It derives its name from the famous rock on the Capitoline Hill in Rome from where prisoners were hurled to their deaths in ancient times.
What is a domain in the function?The domain of a function is the set of values that we are allowed to plug into our function. This set is the x values in a function such as f(x). The range of a function is the set of values that the function assumes. Range = {12, 3, 0}Let y = f(x) be a function with an independent variable x and a dependent variable y. If a function f provides a way to successfully produce a single value y using for that purpose a value for x then that chosen x-value is said to belong to the domain of f.The domain of a function is the set of all possible inputs for the function. For example, the domain of f(x)=x² is all real numbers, and the domain of g(x)=1/x is all real numbers except for x=0.A domain is a particular field of thought, activity, or interest, especially one over which someone has control, influence, or rights.To find the domain and range, we simply solve the equation y = f(x) to determine the values of the independent variable x and obtain the domain. To calculate the range of the function, we simply express x as x=g(y) and then find the domain of g(y).
This question isn't history; it's mathematics.
However, the solution is as follows:
Given
f(x) = 3x²
Domain = {-2, -1, 0}
Required
Calculate the Range
To calculate the range, we simply plug in the values of the domain in the given function
Let the domain be represented by x; such that
x = {-2, -1, 0}
When x = -2
f(x) = 3x²
f(-2) = 3 * (-2)²
f(-2) = 3 * 4
f(-2) = 12
When x = -1
f(x) = 3x²
f(-1) = 3 * (-1)²
f(-1) = 3 * 1
f(-1) = 3
When x = 0
f(x) = 3x²
f(0) = 3 * 0²
f(0) = 3 * 0
f(0) = 0
The range are the values of f(-2), f(-1) and f(0)
Hence, Range = {12, 3, 0}
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How do I know my SSS or SAS?
The triangles are congruent if all three sets of comparable sides are present. The side-side-side shortcut is a congruence technique (SSS). Side-angle-side (SAS), which uses two sets of sides and an angle between them that is known to be congruent, is another shortcut.
SSS, which stands for "side, side, side," denotes that there are two triangles with identical angles on all three sides. The triangles are congruent if their third sides are the same as those of another triangle. The triangles are congruent if two pairs of corresponding angles and the included sides are both true. This standard is called angle-side-angle (ASA).
Angle-angle-side (AAS) is another criterion that takes into account the congruence of two pairs of angles as well as the non-included side. SSS stands for "side, side, side," which signifies that we have two triangles with equal sides on all three sides. SAS, ASA, and AAS are acronyms for these rules. "Side, Angle, Side" stands for two triangles whose two sides and one included angle are known to be equal.
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Solve this system of equations by graphing. First graph the equations, and then type the solution.
The solution of the system of equations:
2x - 3y = -12
y = (-5/3)x - 3
Is (-3, 2)
How to solve the system of equations?Here we have the following system of equations:
2x - 3y = -12
y = (-5/3)x - 3
To solve it graphically, we just need to graph the two lines and see where do they intersect. The graph of the system can be seen below.
We can see that the intersection is at the point (-3, 2), so that is the solution of the system.
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Or what is the probability of rolling a five on the first die and a one on the second die?
0.25 is the probability of rolling a five on the first die and a one on the second die
How do you calculate probability?
Probability is calculated by dividing the number of ways the event can occur by the total number of outcomes. Probability and odds are different concepts. Odds are the probability that something happens divided by the probability that it doesn't happen
Very interesting problem.
1 1
1 2
1 3
1 4
2 1
2 2
2 3
2 4
3 1
3 2
3 3
3 4
4 1
4 2
4 3
4 4
There are 16 possible out comes
1 4
4 1
2 3
3 2
4 out of the 16 outcomes are possible
P(5) = 4/16 = 0.25
The theoretical out come would be 4 times
4/16 = 0.25
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Complete the following proof by providing the reason for each statement.
Solve 6m + 3 = 51
Please write your answer with a clear explanation.
