The water stream's parabola has the equation y = 48 - (x2)/(20*sqrt(3)), with the vertex at (0, 48) and the point of impact at (10sqrt(3), 0).
The equation of the parabola created by the water stream has a vertex at (0, 48), which is where the pipe ends. It is a quadratic equation. The pipe serves as the middle of the parabola's base, which is symmetrical and has a vertex at that location. The vertex form of a parabola can be used to determine the equation of the parabola, which is y = 48 - (x2)/(20*sqrt(3)). The parabola opens downward, with the highest point at (0, 48) and the lowest point at (10sqrt(3), 0), where the water stream hits the ground, according to the equation. The parabola's vertex and point of impact with the ground are described by the equation for the water's journey.
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What is the distance between the points (-7.5, -11) and (2, -11)?
Answer:
9.5
Step-by-step explanation:
Distance (d) = [tex]\sqrt{(2-(-7.5)^2)+(-11-(-11)^2)}\\ \sqrt{(9.5)^2+(0)^2}\\ \sqrt{90.25} \\9.5[/tex]
Solve for x: 2 over 3 equals 8 over quantity x plus The swimming team has competed in 45 races this season. They have won 30 races so far. How many races will the team need to win today for the team to have a 75% success rate?
Answer:
x = 12
4 races
Step-by-step explanation:
2/3 = 8/x
Cross multiply.
2x = 8 × 3
x = 4 × 3
x = 12
Answer: x = 12
0.75 × 45 = 33.75
Since the number of races must be an integer, they must win a total of 34 races to have at least a 75% success rate.
They already won 30 races.
34 - 30 = 4
Answer: 4 races
John had a yard full of dogs and chickens. He counts 25 heads and 78 legs. How many dogs does John have?
In the problem, it is solved that the number of dogs John has is 14
How to solve for the number of dogs John hasThe problem is solved by expression the word problem into a simultaneous equation as follows
let d be the number of dogs and c d number of chickens
d + c = 25 (since all must have a head)
4d + 2c = 78 (2 legs for chicken and 4 legs for dog)
using calculator to solve gives
d = 14 and c = 11
hence the number of dogs is 14
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(1 point) the following question is from the four steps of statistical inference. if you respond with a summary of all four steps, you will receive no credit on this problem: what is assumed when considering the likelihood of the occurrence of an outcome? hint: this is a question about statistics, not probability.
When evaluating the likelihood of an outcome, the claim or hypothesis statement is assumed. The required answer is a hypothesis claim or statement.
It is possible to test one's assumptions regarding a population parameter through the statistical analysis known as hypothesis testing. The association between two statistical variables can then be estimated by this hypothesis.
We start by writing the claim mathematically and determining if it is the null or alternative hypothesis. The null hypothesis is the assertion that there is no change or no relationship between the two variables; otherwise, the alternative hypothesis is the assertion that tells that there is a change or relationship.
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a population of bacteria growing exponentially can be modeled as P(t)= P0e kt , where is the time in hours and P0 is the initial population. if the population has a doubling time of 3 hours, calculate the growth constant .
A population of bacteria growing exponentially can be modeled as P(t)= P0e kt, where is the time in hours and P0 is the initial population. if the population has a doubling time of 3 hours, the growth constant is k = ln(2) / 3 = 0.231049.
The growth constant (k) can be calculated by taking the natural log of 2 (ln(2)) and dividing it by the doubling time (3 hours). Therefore, the growth constant is 0.231049. This equation models exponential growth, which is a type of growth where the rate of increase is proportional to the population size. In this case, the population doubles every 3 hours.
This exponential growth is modeled using the equation P(t)= P0e^kt, where P(t) is the population size at a given time, P0 is the initial population size, and k is the growth constant. By finding the growth constant, we can predict the population size at any given time. The growth constant is found by taking the natural log of 2 (ln(2)) and dividing it by the doubling time (3 hours).
This equation is used to find the amount of growth per unit time and is the same regardless of the population size. This equation can be used to predict the population size at any given time, allowing us to estimate the population size in the future.
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Which inequality is true when x= 4?
For the value of x = 4, the inequality equation that is true is option C: x/2 < 3.
What is an inequality?
In Algebra, an inequality is a mathematical statement that uses the inequality symbol to illustrate the relationship between two expressions. An inequality symbol has non-equal expressions on both sides. It indicates that the phrase on the left should be bigger or smaller than the expression on the right, or vice versa.
The first inequality equation is - x + 5 < 3
Substitute the value of x = 4 in the equation.
4 + 5 < 3
Now, simplify the equation -
9 < 3
It is known that 9 is not less than 3, but greater than 3.
Therefore, this inequality is false.
The second inequality equation is - 9x > 36
Substitute the value of x = 4 in the equation.
9(4) > 36
Now, simplify the equation -
36 < 36
It is known that 36 is not less than 36, but equal 36.
Therefore, this inequality is false.
The third inequality equation is - x/2 < 3
Substitute the value of x = 4 in the equation.
4/2 < 3
Now, simplify the equation -
2 < 3
It is known that 2 is less than 3.
Therefore, this inequality is true.
The fourth inequality equation is - 18 < x + 8
Substitute the value of x = 4 in the equation.
18 < 4 + 8
Now, simplify the equation -
18 < 12
It is known that 18 is not less than 12, but greater than 12.
Therefore, this inequality is false.
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Which inequality is true when x = 4?
A. x + 5 < 3
B. 9x > 36
C. ×/2 < 3
D. 18 < x + 8
A school staff meeting had 5 teachers in attendance, 60% of whom were first-year teachers.
How many first-year teachers were in the meeting?
Answer: 3
Step-by-step explanation: 60 x 5/100 = 3
There were three first-year teachers in the meeting.
shola collects N2x salary every month. when he takes away his expenditure of N5000, the salary is less than or equal to N2500. How much does Shila collects every months?
Answer:
less than or equal to N7500
Step-by-step explanation:
N2x - N5000 = N2500
N2x = N7500
Complete the square to write the equation of the sphere in standard form. x2 + y2 +Z2 + 9x-2y + 12z + 20 = 0 2 V149 Find the center and radius. (x,y,z)=(1-2 center V149 radius
Center of the sphere would be (-4.5, 1, -6) and radius be 6.086.
Write the equation of the sphere?
A sphere's general equation is (x - a)2 + (y - b)2 + (z - c) 2 = r2, where (a, b, c) represents the sphere's center, r represents the radius, and x, y, and z are the coordinates of points on the sphere's surface.
To complete the square, we need to add and subtract the square of half of the x coefficient and y coefficient, and the square of half of the z coefficient.
The equation will be : [tex](x + 9/2)^2 + (y - 1)^2 + (z + 6)^2 = (9/2)^2 + 1^2 + 6^2[/tex]
So the standard form of the equation of the sphere is,
[tex](x + 4.5)^2 + (y - 1)^2 + (z + 6)^2 = 37[/tex]
The center of the sphere is (x, y, z) = (-4.5, 1, -6) and the radius is √37 ≈ 6.086
Therefore, Center of the sphere would be (-4.5, 1, -6) and radius be 6.086.
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Which of the following is equivalent to the expression j ^ 41 ?
The equivalent expression of i⁴¹ is i.
What are the equivalent expressions?Expressions that are equivalent to the same thing, even when they have distinct appearances. When we enter the same value(s) for the variable, two algebraic expressions that are equivalent have the same value (s).
Given:
An expression i⁴¹.
Simplifying,
i⁴¹ = {(i⁴)¹⁰} i
i⁴¹ = {(1)¹⁰} i {i⁴ = 1}
i⁴¹ = i
Therefore, the equivalent expression is i.
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In the equation 10+4y=-4y+2,the variable y represents the same value. Is y = 1, 0, -1, or -2 the solution of this equation explain
The solution to the equation 10+4y=-4y+2 is -1 because the variable y represents the same value.
What is equation?An equation is a formula in mathematics that expresses the equality of two expressions by connecting them with the equals sign =. In its most basic form, an equation is a mathematical statement that shows that two mathematical expressions are equal. 3x + 5 = 14, for example, is an equation in which 3x + 5 and 14 are two expressions separated by a 'equal' sign. A mathematical equation that depicts the relationship between two expressions on opposite sides of the sign. It mostly consists of one variable and one equal to symbol. 2x - 4 = 2 is an example.
Here,
10+4y=-4y+2
8y=-8
y=-1
The solution of equation 10+4y=-4y+2 is -1 as the variable y represents the same value.
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Sudoku is a puzzle consisting of squares arranged in 9 rows and 9 columns. The 81 squares are further divided into nine 3 ✕ 3 square boxes. The object is to fill in the squares with numerals 1 through 9 so that each column, row, and box contains all nine numbers. However, there is a requirement that each number appear only once in any row, column, or box. Each puzzle already has numbers in some of the squares.
Alisha wants to do a statistical study to determine how long it takes people to complete a Sudoku puzzle. Her plan is as follows.
Download 10 different puzzles from the Internet.
Find 10 friends willing to participate.
Ask each friend to complete one of the puzzles and time him- or herself.
Gather the completion times from each friend.
Describe some of the problems with Alisha's plan for the study. (Note: Puzzles differ in difficulty, ranging from beginner to very difficult. SELECT ALL THAT APPLY.)
A. There are actually only 9 different Sudoku puzzles.
B. Some Sudoku puzzles don't have solutions.
C. It is not clear that all puzzles have the same difficulty.
D. Self-timing may lead to some inaccurate measurements.
E. Friends having different levels of experience.
The problems with Alisha's statistical study are that the difficulty levels of the sudoku puzzles might be different, self timing can lead to inaccurate measures of time and also the experience and skill level of her friends will be different.
In her statistical study, Alisha asked 10 of her friends to try 10 different sudoku puzzles from the internet and time themselves while doing it. In this study there are a few errors. The first one being that the difficulty level of the puzzles that her friends will be solving are going to be different.
Another issue is that since her friends are self-timing, there can be inaccurate measures of time and lastly, the experience and skill of her friends for sudoku is going to create a bias in her study.
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Assume A,B,C are invertible matrices of appropriate dimension. Solve for X:
AX + B = CX
The solution of the given equation is X = B(C - A)⁻¹.
To solve for X in the equation AX + B = CX, we can rearrange the equation as follows:
AX - CX = -B
Factor out X on the left side:
(X(A - C)) = -B
To isolate X, we can multiply both sides of the equation by the inverse of (A - C), assuming it exists:
X = -(A - C)⁻¹ × B
X = (C - A)⁻¹ × B
Therefore, the solution for X is:
X = B(C - A)⁻¹
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What is the value of x?
Answer:
X = 11
Step-by-step explanation:
The total degrees of a line is 180
They gave us 39 and 13x-2
We can get rid of the 39 by subtracting it from 180
180-39=141
That means 13x-2 = 141
Now to find X. Adding 2 on both sides, gets rid of the 2 on the left side
13x = 143
Dividing 13 on both sides, we can get X alone
X = 11
Find the average rate of change of each function on the interval specified for the real numbers b or h in the simplest form.
1) the rate change of function f(x) in given interval =4(b+1)
2) the rate change of function g(x) in given interval =1
3) the rate change of function j(x) in given interval =[tex]3h^2+9h+9[/tex]
To find out the average rate change of function on given interval is -
Use the graph of f to determine f (a) and f (b) for the provided range [a,b]. Remember that the graph of f's point with the y-coordinate of f (a) and the x-coordinate of an is called f. Similar to that, f ( b ) is the y-coordinate of the point on the f graph whose x-coordinate is b.
Step 2: Calculate the average rate of change of f over the range [a, b] using the average rate of change formula.
[tex]\frac{f(b)-f(a)}{b-a}[/tex]
1)
[tex]f(x)=4x^2-7 \ on\ [1,b]\\\\f(1)=4-7=-3\\\\f(b)=4b^2-7\\\\the \ rate \ change =\frac{4b^2-7+3}{b-1}\\\\=4(b+1)[/tex]
2)
[tex]p(x)=3x+4 \ on\ [2,2+h]\\\\p(2)=10\\\\p(2+h)=10+h\\\\The\ average\ rate \ change= \frac{10+h-10}{2+h-2}\\\\=1[/tex]
3)
[tex]j(x)=3x^3 \ on \ [1,1+h]\\\\j(1)=3\\\\j(1+h)= 3(1+h)^3\\\\\\so, the\ rate\ change = 3h^2+9h+9[/tex]
The complete Question is: -
For the following exercises, find the average rate of change of each function on the interval specified for real numbers b or h in simplest form.
1. f(x)= 4x^2 - 7 on [1, b]
2. p(x)= 3x+4 on [2,2+h]
3. j(x)= 3x3 on [1, 1+h]
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for each of the following sets of functions either find a function f(x) in their span such that f(x) > 0 for all x
f(x) = 7x - 1, which is a linear equation with a positive leading coefficient, making f(x) > 0 for all x.
Set 1: {f(x) = x + 1, f(x) = x - 1}
Function f(x) = x^2 + 2 can be found in the span of the two given functions. This can be seen by expanding the equation:
f(x) = x^2 + 2 = (x + 1) + (x - 1) = 2x;
thus, f(x) = 2x + 2, which is a quadratic equation with a positive leading coefficient, making f(x) > 0 for all x.
Set 2: {f(x) = 4x - 2, f(x) = 3x + 1}
Function f(x) = 7x - 1 can be found in the span of the two given functions. This can be seen by expanding the equation:
f(x) = 7x - 1 = (4x - 2) + (3x + 1) = 7x;
thus, f(x) = 7x - 1, which is a linear equation with a positive leading coefficient, making f(x) > 0 for all x.
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Complete question:Find a function f(x) in the span of the functions f1(x) = x and f2(x) = -x such that f(x) > 0 for all x.
determine the relative order of the metric prefixes of kilo-, micro-, centi-, and milli-. for the same base unit, choose... is less than choose... , which is less than choose... , which is less than choose... .
The relative order of the metric prefixes Milli- < Centi- < Micro- < Kilo-
The relative order of the metric prefixes of kilo-, micro-, centi-, and milli- is milli-, centi-, micro-, and kilo-. This order is determined by the exponential values of each prefix.
Milli- is equal to 10-3, centi- is equal to 10-2, micro- is equal to 10-6 and kilo- is equal to 103. The exponential values are used to determine the relative order of the prefixes. The lowest exponential value is milli-, making it the smallest metric prefix and the highest exponential value is kilo-, making it the largest metric prefix.
When the exponential values are compared, it is clear that the order of the prefixes is milli- < centi- < micro- < kilo-. This order is used to determine the relative size of the metric prefixes when measuring the same base unit.
For example, if the base unit is meter, then millimeter is the smallest measure and kilometer is the largest measure. The exponential values of the metric prefixes determine the relative order of the base unit.
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A new apartment building has 33 floors, with 24 apartments on each floor. How many apartments are in the building?
(Partial product)
Red :
Blue :
Green :
Yellow :
Total Product:
Simple equation when u break it down: 33 x 24=792 apartments
How many apartments are in the building?A building, or edifice, is an enclosed structure with a roof and walls that is standing in one location more or less permanently, such as a house or factory (although there are also portable buildings). Buildings come in a variety of sizes, shapes, and uses, and they have been modified throughout history for a wide range of reasons, including the availability of building materials, weather, land prices, ground conditions, particular uses, prestige, and aesthetic considerations.
given:
new apartments' building =33 floor
apartments on each =24 floor
33*24=792
792 apartments are in the building
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For a normal distribution with mean 0 and standard deviation 1, which of the following Python lines outputs the probability P(x<0.325)?
