The solution for the inequality is x∈(-∞,4)U(1,+∞)
What is inequality?
Inequality is a statement that compares two values and states that one value is greater than, less than, or not equal to the other value.
To solve the inequality (x-4)(x-1)>0, we can first factor it:
(x-4)(x-1)>0
We can then use the Zero Product Property, which states that if the product of two factors is equal to zero, then at least one of the factors must be equal to zero.
So we get:
x-4=0 or x-1=0
x = 4 or x = 1
Now we will test the sign of inequality for x-4 and x-1.
x<4 or x>1
Hence, the solution for the inequality is x∈(-∞,4)U(1,+∞)
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determine whether the underlined number is a statistic or a parameter.
in a study of all 2462 seniors at a college, it is found that 55% own a vehicle.
choose the correct statement below.
a. statistic because the value is a numerical measurement describing a characteristic of a population
b. parameter because the value is a numerical measurement describing a charateristic of a sample
c. parameter because the value is a numerical measurement describing a characteristic of a population
d. statistic because the value is a numerical measurement describing a characteristic of a sample
Since the value is a numerical measurement representing a property of a sample, it is statistical.
Given that a sample of workers is chosen, and it is discovered that 55% of them possess a car.
Let's first clarify the distinction between a parameter and a statistic before moving on to the questions.
Parameters are numerical summaries of population statistics. However, statistics are numerical summaries of sample data.
Sample is a subset of the population; as such, it is just a small percentage of the whole population.
The percentage of the sample of employees in this case is 55%. Statistic refers to a numerical representation of data about a sample.
The value is statistical since it is a numerical measurement that describes a property of a sample.
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Tristan goes to a restaurant and the subtotal on the bill was
x
x dollars. A tax of 7% is applied to the bill. Tristan decides to leave a tip of 16% on the entire bill (including the tax). Write an expression in terms of
x
x that represents the total amount that Tristan paid
The expression for the total amount Tristan paid is 1.1342x.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
Total bill = $x
Tax = 7%
This means,
= (7/100)x
= 0.07x
Tip = 16%
This means,
= (6/100) x (x + 0.07x)
= 0.06 x (1.07x)
= 0.0642x
The total amount paid.
= total bill + tax + tip
= x + (7% of x) + 16% of (x + 7% of x)
= x + 0.07x + 0.0642x
= 1.1342x
Thus,
The total amount paid is 1.1342x.
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Which expression is equivalent to 3x2 - 10x - 8?
We can rewrite the quadratic to get the equivalent expression:
3*(x - 4)*(x + 2/3)
How to find an equivalent expression?We want to find an expression equivalent to the quadratic equation:
3x^2 -10x -8
Remember that if the quadratic equation has the roots a and b, then we can rewrite the equation as:
3*(x - a)*(x - b)
So let's find the roots, using the quadratic formula we will get:
[tex]x = \frac{10 \pm \sqrt{(-10)^2 - 4*3*(-8)} }{2*3} \\\\x = \frac{10 \pm 14 }{6}[/tex]
So the two roots are:
x = (10 + 14)/6 = 4
x = (10 - 4)/6 = -4/6 = -2/3
Then the equivalent expression is:
3*(x - 4)*(x + 2/3)
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A frequency table of grades has five classes (A, B, C, D, F) with frequencies of 4, 14, 15, 5, and 1 respectively.
Using percentages, what are the relative frequencies of the five classes?
So the relative frequencies of the five classes are:
A: 10.25%
B: 35.89%
C: 38.46%
D: 12.82%
F: 2.56%
What is the Frequency?
Frequency refers to the number of times a specific event or value occurs within a set of data. It is a measure of how often something happens or occurs.
A relative frequency is a measure of how often a certain event or value occurs within a set of data, expressed as a proportion or percentage of the total number of events or values.
To find the relative frequencies of the five classes in percentage, you need to divide the frequency of each class by the total number of observations, and then multiply by 100 to express the result as a percentage.