Answer:
subtract 3 from both sides
6m+3=51
6m+3-3=51-3
simplify
6m=48
divide both sides
6m/6 = 48/6
simplify
divide the numbers
m=8
solution.
M = 8
Answer question please
Answer:
u-41+u-40=u
2u-u=41+40
u=81
What is an example of a geometric series?
An example of geometric series is 2 + 6 + 18 + 54.
When a set of numbers follow a particular order, they are said to be in sequence.
A set of numbers are said to be in geometric sequence if the ratio between second and first term is same as the ratio between third and second term and so on. The geometric sequence is presented as
Sum of n terms = a, ar, ar², ar³, ......, arⁿ⁻¹, arⁿ.
where,
The first term is a.
Every two consecutive terms, r is the common ratio.
The number of terms is n.
When the numbers in geometric sequence are added together, it is called a geometric series. The geometric series is presented as
Sum of n terms = a + ar + ar² + ar³ + ...... + arⁿ⁻¹ + arⁿ.
where,
The first term is a.
Every two consecutive terms, r is the common ratio.
The number of terms is n.
Let us take an example.
The numbers 2, 6, 18, 54 are in geometric sequence because 6:2 = 18:6 = 54:18 and when we will write it as 2 + 6 + 18 + 54, it will become a geometric series.
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How do you find the vertical asymptote and removable discontinuity?
To find the vertical asymptote, look for the values of x where the denominator of a function equals 0. To find the removable discontinuity, look for the values of x where the numerator of a function equals 0.
Vertical asymptotes are x-values where the denominator of a fraction is equal to 0. To find the vertical asymptote, we need to set the denominator equal to 0 and solve for x. This will give us the x-values where the graph of the function has a vertical asymptote. Removable discontinuities are x-values where the numerator of a fraction is equal to 0. To find the removable discontinuity, we need to set the numerator equal to 0 and solve for x. This will give us the x-values where the graph of the function has a removable discontinuity. In both cases, once we have the x-values, we can plot the graph of the function and see where the vertical asymptote and removable discontinuity are located. We can also use these x-values to determine the behavior of the function in the vicinity of the vertical asymptote or removable discontinuity.
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Use the Law of Cosines to find the values of x°and y°. Round to the nearest tenth.
The value of x and y° are 29.1 and 76.6°.
What is rounding to tenth?
Look at the hundredth number to round the decimal number to the nearest tenth. If it's more than 5, add one to the tenth value. Remove all the numbers that are present after the tenth place and leave the tenth place value alone if it is less than 5.
The length of sides of the triangle are x, 35, and 40.
Assume that AB = c = x, BC = a = 35, and AC = b = 40
m∠C = 45° and m∠B = y°.
Cosine law:
c² = a² + b² - 2ab cos C ....(i)
b² = a² + c² - 2ac cos B ....(ii)
a² = b² + c² - 2bc cos A ....(iii)
Putting a = 35, b = 40, c = x, and C = 45° in law (i)
x² = 35² + 40² - 2×35×40 cos 45°
x² = 2825 - 2800 × (1/√2)
x = 29.07
x = 29.1 (nearest tenth)
Putting a = 35, b = 40, c = 29.1, and B = y° in law (ii)
40² = 35² + 29.1² - 2×35×29.1 cos y
1600 = 1225 + 846.81 - 2037 cos y
2037 cos y = 471.81
cos y = 471.81/2037
y = 76.60°
y = 76.6°
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How do you describe the end behavior of the graph if the degree is cold and the leading coefficient is negative?
The answer for the given question is following:
If the degree of a polynomial is odd and the leading coefficient is negative, the end behavior of the graph of the polynomial will be as follows:
If the degree of the polynomial is odd, the graph of the polynomial will have an odd number of turning points.If the leading coefficient is negative, the leftmost and rightmost parts of the graph of the polynomial will both approach negative infinity as x approaches negative infinity and positive infinity, respectively.For example, consider the polynomial f(x) = -x^3 + 3x^2 - 5x + 2. This polynomial has a degree of 3 (which is odd) and a leading coefficient of -1 (which is negative). The graph of this polynomial will have 1 turning point (which is odd) and will approach negative infinity as x approaches negative infinity and positive infinity.
