let the age of three brother be x, y and z.
so, x + y + z = 36
x = y + z
After 8 year, (z+ 8) = 2(x+8)
z+ 8 = 2x+ 16
2x - z +8=0
Thus, the age of oldest is 44 and age of youngest is 18.
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The Translation of the given question is:
The sum of the ages of 3 brothers is 36. The age of the eldest is equal to the sum of the two younger brothers, within 8 years the younger will double the age of the older, what is the age of the brothers?
Write the following statements as P^Q, PVQ, -P, P then Q, P <-> Q State what P and Q are.
a) If it is a rock, then it contains magnesium.
b) The weather is nice or I am chilly
c) x ∈ A ∩ B
In statement c), A and B are sets, and x is an element that belongs to both sets A and B.
What is equation?
An equation is a mathematical statement that shows the equality between two expressions, often denoted by placing an equals sign (=) between the two expressions. The expressions on either side of the equals sign are typically composed of variables, constants, and mathematical operations such as addition, subtraction, multiplication, division, exponentiation, and so on.
An equation is said to be true if the expressions on both sides of the equals sign represent the same quantity or value. Equations are often used in mathematics and science to model real-world phenomena, to make predictions, and to solve problems.
a) P: It is a rock.
Q: It contains magnesium.
P → Q
b) P: The weather is nice.
Q: I am chilly.
P ∨ Q
c) P: x belongs to set A.
Q: x belongs to set B.
P ∧ Q
d) P: It is raining.
Q: The ground is wet.
P → Q
e) P: The food is hot.
Q: I will blow on it.
P → Q
f) P: The car is red.
Q: It is a convertible.
P ↔ Q
Note: In statement c), A and B are sets, and x is an element that belongs to both sets A and B.
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Please help! What is slope of the line? y+6=1/3(x−4) will give you brainlist and good ratings plus 70 points.
Answer:
The slope is 1/3
Step-by-step explanation:
y+6=1/3(x-4)
-6 -6
-----------------
y = 1/3 * x + 1/3 * (-4) - 6
y = 1/3x -7 1/3
Answer:
[tex]\frac{1}{3}[/tex]
Step-by-step explanation:
First, start by simplifying the right side of the equation, [tex]y+6=\frac{1}{3}(x-4)[/tex].
When we simplify the right side using distributive property, we will get:
[tex]y+6=\frac{1}{3}x-\frac{4}{3}[/tex]
Subtract 6 from both sides to get:
[tex]y=\frac{1}{3}x-\frac{4}{3}-6[/tex]
Simplify further and get:
[tex]y=\frac{1}{3}x-\frac{22}{3}[/tex]
By viewing the equation, we can tell the slope is 1/3.
Brainliest, good ratings, and 70 points, please!
Jayden is packing for college.If each of his boxes are 4.5 ft x 2 ft x 4 ft.,how many boxes can he fit in his 185ft^3 closet?
Volume is Length x width x height
1 box = 4.5 x 2 x 4 = 36
Each box is 36 cubic feet. Now divide the closet size by box size
185 cubic feet/36 cubic feet per box = 5.138
Since you can't have .138 of a box, and rounding up to 6 boxes is too much, the closet will hold 5 boxes (with .138 cubic feet left over).
Question content area top
Part 1
In a different plan for area codes, the first digit could be any number from 0 through 6, the second digit was either 2,3, or,4 and the third digit could be any number except 0 or 3. With this plan, how many different area codes are possible?
There are 168 different area codes possible with this plan by using the multiplication principle of counting.
What is multiplication principle ?
The multiplication principle of counting, also known as the rule of product, is a counting principle in combinatorics that states that if there are m ways to perform one task and n ways to perform another task, then there are m x n ways to perform both tasks together.
There are 7 possible choices for the first digit (0 through 6), 3 possible choices for the second digit (2, 3, or 4), and 8 possible choices for the third digit (any digit except 0 or 3). To find the total number of possible area codes, we can use the multiplication principle of counting:
Total number of area codes = Number of choices for first digit x Number of choices for second digit x Number of choices for third digit
Total number of area codes = 7 x 3 x 8
Total number of area codes = 168
Therefore, there are 168 different area codes possible with this plan.
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A 3cm by 3cm by 3cm cube has three holes, each with a 1cm by 1cm cross section
running from the centre of each face to the centre of the opposite face. What is
the total surface area of the resulting solid (including the internal surfaces)
The total surface area of the resulting solid is [tex]54 cm^2 + 9 cm^2 = 63 cm^2.[/tex]
What is area of solid?
