Answer:
A quadratic equation is an equation of the form ax^2 + bx + c = 0, where a, b, and c are constants, and x is a variable.
The equations that are quadratic equations are:
(i) x^ 2 + 6 x − 4 = 0
(v) 2 x^ 2 − √ 3 x + 9 = 0
The equations that are not quadratic equations are:
(ii) √ 3 x^ 2 − 2 x + 1/ 2 = 0
(iii) x^ 2 + 1/ x^ 2 = 5
(iv) x − 3/ x = x ^ 2
(vi) x ^ 2 − 2 x − √ x − 5 = 0
(vii) 3 x ^ 2 − 5 x + 9 = x 2 − 7 x + 3
(viii) x + 1 x = 1
In (ii) √ 3 x^ 2 − 2 x + 1/ 2 = 0 the coefficient of x^2 is not a real number.
In (iii) x^ 2 + 1/ x^ 2 = 5 the equation is not in the form of ax^2 + bx + c = 0
In (iv) x − 3/ x = x ^ 2 the equation is not in the form of ax^2 + bx + c = 0
In (vi) x ^ 2 − 2 x − √ x − 5 = 0 the equation is not in the form of ax^2 + bx + c = 0
In (vii) 3 x ^ 2 − 5 x + 9 = x 2 − 7 x + 3 both sides are not equal
In (viii) x + 1 x = 1 the equation is not in the form of ax^2 + bx + c = 0
So, the equations that are quadratic equations are (i) and (v).
Step-by-step explanation:
Over which of the following is decreasing?
The correct option is C.
Describe Graph?A graph is a visual representation of data or a function, typically shown on a coordinate plane. It can be used to display information in a clear and concise way, and can be used to identify patterns, trends, or relationships within the data. Graphs can take many forms, including line graphs, bar graphs, scatter plots, and pie charts. They are used in many different fields, including mathematics, science, engineering, economics, and statistics. A right angled triangle is a type of triangle in which one angle is 90 degrees. The side opposite the right angle is called the hypotenuse and the other two sides are called the legs. The Pythagorean theorem states that the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the legs.
There are several types of graphs that can be used to represent data and information, including:
Line graphs: these are used to show the change in a variable over time. They are often used to represent continuous data.Bar graphs: these are used to show the frequency or quantity of different categories of data. They are often used to represent discrete data.Pie charts: these are used to show the proportion of different categories of data as a percentage of the whole. They are often used to represent data that is divided into parts of a whole.Scatter plots: these are used to show the relationship between two variables. They are often used to represent data that is spread out over a large range.Histograms: these are used to show the distribution of numerical data. They are similar to bar graphs, but they are used to represent continuous data rather than discrete data.Line plots: A line plot is a way to display data along a number line. It is a graph that shows frequency of data items in specific intervals or ranges along the number line.Dot Plots: A dot plot is a way to display data by using dots. Each dot represents a value.Box and Whisker plots: Box and whisker plots are a way to show the spread of data in a compact form and to identify outliers.To know more about coordinate plane visit:
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49 is 73% of what number?
Answer:
67.1
Step-by-step explanation:
Writing the statement '49 is 73% of what number?' where x is the number we are trying to find:
[tex]49 = 73\% \: of \: x[/tex]
To find the percentage of a number, we multiply the number by the decimal equivalent of the percentage, so can be rewritten as:
[tex]49 = \frac{73}{100} \times x[/tex]
[tex]49 = 0.73x[/tex]
[tex] \frac{49}{0.73} = x[/tex]
[tex]x = 67.1 \: rounded \: to \: 3 \: signifiant \: figures[/tex]
Examine the triangle below, solve for x, rounded to two decimal places
On solving the question, The value of x in Right Angle Triangle is .The value of x is .[tex]16\sqrt{2}[/tex]
What is a Right Angle Triangle ?A right triangle, also known as a right-angled triangle, right-perpendicular triangle, orthogonal triangle, or previously rectangled triangle, is a triangle with one right angle, or two perpendicular sides. The foundation of trigonometry is the relationship between the sides and various angles of the right triangle.