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If the degree of the polynomial is odd, the graph of the polynomial will have an odd number of turning points.
For example, consider the polynomial
f(x) = -x^3 + 3x^2 - 5x + 2.
This polynomial has a degree of 3 (which is odd) and a leading coefficient of -1 (which is negative).
The graph of this polynomial will have 1 turning point (which is odd) and will approach negative infinity as x approaches negative infinity and positive infinity.
What is meant by continuity of a function explain with an example?
Continuity of a function is when the function is continuous over the range of its domain. An example is a function f(x) = x^2, which is continuous over its domain of x∈R.
Continuity of a function is when the function is continuous over the range of its domain. A function is continuous if the graph of the function is a single, connected curve with no breaks or gaps. This means that for any point on the curve, the function is non-discontinuous. An example of a continuous function is f(x) = x^2, which is continuous over its domain of x∈R. This means that, no matter what value is put into the function, the output will always be a single value and the graph of the function will be a single, connected line. This is because the function is continuous over its entire domain, and therefore there are no breaks or discontinuities in the function. This is an example of continuity of a function.
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What is the quotient of 2.4 divided by 3?
0.8 is the quotient when 2.4 is divided by 3.
what is quotient?In the end, the quotient is what we obtain when we divide a number. A mathematical procedure called division involves separating objects into equal groups. The letter (÷) is used to symbolize it.
How to divide fractions?When two fractions are divided, the first fraction is multiplied by the second fraction's reciprocal. Finding the reciprocal of the second fraction and this can be obtained by reversing its numerator and denominator—is and then dividing the fractions. Multiply the two numerators after that. Multiply the two denominators after that, After that we need to simplify the fraction to its lowest form.
Mathematically quotient is defined by:
= 2.4 ÷ 3
=> 2.4/ 3
=>0.8
so 0.8 is the quotient when 2.4 is divided by 3
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I struggle with math a lot.
The answer is:
3 and 4
Step-by-step explanation:
multiplying 7/10 miles by 3 will give you 21/10 which is 2.1 miles
multiplying 7/10 miles by 4 will give you 28/10 which is 2.8 miles
Answer:
i think is 3 times and 4 times because.....
Step-by-step explanation:
For Tristan to jog between 2 and 3 miles, the number of times he would have to jog the route that is 7/10 mile must be such that the product of the number of times and 7/10 miles gives a number between 2 and 3.
Considering the options given
A. 2 * 7/10 = 1.4 miles (this is not within the range)
B. 3 * 7/10 = 2.1 miles (this is within the range)
C. 4 * 7/10 = 2.8 miles (this is within the range)
D. 5 * 7/10 = 3.5 miles (this is not within the range)
What is an example of a linear function graph?
y = 3x - 2 is an example of a linear function graph.
What are the steps of draw the linear function graph?For graphing linear functions, there are three fundamental techniques. The first method involves tracing a line across a set of points that have been plotted. The second method makes use of the slope and y-intercept. Applying transformations to the identity function f(x)=x f(x) = x is the third step.
Those with a straight-line graph are considered to be linear functions. The following is the form of a linear function. a + bx = y = f(x). In the linear function there are one independent and one dependent variables . X is an independent variable, whereas Y is a dependent variable.
Example: The equation y = 3x – 2 depicts a linear function since it is a straight line in the coordinate plane. This function may be expressed as f(x) = 3x - 2 since y can be substituted with f(x).
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What is the relationship between the volumes of a pyramid and a prism If the pyramid and prism have the same base areas and heights?
The volumes of pyramid as well as a prism are always 1:3 Volume of prism if their bases and heights are the same.
Define relationship between the volumes of pyramid and prism?A pyramid is just a three-dimensional object that has faces made of triangles and a base made of polygons.
The base seems to be the bottom, while the faces are the sides. A two-dimensional form with straight sides is called a polygon.A prism is indeed a three-dimensional object having two identically shaped and sized polygonal bases and rectangular sides.
In the actual world, a cardboard box serves as an illustration of a prism. When a pyramid and a prism have bases and heights that are equivalent, the pyramid can fit inside the prism. In reality, when this is the situation, its pyramid occupies precisely one-third of the prism's volume.Thus, the volumes of a pyramid as well as a prism are always 1:3 Volume of prism if their bases and heights are the same.
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Jane bought a new car three years ago.
At the end of the first year the value of the car had decreased by 12.5%
The value of the car then decreased by 10% each year for the next two years.
At the end of the three years, the value of the car was £17 010
Work out the value of the car when Jane bought it three years ago.
The value of the car when Jane bought it three years ago would be = £52,338.46
What is the value of a product?The value of a product is the cost or worth of that product which can decrease or increase over time and this can affect it's cost outcome.
The value of the car bought by Jane decreases in the first year = 12.5%
The value of the car decreased next two years by 10% each = 10× 2 = 20%
The total percentage decrease in value = 20+12.5 = 32.5%
The amount decreases to.= £17010
That is 32.5% = £17010
100% = X
Make X the subject of formula;
X = 100 × 17010/32.5
X = 1701000/32.5
X= £52,338.46
Therefore, in conclusion, the value of the new car three years ago = £52,338.46.
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What is the correct order of steps for copying angle ABC?
To duplicate angle ABC, draw a line segment, position the compass on point A, and then draw an arc that intersects the line segment. Next, position the compass on point B, and then draw a second arc that intersects the first arc at a point on the line segment. Finally, position the compass on the point where the two arcs intersect, but without changing the width, and draw a third arc that intersects the line segment.
What is an angles?When two straight lines or rays intersect at a single endpoint, an angle is created. The vertex of an angle is the location where two points come together. The Latin word "angulus," which means "corner," is where the term "angle" originates.
What are common instruments used to measure angles?Common instruments used to measure angles are:
1. Protractor
2.Compass
3.Digital Angle finder
4.Angle finder
5.Clinometer
6. Inclinometer
You can take the following actions to copy angle ABC:
Create a line segment that will serve as the foundation for the new angle you're going to create.
Draw an arc that crosses the line segment you produced in step 1 by positioning the compass on point A.
Draw a second arc that crosses the previous arc at a point on the line segment by setting the compass on point B.
Place the compass on the intersection of the two arcs without adjusting the compass's width, then create another arc that crosses the line segment.
Point D is where the second arc crosses the line segment. To finish the new angle, join points D and C.
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Without using table or calculator simplify √50-3√2(2√2-5)-5√3-2
-12
step by step:
√50-3√2(2√2-5) -5√32
= 5√2 -12+15√2-5(4)√2
= 5√2 -12+15√2-20√2
= -12
How to find the angle of a triangle given 3 sides and 1 right angle?
When the two sides and one angle of a triangle are given then we can find out the other two remaining angles by the law of sins.
Law of Sin :
In trigonometry, the law of sines, sine law, sine formula, or sine rule is an equation relating the lengths of the sides of any triangle to the sines of its angles.
According to the law of sine s
[tex]\frac{sina}{A}[/tex] = [tex]\frac{sin b}{B}[/tex]
[tex]\frac{sin90}{A}[/tex] = [tex]\frac{sin b}{B}[/tex] ( since it is given that one angle is 90 degrees)
[tex]\frac{1}{A}[/tex] =[tex]\frac{sin b }{B}[/tex]
sin b = B/A
b = [tex]sin^{-1}[/tex](B/A) where B and A are sides of the triangle and known values.
