Answer:
The roots are imaginary.
Step-by-step explanation:
⭐ What is "the nature of the roots"
The nature of the roots are how the roots of a quadratic exist.⭐What are the different types of "the nature of the roots"?
The roots could be real numbers, distinct, and rational/irrationalThe roots could be real, equal, and rationalThe roots could be imaginary⭐How do we determine "the nature of the roots"?
Substitute the values of the coefficients (a,b, and c) of a quadratic equation into the quadratic formula( [tex]x =\frac{ -b+/-\sqrt{b^2-4ac} }{2a}[/tex])If the value of the discriminant in the quadratic formula ([tex]b2-4ac[/tex])>0: the roots are real numbers, distinct, and rational/irrationalIf the value of the discriminant in the quadratic formula ([tex]b2-4ac[/tex])=0: the roots are real, equal, and rationalIf the value of the discriminant in the quadratic formula ([tex]b2-4ac[/tex])<0: the roots are imaginaryTo solve this problem, substitute the values of the coefficients of the given quadratic equation into the quadratic formula:
[tex]x =\frac{ -6+/-\sqrt{6^2-4(2)(30)} }{2(2)}[/tex]
Now, compute only the discriminant ([tex]b^2-4ac[/tex]).
[tex]b^2-4ac = 36-4(60)[/tex]
[tex]b^2-4ac = 36-240[/tex]
[tex]b^2-4ac = -204[/tex]
[tex]b^2-4ac[/tex]< 0. Therefore, the roots are imaginary.
Is 2x 3y a binomial?
2x + 3y is a binomial is a true statement.
A polynomial is of various types like binomial, trinomial and multinomial.
Monomial is said to contain only one term, trinomial is said to contain exactly three terms, multinomial contains n number of terms.
An mathematical expression known as a binomial has exactly two terms.
Examples of binomials are 4x² + 5y², xy² + y, x² + 3, x + y, etc.
Here, the given algebraic expression is 2x + 3y, where 2x is one term and 3y is another term. The coefficient of x is 2 and coefficient of y is 3 where as the exponent of x is 1 and the exponent of y is 1.
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How will you compare the graph of a function and the graph of its inverse?
The graph of a function and the graph of its inverse are reflected across the line y = x.
Connsider a function f(x).
The inverse of function f(x) is represented as f^-1(x).
The inverse of a function is a function that reverses the effect of the original function.
We know that if we take the inverse of function then the domain of a function will be the range of inverse function and the range of a function will be the domain for its inverse.
This means if the point (3, -6) is in the original function then itwill be represented by the point (-6, 3) in the inverse function.
Also, we can obtain the graph of an inverse function as a reflection of the graph of original function across the line x = y.
Hence, the inverse functions' graphs are reflections over the line x = y
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Are quadrilaterals 11 sides?
Therefore , the 11 sides polygon cannot be a quadrilateral.
Describe quadrilateral.A polygon with four sides, four angles, and four vertices is referred to as a quadrilateral. A sort of polygon called a quadrilateral has sides that are defined in a certain way. The quadrilateral in the illustration below, for instance, can be defined as ABCD, ADCB, BCDA, CDAB, etc.
Here,
the quadrilateral
Each of them consists of four vertices.
Each side consists of four sides.
360 degrees is the sum of all interior angles.
Two diagonals are present.
There are both regular and irregular quadrilaterals.
It must have four equal sides, four equal angles, and diagonals that cross in order to be regarded as a quadrilateral.
Therefore , the 11 sides polygon cannot be a quadrilateral.
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1. What does the trend look like
2. Do the variables show a positive, negative correlation? Or is there no apparent relationship between them
Answer:
No relationship
Step-by-step explanation:
How does a graph of a linear equation in two variables look like?
The graph of a linear equation in two variables is a straight line.
The general linear equation in two variables is ax + by + c = 0, where a, b, c are constants. Also, a and b cannot both equal zero at the same time. In order to graph of a linear equation in two variables ax + by + c = 0, we simply assume a set of values for x and calculate the respective set of values for y.
So we have a set of coordinates (x, y). Now plot the points on graph and join them.
The graph formed will be a straight line.
The point at which the line (graph of a linear equation) crosses the y-axis is the y-intercept and the point at which the line (graph of a linear equation) crosses the x-axis is the x-intercept.
Therefore, the graphing of all ordered pairs that satisfies a linear equation in two variables gives a straight line.
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Which graph represents the line described by the given point (- 2, 3) and slope 0
The graph of the line parallel to x-axis and passes trough the point (-2,3).
What is slope of a line?
A line's slope in mathematics is defined as the ratio of the change in the y coordinate to the change in the x coordinate.
Both the net change in the y-coordinate and the net change in the x-coordinate are denoted by Δy and Δx, respectively.
Consequently, the formula for the change in y-coordinate with respect to the change in x-coordinate is
m = Δy/Δx = change in y/change in x
where "m" represents a line's slope.
Additionally, the slope of the line can be shown as
tan θ = Δy/Δx.
Given that the slope of the line is 0. Thus the angle between the line with the x-axis is 0 degree as tan 0° = 0.
The line is parallels to x-axis.
The equation of the line that is parallel to x-axis is y = a.
Since the line passes through the point (-2,3), thus it will be satisfies the equation line.
Putting x = -2 and y = 3
a = 3
The equation of the line is y = 3
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What is the most approved disability?
The most often recognized impairments for social security disability benefits are musculoskeletal system disorders like arthritis.
This is due to the prevalence of arthritis. A total of 58 million Americans suffer from arthritis. You might be eligible for disability benefits if your arthritis makes it difficult for you to move or carry out basic daily tasks.
If your condition should automatically qualify you for disability benefits, a social security disability lawyer can analyze your case and make that determination. Your attorney may walk you through the disability application process and advise you on the kinds of records you might need to substantiate the seriousness of your disease.
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What is the slope of the line that passes through the points (4, 7) and (7, 16)? Write your answer in simplest form.
Answer:
3
Step-by-step explanation:
Lets use the slope formula, Which is given as :-
[tex]\sf{ \dfrac{y2-y1}{x2-x1} }[/tex]
Substitute the points we have to the formula :-
[tex]\begin{gathered}\sf \longmapsto {\dfrac{16 - 7}{7-4 }} \\ \sf{ \longmapsto {\dfrac{9}{3}} \\ \sf{\longmapsto 3} \end{gathered}[/tex]
Thus, The correct answer is 3!!
A 12-foot ladder is placed against a vertical wall of a building, with the bottom of the ladder standing on level ground 10 feet from the base of the building. How high up the wall does the ladder reach?
The height of the wall where the ladder reaches will be 6.33 feet.
What is a Pythagoras theorem?It expresses that the region of the square whose side is the hypotenuse is equivalent to the amount of the region of the squares on the other different sides.
The Pythagoras theorem formula is given as
H² = P² + B²
A 12-foot stepping stool is set against an upward mass of a structure, with the lower part of the stepping stool remaining on level ground 10 feet from the foundation of the structure.
The height of the wall where the ladder reaches will be calculated as,
12² = P² + 10²
144 = P² + 100
P² = 44
P =6.33 feet
The level of the wall where the stepping stool arrives freely will be 6.33 feet.
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25. how many strings of three decimal digits a) do not contain the same digit three times? b) begin with an odd digit? c) have exactly two digits that are 4s?
Using combination formula and analyzing the cases provided, The answer is 120,225 and 30.
What do you mean by combination?Combinations are mathematical operations that count the number of potential configurations for a set of elements when the order of the selection is irrelevant.
What is the formula to calculate combination?The required formula is:
[tex]C(n,r) = \frac {n!}{r!(n-r)!}[/tex]
number of digits that can be asserted in a position = 10 (0-9)
places to be filled = 3
If it do not contain the same digits three times, The number of strings of three decimal digits = C(10,3)
=[tex]\frac {10!}{3!*(10-3)!}[/tex]
=120.
If it begin with odd numbers, The numbers that can be filled at the start=5
for last two places = C(10,2)
=[tex]\frac {10!}{2! * (10-2)!}[/tex]
=45
Total number of strings=5*45 = 225
If it have two digits 4s, The number of possible cases of having two 4s= 3
For a remaining spot= C(10,1)
=[tex]\frac {10!}{1!(10-1)!}[/tex]
=10
Total number of strings = 3*10=30
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What is the y-intercept of Y =- 2x 6?
Answer:
y-intercept: 6
Step-by-step explanation:
Y = -2x 6
The equation is y = mx + b
m = the slope
b = y-intercept
So, the y-intercept is 6
What is the formula of rectangle pyramid?
The volume of a rectangular pyramid is one-third of the volume of a cuboid the pyramid is inscribed in with same base. That is the formula for volume of pyramid is,
V = l×b×h/3
A rectangular pyramid is a solid with a rectangular base area and 4 triangular faces, one face on each edge of the base joining at the top vertex. Generally, a rectangular pyramid is a right rectangular pyramid.
Let us say the rectangular pyramid we are considering has a dimension of l×b base, where l and b are the length and breadth of the base area and h is the height of the pyramid. Then the formula of volume of rectangular pyramid is
V = l×b×h/3
--The question is incomplete, answering to the question given below--
"What is the formula of volume of rectangular pyramid?"
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The equation and graph show the distance traveled by a minivan and a puck truck in miles, y, as a function of time in hours, x.
The rate of change of the pickup is greater than the rate of change of the minivan
How to compare the rates of change?From the question, we have the graph that can be used in our computation:
On the graph, we have the following points
(x, y) = (0, 0) and (1, 50)
The equation of the proportional relationship is then calculated as
y = Y/X * x
Where
(X, Y) = (1, 50)
Substitute the known values in the above equation, so, we have the following representation
y = 50/1 * x
Evaluate
y = 50x
This means that the rate of the pickup is 50 miles per hour for the pickup
For the minivan, we have
y = 45x
This means that the rate of the pickup is 45 miles per hour for the minivan
50 is greater than 45
Hence, the rate is greater
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What is equidistant from both endpoints?
In geometry, the midpoint is the middle point of a line segment. It is equidistant from both endpoints, and it is the centroid both of the segment and of the endpoints.
A point is said to be equidistant from a set of objects if the distances between that point and each object in the set are equal.
In two-dimensional Euclidean geometry, the locus of points equidistant from two given (different) points is their perpendicular bisector. In three dimensions, the locus of points equidistant from two given points is a plane, and generalising further, in n-dimensional space the locus of points equidistant from two points in n-space is an (n−1)-space.
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What additional information is needed for an AAS congruence theorem?
You must be aware that pairs of two angles are congruent as well as the pair of sides that are next to one of the specified angles in order to utilize the AAS Theorem to verify congruence.
Triangles are said to be congruent if two of their matching angles and one of their excluded sides are congruent with those of two other triangles. Because it can be demonstrated, this is a theorem.
The AAS Theorem uses two angles and a side to demonstrate triangle congruence, just as the ASA Postulate. The letters are arranged differently from the angles and sides they represent.
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Help meeeeeeeeeeeeeeeeeeeeeee pleaseeeeeeeeeeeeee!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
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Answer:
f(-3)= -6
f(0) = 0
f(4)= 36
What is the median of data 4 6 8 9 11?
Answer:
8
Step-by-step explanation:
its the middle number when the given values are listed least to greatest.
*count from each minimum and maximum values til you have the number in exact center.
7(h + k)² - 21(h + k)
factorise completely
Multiple choice math
The only graph that correctly shows the given piecewise function is; Graph B
How to interpret Piecewise functions?It is pertinent to note that when it comes to piecewise functions and inequalities, a closed, or shaded circle is typically used to represent the inequalities greater than or equal to (≥) or less than or equal to (≤) . However, an open, or unshaded circle is typically used to represent the inequalities greater than or less than.
Now, the first part of the piecewise function states that;
f(x) = x + 1 if x < 1
Thus, it will be an unshaded circle pointing to the left direction indicating less than.
The second inequality says 4 provided that x ≥ 1.
Thus;
The line will be a horizontal line pointing right with a shaded circle. Therefore we conclude that only option B is correct.
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The cost of ms. Clark's restaurant meal is $25. 50. As a tip, ms. Clark gives the waiter 20% of the meal's cost. What is the total amount ms. Clark pays, including tip? responses $26. 01 $26. 01 $30. 60 $30. 60 $32. 64 $32. 64 $33. 5.
As per the given percentage, the total amount Ms. Clark pays, including tip is $30.1
The term percentage is referred as a portion of a whole expressed as a number between 0 and 100 rather than as a fraction.
Here we have given that the cost of Ms. Clark's restaurant meal is $25. 50. And as a tip, Ms. Clark gives the waiter 20% of the meal's cost.
Now, we need to find the total amount Ms. Clark pays, including tip.
While we looking into the given question,
The following values are given in the question,
Total amount of bill for Ms. Clark = $25.50
Percentage of tip = 20%
Then the amount of tip is calculated as,
=> 25.50 x 20/100
=> 25.50 x 0.20
=> 5.1
Then the total amount paid by Ms. Clark is
=> 25.50 + 5.1
=> 30.1
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What does it mean to have 2 equal roots?
Therefore , it means if an equation have 2 roots , it means it is a quadratic function .
What is square root ?A number's root is that factor of the number that, when multiplied by itself, yields the original number. Specifically, squares and square roots are exponents. Think of the number nine. This can be expressed as or as 3 x 3.
Here,
If an equation have 2 roots , it means it is a quadratic function
If D=0, a quadratic function has two roots that are equal.
D (discriminant) = 0
=>b24ac=0 is required for a polynomial function to have equal roots.
Therefore , it means if an equation have 2 roots , it means it is a quadratic function .
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What is are the things s2 considered to show that the two triangles are congruent?
Answer:
Congruence in two or more triangles depends on the measurements of their sides and angles. The three sides of a triangle determine its size and the three angles of a triangle determine its shape. Two triangles are said to be congruent if pairs of their corresponding sides and their corresponding angles are equal.
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Step-by-step explanation:
Solve the system by substitution. y= y= \,\,-2x −2x y= y= \,\,-6x+36 −6x+36
The solution to the system of equations, y = -2x and y = -6x + 36, is: (9, -18).
How to Solve a System of Equations by Substitution?Given the following equations of the system as:
y = -2x --> eqn. 1
y = -6x + 36 --> eqn. 2
To solve, substitute y = -2x into equation 2:
-2x = -6x + 36
Solve for x
-2x + 6x = 36
4x = 36
x = 9
To find the value of y, substitute x = 9 into equation 1:
y = -2(9)
y = -18
The solution is: (9, -18).
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he graph for the equation y = x minus 4 is shown below. On a coordinate plane, a line goes through (0, negative 4) and (4, 0). Which equation, when graphed with the given equation, will form a system that has an infinite number of solutions? y minus x = negative 4 y minus x = negative 2 y minus 4 = x y + 4 x = 1
A system of equations with an infinity number of solutions, along with y = x - 4, is formed with the following equation:
y - x = -4.
What are linear functions?The slope-intercept definition of a linear function is given as follows:
y = mx + b.
The coefficients of the function are given as follows:
m is the slope.b is the y-intercept.The combination of two linear functions results in a system of equations.
Each intersection point of the linear functions is a solution to the system of equations, then a system with infinity solutions will only happen when the two lines are the same, that is, they have the same slope and the same intercept.
Hence the desired equation in this problem is given as follows:
y - x = -4.
Which in slope-intercept form is given by:
y = x - 4.
Which is equals to the graphed equation, hence they intersect infinite times.
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Answer:
A) y - x = -4
Step-by-step explanation:
How to find the missing number in integer array of 1 to 100 in Java?
Finding the missing number from the first 100 numbers in the given array arr[] of size N-1 with integers in the range [1, N] is the task. The list doesn't contain any duplicates.
Java method for locating a missing integer in an array of integers from 1 to 100
Make a temp array temp[] of size n + 1 with a value of 0 for each element.For each element in the input array arr[i], perform the following.If (temp[arr[i]] == 0), then temp[arr[i]] is 1.traverse temp[] and output an element of an array with the value of 0. (This is the missing element).class GFG; import java.io.*; import java.util.*
public static void findMissing(int arr[], int N)
{
int i;
int temp[] = new int[N + 1];
for (i = 0; i <= N; i++) {
temp[i] = 0;
}for (i = 0; i < N; i++) {
temp[arr[i] - 1] = 1;
} int ans = 0;
for (i = 0; i <= N; i++) {
if (temp[i] == 0)
ans = i + 1;
} System.out.println(ans);
}
public static void main(String[] args) {
int arr[] = { 1, 3, 7, 5, 6, 2 };
int n = arr.length; // Function call
findMissing(arr, n);
}
}
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if you fit your data to this function with n set exactly equal to 2, what is vx equivalent to?
(a) If you fit your data to this function with n set exactly equal to 2, then we have to find v(x, i) is equivalent to -2At(0).
(b) If you fit your data to this function with n set exactly equal to 2, then we have to find v(x, i) is equivalent to At(0)^2+B.
The given equation is x(f) = x(i)+v(x, i)Δt+12a(x)(Δt)^2.
Here x = x(f)-x(i)
So the equation is
x = v(x, i)Δt+12a(x)(Δt)^2..................(1)
The function in the program
x = A(t-t(0))^n+B
(a) If you fit your data to this function with n set exactly equal to 2, then we have to find v(x, i) is equivalent to.
If we set n = 2. Then;
x = A(t-t(0))^2+B..................(2)
On comparing the equation (1) and (2), we get
A = 1/2 a(x)
So, a(x) = 2A
x(f) = At^2+At(0)^2-2Att(0)+B.......................(3)
Now comparing the equation (1) and (3)
v(x, i) = -2At(0)
(b) If you fit your data to this function with n set exactly equal to 2, then we have to find x(i) is equivalent to.
On comparing the equation (2) and (3), we get
x(i) = At(0)^2+B
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Complete question is:
Equation 3.8 in the textbook states x(f) = x(i)+v(x, i)Δt+12a(x)(Δt)^2. In this lab you will collect data for the position, x, as a function of time, t. The software you will use will allow you to fit data using a function of the form x=A(t−t(0))^n+B.
1. If you fit your data to this function with n set exactly equal to 2, what is v(x, i) equivalent to?
2. If you fit your data to this function with n set exactly equal to 2, what is x(i) equivalent to?
How do you describe the transformation of a function?
The transformation of function is the process of modifying the existing graph of a function.
We know that in a function transformation, the graph of parent function either moves to left/right/up/down or resizes or reflects. There types of function transformations are: Translation, Dilation and Reflection
There are two types of translations of functions.
1) Horizontal translations: a function y = f(x) into the form y = f(x ± m)
if m > 0, then the function f(x ) moves to the left side by 'm' units.
if m < 0, then the function f(x) moves to the right by 'm' units.
2) Vertical translations: a function y = f(x) into the form f(x) ± m
if m > 0, then the function f(x) moves up by 'm' units.
if m < 0, then the function f(x) moves down by 'm' units.
Similarly there are two types of dilations.
1) Horizontal Dilation: a function y = f(x) into the form y = f(kx)
2) Vertical Dilation: a function y = f(x) into the form y = k f(x)
In both the cases, if k > 1, then the graph stretches and if 0 < k < 1, then the graph shrinks.
In case of reflection transformation of function y = f(x),
y = - f(x) is the reflection with respect to the x-axis and y = f(-x) is reflection with resepct to the y-axis.
Therefore, in a function transformation, the original graph of function either moves to left/right/up/down or resizes or reflects.
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A, B and Care points on the circumference of a circle with centre O.
LACB = 74°
74
Diagram not drawn to scale
Calculate the value of x.
(4 marks)
0x =
Submit Answer
O
Answer:
x = 16°
Step-by-step explanation:
AOB = 74 · 2 = 148°
triangle AOB is isosceles
2x + 148 = 180
2x = 180 - 148
2x = 32
2/2 x = 32/2
x = 16°
How many turning points can a degree 5 function have?
A degree 5 function can have up to five turning points. These turning points are also known as stationary points, inflection points, or extrema.
A degree 5 function is a polynomial of degree 5. This means that it is a function of the form f(x) = ax^5 + bx^4 + cx^3 + dx^2 + ex + f, where a, b, c, d, e, and f are constants. The degree of a function is determined by the highest power of the variable in the equation. In this case, the highest power of x is 5, and so the degree is 5. A degree 5 function can have up to five turning points. These turning points are also known as stationary points, inflection points, or extrema. A stationary point is a point on the graph of the function where the slope of the graph is either 0 or undefined, and an inflection point is a point on the graph of the function where the concavity of the graph changes. In order for a function to have a turning point, the derivative of the function must equal 0 at that point, and the second derivative of the function must not equal 0. If the second derivative does equal 0 at the point, then the point is a point of inflection, rather than a turning point. The number of turning points of a degree 5 function can be determined by finding the number of real roots of the equation f'(x) = 0, where f'(x) is the derivative of the function f(x). Since the degree of the derivative of a degree 5 polynomial is 4, this equation will have up to 4 real roots. This means that the degree 5 function can have up to five turning points.
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How do you explain temperature on a graph?
Temperature is typically represented on a graph by plotting points along the vertical (y-axis) to represent the temperature. The horizontal (x-axis) is typically used to represent time or location.
Temperature is typically represented on a graph by plotting points along the vertical (y-axis) to represent the temperature. The horizontal (x-axis) is typically used to represent either time or location. Each point on the graph is a measurement of temperature at a specific moment in time or location. The data points can be connected with a line to create a line graph, which can show temperature trends over time or in different locations. If two sets of data are being compared, such as indoor and outdoor temperatures, two lines can be drawn on the same graph to compare the two. By looking at the graph, one can easily identify the highest and lowest temperatures, as well as any trends over time. Additionally, the graph can be used to identify when temperatures are above or below a certain threshold. Graphs can be used to quickly and easily represent data, making them a powerful tool in understanding temperature.
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