The area of a solid refers to the total amount of surface space that the solid occupies. This can be measured in square units, such as square centimeters or square meters, depending on the unit of measurement being used.
To calculate the surface area of the resulting solid, we need to consider the surface area of each of the six faces of the cube, as well as the surface area of the three internal hole walls.
The surface area of each face of the cube is 3 cm x 3 cm = [tex]9 cm^2[/tex]. Since there are six faces, the total surface area of the cube is 6 x 9 [tex]cm^2[/tex] = 54 [tex]cm^2[/tex].
Each hole has a length of 3 cm, so the surface area of the internal walls of each hole is 3 cm x 1 cm = 3 [tex]cm^2[/tex]. Since there are three holes, the total surface area of the internal walls is 3 x 3 [tex]cm^2[/tex] = 9 [tex]cm^2[/tex].
Therefore, the total surface area of the resulting solid is 54 [tex]cm^2[/tex] + 9 [tex]cm^2[/tex] = 63 [tex]cm^2[/tex].
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I need help with this problem
The value of x when lines MN and PQ are equal is 7
How to determine the value of the variableLet take note of the properties of a quadrilateral, they include;
A quadrilateral has four vertices.It has four sides.The sum of all interior angles of a quadrilateral shape is equal to 360° degrees.The shape could be a regular or an irregular shape.From the information given in the diagram, we have that;
Line MN = Line PQ
Also, the expressions are;
MN = 7x + 13
PQ = 10x - 8
Now, equate the values, we get;
7x + 13 = 10x - 8
collect the like terms
7x - 10x = -8 - 13
subtract the like terms
-3x = -21
Divide both sides by the coefficient of x, we get
x = 7
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Which are correct representations of the inequality –3(2x – 5) < 5(2 – x)? Select two options
Answer:
-6x + 15 < 10 - 5x or 11x > 5
Step-by-step explanation:
What is the value of x?
(2x + 4)
(3x+6)
(4x-23)
(3x-18)
(2x-3)
Answer:
x=41
Step-by-step explanation:
If this is a polygon, I'm going to assume that it has 5 sides.
s=(5-2)(180)
s=3(180)
=540
(2x+4)+(3x+6)+(4x-23)+(3x-18)+(2x-3)=540
Now simplify. Add the x's and the numbers together. Then divide.
14x-34=540
14x=540+34
14x=574
x=574/14
x=41
You need a 25% alcohol solution. On hand, you have a 360 mL of a 10% alcohol mixture. You also
have 55% alcohol mixture. How much of the 55% mixture will you need to add to obtain the desired
solution?
You will need
mL of the 55% solution
you will need 180 mL of the 55% alcohol mixture to create a 25% alcohol solution.
How to solve the question?
To find out how much of the 55% alcohol mixture is needed to create a 25% alcohol solution, we can use the formula:
(amount of pure alcohol in the 10% mixture + amount of pure alcohol in the 55% mixture) / total volume of solution = desired alcohol concentration
Let x be the amount of the 55% alcohol mixture needed.
First, we need to calculate the amount of pure alcohol in the 10% mixture. We know that the 10% mixture contains 10% alcohol, which means that there are 0.10 x 360 = 36 mL of pure alcohol in the mixture.
Next, we need to calculate the amount of pure alcohol in the 55% mixture. We know that the 55% mixture contains 55% alcohol, which means that there are 0.55 x x = 0.55x mL of pure alcohol in the mixture.
The total volume of the solution will be 360 mL + x mL.
Using the formula above, we can set up the equation:
(36 + 0.55x) / (360 + x) = 0.25
Simplifying the equation, we get:
36 + 0.55x = 0.25(360 + x)
36 + 0.55x = 90 + 0.25x
0.3x = 54
x = 180 mL
Therefore, you will need 180 mL of the 55% alcohol mixture to create a 25% alcohol solution.
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What is the slope of the line below ?
Step-by-step explanation:
Slope = rise / run
Using points ( -1/2 - 1/2 ) and (1/2, 0 )
rise = 1/2 run = 1
rise / run = 1/2 /1 = 1/2 = slope
What are the coordinates of the reflection of point R across the x-axis?
(-2, -3)
(-3, 2)
(-2, 3)
(2, -3)
Which of the following is best described as a line segment that has both
endpoints on a circle?
O A. Center
OB. Radius
O C. Chord
O D. Tangent
SUBMIT
Answer:
C. Chord
Step-by-step explanation:
Chord: Any segment whose endpoints lie on the circle is a chord.
Find the distance between:
(0, -7) and (-8,5)
Round your answer to the nearest hundredth.
[tex]~~~~~~~~~~~~\textit{distance between 2 points} \\\\ (\stackrel{x_1}{0}~,~\stackrel{y_1}{-7})\qquad (\stackrel{x_2}{-8}~,~\stackrel{y_2}{5})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ d=\sqrt{(~~-8 - 0~~)^2 + (~~5 - (-7)~~)^2} \implies d=\sqrt{(-8 +0)^2 + (5 +7)^2} \\\\\\ d=\sqrt{( -8 )^2 + ( 12 )^2} \implies d=\sqrt{ 64 + 144 } \implies d=\sqrt{ 208 }\implies d\approx 14.42[/tex]
Answer:
4√13 or 14.422205101856
Step-by-step explanation:
Distance (d) = √(-8 - 0)2 + (5 - -7)2
= √(-8)2 + (12)2
= √208
= 4√13
= 14.422205101856
Which expression has an aproxímate value be between 6 and 7 select all that apply
The expression which has an approximate value be between the numbers 6 and 7 are (a) π + 3 and (b) √39.
In order to determine which expression has an approximate value between the numbers, 6 and 7, we can estimate the value of each expression and compare them to 6 and 7.
Option(a) π + 3 ;
We know that the approximate value of "π" is 3.14,
So, 3.14 + 3 = 6.14 (it is between 6 and 7)
Option(b) : √39 ≈ 6.24 (it is between 6 and 7)
Option (c) : 6π , We substitute, π ≈ 3.14,
We get, ≈ 18.85 (it is not between 6 and 7)
Option (d) : √35 ≈ 5.92 (it is not in between 6 and 7)
Therefore, the correct options are (a) and (b).
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The given question is incomplete, the complete question is
Which expression has an approximate value be between 6 and 7?
Select all that apply
(a) π + 3
(b) √39
(c) 6π
(d) √35
The table represents equivalent ratios. What is the missing value of x in the table
9
7
6
5
Answer:
Step-by-step explanation:
can someone help me on number 2
Answer:
P=32 yards, A=64 yards^2
Step-by-step explanation:
We know that P = 4 x s, where s is the side length. In this case, we know that s=8. So, the perimeter is 32 yards. We know that A= s^2. Substituting for s=8 makes the area 64 yards^2. Thus, the perimeter of this square is 32 yards, while the area is 64 yards squared.
NO LINKS!! URGENT HELP PLEASE!!!
1.Change to exponential form
a. ln w = 7 + 6x
2. Solve for t using a logarithm with base a
a. 3a^(t/2) = 7
Answer:
1. w = [tex]\bold{e^{7+6x}}[/tex]
2. [tex]\bold{t = 2(log_a(7) - log_a(3))}[/tex]
Step-by-step explanation:
1.
a. The exponential form of a logarithmic equation is given by:
[tex]\bold{log_a(b) }[/tex]= c is equivalent to [tex]a^c = b[/tex]
Using this rule, we can rewrite the equation:
ln w = 7 + 6x as w = [tex]\bold{e^{7+6x}}[/tex]
Therefore, the exponential form of the given equation is w = [tex]\bold{e^{7+6x}}[/tex]
2.
a. To solve for t using a logarithm with base a, we can take the logarithm of both sides of the equation:
[tex]\bold{3a^\frac{t}{2} = 7 }\\\bold{log_a3a^\frac{t}{2}= log_a(7)}[/tex]
Using the rule of logarithms that log_a(b^n) = n*log_a(b), we can simplify the left side:
[tex]\bold{log_a(3) +\frac{t}{2} log_a(a) = log_a(7)}[/tex]
Since log_a(a) = 1 for any base a, we can simplify the expression further:
[tex]\bold{log_a(3) + \frac{t}{2}*1= log_a(7)}[/tex]
Now we can solve for t by isolating it on one side of the equation:
[tex]\bold{ \frac{t}{7} = (log_a(7) - log_a(3))} \\ \bold{t = 2(log_a(7) - log_a(3))}[/tex]
Therefore, the solution for t using a logarithm with base a is[tex]\bold{t = 2(log_a(7) - log_a(3))}[/tex]
Answer:
[tex]\textsf{1.} \quad w = e^{7 + 6x}[/tex]
[tex]\textsf{2.} \quad t= \log_a\left(\dfrac{49}{9}\right)[/tex]
Step-by-step explanation:
Question 1Exponential form is a way to represent a number using an exponent, where the base is raised to a power.