Remaining angle c = 180- [tex]sin^{-1}[/tex](B/A)
Therefore if one angle and at least two sides are given then we can find out the remaining by the law of sin
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What is the constant of 5x =- 3y?
The equation represents a direct variation, and the constant of variation for 5x = -3y is k = -5 / 3.
What is the Proportionality?Proportionality is an essential topic with several applications in everyday life. Proportionality can be used to compare different quantities. Volume, for example, is inversely related to density.
The equation is given in the question as:
5x = -3y
We can rearrange it as y = -5x / 3
Hence, we see that y ∝ x, and the equation is of the form y = kx, where k is the proportionality constant. This denotes that y varies directly with x.
Here k = -5 / 3.
Hence, the constant of variation is k = -5 / 3.
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Find the slope and the y-intercept of the following linear equation.
15x – 10y = 10
Answer:
The slope of the line described by the equation 15x – 10y = 10 is m = 15/10 = 1.5, and the y-intercept is b = 10/15 = 2/3.
Step-by-step explanation:
Answer:Slope is 1.5, and the y-intercept is -1
Step-by-step explanation:
So in order to get the slope and y-intercept, you have to put the equation in slope form, y=mx+b
Here’s the work for it
15x-10y=10
-15x -15x
-10y=-15x+10
Now divide -10 on both sides
y=1.5x-1
Now that it’s in the right form, you can easily see the slope is 1.5 and the y-intercept is -1
I hope this helps, please let me know if it was right!
I need help please! It’s asap
The Frequency of graph is 3
What is the frequency of the graph?The frequencies of each category are represented individually in a frequency graph; the frequencies of each category are shown cumulatively. By doing so, we are able to analyze the data's distribution in greater detail than we could have done by using a Frequency polygon and performing statistics.
A frequency polygon can also be used to display grouped data. This sort of line graph exists. The horizontal axis is a continuous scale, therefore the frequencies can be connected using straight line segments.
Calculation:Looking at the graph we can see that the graph is oscillating between -3 and 3 and as frequency is a positive term taking modulus of this oscillation we get to know that the frequency is 3.
The Frequency of graph is 3
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which statement about correlation is false? correlation is used to define the variables of only non-linearly related data sets. correlation is the degree to which the two variables of a data set resemble each other. the correlation of a data set can be positive, negative, or 0. correlation between the variables of the data set can be measured.
The statement that is false is: Correlation is used to define the variables of only non-linearly related data sets.
Correlation is used to measure the relationship between two variables in a data set, regardless of whether the data set is linear or non-linear.Understanding Correlation in Data Sets
Correlation is a measure of the relationship between two variables of a data set and can be positive, negative, or 0. It is used to measure the degree to which the two variables of a data set resemble each other, regardless of whether the data set is linear or non-linear. The correlation between any two variables can be easily measured and compared, allowing for more detailed analysis of the data set.
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Determine whether the following sequence is an arithmetic or geometric progression.Give a reason for your answer.
100p,50p,25p,...
Answer: geometric
Step-by-step explanation:
the first number, 100, is divided by 2 to become 50, and the second number, 50, is divided by 2 to get 25 and so on
Find the distance between the two points rounding to the nearest tenth (if necessary). (0,1) and (6,−7)
The distance between the two points (0,1) and (6,−7) is 10.
What is distance?Distance can be defined as the length between two points.
To calculate the distance between the two points, we use the formula below.
Formula:
d = √[(x₂-x₁)²+(y₂-y₁)²].................. Equation 1Where:
d = Distance between the two points.From the question,
Given:
x₂ = 6x = 0y₂ = -7y₁ = 1Susbtitute these values into equation 1
d = √[(6-0)²+(-7-1)²]d = √(36+64)d = √100d = 10Hence, the distance between the two points is 10.
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1.Solve this equation by completing the square x^2-14x+49=40. Show your work. No other method will be accepted.
2. Solve this equation by factoring by grouping x²-x = 12. All work must be shown and no other method will
be accepted.