The total number of observations can be found by adding up the frequencies of all five classes: 4 + 14 + 15 + 5 + 1 = 39
To find the relative frequency of class A, divide the frequency of class A (4) by the total number of observations (39) and then multiply by 100: 4/39 * 100 = 10.25%
Similarly, you can find the relative frequencies for the other classes:
Class B: 14/39 * 100 = 35.89%
Class C: 15/39 * 100 = 38.46%
Class D: 5/39 * 100 = 12.82%
Class F: 1/39 * 100 = 2.56%
So the relative frequencies of the five classes are:
A: 10.25%
B: 35.89%
C: 38.46%
D: 12.82%
F: 2.56%
It's worth noting that the sum of all relative frequencies should be equal to 100%.
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A bicyclist starts from rest and accelerates along a straight path to a speed of 12.15 m/s in a time of 4.5 seconds. What is the bicyclist’s acceleration in m/s2?
A. .37
B. 54.7
C. 2.7
D. 6.8
The bicyclist’s acceleration is 2.7 m/s²
the correct answer is an option (C)
We know that the acceleration is nothing but the change in velocity over the change in time.
A = Δv / Δt
where, Δv = change in velocity
Δt = change in time
A = acceleration
Here, we have been given a bicyclist starts from rest and accelerates along a straight path to a speed of 12.15 m/s in a time of 4.5 seconds.
So, Δv = 12.15 m/s and Δt = 4.5 seconds
Using above formula of the acceleration would be,
A = Δv / Δt
A = 12.15 / 4.5
A = 2.7 m/s²
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Which of the following 3D figures is created when the triangle shown is rotated about the vertical axis?
A
B
C
D
3
cylinder
cone
pyramid
triangular prism.
The 3D figure that is created when the triangle shown is rotated about the vertical axis is; A cone
How to interpret the rotation of a shape?A three dimensional figure is defined as one that has a length, width and height.
Let us look at some options;
1) Prism; This is not formed by rotating a two-dimensional figure around the y-axis because of the presence of both a rectangle and a triangle face.
2) Cylinder; This is a three dimensional figure formed by rotating a rectangle which is a two-dimensional figure around the y-axis.
3) Circle; This is a two dimensional figure
4) Cone; This is a three dimensional figure formed by rotating a triangle which is a two-dimensional figure around the y-axis.
5) Sphere; This is a three dimensional figure formed by rotating a semi circle which is a two-dimensional figure around the y-axis.
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For what value of k will roots of the equation be real and equal if 9x 2 3kx 4 0?
A quadratic equation 9x² + 3kx + 4 = 0 has equal roots. Thus, the values of k are -4, and +4.
What is quadratic equation?The equation of the second degree is a quadratic equation. This indicates that it contains a phrase that is squared, at least once. ax² + bx + c = 0, which uses constants or numerical coefficients for the variables a, b, and c, is one of the classic formulae for solving quadratic equations. Unknown variable 'x' is used here.
The given problem can be solved using the concepts of quadratic equations.
1. The given quadratic equation is 9x² + 3kx + 4 = 0.
2. For an equation to have equal roots the value of the discriminant is 0,
=> The discriminant of a quadratic equation ax² + b x + c = 0 is given by the formula,
=> Discriminant ( D ) = [tex]\sqrt{b^2 - 4ac}[/tex]
=> For equal roots D = 0.
3. Substitute the values in the above formula:
⇒ [tex]\sqrt{(3k)^2 - 4*9*4}[/tex] = 0
⇒ [tex]{9k^2 - 144}[/tex] = 0
⇒9k² = 144
⇒ k² = 16
⇒ k = ± 4
Therefore, the values of k are -4, and +4.
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Solve.
12. Which team used the greatest percent of water in their recipe?
13. Some people say that the ideal recipe for sand sculptures contains 88.9%
sand. Which team's recipe is closest to the ideal recipes?
Their recipe contains 88.6% sand.
Which team's formula comes the closest to being ideal?Team 1 used the greatest percent of water in their recipe with a total of 48.3%. Team 2’s recipe had 45.5% water, while Team 3’s recipe had a total of 41.2%.When looking at the recipe closest to the ideal 88.9% sand, Team 3's recipe is the closest. Team 3's recipe contains a total of 87.7% sand, while Team 1's recipe contains 84.6% and Team 2's recipe contains 82.2%.This indicates that Team 3 used the most efficient ratio of sand to water, with the closest recipe to the ideal 88.9% sand. Team 3's recipe also used the least amount of water, indicating that they were able to achieve the desired consistency and strength of the sand sculpture without having to use too much water.Overall, Team 3 was the most successful in creating a recipe closest to the ideal sand sculpture recipe. Their recipe was the least wasteful of water, while still being able to achieve the desired consistency and strength of the sand sculpture.To learn more about The theory of ideal sand sculpture recipes refer to:
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find the midpoint of the line segment.
Answer:
(-3,0)
Step-by-step explanation:
Step-by-step explanation:
Bottom line point
( -5, -3 )
( -1, 3 )
Midpoint:
( -3, 0 )
pls I need some help with this question and teach me how to go about it when solving for this work given in this question.
Answer:
GH₵10.50 per girlGH₵20.50 per boyStep-by-step explanation:
Given GH₵960 contributed by 80 students of which 68 are girls who contributed a total of GH₵714, you want to know the amount per girl and the amount per boy that was contributed.
RateThe amount per girl or boy is found by dividing their total contribution by the corresponding number of girls or boys.
ApplicationIf 68 girls contributed GH₵714, then the amount per girl is ...
(GH₵714)/(68 girls) = GH₵10.50 /girl
Each girl contributed GH₵10.50.
The remaining 12 students were boys, and the amount they contributed was (GH₵960 -714) = GH₵246. Then the amount per boy is ...
(GH₵246)/(12 boys) = GH₵20.50 /boy
Each boy contributed GH₵20.50.
Calculating Volume Practice
In a shape or space, volume refers to the quantity that can be accommodated.
Exactly how is volume determined?It's a formula: V = lwh. six-faced solid object in three dimensions. an indication of an object's length. an indicator of an object's width.
In a shape or space, volume refers to the quantity that can be accommodated. Remember that volume is equal to the number of cubes that can completely occupy a space. Area is the number of squares that can cover a space (in square units) (cubic units). For calculating volume, each 3D shape has a formula.
In a shape or space, volume refers to the quantity that can be accommodated.
The complete question is,
In 7th grade mathematics, what is volume?
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18x^2+4-[6(x^2-2)+5]
The simplified form of the expression 18x² + 4 - [6(x² -2) + 5] is 12x² + 11.
What is an expression?Mathematical statements are called expressions if they have at least two words that are related by an operator and contain either numbers, variables, or both. Addition, subtraction, multiplication, and division are all possible mathematical operations.
The given expression is
18x² + 4 - [6(x² -2) + 5]
We can rewrite it as
= 18x² + 4 - [6x² - 12 + 5]
= 18x² + 4 - [6x² - 7]
= 18x² + 4 - 6x² + 7
= 12x² + 11
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The complete question is:
Simplify the expression: 18x² + 4 - [6(x² -2) + 5]
Two different plants that grow each month at different rates are represented by the functions f(x) and g(x). In what month does the height of the f(x) plant exceed that of the g(x) plant? month (x) f(x) = 3x g(x) = 5x + 12 1 3 17 2 9 22.
In the 4th month, the height of the f(x) plant exceeds that of the g(x) plant. This can be solved using the concept of polynomials.
What is polynomials?When exponents, constants, and variables are joined using mathematical operations like addition, subtraction, multiplication, and division, the result is a polynomial (No division operation by a variable).
Exponents that may be added, subtracted, or multiplied are a part of algebraic expressions called polynomials.Different forms of polynomials exist. linear equations with monomial coefficientsa polynomial with a single term called a monomial.Binomial quadratic equation (A binomial is a polynomial with two, unlike terms).Month (x)
f(x) = 3x / g(x) = 5x + 12
⇒f(x) × g(x) = 3X
⇒g(x) = 3X/ 5x + 12
At 4th month let x = 4
f(x) =g(x)
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The complete question is as follows:
Two different plants that grow each month at different rates are represented by the functions f(x) and g(x). In what month does the height of the f(x) plant exceed that of the g(x) plant?
Month (x) / f(x) = 3x / g(x) = 5x + 12
1 / 3 / 17
2 / 9 / 22
A) Month 3
B) Month 4
C) Month 5
D) Month 6
A restaurant’s goal is to serve 600 customers in 8 hours and 900 customers in 12 hours. Write an equation in point-slope form that represents the number of customers served per hour
y = 75x - 450 represents the number of customers served per hour where y is the number of customers served and x is the number of hours.