A right triangle's three sides are related in Euclidean geometry by the Pythagorean theorem, also known as Pythagoras' theorem. According to this statement, the areas of the squares on the other two sides add up to the size of the square whose side is the hypotenuse.
In the triangle 2 angles are respectively.
The third angle is = 45
The triangle is issosceles triangle
So the side which is not x is 16.
Now by using pythagorus Theorem
The value of x is .[tex]16\sqrt{2}[/tex]
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Are prime numbers only divisible?
No, prime numbers are not divisible by any other number apart from one and number itself.
As given in the question,
Given numbers are prime numbers,
Condition to be asked :
Prime numbers are divisible.
Prime numbers are those numbers which are only divisible by only two numbers one and number itself.
Prime numbers has only two factors one and number itself.
Example of prime numbers are as follow :
2, 3, 5, 7, 11,.....so on.
If the number has more than two factors then the numbers are considered as composite numbers.
One is neither prime nor composite.
Therefore, prime numbers are not divisible by any other number.
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What is an example of a perpendicular bisector?
A perpendicular bisector is a line that passes through the midpoint of two points, and is perpendicular to the line connecting the two points.
An example of a perpendicular bisector is the line between points A(2,4) and B(4,6). The midpoint of A and B is (3,5), and the equation of the line perpendicular to A and B is y= -x+10. To verify that the equation is perpendicular to A and B, we can calculate the slope of the line connecting A and B. The slope of A and B is (6-4)/(4-2) which is equal to 2. The slope of a perpendicular line is the negative reciprocal of 2, which is -1/2. Therefore, the equation of the perpendicular line is y = -(1/2)x + 10. This equation passes through the midpoint (3,5) which verifies that it is a perpendicular bisector of A and B.
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Which of the following are quadratic equation 2x² √ 3x 9 0?
Yes, 2x²-√3x+9=0 is a quadratic equation.
A quadratic equation is a type of polynomial equation that can be written in the form of ax² + bx + c = 0, where a, b, and c are constants and x is the variable. In this case, the equation 2x²-√3x+9=0 can be written in the form of ax² + bx + c = 0, where a = 2, b = -√3 and c = 9. Therefore, it is a quadratic equation. Quadratic equations have solutions in the form of x = (-b ± √(b² - 4ac))/2a, which is also known as the quadratic formula. In this case, if we substitute the values of a, b, and c into the quadratic formula, we can find the solutions for x in the equation 2x²-√3x+9=0.
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Complete question:
2x²-√3x+9=0 is it a quadratic equation?
The amount of potage placed on a firt-cla letter depend on the weight of the letter
Triangle ABC is congruent to Triangle PDF. Side AC corresponds to what side in Triangle PDF?
Triangle ABC and Triangle are congruent, but PF is the corresponding side.
What are triangle?A triangle in geometry is a three-sided polygon with three edges and three vertices.
The fact that a triangle's internal angles add up to 180 degrees is its most crucial characteristic.
This characteristic is known as the triangle's angle sum property.
If ABC is a triangle, it is written as ABC, where A, B, and C represent the triangle's vertices.
In Euclidean geometry, a triangle is a two-dimensional shape that is represented by three non-collinear points in a single plane.
A closed, two-dimensional shape is a triangle. It is a polygon with three sides. Straight lines make up all of the sides.
The vertex is the intersection of two straight lines. The triangle therefore has three vertices.
According to our question-
The matching parts of two figures that are congruent are identified by their respective vertices in the same order.
The side PF of PDF corresponds to the side AC of ABC (the first and last letters of the name or vertices) (corresponding letters in the name).
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Is this a function or just a relation?
From the given figure, we can say that it is a relation as 0 is input for both -2 and 1.
What is the Onto function ?
Onto function can be defined as the function in which the range is equals to codomain.
We know that relation can be defined as the relationship between sets of values and it is denoted by R.
And Function can be defined as the it is a relation where with only one output to each input.
From the given figure,
(0,-2) (0,1) (1,2) (2,1) (3,4) are the ordered pairs and here 0 is input for both -2 and 1
Hence , From the given figure, we can say that it is a relation as 0 is input for both -2 and 1.