3. Given this quadratic equation, 2x^2-15x-8=0
A) list the factors of the equation
B) determine the x-intercepts. Show your work algebraically
Can you please do the work in handwriting please
The values of x are -3 and 4.
What is factoring polynomial?
The term "factorization of polynomials" or "polynomial factorization" refers to the process of combining irreducible factors with coefficients in the same domain to express a polynomial with coefficients in a given field or in integers.
Consider, the given equation
x^2 - x = 12
Subtract 12 from both sides
x^2 - x - 12 = 12 - 12
x^2 - x - 12 = 0
Since -12 = -4 x 3
⇒ x^2 - 4x + 3x - 12 = 0
x(x - 4) + 3(x - 4) = 0
(x + 3)(x - 4) = 0
⇒ (x + 3) = 0, (x - 4) = 0
x = -3, x = 4
Hence, the values of x are -3 and 4.
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find the distance between the points R(a+b,a-b) and S(a-b,a+b)
Answer:
The distance between the points R(a+b,a-b) and S(a-b,a+b) is 2*sqrt(2)*sqrt(a^2+b^2).
Step-by-step explanation:
To find the distance between the two points, we can use the distance formula:
distance = sqrt((x2-x1)^2 + (y2-y1)^2)
Plugging in the coordinates of the two points, we get:
distance = sqrt((a-b-a-b)^2 + (a+b-a+b)^2)
Simplifying, we get:
distance = sqrt(2*(a^2 + b^2))
Multiplying both sides by sqrt(2) gives us:
distance = 2*sqrt(2)*sqrt(a^2+b^2)
Therefore, the distance between the points R(a+b,a-b) and S(a-b,a+b) is 2*sqrt(2)*sqrt(a^2+b^2).
R, S, T and U are points on the circumference of a circle, centre O.
The angle RUS is 46° and the angle URT is 36°
R
36%
46°
U
Calculate the angle RTS.
(1 mark)
T
The angle RST of the arc will be equal to 46°.
What is an arc of the circle?A circle's arc is defined as a portion or segment of its circumference. A chord of a circle is a straight line that can be drawn by connecting the two ends of an arc. A semicircular arc is one whose length is exactly half that of a circle.
Given that the angle RUS is 46 and the angle URT is 36.
The angle RST has the same arc that is made by the angle RUS. From that theorem, we can conclude that the angle RUS will be equal to the angle RST.
∠RUS = ∠RST
∠RST = 46°
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HELP ME if u can i'll give brainilest if yuor answer is correct.
Answer:
$1.60
Step-by-step explanation:
1 pound of rice divided into eight sections. Five sections cost $1, thus divide by 5 and multiply by 8
1/5*8 = $1.6
Answer: $1.60 (I think)
Step-by-step explanation: I'm not sure, but when it said the whole diagram = 1 whole pound of rice. So, we know there are 8 parts. So, if 5 of the 8= $1.00. So, the 100 / 5 = 20, now we can ASSUE each tile = 0.20 cents. So, 0.20 x 8 = $1.60. I hope I am right
What is the best example of discontinuity?
The best example of discontinuity is a graph of a function with a "hole" or "jump" in it, where the value of the function suddenly changes without any gradual change.
Discontinuity occurs when a graph of a function has an abrupt change, either in the form of a "hole" or "jump" in it. In a graph of a continuous function, the values gradually change in a smooth manner. However, with a graph of a discontinuous function, the function suddenly changes without any gradual transition. This sudden change is often caused by a discontinuity in the domain or range of the function. For example, a discontinuity may occur where a function is undefined or has an undefined limit. Graphically, this is usually illustrated as a gap or jump in the graph of the function. This type of discontinuity is known as a removable discontinuity, since it can be removed by redefining the function at the point of discontinuity. Other types of discontinuity include infinite discontinuity, which occurs when the graph of a function approaches either positive or negative infinity, and jump discontinuity, which occurs when the graph of a function jumps from one value to another without any transition.
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