Question 1 options:
a)
import scipy.stats as st
print(st.norm.cdf(0.325, 0, 1))
b)
import pandas as pandas
print(st.norm.pdf(0.325, 0, 1))
c)
import scipy.stats as st
print(st.norm.sf(0.325, 0, 1))
d)
print(normal(0.325, 0, 1))
Python lines to get the output for the probability P(x<0.325) are -
a) import scipy.stats as
st print(st.norm.cdf(0.325, 0, 1))
Hence, option a is the correct answer.
The Python code -
import scipy.stats as
st print(st.norm.cdf(0.325, 0, 1))
This line of code imports the scipy.stats module as "st", and then uses the norm.cdf function to calculate the cumulative distribution function (CDF) of a normal distribution with mean 0 and standard deviation 1, evaluated at x=0.325.
The CDF gives the probability that a random variable from the normal distribution is less than or equal to a certain value, so this line of code is outputting the probability P(x<0.325).
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Example 1. 15+6x3 This problem is modeled after example 1. Find the requested pattern. (Enter the first three numbers of the pattern as a comma-separated list.) three pattern
Therefore, the 3 patterns are
3,6,9,3,6,9
Explanation:
Given that,
we will carry out the multiplications of succession counting number by 3 and if there is more than a single digit answer .we add the digits.
we are looking for is a pattern for there single digit numerals.
carryout the plan
1x3=3→3
2x3=6→6
3x3=9→9
4x3=12→1+2=3
5x3=15→1+5=6
and so on
continue with some additional at terms.
6x3=18→1+8=9
7x3=21→2+1=3
∵ Therefore the 3 patterns are
3,6,9,3,6,9
A pattern is defined in mathematics as a sequence of repeating objects, shapes, or numbers. A pattern can be associated with any type of event or object. A pattern has a rule that tells us which objects belong to the pattern and which objects do not belong to the pattern.
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Matt has a piggy bank with 250 coins all dimes and quarter.The total dollar amount in the piggy bank is $39.25. How of each type of coin are in the piggy bank?
The piggy bank has 200 dimes and 50 quarters.
To find this, we can set up the following equation:
(number of dimes x $0.10) + (number of quarters x $0.25) = $39.25
We know that the piggy bank contains 250 coins, so we can substitute that in:
(x x $0.10) + (250-x x $0.25) = $39.25
Now we can solve for x, the number of dimes:
x0.10 + (250-x)0.25 = 39.25
x0.10 + 62.5 - x0.25 = 39.25
0.1x + 62.5 - 0.25x = 39.25
-0.15x = -23
x= 153
So there are 153 dimes in the piggy bank, and 250-153 = 97 quarters.
But we know that the piggy bank contains 250 coins, so we can check that 153 dimes + 97 quarters = 250 coins.
What is 2.4 divided by -0.06?
(With work pls)
Answer:
To find the result of 2.4 divided by -0.06, we need to use the following steps:
Step 1: Change the division problem into a multiplication problem by flipping the divisor and multiplying by its reciprocal.
-0.06 ÷ 2.4 = -0.06 x 1/(2.4)
Step 2: To find the reciprocal of 2.4, we need to divide 1 by 2.4
1/(2.4) = 0.416666666666667
Step 3: Multiply the original dividend (2.4) by the reciprocal of the divisor (0.416666666666667)
2.4 x 0.416666666666667 = -0.1
So, 2.4 divided by -0.06 is equal to -0.1
It's worth noting that -0.1 is a negative number which makes sense since the divisor is negative, hence the result is the opposite of the result when dividing by a positive number.
Andrew and his brothers want to put their money together to buy a new game system . Costs $168.69 , how much money will each boy need to contribute so they put in equal amount.
The amount each boy will have to contribute is $56.23
How to calculate the amount that each boy will contribute?