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i need the answer to this simplifying radicals
Answer:
9√6
Step-by-step explanation:
3√2 × 3√3
3√2×3 ×3
3√6×3
9√6
Find the area of the trapezoid
Step-by-step explanation:
we need Pythagoras for right-angled triangles
c² = a² + b²
with c being the Hypotenuse (the side opposite of the 90° angle), a and b being the legs.
we also need to remember that the sum of all angles in a quadrilateral (4-sided shape) is 360°.
so, as 3 angles in the main quadrilateral are 90°, so is also the 4th angle. and that makes the quadrilateral a regular rectangle.
we know the length of the rectangle (15 ft).
the width is also the second leg of the attached right-angled triangle.
so, we know
13² = 5² + (leg2)²
169 = 25 + (leg2)²
144 = (leg2)²
leg2 = sqrt(144) = 12 ft
the total area is
the area of the rectangle
+
the area of the triangle
the area of the rectangle is
length × width = 15 × 12 = 180 ft²
the area of the right-angled triangle is
leg1 × leg2 / 2 = 5 × 12 / 2 = 5×6 = 30 ft²
the total area is
180 + 30 = 210 ft²
FYI - a different way is to directly calculate the area of the trapezoid :
(base1 + base2)×height/2
height = the width of the rectangle or leg2 of the right-angled triangle.
so, we have
(15 + (15 + 5))×12/2 = (15 + 20)×6 = 35×6 = 210 ft²
The following table represents the highest educational attainment of all adult residents in a certain town. If a resident who is 40 or older is chosen at random, what is the probability that they have completed a bachelor's or master's degree? Round your answer to the nearest thousandth.
....................
What is the formula for scale factor?
The formula for scale factor is: Scale Factor = New Length / Original Length.
What is scale factor?Scale factory the rescue between two corresponding length, area or the volumes of two similar figure it is used to compare the size of one figure to another as well as to the enlarge of reduced to size of a figure the scale factor is expressed as a ratio such as one is to to fit the first number is the original size and the second is the new size.
This is used to determine the factor by which an object has been scaled up or down. For example, if an object was originally 8 inches long and then scaled up to 16 inches long, the scale factor would be 2, as 16 is twice the length of 8.
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Boden's account has a principal of $800 and a simple interest rate of %3.2 Complete the number line. How much money will be in the account after 4 years, assuming Boden does not add or take out any money?
Answer:
The simple interest is calculated by multiplying the principal amount by the interest rate and the number of years.
Simple Interest = Principal x Interest Rate x Time
The simple interest on Boden's account is:
800 x 3.2% x 4 = 800 x 0.032 x 4 = $256
To find the total amount in the account after 4 years, we add the interest to the principal:
800 + 256 = $1056
So, Boden's account will have $1056 after 4 years.
What is the formula of a pair?
An ordered pair is a set of two values, (x,y), that represents a point on a coordinate plane. The x-coordinate represents the horizontal position and the y-coordinate represents the vertical position. The formula for an ordered pair is (x,y). where x and y are the coordinates.
Which is true about adding and subtracting polynomials?A.In adding and subtracting, we copy the common base, then add or subtract their exponents.B.To add and subtract polynomials, we copy the common variable, then multiply their exponents.C.We can add and subtract terms regardless if they have the same base.D.We can only add and subtract like terms
The correct answer is C. We can add and subtract terms regardless if they have the same base.
To add polynomials, we add the coefficients of the like terms together. For example, to add 2x^3 + 5x^2 + 6x + 3 and 3x^2 + 7x + 8, we would first identify the like terms, which in this case are x^2 and x. The coefficients of the like terms are then added together, so 2x^3 + (5+3)x^2 + (6+7)x + (3+8). The result is 2x^3 + 8x^2 + 13x + 11.
To subtract polynomials, we subtract the coefficients of the like terms. For example, to subtract 3x^2 + 7x + 8 from 2x^3 + 5x^2 + 6x + 3, we would identify the like terms, which in this case are x^2 and x. The coefficients of the like terms are then subtracted, so 2x^3 + (5-3)x^2 + (6-7)x + (3-8). The result is 2x^3 + 2x^2 - x - 5.
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write an equation of the perpendicular bisector of the segment with endpoints G (-2,0) and H(8,-6)
The equation of the perpendicular bisector of the segment with endpoints G (-2,0) and H(8,-6) would be, y = -(3/4)x + (9/2)
What is Perpendicular bisector of the segment?
A perpendicular bisector is a line that cuts another line segment through the junction point at a straight angle. As a result, a perpendicular bisector always cuts a line segment through its midway. The term bisect means to divide equally or uniformly.
The midpoint of the segment GH is the point (3,-3).
The slope of the line perpendicular to GH is the negative reciprocal of the slope of GH, which is -6/8 = -3/4
The slope-intercept form of the equation of the line is y = mx + b, where m is the slope and b is the y-intercept.
The point-slope form of the equation of the line is y - y1 = m(x - x1)
So we have
y - (-3) = (-3/4)(x - 3)
y + 3 = (-3/4)x + (9/2)
We can find the equation of the perpendicular bisector of the segment G(x1, y1) and H(x2, y2) by using the midpoint of the segment, (x1 + x2)/2, and (y1 + y2)/2, and the slope of the segment, (y2 - y1)/(x2 - x1)
so our final equation is y = -(3/4)x + (9/2)
Therefore, equation of the perpendicular bisector of the segment with endpoints G (-2,0) and H(8,-6) would be, y = -(3/4)x + (9/2)
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3 years ago, the residents of Planet X found a black hole leading to another galaxy. Since then,
they have been leaving Planet X at a rate of 120 residents per year.
The following equation describes this situation:
-120-3=-360
What does - 360 tell us?
Choose 1 answer:
A total of 360 residents left Planet X in the past three years. or
360 residents left Planet X each year. or
None of the above
A aggregate of 360 residers left Planet X in the once three times.
What's Linear Equation?
A direct equation is an algebraic equation of the form y = mx b, where m is the pitch and b is the y- intercept, and only a constant and a first- order( direct) term are included. The variables in the antedating equation are y and x, and it's sometimes appertained to as a" direct equation of two variables."
The point- pitch form, standard form, and pitch- intercept form are the three main types of direct equations.
At a pace of 120 occupants every time, they've been departing earthX.
So, by the formuls;
- 120x 3 = 360
thus, A aggregate of 360 residers left Planet X in the once three times.
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What are bases Grade 7?
Bases are chemical compounds that can accept hydrogen ions (H+) when added to water. Bases have a pH higher than 7 on the pH scale. Common bases include baking soda (sodium bicarbonate), lye (sodium hydroxide), ammonia (NH3), and calcium hydroxide (CaOH2).
The Importance of Understanding Bases in Grade 7 ChemistryBases are an important concept to understand in Grade 7 Chemistry. They are chemical compounds that have a pH higher than 7 on the pH scale and are capable of accepting hydrogen ions (H+) when added to water. Knowing the basics of bases can help students in a variety of ways, from understanding the properties of solutions to being able to identify and use different bases in lab experiments.
To begin with, understanding the properties of bases is essential in order to properly identify and use them in experiments. Bases can be divided into two categories: alkalis and acids. Alkalis are bases that are soluble in water, while acids are bases that are insoluble in water. Each type of base has its own unique properties and uses. For example, baking soda (sodium bicarbonate) is a common alkali that can be used for baking, cleaning, and even as an antacid. Meanwhile, lye (sodium hydroxide) is an acid that is used in many industrial processes, such as soap and textiles manufacturing.
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Which graph BEST represents the equation:
y=10−2x
the equation 10-2x is plotted below.
What is equation straight line?
Y = mx + c is the general equation for a straight line, where m denotes the line's slope and c the y-intercept. It is the version of the equation for a straight line that is used most frequently in geometry. There are numerous ways to express the equation of a straight line, including point-slope form, slope-intercept form, general form, standard form, etc. A straight line is a geometric object with two dimensions and infinite lengths at both ends. The formulas for the equation of a straight line that are most frequently employed are y = mx + c and axe + by = c. Other versions include point-slope, slope-intercept, standard, general, and others.
The equation of the line y=10−2x
m=-2
intercept = 10
Hence the equation 10-2x is plotted below.
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A student is studying the ways different elements are similar to one another. Diagrams of atoms from four different elements are shown below.
Which two atoms are of elements in the same group in the periodic table?
Answer:
Step-by-step explanation:
the way to determine if two atoms are of elements in the same group in the periodic table is to look at the number of valence electrons in the outermost energy level of the atom. Elements in the same group have the same number of valence electrons. For example, elements in Group 1 have 1 valence electron, elements in Group 2 have 2 valence electrons, and so on.
It's worth mentioning that the group in the periodic table is also known as family or column.
3. Karrie was late to work 14 times last year.
she worked 250 days last year, what perc
of the days was she late?
On solving the provided question, we can say that percentage of the days was she late = 14/250 * 100 = 5.6%
What is percentage?A percentage in mathematics is a figure or ratio that is stated as a fraction of 100. The abbreviations "pct.," "pct," and "pc" are also occasionally used. It is frequently denoted using the percent symbol "%," though. The amount of percentages has no dimensions. With a denominator of 100, percentages are basically fractions. To show that a number is a percentage, place a percent symbol (%) next to it. For instance, if you correctly answer 75 out of 100 questions on a test (75/100), you receive a 75%. To compute percentages, divide the amount by the total and multiply the result by 100. The percentage is calculated using the formula (value/total) x 100%.
Karrie was late to work = 14 times last year.
she worked = 250 days last year
percentage of the days was she late = 14/250 * 100 = 5.6%
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what is the slope of the line connecting (5,1) and (-1,3)? Please exlplain how you got the answer. I will mark you brainliest.
The slope of the line connecting the points (5,1) and (-1,3) will be - 1/3.
What is a linear equation?A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.
The linear equation is given as,
y = mx + c
Where m is the slope of the line and c is the y-intercept of the line.
The slope of the line is given as,
m = (y₂ - y₁) / (x₂ - x₁)
The points are given below.
(5, 1) and (-1, 3)
The slope of the line is given as,
m = (3 - 1) / (- 1 - 5)
m = 2 / (-6)
m = - 1/3
The slope of the line connecting the points (5,1) and (-1,3) will be - 1/3.
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Give a algebra equation to represent this pattern
In January, the number of days shown by the equation m = 4w + 3.
What is linear equation?Equations whose variables have a power of one are called linear equations. One example with one variable is where ax+b = 0, where a and b are real values and x is the variable.
Given:
A pattern shown in the image.
Let m is the number of days in a month.
And w represents the number of days in the weeks.
So, algebraic equation,
m = 4w + 3.
Therefore, the equation is m = 4w + 3.
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The value of y is 37 times the value of x.
Answer:
y = 37x
Step-by-step explanation:
We know
The value of y is 37 times the value of x, so our equation is
y = 37x
What are the 2 methods of solving equations?
There are many methods for solving equations, but the two main methods are algebraic method and graphic method.
Algebraic methods: These methods involve using algebraic manipulation to isolate the variable on one side of the equation and find its value. This can include using operations such as addition, subtraction, multiplication, and division, as well as the use of inverse operations (e.g. undoing addition with subtraction) and properties of equality (e.g. transitive property).
Graphic methods: These methods involve using graphs to represent the equation and find the solution. This can include plotting the equation on a coordinate plane and finding the points of intersection, or using a graphing calculator or software to plot the equation and find the solution.
It's worth noting that the method used to solve an equation will depend on the complexity of the equation and the information available. Some equations can be easily solved using algebraic methods, while others may require a combination of algebraic and graphic methods or an entirely different approach.
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Simplify the expression to a polynomial in standard form: (2x+3)(3x^2-6x+2) (2x+3)(3x 2 −6x+2)
Answer:
6x^3 + x^2 - 12x^2 - 18x - 6x - 6 = 6x^3 - 18x^2 - 12x - 6.