The natural logarithm function is the inverse of the exponential function:
[tex]\boxed{\ln x=y \iff x=e^y}[/tex]
Therefore we can use this definition to change the given equation to exponential form:
[tex]\begin{aligned}\ln w & = 7 + 6x\\\\e^{\ln w} & = e^{7+6x}\\\\w&=e^{7+6x}\end{aligned}[/tex]
Therefore, the exponential form of the equation is:
[tex]w = e^{7 + 6x}[/tex]
[tex]\hrulefill[/tex]
Question 2To solve for t using a logarithm with base a, begin by taking the logarithm of both sides of the equation with base a:
[tex]\log_a (3a^{\frac{t}{2}})=\log_a(7)[/tex]
[tex]\textsf{Apply the log product law:} \quad \log_axy=\log_ax + \log_ay[/tex]
[tex]\log_a (3)+\log_a(a^{\frac{t}{2}})=\log_a(7)[/tex]
Subtract logₐ(3) from both sides of the equation:
[tex]\log_a (3)+\log_a(a^{\frac{t}{2}})-\log_a (3)=\log_a(7)-\log_a (3)[/tex]
[tex]\log_a(a^{\frac{t}{2}})=\log_a(7)-\log_a (3)[/tex]
[tex]\textsf{Apply the log quotient law:} \quad \log_ax - \log_ay=\log_a \left(\dfrac{x}{y}\right)[/tex]
[tex]\log_a(a^{\frac{t}{2}})=\log_a\left(\dfrac{7}{3}\right)[/tex]
[tex]\textsf{Apply the log power law:} \quad \log_ax^n=n\log_ax[/tex]
[tex]\dfrac{t}{2}\log_a(a)=\log_a\left(\dfrac{7}{3}\right)[/tex]
Apply the log law: logₐ(a) = 1
[tex]\dfrac{t}{2}(1)=\log_a\left(\dfrac{7}{3}\right)[/tex]
[tex]\dfrac{t}{2}=\log_a\left(\dfrac{7}{3}\right)[/tex]
Multiply both sides of the equation by 2:
[tex]2 \cdot \dfrac{t}{2}=2 \cdot \log_a\left(\dfrac{7}{3}\right)[/tex]
[tex]t=2 \log_a\left(\dfrac{7}{3}\right)[/tex]
Finally, apply the log power law:
[tex]t= \log_a\left(\dfrac{7}{3}\right)^2[/tex]
[tex]t= \log_a\left(\dfrac{7^2}{3^2}\right)[/tex]
[tex]t= \log_a\left(\dfrac{49}{9}\right)[/tex]
Therefore, the solution for t in terms of logarithm with base a is:
[tex]\boxed{t= \log_a\left(\dfrac{49}{9}\right)}[/tex]
David invested his profit of $50,000 from the sale of his business into an aggressive stock fund. After 15 years, the account had a total of $132,558.36 in it. A. What annual interest rate, compounded continuously, produced this return? (Enter the value of r rounded to three decimal places.). B. E termine the approximate number of years (from the original investment) it will take for the account to grow to $300,000. Round answer to the nearest tenth
Answer:
Step-by-step explanation:
A. To find the annual interest rate, compounded continuously, we can use the formula:
A = Pe^(rt)
where A is the final amount, P is the principal amount (initial investment), e is the mathematical constant approximately equal to 2.71828, r is the annual interest rate, and t is the time in years.
We are given that P = $50,000, A = $132,558.36, and t = 15 years. We need to solve for r.
Substituting the given values into the formula, we get:
$132,558.36 = $50,000 e^(15r)
Dividing both sides by $50,000 and taking the natural logarithm of both sides, we get:
ln(2.6511672) = 15r
Solving for r, we get:
r = ln(2.6511672) / 15
r ≈ 0.045 (rounded to three decimal places)
Therefore, the annual interest rate, compounded continuously, that produced this return is approximately 0.045 or 4.5%.
B. To determine the approximate number of years it will take for the account to grow to $300,000, we can again use the formula:
A = Pe^(rt)
where A is the final amount we want to reach, P is the initial investment ($50,000), e is the mathematical constant approximately equal to 2.71828, r is the annual interest rate we just found (0.045), and t is the time in years we want to solve for.
Substituting the given values into the formula, we get:
$300,000 = $50,000 e^(0.045t)
Dividing both sides by $50,000 and taking the natural logarithm of both sides, we get:
ln(6) = 0.045t
Solving for t, we get:
t = ln(6) / 0.045
t ≈ 27.6 years (rounded to the nearest tenth)
Therefore, it will take approximately 27.6 years from the original investment for the account to grow to $300,000.
Question 2 (Essay Worth 10 points)
(01.03 MC)
Solve the equation √x+3+4=5 for the variable. Show each step of your solution process.
Solving the radical expression √(x + 3) + 4 = 5 for x gives x = -2
Solving the radical expressionFrom the question, we have the following parameters that can be used in our computation:
√(x + 3) + 4 = 5
Subtract 4 from both sides of the equation
So, we have
√(x + 3) = 1
Take the square of both sides
x + 3 = 1
So, we have
x = -2
Hence, the solution for x is -2
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Find the area of the shape below. Give your answer in cm².
9 cm
4 cm
12 cm
Not to scale
The area of the shape is equal to 60 square centimeters
How to calculate for the area of the shapeThe shape is observed to be made up of a triangle and a rectangle, so we shall calculate for each area and sum the results to get the total area of the shape as follows:
area of triangle = 1/2 × 4 cm × 12 cm
area of the triangle = 24 cm²
area of the rectangle = 9 cm × 4 cm
area of the rectangle = 36 cm²
total area of the shape = 24 cm² + 36 cm²
total area of the shape = 60 cm²
Therefore, the area of the shape is equal to 60 square centimeters
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PLEASE I NEED HELP!! WILL MARK BRAINLIEST IF CORRECT!! TYY
Answer:
6.2
Step-by-step explanation:
For this we use a method called Pythagoras theorem.
to find '?' we will have to use this method
[tex]A^{2}[/tex] +[tex]B^{2}[/tex] =[tex]C^{2}[/tex]
since we don't know what A is we will name it x
[tex]x^{2}[/tex]+[tex]5^{2}[/tex]=[tex]8^{2}[/tex]
x+25=64
64-25=39
[tex]x^{2}[/tex]=39
x=[tex]\sqrt{39}[/tex]
x=6.2
Using the horizontal line test, which of the following can be concluded about
the inverse of the graph of the function below?
OA. It is a vertical shift.
OB. It is a function.
OC. It is not a function.
OD. It is a horizontal shift.
PLEASE HELP FAST!!
The correct answer would be option B i.e. The inverse of the function x = -y² + 4 is a function.
What is a horizontal shift?
A horizontal shift is a type of transformation in which a function is shifted left or right along the x-axis without changing its shape or orientation. If a function f(x) is shifted to the right by a distance of c units, the resulting function is denoted by f(x - c), and if it is shifted to the left by a distance of c units, the resulting function is denoted by f(x + c). Horizontal shifts are commonly used in calculus, geometry, and other branches of mathematics to analyze the behavior of functions and to solve problems related to graphs and equations.
By plotting the inverse of the function the following graph is obtained.
We know that the function is x = -y² + 4.
The inverse of the function x = -y² + 4 would be y = , which is a vertical parabola opening upwards. When we use the horizontal line test, we find that any horizontal line would intersect the once, which means that a single input (x) would have single corresponding output (y). Therefore, the inverse of the function x = -y² + 4 is a function.
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For the given triangle, find the missing length(s). Give an exact answer and, where appropriate, an approximation to three
decimal places.
Select the correct choice below and, if necessary, fill in the answer box(es) to complete your choice.
A. Using radicals, the shorter leg is exactly The shorter leg, up to three decimal places, is approximately
B. The shorter leg is exactly No approximation is necessary.
Select the correct choice below and, if necessary, fill in the answer box(es) to complete your choice.
OA. Using radicals, the hypotenuse is exactly The hypotenuse up to three decimal places, is approximately
B. The hypotenuse is exactly No approximation is necessary.
This question: 1 point(s) poss
15
The missing length of the triangle above would be =
A.Using radicals, the shorter leg is exactly 9. The shorter leg, up to three decimal places, is approximately 8.660.
How to calculate the missing length of the given triangle?To calculate the missing length of the given triangle, the sine formula is used such as;
a/sinA = c/sinC
where;
a = 15
A = 60°
c= ?
V= 90°
15/sin60° = b/sin90°
Make be the subject of formula;
c = 15× 1/0.866025403
c = 17.32
Using the Pythagorean formula;
c² = a² + b²
17.32² = 15² + b²
b² = 300 - 225
b² = 75
b = √75
b = 8.660.
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What is the result of multiplication of complex numbers
[tex] - \sqrt{3} + i \: and \: \frac{1}{8} (cos \: \frac{5\pi}{3} + i \: sin \: \frac{5\pi}{3} )[/tex]
The result of multiplication of complex numbers is ¹/₈sin5π/3 -√3/8 cos5π/3 + i¹/₈(cos5π/3 - √3sin5π/3).
What is the result of multiplication of the complex number?The result of the multiplication of the complex number is determined as follows;
-√3 + i x ¹/₈ (cos 5π/3 + i sin 5π/3)
Multiply the bracket by grouping them as shown below;
= -√3 x ¹/₈ (cos 5π/3 + i sin 5π/3) + i x ¹/₈ (cos 5π/3 + i sin 5π/3)
Multiply out the bracket;
= -√3/8 cos5π/3 - i√3/8 sin5π/3 + i¹/₈cos5π/3 + ¹/₈sin5π/3
note: i x i = 1
Collect similar terms together and add them if any;
= ¹/₈sin5π/3 -√3/8 cos5π/3 + i¹/₈(cos5π/3 - √3sin5π/3)
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What is the formula for the nth term of the given sequence? 48,72,108….
The explicit formula for an, the nth term of the sequence is f(n) = 48 * (3/2)ⁿ ⁻ ¹
How to determine the nth term of the sequenceFrom the question, we have the following parameters that can be used in our computation:
48, 72, 108…
The above definitions imply that the sequence is a geometric sequence with the followin features
First term, a = 48
Common ratio, r = 72/48 = 3/2
Using the above as a guide,
So, we have the following representation
f(n) = a * rⁿ ⁻ ¹
So, we have
f(n) = 48 * (3/2)ⁿ ⁻ ¹
Hence, the sequence is f(n) = 48 * (3/2)ⁿ ⁻ ¹
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Use the following table to help answer the question below.
State
Single-Earner
2-Person
3-Person
4-Person
Florida
$41,226
$52,259
$58,574
$69,009
Georgia
$40,691
$55,258
$61,104
$68,502
Missouri
$39,645
$51,568
$60,371
$71,059
Texas
$38,940
$55,859
$59,222
$66,381
Virginia
$48,362
$65,122
$74,151
$85,939
A family of three living in Georgia is thinking about filing bankruptcy. In order to file for Chapter 7 bankruptcy, what must be true about their monthly income?
a.
The family's monthly income must be less than $5,092.
b.
The family's monthly income must be more than $5,092.
c.
The family's monthly income must be less than $4,605.
d.
The family's monthly income must be more than $4,605.
The true statement about monthly income is "The family's monthly income must be less than $5,092." (option a).
The table provided shows the median income levels for different family sizes in various states, including Georgia. To determine whether the family of three is eligible for Chapter 7 bankruptcy, we need to compare their monthly income to the median income for a three-person family in Georgia, which is $61,104.
If the family's monthly income is less than the median income for their family size in their state, they are presumed to be eligible for Chapter 7 bankruptcy. In this case, the family's monthly income must be less than $61,104.
Looking at the table, we can see that the median income for a three-person family in Georgia is $61,104, which means that the family's monthly income must be less than $5,092 in order to be eligible for Chapter 7 bankruptcy.
Therefore, the correct answer is (a) - the family's monthly income must be less than $5,092 for them to be eligible to file for Chapter 7 bankruptcy.
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Given 3 positive intergers a, b, and c. Knowing a < b < c. If 42ª + 2² +2²=2336, what is the value of a?
Answer: We are given that:
42^a + 2^2 + 2^2 = 2336
Simplifying the expression on the left-hand side, we get:
42^a + 4 = 2336
Subtracting 4 from both sides, we get:
42^a = 2332
Taking the logarithm of both sides with base 42, we get:
a = log₄₂₂₋₃₂ ≈ 1.417
Since a is a positive integer, the closest integer to 1.417 is 1. Therefore, the value of a is 1.
Step-by-step explanation:
The radius of a cylindrical pipe is 2 ft. If the pipe is 19 ft long, what is its volume
Answer: The volume of the cylindrical pipe is 76pi cubic feet.
Step-by-step explanation: Sincerely, answered by Lizzy ♡ :: as an A+ student, I want to make sure other students can succeed as well, so in my free time: i answer questions like yours on Brainly! if you could click the thanks heart, give me brainliest by clicking the crown, and rate my answer 5 stars, it would be appreciated! have a lovely day! (ᵔᴥᵔ)
Answer:
Step-by-step explanation:
239 cubic feet
i asked my math teacher
