The formula g(x) = 2 * 0{-10≤x+3≤10} represents a function that has been horizontally shifted left by 3 units, reflected about the y-axis, and vertically scaled by a factor of 2.
What is Function?A function is a mathematical rule that assigns each input from a set (domain) a unique output from another set (range), typically written as y = f(x).
The notation "0{-10≤x≤10}" typically represents the domain of a function or an inequality. It means that the function is defined only for the values of x that are between -10 and 10 (including -10 and 10).
Assuming that the function in question is a constant function equal to zero, the parent function is f(x) = 0.
To describe the transformations that happened to this function, we need more information about the specific formula. For example, if the formula is:
g(x) = 0{-10≤x≤10}
Then there are no transformations from the parent function. The function is simply a constant function that is equal to zero over the interval [-10, 10].
However, if the formula is something like:
g(x) = 2 * 0{-10≤x+3≤10}
Then we can describe the transformations as follows:
Horizontal translation: The function has been shifted horizontally to the left by 3 units. This means that the point (3, 0) on the parent function is now located at the origin (0, 0) on the transformed function.
Dilation/reflection: The function has been reflected about the y-axis and vertically scaled by a factor of 2. This means that the point (-1, 0) on the parent function is now located at (-4, 0) on the transformed function, and the point (1, 0) on the parent function is now located at (2, 0) on the transformed function.
Vertical translation: There is no vertical translation in this case, since the constant function is already centered at y = 0.
To summarize, the formula g(x) = 2 * 0{-10≤x+3≤10} represents a function that has been horizontally shifted left by 3 units, reflected about the y-axis, and vertically scaled by a factor of 2.
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The formula g(x) = 2 * 0{-10≤x+3≤10} represents a function that has been horizontally shifted left by 3 units, reflected about the y-axis, and vertically scaled by a factor of 2.
What is Function?A function is a mathematical rule that assigns each input from a set (domain) a unique output from another set (range), typically written as y = f(x).
The notation "0{-10≤x≤10}" typically represents the domain of a function or an inequality. It means that the function is defined only for the values of x that are between -10 and 10 (including -10 and 10).
Assuming that the function in question is a constant function equal to zero, the parent function is f(x) = 0.
To describe the transformations that happened to this function, we need more information about the specific formula. For example, if the formula is:
g(x) = 0{-10≤x≤10}
Then there are no transformations from the parent function. The function is simply a constant function that is equal to zero over the interval [-10, 10].
However, if the formula is something like:
g(x) = 2 * 0{-10≤x+3≤10}
Then we can describe the transformations as follows:
Horizontal translation: The function has been shifted horizontally to the left by 3 units. This means that the point (3, 0) on the parent function is now located at the origin (0, 0) on the transformed function.
Dilation/reflection: The function has been reflected about the y-axis and vertically scaled by a factor of 2. This means that the point (-1, 0) on the parent function is now located at (-4, 0) on the transformed function, and the point (1, 0) on the parent function is now located at (2, 0) on the transformed function.
Vertical translation: There is no vertical translation in this case, since the constant function is already centered at y = 0.
To summarize, the formula g(x) = 2 * 0{-10≤x+3≤10} represents a function that has been horizontally shifted left by 3 units, reflected about the y-axis, and vertically scaled by a factor of 2.
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The salaries of six bank employees are $37,000, $38,500, $35,000, $37,000, $45,000, $40,000, and $75,000.
Which statement is true?
Question 1 options:
Both the median and mode are appropriate measures of center.
The mean, median, and mode are all appropriate measures of center.
Both the mean and median are appropriate measures of center.
The median is the only appropriate measure of center.
The correct answer is: Both the mean and median are appropriate measures of center.
What is statistics?Statistics is a branch of mathematics that deals with the collection, analysis, interpretation, presentation, and organization of data. It involves the use of mathematical and computational tools to summarize and analyze large sets of data, with the goal of extracting meaningful insights and identifying patterns or trends.