Step-by-step explanation:
simplify the expression (2x+3)(3x^2-6x+2)
First, we'll use the distributive property to expand the product of the two binomials:
(2x+3)(3x^2-6x+2) = 2x(3x^2-6x+2) + 3(3x^2-6x+2)
Next, we'll expand the product of each term in the first binomial with each term in the second binomial, using the distributive property again:
= 2x3x^2 + 2x(-6x) + 2x2 + 33x^2 + 3*(-6x) + 3*2
We can now simplify the resulting terms by combining like terms and combining the coefficients:
= 6x^3 -12x^2 + 4x + 9x^2 -18x + 6
we will combine the like terms
= 6x^3 - 18x^2 + 4x + 6
This is our final expression in standard form
what expression is equivalent to 6(x+2y) + 3 + 4y + 5
Answer:
6(x+2y) + 3 + 4y + 5
6x+12y+3+4y+5
Simplified: 6x+16y+8
Step-by-step explanation:
Is it possible to define all terms in geometry?
No, it is not possible to define all terms in geometry. The point, line, and plane are only a few of the many undefined terms in geometry. All other concepts in geometry may be defined from these three undefined terms.
Who named geometry?The father of geometry, Euclid was a brilliant mathematician. Learn more about Euclid and the history of some of the math ideas we use today to see how important they have become.
The terms "ge" and "metria," which both imply "measuring," are the origins of geometry. For more than 2000 years, the Greeks' method of approaching geometry has served as the foundation for geometry.
The study of various mathematical or actual-world forms, figures, and sizes is known as Geometry. We learn about various angles, transformations, and similarities between the forms in geometry. The point, line, and plane are the main building blocks of geometry.
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No, it is practically not possible to define all terms in geometry. Points, lines, and planes are just a few of the many terms not defined in geometry.
Which term is not defined in geometry?The point, line, and plane are only adequately described by examples and descriptions, hence they are regarded as undefined words in geometry. Give the points, lines, and planes a name. Points that are on the same line are known as collinear points.
A legal document's definitions are often located at the outset, or at the start of a standalone portion like a schedule or section.
The study of different mathematical or real-world shapes, sizes, and figures is known as Geometry. You will learn about points, lines, planes, angles, parallel lines, triangles, similarity, quadrilaterals, transformations, circles, and area in geometry.
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Solving systems of equations by elimination worksheet
1. y = 6x-11
-2x-3y = -7
2. 2x-3y = -1
y = x-1
1. steps to find the value of x
The first step is to equalize the form of the equation.
y = 6x-11 = -6x+y= -11
-2x-3y = -7
thus becoming:
-6x+y= -11
-2x-3y = -7
Then eliminate y:
-6x+y= -11 | times -3| becomes 18x-3y=33
18x-3y=33
-2x-3y = -7
y in the equation can be eliminated to become:
20x=40
x=40/20
x=2
steps to find the value of y:
The first step is to equalize the form of the equation.
y = 6x-11 = -6x+y= -11
-2x-3y = -7
thus becoming:
-6x+y= -11
-2x-3y = -7
Then eliminate x:
-2x-3y = -7 | multiplied by 3| becomes -6x-9y=-21
-6x+y= -11
-6x-9y=-21
x in the equation can be eliminated to become:
10y=10
y=-10/10
y=1
2.
1. steps to find the value of x
The first step is to equalize the form of the equation.
2x-3y = -1
y = x-1 becomes -x+y=-1
thus becoming:
-2x-3y = -1
-x+y=-1
Then eliminate y:
-x+y=-1| times -3| to 3x-3y=3
-2x-3y = -1
3x-3y=3
y in the equation can be eliminated to become:
-5x=-4
x=4/5
Steps to find the value of y:
The first step is to equalize the form of the equation.
2x-3y = -1
y = x-1 becomes -x+y=-1
thus becoming:
-2x-3y = -1
-x+y=-1
Then eliminate x:
-x+y=-1| multiplied by 2| becomes -2x+2y=-2
-2x-3y = -1
-2x+2y=-2
x in the equation can be eliminated to become:
-5y=1
y=-1/5
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