The point-slope form of a linear equation is y - y1 = m(x - x1), where m is the slope and (x1, y1) is a point on the line.
To find the equation representing the number of customers served per hour, we can first find the slope of the line by using the information given. The slope of a line is the change in y over the change in x.
In 8 hours, the restaurant serves 600 customers and in 12 hours, 900 customers. Therefore, the change in y is 900 - 600 = 300 and the change in x is 12 - 8 = 4. The slope of the line is 300/4 = 75.
We also know that the restaurant serves 600 customers in 8 hours. This means that when x = 8, y = 600.
Using this information, we can write the equation in point-slope form:
y - 600 = 75(x - 8)
So the equation of the line representing the number of customers served per hour is:
y = 75x - 450
Where y is the number of customers served and x is the number of hours.
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What are the solutions roots of 2x² 5x 3 0?
The roots of the equation 2x² 5x 3 0 are the two values of x that make the equation equal to 0. In this case, the two roots are x = -3 and x = 0.5.
To find the solutions roots of 2x² 5x 3 0:
1. Rearrange the equation to make it equal to 0: 2x² 5x - 3 = 0
2. Use the quadratic equation to solve for x: x = (-b ± √(b² - 4ac)) / 2a
3. Substitute the coefficients of the equation: x = (5 ± √(25 - 4(2)(-3))) / 4
4. Simplify the equation: x = (5 ± √49) / 4
5. Calculate the two solution roots: x = -3 and x = 0.5
The solutions roots of 2x² 5x 3 0 can be found by rearranging the equation to make it equal to 0 and then using the quadratic equation to solve for x. The coefficients of the equation (2, 5, and -3) must be substituted into the equation to calculate the two solutions roots. When this is done, the two solutions roots are x = -3 and x = 0.5. This means that if x is equal to either -3 or 0.5, the equation 2x² 5x 3 0 will equal 0.
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Find the slope of the line graphed below.
Answer:
-4/4 = -1
Step-by-step explanation:
Answer: -4/4
Step-by-step explanation:
m = slope
(x1, y1) = coordinates of first point in the line
(x2, y2) = coordinates of second point in the line
-3,-1 1,-5 are the corrdinates
(-5) - (-1) = -4
1 - (-3) = 4
What is K in the equation y?
The amount of the constant k is known as the "constant of proportionality".
What is K in an equation?Given any position, we can calculate k by dividing the y-coordinate by the x-coordinate because k is constant (the same for every point). Where k is the constant of variation, y = kx.
We refer to a relationship between two variables as having a direct relationship when the equation for the relationship is of the form y = kx, where k is a constant. The "constant of proportionality" is the value of the constant k.
For some constant k, often known as the proportionality or variational constant, y=kx. (Some textbooks will refer to direct variation as "y varies as x," "y varies proportionally as x," or "y is directly proportional to x.
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Add the expressions.
the quantity negative 6 minus one sixth times p end quantity plus the quantity two-thirds times p minus 8 end quantity
negative 3 over 12 times p plus negative 2
1 over 9 times p minus 2
1 over 2 times p minus 14
1 over 3 times p plus negative 14
The addition of the expression; negative 6 minus one sixth times p end quantity plus the quantity two-thirds times p minus 8 is "1 over 2 times p minus 14".
The correct answer choice is option C
How to add expression?-6 - (1/6 × p) + (2/3 × p) - 8
open parenthesis
-6 - 1/6p + 2/3p - 8
-6 - 8 - 1/6p + 2/3p
-14 - p+ 4p/ 6
= -14 + 3p/6
= -14 + 1/2p
It can also be written as;
1/2p - 14
Therefore, the addition of the expression is 1 over 2 times p minus 14.
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Answer:its c
Step-by-step explanation:the answer is c
Unit 7: right triangles and trigonometry 7-5H
Applying the trigonometric ratios, the values of x are:
1. x = 7.3
2. x = 33.3
3. x = 21.3
4. x = 31.9
5. x = 25.6
6. x = 11.0
7. x = 41.8°
8. x = 64.2°
What are the Trigonometric Ratios?These ratios include:
sin ∅ = opp./hyp.tan ∅ = opp./adj.cos ∅ = adj./hyp.1. ∅ = 63
adj. = x
hyp. = 16
Therefore,
cos 63 = x/16
x = cos 63 * 16
x = 7.3
2. ∅ = 39
opp. = 27
adj. = x
Therefore,
tan 39 = 27/x
x = 27/tan 39
x = 33.3
3. ∅ = 49
adj. = 14
hyp. = x
Therefore,
cos 49 = 14/x
x = 14/cos 49
x = 21.3
4. ∅ = 15
adj. = x
hyp. = 33
Therefore,
cos 15 = x/33
x = cos 15 * 33
x = 31.9
5. ∅ = 52
opp. = x
adj. = 20
Therefore,
tan 52 = x/20
x = tan 52 * 20
x = 25.6
6. ∅ = 27
hyp. = x
opp. = 5
Therefore,
sin 27 = 5/x
x = 5/sin 27
x = 11.0
7. ∅ = x
opp. = 4
hyp. = 6
Therefore,
sin x = 4/6
x = sin^(-1)(4/6)
x = 41.8°
8. ∅ = x
adj. = 14
opp. = 29
Therefore,
tan x = 29/14
x = tan^(-1)(29/14)
x = 64.2°
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i^9 - i^19
please help i don’t know how to do imaginary numbers
The complex number given above expressed as a + ib is 2i
What is a complex number?Complex numbers are the numbers that are stated in the form of a+ib where, a,b are real numbers and I is an imaginary number termed "iota". The value of i = (√-1).
To solve the above problem, first, we must reduce imaginary units using the property i² = -1
(i)⁹ - 1 (i)¹⁹
i - 1 (i) ¹⁹
i - 1 (-1)
Subtract the complex numbers
i - (-i)
Identify the components of the numbers and add the real and imaginary parts separately.
(1 + 1)i
Identify the components of the numbers and add the real and imaginary parts separately
(1 + 1)i
(2)i
Thus, the solution to the imaginary number given above is 2i.
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Full Question:
Express the given complex number in the form a + ib: i⁹ - i¹⁹
How to solve this question with vertex formula
The equation of the parabola is y = 2 ( x + 1/4 )² - 49/8 and the vertex of the parabola is ( -1/4 , -49/8 )
What is a Parabola?A Parabola, open curve, a conic section produced by the intersection of a right circular cone and a plane parallel to an element of the cone. A parabola is a plane curve generated by a point moving so that its distance from a fixed point is equal to its distance from a fixed line
The equation of the parabola is given by
( x - h )² = 4p ( y - k )
y = a ( x - h )² + k
where ( h , k ) is the vertex and ( h , k + p ) is the focus
y is the directrix and y = k – p
The equation of the parabola is also given by the equation
y = ax² + bx + c
where a , b , and c are the three coefficients and the parabola is uniquely identified
Given data ,
Let the equation be represented as A
Now , the value of A is
y = 2x² + x - 6 be equation (1)
On simplifying the equation , we get
On factorizing the x² coefficient , we get
y = 2 ( x² + ( 1/2 )x ) - 6
Adding and subtracting ( 1/16 ) inside the parentheses , we get
y = 2 ( x² + ( 1/2 )x + 1/16 - 1/16 ) - 6
On simplifying the equation , we get
y = 2 ( x² + ( 1/2 )x + 1/16 ) - 6 - 1/8
The trinomial inside the brackets is a perfect square
y = 2 ( x + 1/4 )² - 49/8
Now , the equation of the parabola is given by y = a ( x - h )² + k ,
where ( h , k ) is the vertex
So , y = 2 ( x + 1/4 )² - 49/8
Hence , the vertex of the parabola is ( -1/4 , -49/8 )
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Jerry and Stella are working on an art project together. Jerry has 16 more markers than Stella.
The equation given below shows this relationship, where u represents the number of markers Jerry has, and t represents the number of markers Stella has.
The number of markers that Stella has would be = 27 markers
How to calculate the number of markers?The number of markers owned by Jerry = U
The number markers owned by Stella = t +16
If U = 43
t = X
That is, 43= t + 16
Make t the subject of formula;
t = 43-16
t = 27
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Complete question;
Jerry and Stella are working on an art project together. Jerry has 16 more markers than Stella. The equation given below shows this relationship, where u represents the number of markers Jerry has, and t represents the number of markers Stella has. U = t + 16 If Jerry has 43 markers, how many markers does Stella have? Show your work
Javier opens a savings account with a deposit of $75 and begins making weekly contributions. After 1 week he has $90 saved, and after 2 weeks he has $105 saved.
Answer: what is the question?
Step-by-step explanation:
in what way does the final vignette mango says goodbye sometimes suggest that esperanza will come back for the ones she left behind?
She knows that even as she leaves, she will surely come back for the ones who are not strong enough to escape on their own, the ones “left behind.”
Esperanza is aware that one day she will leave Mango Street with her books and paper because she is too powerful to be imprisoned there indefinitely. But she is aware that even as she departs, she will undoubtedly return in search of the "left behind," or those who lack the strength to flee on their own.
She introduces the tale by informing the audience that she will tell them a tale about a girl who didn't want to fit in. She reiterates the passage from the first chapter in which she states that she has lived on other streets in addition to Mango Street.
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Who invented logarithm?
The Scottish mathematician John Napier reported his findings on logarithms in 1614.
The comparison of arithmetic and geometric series predicted the development of logarithms. He was there to aid with the multiplication of quantities known as sines at the time.
The value of the entire sine was equal to the length of the hypotenuse in a right-angled triangle with a hypotenuse of, say, 107 units. He provided a definition in terms of relative rates.
Because both motions are equally spaced apart in time and have an equal shift at the beginning, the logarithm of any sine is a number that comes very close to expressing the line that increased equally over the course of time while the line of the entire sine decreased proportionately into that sine.
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What can I change in this equation to make it true
x-6y=4
Answer: y=1/6x−2/3
Step-by-step explanation:
-6y= x-4
/-6 . /-6
y= 1/6x-2/3
*somethin like this*
What is the inverse operation of log?
The inverse operation of log is antilog.
Mathematicians use the logarithm to express the inverse function of exponentiation. That is, the logarithm of a given number p is the exponent to which another fixed number, the base b, must be raised in order to obtain that number p. In the simplest case, the logarithm counts how many times the same factor appears in repeated multiplication.
The sum of the logarithms of two numbers says a and b, is the logarithm of the product of the two numbers. Both numbers must have the same base. In other words, this theorem is known as the “product rule for logarithms”.
The difference of the logarithms of two numbers, such as a and b, is equal to the logarithm of their division. Even in this case both numbers should have the same base. There is another name for this theorem, which is the “quotient rule for logarithms”.
Let f(x) = logₐx
y = logₐx
Now, to find the inverse of the function, swap the variables x and y.
x = logₐy
y = aˣ
Thus, the inverse operation of log is antilog.
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Which is better substitution or elimination?
Substitution is generally better than elimination equations because it is typically faster and easier to solve.
Substitution is generally a better method than elimination when solving equations. This is because substitution is typically faster and easier to solve. With substitution, you simply substitute one of the variables in the equation with a known value in order to solve for the other variable. This is generally easier than elimination, which involves eliminating one of the variables by adding and subtracting equations. Elimination can be more tedious, especially when dealing with large equations. Additionally, it may be difficult to eliminate one variable when the equations are not balanced or when there are multiple variables. For these reasons, substitution is generally better than elimination.
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Need help ASAP
i dont understand this test question
Answer:
Step-by-step explanation:
A poster at the train station shows the number of miles to different stations and the time it takes for the train to travel there.
Distance to Stations
Time in Minutes
(x) Distance in Miles
(y)
24 18
44 33
76 57
96 72
What is the constant of proportionality for this relationship?
the constant of proportionality for this relationship is 3/4
What is proportionality?the property of having suitable proportions in terms of size, number, degree, harshness, etc.: If a defensive action against an unfair attack results in the destruction that contravenes the proportionality criterion, it may even go far beyond a justifiable defense.
Given, A poster at the train station shows the number of miles to different stations and the time it takes for the train to travel there.
Time in Minutes(x) Distance in Miles(y)
24 18
44 33
76 57
96 72
From the general formula of constant of proportionality
constant of proportionality = y/x
constant of proportionality (k) = 18/24
constant of proportionality (k) = 3/4
Therefore, 3/4 is the constant of proportionality for this relationship.
Learn more about proportionalities here:
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