Andrew and his two brother want to contribute money together to buy a new game system
The cost of the game system is $168.69
Each boy want to contribute the same amount
Therefore the amount that each boy will contribute can be calculated as follows
There are 3 boys in total, Andrew and his two brothers
= 168.69/3
= 56.23
Hence each boy will contribute an amount of $56.23
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Answer the following
One can infer some information about a line's slope just by looking at its graph, especially in comparison to other lines plotted on the same coordinate plane.
What is Identify slope from a graph?Slope has a meaning in mathematics that is remarkably similar to what it means in everyday language. When describing the steepness and direction of lines in mathematics, slope is utilized. The three lines' graphs are displayed below; take a look:Lines A and B will be examined first. Line B is steeper than line A, if these lines were hills, in your mental model. Line A and line B have different slopes.Then, as you walk from left to right, observe how lines A and B incline up. Assuming a positive slope for these two lines. Between left and right, Line C slopes downward. It slopes down on line C. The rise and run of the line may be determined using two of its points, and the slope can be calculated. The rise and run are terms for the vertical and horizontal changes between two places, respectively. Divide the rise by the run to get the slope.
Rise / run = a slope.
A slope of 1.2 will be present on this line.regardless of the line's two points that you choose. Try calculating the slope between the point ( 6, 3 ) and the origin, ( 0, 0). The ascent will equal 3 and the run will equal 6. Rise run equals 3 / 6 plus 1 2 is the slope. It remains the same.The Complete Question is line's slope.
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I need assistance for this problem below:
The image of quadratic function f(x) = x² is equal to g(x) = 6 · x².
How to derive and graph the image of a quadratic equation
In this question we see the representation of quadratic equation f(x) = x², from which we need to generate the image of this function, this can be done by a rigid transformation known as vertical dilation:
g(x) = k · f(x), k > 1
Where:
f(x) - Original functiong(x) - Resulting functionIf we know that f(x) = x² and k = 6, then the image of function is:
g(x) = 6 · x²
Whose representation on Cartesian plane is shown in the image attached below.
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Quadrilateral DEFG is similar to quadrilateral HIJK. Find the measure of side JK.
Round your answer to the nearest tenth if necessary.
Quadrilateral DEFG is similar to quadrilateral HIJK The measure of side JK is 8.
Since quadrilateral DEFG is similar to quadrilateral HIJK, we know that the ratio of corresponding side lengths is equal. This means that if we know the length of one side of one of the quadrilaterals, we can use that ratio to find the length of the corresponding side in the other quadrilateral.
For example, if we know that side DE is 8 units long, we can use the ratio of side JK to side DE (x/8) to find the length of side JK. We can also use the same ratio of side IJ to side DF which is x/4.
Let's assume that the length of side DE is 8 units. We can use the ratio of side JK to side DE (x/8) to find the length of side JK.
[tex]x/8 = x/4[/tex]
Cross-multiplying and simplifying the equation we get
[tex]4x = 8x[/tex]
[tex]x = 8[/tex]
Therefore, the measure of side JK is 8 units.
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NO LINKS!!!
55, Write an equation satisfying the given conditions.
Part (a)
The two limit statements tell us that this an exponential decay function.
The curve goes up forever when heading to the left (negative infinity) as indicated by the notation [tex]\displaystyle \lim_{\text{x}\to-\infty}f(x) = \infty[/tex]
At the same time, the curve slowly approaches the horizontal asymptote y = -2, when moving to the right, because of this notation [tex]\displaystyle \lim_{\text{x}\to\infty}f(x) = -2[/tex]
An exponential decay function like [tex]\text{y} = (0.5)^{\text{x}}[/tex] has a horizontal asymptote of y = 0, aka the x axis. The y value approaches 0 but never gets there. Each output is positive.
Shift everything down 2 units to arrive at [tex]\text{y} = (0.5)^{\text{x}}-2[/tex] and this will move the horizontal asymptote down the same amount.
There's nothing really special about the 0.5; you can replace it with any value in the interval 0 < b < 1.
---------
Answer: [tex]\text{f(x)} = (0.5)^{\text{x}}-2[/tex]====================================================
Part (b)
I'll use this template
[tex]\text{y} = ab^{\text{x}}+c[/tex]
Plugging in x = 0 leads to y = a+c which is the y intercept. Set this equal to the stated y intercept 7 and we get a+c = 7.
We want the [tex]ab^{\text{x}}[/tex] portion to approach zero, which leads to c = 4 so we approach the stated horizontal asymptote.
So,
a+c = 7
a+4 = 7
a = 7-4
a = 3
We go from this
[tex]\text{y} = ab^{\text{x}}+c[/tex]
to this
[tex]\text{y} = 3b^{\text{x}}+4[/tex]
The value of b doesn't matter.
I'll go for b = 0.7 so we get to [tex]\text{f(x)} = 3(0.7)^{\text{x}}+4[/tex]
---------
Answer: [tex]\text{g(x)} = 3(0.7)^{\text{x}}+4[/tex]====================================================
Part (c)
The parent function [tex]\text{y} = \log(\text{x}})[/tex] has a domain of [tex](0, \infty)[/tex]. In other words it is the interval [tex]0 < \text{x} < \infty[/tex]
If we replaced each input x with x-5, then we shift the xy axis 5 units to the left. It gives the illusion the log curve moves 5 units to the right.
The vertical asymptote also moves 5 units to the right. We go from a domain of [tex](0, \infty)[/tex] to a domain of [tex](5, \infty)[/tex]
The base of the log doesn't matter.
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Answer: [tex]\text{h(x)} = \log(\text{x}-5)[/tex]Check out the graphs below. I used GeoGebra, but Desmos is another good option.
Determine another point on the line given two points on the line.
(0, 5), (4, 1)
Another point on the line is (2, 3)
How to find another point on the lineTo find another point on the line the equation of the line will be solved as used to get other points
The slope, m of the lines is calculated the formula
m = (y₀ - y₁) / (x₀ - x₁)
where
m = slope
x₂ and x₁ = points in x coordinates
y₂ and y₁ = points in y coordinates
The slope, m of the linear function is calculated using the points (0, 5), (4, 1)
m = (y₀ - y₁) / (x₀ - x₁)
m = (5 - 1) / (0 - 4)
m = (4) / (-4)
m = -1
equation passing through point (0, 5)
(y - y₁) = m (x - x₁)
y - 5 = -1 (x - 0)
y - 5 = -x
y = -x + 5 equation of the line
for x = 2
y = -x + 5 = -2 + 5 = 3
the point is (2, 3)
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#7 in need help with this problem please
You cannot use the Hypotenuse-Leg congruence theorem to prove the similarity of triangles JKM and LKM, as they are not right triangles.
What is the HL congruence theorem?The Hypotenuse-Leg congruence theorem states that if the hypotenuse and one leg of two right triangles have the same measure then these two triangles are said to be congruent to each other.
The triangles JKM and LKM are not right triangles, as they do not have an angle of 90º, hence the HL congruence theorem cannot be used to prove their similarity.
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show that the improper integral g(x0dx is divergent but the average value of g on the interval 4,infinoty is finite
To show that the improper integral g(x)dx is divergent, but the average value of g on the interval 4, infinity is finite, we can consider a function g(x) = 1/x, which is mostly used as an example for a divergent integral.
The improper integral of g(x) from 4 to infinity is given by:
[tex]\int\limits {g(x)} \, dx = \int\limits {(1/x)} \, dx[/tex] from 4 to infinity
= lim (upper limit -> infinity) [ln|x|] from 4 to x
= [ln|x|] from 4 to infinity
= ln(infinity) - ln(4) = infinity - ln(4) = infinity
As the limit of the integral is infinity, the integral is divergent.
However, the average value of g on the interval [4, ∞) is given by:
average value = (1/∞ - 4) * ∫(1/x)dx from 4 to infinity
= (1/∞ - 4) * (infinity - ln(4))
= -4 + ln(4)
= ln(4) - 4
which is a finite value when the integral is divergent
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