Here,
The mean is the sum of all salaries divided by the number of salaries. In this case, the sum is:
37,000 + 38,500 + 35,000 + 37,000 + 45,000 + 40,000 + 75,000 = 307,500
And there are seven salaries. Therefore, the mean is:
307,500 / 7 = 43,928.57
The median is the middle value when the salaries are arranged in order from lowest to highest. First, we need to arrange the salaries in order:
35,000, 37,000, 37,000, 38,500, 40,000, 45,000, 75,000
The median is the middle value, which is 40,000.
The mode is the value that appears most frequently in the set of salaries. In this case, both 37,000 and 40,000 appear twice, so there is no unique mode.
Since the salaries are not symmetrically distributed, the mean is not a perfect measure of central tendency. However, it can still provide useful information about the "average" salary. On the other hand, the median is resistant to extreme values and may be a better measure of central tendency for this dataset. Therefore, both the mean and median are appropriate measures of center for this dataset.
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(a) What is the value of x? Show your work.
(b) What is the measure of angle C? Show your work.
In triangle ABC
a) The value of x = 29⁰
b) The angle c equal to 93⁰
What is a triangle?A triangle is a closed plane figure that is formed by connecting three line segments, also known as sides, at their endpoints. The three endpoints, or vertices, where the sides of the triangle meet are not collinear. Triangles are important in mathematics and geometry because they are the simplest polygon that can exist in two-dimensional space.
According to the given informationIn a triangle, the sum of all interior angles is always 180 degrees. Therefore, we can use this fact to find the value of x and angle c.
We know that:
angle a = 35⁰
angle b = 52⁰
angle c = 3(x+2)⁰
Using the fact that the sum of all interior angles in a triangle is 180 degrees, we can write:
angle a + angle b + angle c = 180
Substituting the values we know, we get:
35 + 52 + 3(x+2) = 180
Simplifying the equation, we get:
87 + 3x + 6 = 180
3x + 93 = 180
3x = 87
x = 29
Therefore, x = 29⁰
To find angle c, we can substitute the value of x into the equation we were given for angle c:
angle c = 3(x+2)
angle c = 3(29+2)
angle c = 3(31)
angle c = 93
Therefore, angle c is equal to 93⁰.
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k^2+6k=0 solve the quadratic equation by factoring
Answer:
K = √-6k
i did the math and got this answer and it was right
please help me in this question is math,solve just d, e&f
Step-by-step explanation:
a) factorize A
A = (2x-1)²+2(3-6x)(4x-7)-4x²+1
expand the terms
(2x-1)²-52x²+108x-41
factorize
(2x-1)²-(26x-41)(2x-1)
factor out the common factor 2x-1
-(2x-1)(24x-40)
A = -8(2x-1)(3x-5)
b) show that B = (3x-11)(2x-1)
6x²-25x+11
6x²-3x-22x+11
3x(2x-1)-11(2x-1)
(2x-1)(3x-11)
c) Expand and reduce A
(2x-1)²+2(3-6x)(4x-7)-4x²+1
-48x²+108x-40
d) Calculate A for x=0 and x=-1
when x=0 -48(0)²+108(0)-40
A=0
x=-1 -48(-1)²+108(-1)-40
A=-196
e) Reduce 2A-3B
A=-48x²+108x-40 B=6x²-25x+11
2(-48x²+108x-40)-3(6x²-25x+11)
-96x²+216x-80-18x²+75x-33
-144x²+291x-113
f) Factorize 2A-B
A=-48x²+108x-40 B=6x²-25x+11
2(-48x²+108x-40)-(6x²-25x+11)
-96x²+216x-80-6x²+25x-11
-102x²+241x-91
x=(241 + sqrt(20953))/204
x=(241 - sqrt(20953))/204
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^4√p7
in exponential form.
Answer:1111
Step-by-step explanation: