The function form of the given function would be [tex]f(x)=log_b(x)[/tex].
What is a function?
In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function.
The given function is f(x) = logbx.
So the function form would be the function of x is equal to the logarithmic of x having base b.
so this can be written as
[tex]f(x)=log_b(x)[/tex]
Hence, the function form of the given function would be [tex]f(x)=log_b(x)[/tex].
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The function form of the given function would be [tex]f(x)=log_b(x)[/tex].
What is a function?
In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function.
The given function is f(x) = logbx.
So the function form would be the function of x is equal to the logarithmic of x having base b.
so this can be written as
[tex]f(x)=log_b(x)[/tex]
Hence, the function form of the given function would be [tex]f(x)=log_b(x)[/tex].
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Given that $k$ is a positive integer less than 6, how many values can $k$ take on such that $3x \equiv k \pmod{6}$ has no solutions in $x$
Supposing the value of x to be an integer, the values of k that donot
satisfy the given equation 3x = k mod 6 are 1,2,4,5.
What is an integer?An integer, which can comprise both positive and negative integers, including zero, is a number without a decimal or fractional portion.
What is the difference between integers and whole numbers?Integers are a set of numbers that include both positive and negative numbers, as well as zero. Whole numbers, on the other hand, only include the set of non-negative numbers starting from 0 (i.e., 0, 1, 2, 3, 4, ...). In other words, whole numbers are a subset of integers.
If 3x = k mod 6 has no solutions in x, then k must not be divisible by 3. The positive integers less than 6 that are not divisible by 3 are 1, 2, 4, and 5. Therefore, k can take on 4 values: 1, 2, 4, and 5.
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Find a counterexample to show that the conjecture is false.
All numbers ending in 6 are divisible by 6.
Therefore ,In other words the solution of the given problem of fraction is even though 21 can be divided by 3, it cannot be divided by 6. (for an integer anyway)
Describe fraction.A fractional or ratio element is a portion of the whole. The numerator a denotes the number of parts that are included, and the denominator b denotes the number of pieces of equal size into which the whole has been divided. The least common multiple (LCD) of two fraction denominators is called the LCM of those denominators.
Here,
21/3 = 7 21/6 = 3.5
18/3 = 6 18/6 = 3
24/3 = 8 24/6 = 4
12/3 = 4 12/6 = 2
Each can be split to get an integer, with the exception of:
21/6 = 3.5
Therefore ,In other words, even though 21 can be divided by 3, it cannot be divided by 6. (for an integer anyway).
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Gregory(g) is 20 years older than his cousin Mark(m). Mark is 6 years younger than his
sister Louanne(L). Write an expression to represent the sum of their ages.
Answer:
Step-by-step explanation:
Let's make Mark x as he is in both equations.
For Gregory in Marks view = x+20
For Marks's sister Louanne = x-6
Now you just add everything!
> x+x+20+x-6
> 3x+14
The sum of their ages is 3x+14
Hope that helped!
Work out
m
and
c
for the line:
2
y
−
4
x
=
2
Answer:
General equation : y = mx + c
2y - 4x = 2
2y = 4x + 2
y = 2x + 1
Therefore m = 2 and c = 1.
I WILL GIVE THANKS AND MARK BRAINLIEST
THIS ANSWER IS INCORRECT, WHAT IS THE CORRECT ANSWER?
On solving the provided question, we can say that - the percentage of the data is 5% = 5/100 = 0.05
What is percentage?A percentage is a figure or ratio stated as a fraction of 100 in mathematics. Although the abbreviations "pct.", "pct.", and occasionally "pc" are also used, the percent symbol, "%," is frequently used to indicate it. A % is a number without dimensions and without a measurement system.
According to the authors, "the bases will be virtually totally present in their most probable forms. If this is the case, then only adenine and thymine and guanine and cytosine are viable base pairs, and the requirements for creating hydrogen bonds are more stringent (lines 31-35).
Options C and D are erroneous because the table does not support the authors' postulated pairing of nitrogenous bases in DNA molecules.
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What is complete angle Class 7?
The angle with the measure 360° is known as a complete angle. A complete angle is one full rotation measuring 360°.
When the final point coincides with the initial point, after one whole rotation, then the angle so created is known as the complete angle. A complete angle is also known as a full angle or a round angle.
The measure of a complete angle is equal to 2π radians = 360 degrees which is the central angle of a circle. Also, if we combine four right angles or two straight angles it makes a complete angle. A complete angle is identical to a zero angle but the difference is only the amount of rotation.
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A kite is shaped like an isosceles triangle. To the nearest tenth what is the length of the spine?
The length of the spine will be;
⇒ 48.2 cm
What is mean by Triangle?A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.
Given that;
A kite is shaped like an isosceles triangle.
Now,
Since, A kite is shaped like an isosceles triangle.
Hence, Two sides of a triangle is equal to each other.
Let the length of the spine = x
So, We can formulate by the Pythagoras theorem,
⇒ Hypotenuse² = Base² + Perpendicular²
⇒ 62² = (78/2)² + x²
⇒ 3844 = 39² + x²
⇒ 3844 = 1521 + x²
⇒ 3844 - 1521 = x²
⇒ 2323 = x²
⇒ x = √2323
⇒ x = 48.2 cm
Thus, The length of the spine = 48.2 cm.
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When merida divides her age by 3 and adds 5, the result is 9 which equation represents this situation where m is meridas age?
a/ 9= (m ~ 3) x 5
b/ m= (9 - 3 ) + 5
c/ m = (9~3) +5
d/ 9= (m~ 3) +5
When Merida divides her age by 3 and adds 5, the result is 9, now the equation becomes: 9 = (m + 3) ÷ 5.
What is an equation?The link between two expressions on each side of the sign is represented by a mathematical equation. One variable and an equal sign are often present.
The definition an equation in algebra is a mathematical expression that indicates the equivalence of two mathematical terms. In equation 6x + 11 = 14, for instance, the two expressions 6x + 11 and 14 are separated by the symbol "equal."
When Merida divides her age by 3 and adds 5, the result is 9, now the equation becomes: 9 = (m + 3) ÷ 5, this represents the situation where m is Merida's age.
correct option: D
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What is the degree of the polynomial 7x 2y 3z 4?
The degree of a polynomial is the highest power of each variable in the equation. In the polynomial 7x2y3z4, the highest power of each variable is 2 for x, 3 for y, and 4 for z. Therefore, the degree of this polynomial is 8.
1. Identify the highest power of each variable.
For 7x2y3z4, the highest power of each variable is 2 for x, 3 for y, and 4 for z.
2. Add the highest powers of each variable.
2 + 3 + 4 = 9
3. Subtract 1 from the sum.
9 - 1 = 8
4. The degree of the polynomial is the result of the subtraction.
Therefore, the degree of the polynomial 7x2y3z4 is 8.
The degree of a polynomial is the highest power of each variable in the equation. To calculate the degree of a polynomial, you must identify the highest power of each variable and add them together. Then, subtract 1 from the sum to get the degree of the polynomial. For example, in the polynomial 7x2y3z4, the highest power of each variable is 2 for x, 3 for y, and 4 for z. Adding these powers together gives us 9. Subtracting 1 from this sum gives us 8, which is the degree of the polynomial. Therefore, the degree of the polynomial 7x2y3z4 is 8.
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What is 72 1/4 in a decimal
Answer:
I think it's 0.18 in decimal
what is 7/8 x 40 equal.
Based on these data, how many students received a score higher than 95?
A. At least 15
B. More than 25
C. 6 or fewer
D. Exactly 10
Bar charts display categorical variables, whereas histograms display numerical or quantitative data.
What is mean by histogram?The frequency distribution of a few data points for one variable is represented graphically by a histogram. Heterogeneous "bins" or "range groups" are frequently used in histograms in order to categorize data and count the number of data points that are part of each bin.
Among graphing tools, the histogram is widely used. It is utilized to encapsulate discrete or continuous data that is measured on an interval scale. It is frequently employed as a convenient way to highlight the key characteristics of the data distribution.
Histograms show numerical or quantitative data, whereas bar charts show categorical factors. The numerical data in a histogram will typically be continuous in most cases (having infinite values). It would be ridiculous to attempt to plot an axis that included every potential value for a continuous variable.
Therefore, the correct answer is option C. 6 or fewer.
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Terms nd coefficients and constants of 6+n2 + 1/2d
A lottery game contains 24 balls numbered 1 through 24. What is the probability of choosing a ball numbered 25
Selecting ball number 25 has no chance of happening.
Explain about the probability?Probability is only the likelihood that something will occur. When we don't know how something will turn out, we might discuss the likelihood of various outcomes or the potential of one. Statistics is the scientific study of events that conform to a probability distribution.
It is predicated on the likelihood that something will take place. The rationale for probability serves as the theoretical probability's essential tenet. A coin has a 12% chance of landing on its head, for instance, when it is flipped.
Probability is a statistic that is used to indicate the likelihood or potential for an event to occur. Both fractions from 0 to 1 and percentages from 0% to 100% can be used to indicate probabilities.
In 25th Ball it is 0
Because there is no 25th ball
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Which fraction is equivalent to -3/2
A) 3/-2
b) -(3/-2)
C) -3/-2
D) -(-3/2
HELP ASAP PLS
Answer: A
Step-by-step explanation: The other answer choices have 2 negatives which cancel and make a positive number.
Let ABC be a triangle, and
M, N, and K represent the midpoints of sides AB, BC, and AC respectively.
If area of the triangle ABC is 6.0 square feet, then what is the area of the triangle MAK?
Step-by-step explanation:
please refer to the sketch
What is the length of the missing leg? If necessary, round to the nearest tenth.
The length of the other leg is 65 cm
How to find the length of the other legFrom the question, we have the following parameters that can be used in our computation:
Leg 1 = a
Leg 2 = 72 cm
Hypotenuse = 97 cm
The length of the hypotenuse of the right triangle can then be calculated using
Hypotenuse² = Leg 1² + Leg 2²
Substitute the known values in the above equation, so, we have the following representation
97² = a² + 72²
So, we have
a² = 97² - 72²
Evaluate
a² = 4225
Take the square roots
a = 65
Hence, the other leg is 65 cm
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On a certain hot summer's day, 311 people used the public swimming pool. The daily prices are $1.50 for children and $2.00 for adults. The receipts for admission totaled $525 How many children and how many adults swam at the public pool that day?
The number of children that swam in the public pool that day is 194
and the number of adult that swam in the public pool that day is 117
Let x represent the number of children that swam in the public pool that day.
Let y represent the number of adult that swam in the public pool that day.
On a certain hot summer day, 311 people used the public swimming pool. This means that
x + y = 311
The daily prices are 1.50 for children and 2.00 for adults. The receipts for admission totaled to $525. This means that
$1.50x + $2.00y = $525 - - - - - - - -1
Substituting x = 311 - y into equation 1, it becomes
1.50(311 - y) + 2.00y = 525
466.5 - 1.50y + 2.00y = 525
0.5 y = 58.5
y = 117
Substituting y = 117 into x = 311 - y, it becomes
x = 311 - 117
x = 194
Hence , the number of children that swam in the public pool that day is 194 and the number of adult that swam in the public pool that day is 117.
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How do you write coordinates for translation?
Coordinates (x ,y ) of the given geometrical figure after translation is written as ( x + h , y + k ) where h ∈ R and k ∈ R.
As given in the question,
Let us consider the coordinates of any geometrical figure is represented by ( x, y ) in the coordinate plane.
Translation is the representation of transformation the change in the location of the given geometrical figure without change in the shape and size.
It can be translated in four ways :
Translation to the right is written as ( x + h , y )
Translation to the left is ( x - h, y)
Translation in the up is ( x, y + k )
Translation in the down is ( x , y - k ).
Therefore, the original coordinate ( x ,y ) after translation written as
( x + h , y + k ) where h ∈ R and k ∈ R.
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Isaac's father is 49 years old. He is four years older than three times Isaac's age. How old is Isaac
If Isaac's father is four years older than three times of Isaac's age and the age of father is 49 years old. So, Isaac age will be 15 years old.
How old is Isaac?According to online myth, there is a mathematical equation that regulates the lower bound for a possible dating partner's socially acceptable age: half your age plus 7, or, in mathematical words, if x is your age, the bottom barrier is [tex]f(x) = x/2 + 7[/tex].
Consider Isaac is L
Let us suppose L is x years old.
3 times the age of L = 3x
3 times L’s age plus 4 years = 3x + 4
Furthermore, L’s father’s age is 49 years older than L’s age.
Therefore,
[tex](3x + 4) = (49) (49)\\(3x + 4) -4 = (49) – 4\\3x = 45\\3x/3 = 45/3\\X = 15[/tex]
L’s age is 15 years since we expected L’s age = x (and x=15).
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What is 2x10-2+6 please help
Answer:
24
Step-by-step explanation:
What is 2x10-2+6?
2 × 10 - 2 + 6 = (remember PEMDAS)
20 - 2 + 6 =
18 + 6 =
24
Answer:
24 should be your answer
A researcher is following the growth of a particular type of flower. She writes the given equation to show the height of the flower g(n), in inches, after n days. When the researcher finished his study, the height of the flower was about 11.04 inches. What is a reasonable domain to plot the growth function
After solving, the possible domain in interval notation is (0, 7).
In the given question, a researcher is following the growth of a particular type of flower.
The equation to show the height of the plant f(n), in cm, after days (n) = 8(1.05)^n
According to the given information,
The height of the plant is modeled by the function= f(n)
The height of the plant is approximately 11.04cm when the number of days = 7
The days are started from n > 0 and n<=7
Hence the possible domain in interval notation = (0, 7)
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The complete question is:
A scientist is studying the growth of a particular species of plant. He writes the following equation to show the height of the plant f(n), in cm, after days (n) = 8(1.05)^n
Part A: When the scientist concluded his study, the height of the plant was approximately 11.26 cm What is a reasonable domain toplot the growth function?
Part B: What does the y-intercept of the graph of the function () represent?
Part C: What is the average rate of change of the function f(n) from n = 2 ton, and what does it represent?
Find whether x^n+y^h is disable by x-y(y not equal o)or not
Adam is trying to spot a meteor. The probability he will see one in the next 10 minutes is 0.56. What are the odds in favor of Adam seeing a meteor in the next 10 minutes?
The odds from the probability is 14 : 11
How to determine the odds from the probability ?The value of the probability is given as
Probability in the next 10 minutes = 0.56
This means that
p = 0.56
Represent the probability as a fraction
So, we have the following representation
p = 56/100
Simplify the fraction
p = 14/25
To convert the probability to odds, we make use of the following equation
Probability = Odds/(1 + Odds)
Substitute the known values in the above equation, so, we have the following representation
14/25 = Odds/(1 + Odds)
So, we have
(1 + Odds) * 14/25 = Odds
This gives
14/25 + Odds * 14/25 = Odds
Evaluate the like terms
11/25 * Odds = 14/25
So, we have
Odds = 14/11
Express as ration
Odds = 14 : 11
Hence, the odds is 14 : 11
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Mason worked at the water park over the summer. He made $425 in June and $680 in July if he made twice as much money in august as he did june. What is the ratio of money earned in august to July
The ratio of money earned in August to July is 5/4.
Now, According to the question:
Let's know
What is Ratio?
A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0. A proportion is an equation in which two ratios are set equal to each other. For example, if there is 1 boy and 3 girls you could write the ratio as: 1 : 3 (for every one boy there are 3 girls) 1 / 4 are boys and 3 / 4 are girls.
Mason worked at the water park over the summer. He made $425 in June and $680 in July.
And if he made twice as much money In August as he did in June.
That means, he made $850 in August.
Then, The ratio will be :
= August / June
= 850/680
= 5/4
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Describe a sequence of transformation that maps DOG onto CAT
Reflect it across the x-axis, then translate it up 6 units and left 1 unit before reflecting it across the y-axis.
what is sequence ?A collection of numbers, or "terms," is referred to as a sequence. Examples of terms include 2, 5, and 8. Some sequences can be made endlessly long by taking advantage of a particular pattern they follow. Use the example of 2,5,8 and add 3 to continue the series. There are formulas that demonstrate where to look for words within a sequence. A collection of objects that are in some order is known as a sequence in mathematics (or events). It resembles a set in that it has pieces (also called elements or terms). The total, perhaps infinite number of ordered objects are referred to as the sequence's length. the act of placing two or more objects in a logical order.
given
Δ DOG AND ΔCAT
According to Chanel, the series of transformations that maps triangle ABC onto triangle DEF is as follows:
Reflect it across the x-axis, then translate it up 6 units and left 1 unit before reflecting it across the y-axis.
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In a triple batch of spice mix, there are 6 teaspoons of garlic powder and 15 teaspoons of salt. Answer the following questions about the mix. If you get stuck, create a double number line.
In a double number line diagram, equal ratios are represented by two parallel number lines. On both number lines, the tick marks are in the same places. Though the other numbers are frequently varied, the tick marks labeled with 0 always line up.
How to create a double number line?According to question:-
How much more garlic powder than salt is in the triple batch?
Answer: 6 teaspoons of garlic powder - 15 teaspoons of salt = -9 teaspoons. So there is 9 teaspoons less garlic powder than salt in the triple batch.
How much spice mix is in the triple batch?
Answer: 6 teaspoons of garlic powder + 15 teaspoons of salt = 21 teaspoons of spice mix.
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How do you graph a parent graph?
This is how you construct a parent graph - it is the simplest form of the function, and has a basic shape.
The most basic form of a function is a parent function. Its essential shape is not changed in any manner. In mathematics, some graphs are frequently seen. Because of this, the graphs of quadratic functions, square roots, absolute values, cubics, and cube roots are among the original, widespread functions that are referred to as parent graphs.
For instance, you should still be able to identify the parabola that has undergone various transformations when you view a u-shaped graph that has been inverted and stretched vertically.
We can take a few examples to understand this concept further.
For a quadratic equation, the parent graph is [tex]f(x) = x^{2}[/tex], which is a parabola. For a cubic equation, the parent graph is [tex]f(x) = x^{3}[/tex].Hence, this is how you construct a parent graph - it is the simplest form of the function, and has a basic shape.
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i need help with number seven with a full explanation please
The value of x would be 32.
What are a congruent quadrilaterals?
In geometry, two figures are congruent if they have the same size and shape. Congruent figures can be moved or oriented in different ways, but they will always match up exactly. In the case of quadrilaterals, they are congruent when they have the same side lengths and corresponding angles.
In the given figure PQRS ~ WXYZ
x = YZ
x = 32.
Hence, the value of x would be 32.
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By analyzing the figure, The value of x would be 32.
What are a congruent quadrilaterals?In geometry, two figures are congruent if they have the same size and shape. Congruent figures can be moved or oriented in different ways, but they will always match up exactly. In the case of quadrilaterals, they are congruent when they have the same side lengths and corresponding angles.
In the given figure PQRS ~ WXYZ
x = YZ
x = 32.
Hence, the value of x would be 32.
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Which is the algebraic sequence of 1,4,7,10
The algebraic sequence of 1,4,7,10 is aₙ = 3n - 2
How to determine the explicit formula of the sequence?From the question, we have the following sequence that can be used in our computation:
1,4,7,10
In the above sequence, we can see that 3 is added to the previous term to get the current term
Using the above as a guide,
So, we have the following representation
aₙ = aₙ₋₁ + 3
Also, we have
a = 1 i.e. the first term
d = 3 i.e he common difference
When represented explicitly, we have
aₙ = a + (n - 1) * d
So, we have
aₙ = 1 + (n - 1) * 3
Evaluate the products
aₙ = 3n - 2
Hence, the explicit formula is aₙ = 3n - 2
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