The probability that they share the same color is 7/15.
What is probability ?The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true.
An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.
The likelihood that an event will occur increases with its probability.
A straightforward illustration is tossing a fair (impartial) coin.
The chance of both outcomes ("heads" and "tails") is equal because the coin is fair, "heads" is more likely than "tails," there are no other conceivable outcomes, and the likelihood of either outcome is half (which may also be.
According to our question-
Then n(S)= number of ways of drawing 2 balls out of (6+4)=10
Let E= event of getting both balls of same color
Then, n(E)= no of ways (2 balls out of six) or (2 balls out of 4)
= 6C 2+ 4c2
∴P(E)= n(S)/n(E)= 45/21= 15/7
7/15
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Is x 8 a factor of the function f x 2x3 17x2 64?
A factor of a polynomial function is a polynomial that divides the function evenly when using polynomial division.
To check if x - 8 is a factor of the function f(x) =[tex]2x^3 - 17x^2 + 64[/tex] , we can use polynomial division.
When dividing f(x) by x - 8, the remainder should be zero.
x - 8 is a factor of the function when the remainder is zero.
In this case, the quotient is [tex]2x^2 + x + 8[/tex] , and the remainder is zero, so x - 8 is a factor of the function f(x) = [tex]2x^3 - 17x^2 + 64.[/tex].
So we can say [tex]f(x) = (x-8)(2x^2 + x + 8)[/tex]
Alternatively, we can also use synthetic division to check if x - 8 is a factor of the function.
Synthetic division is a shorthand method of dividing a polynomial by a linear factor such as x - 8.
If the remainder is zero, then x - 8 is a factor of the function.
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In a school election, Jessie received 60 votes, Rachel received 50 votes and Mario received 40 votes. What is the ratio of votes Rachal received to the votes Jessie received?
Therefore , the solution of the given problem of ratio comes out to be Jessie votes to Rachel votes is 6:5.
A ratio is what?A ratio is the simple expression "a / b," where "b" must not be greater than zero, for an ordered pair of numbers "a" and "b." Two ratios are combined to form a ratio. The ratio might be represented as 1:3 if there was just one man and three girls. 3/4 are girls, while 1/4 are boys. A part is a statistic, a percentage of something's size, or a distinction between two or more objects.
Here,
Given: Rachel received 50 votes,
Mario got 40 votes, and Jessie got 60.
To calculate the proportion of Jessie votes to Rachal votes:
Thus,
=> 60 : 50
=>6:5
Therefore , the solution of the given problem of ratio comes out to be Jessie votes to Rachel votes is 6:5.
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The car travels at a constant speed. After 6 seconds, it travels 180 meters.
Write a proportional equation to find the car's distance, d, at any time,
The equation that can be used to find the car's distance, d, at any time is d = 30 × t.
What is the equation that can be used to find the car's distance, d, at any time?Speed is simply referred to as distance traveled per unit time.
Mathematically, Speed = Distance ÷ time.
Given that;
Elapsed time t = 6 secondsDistance traveled d = 180Speed s = ?First, we determine the speed of the car.
Speed = Distance ÷ time
Speed = 180 / 6
Speed = 30 m/s
Now, to get the distance traveled at any time, plug the value of the speed of the car into the speed formula and solve for distance d.
Speed = Distance ÷ time
Speed = d / t
d = Speed × t
d = 30 × t
Therefore, the equation is d = 30 × t.
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contents of 2x + 3y answer
The Slope Intercept Form Of 2x + 3y = 8 Is y = -2x/3 + 8/3
How to determine the slope intercept formFrom the question, we have the following parameters that can be used in our computation:
2x + 3y = 8
Make 3y the subject of the formula
So, we have the following representation
3y = -2x + 8
Divide through by 3
This gives
y = -2x/3 + 8/3
Hence, the equation is y = -2x/3 + 8/3
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Complete question
contents
The Slope Intercept Form Of 2x + 3y = 8 Is
help me solve this pls because i need to solev this fast help me
The value of K that will make the expressions equivalent is 10.
How to evaluate the equivalent expression for the value of KConsidering the two expressions:
7 + (1/2)x - 3 + (3/4)x and 1 whole number (1/4)x + k - 6
we shall write the expression 7 + (1/2)x - 3 + (3/4)x in the form of the expression having k and then compare to know the value of k as follows;
(1/2)x + (3/4)x = (2x + 3x)/4
(1/2)x + (3/4)x = 5x/4
7 - 3 = 10 - 3 - 3
7 - 3 = 10 - 6
so;
7 + (1/2)x - 3 + (3/4)x = 5x/4 + 10 - 6
by comparison;
5x/4 is equal to the mixed fraction 1 whole number (1/4)x
k = 10 as obviously -6 is equal to -6.
Therefore, 10 is the value of k that will make expressions equivalent.
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Can anybody help me solve this
Answer: (5x^2-7)(x-4)
Step-by-step explanation:
5x^2(x-4)-7(x-4)
= (5x^2-7)(x-4)
The Davenports just got plans approved to install a Rectangular patio in their backyard a scale drawing of the paddle using a scale of 3in.: 10ft on the scale drawing, the patio measures 6 in. by 12 in. How many square feet will their patio cover?
The total area of the patio will be 20 * 40 = 800 square feet.
What is area of the scale model?The proportionate relationship between a linear dimension of a feature on a model, map, or drawing of an object and the same feature on the genuine thing. A scale model is a physical representation of an object that is geometrically equivalent (known as the prototype).
Since the scale drawing is 3 inches : 10 feet, this means that every 3 inches on the drawing represents 10 feet in real life. Hence, 1 inch on the drawing represents 10/3 = 3.33 feet in real life.
So the patio measures 6 inches by 12 inches on the drawing, which corresponds to 6 * 3.33 feet by 12 * 3.33 feet in real life, or 20 feet by 40 feet.
Therefore, the total area of the patio will be 20 * 40 = 800 square feet.
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what is 5/16 - 3/8 in simplest form
Answer: -1/16
Step-by-step explanation:
3/8 ---> 6/16
5/16 - 6/16 = (-1/16)
What are the 2 parts of exponential notation?
The two parts of the exponential notation can be named as the "Base" and the second part is number raised to base called as Exponent .
Consider the Exponential Expression : aⁿ ;
The above exponent notation is read as the number "a" to the power of "n" ,
it means that the number "a" is multiplied "n" number of times .
The two parts of this Exponential Notations are :
the number "a" is called the base and "n" is called as the power or exponent .
Therefore , the two parts of the exponential notation are the base and the power/exponent .
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What type of triangle has side lengths 5'7 and 11?
As the triangle cannot be equilateral since the sides are not equal. So the obtuse triangle has side lengths 5, 7 and 11.
Assume that a triangle has sides that measure 5, 7, and 11.
Finding the sum of the squares on the triangle's two shorter sides and comparing it to the square on the longest side will reveal the type of triangle.
A triangle must be sharp in order to:
Let a = 5, b = 7 and c = 11
a^2 + b^2 = (5)^2 + (7)^2 = 25 + 49 = 74
c^2 = (11)^2 = 121
(1) If the triangle is
a^2 + b^2 > c^2
Therefore, the triangle is not acute.
(2) Eqviangular means that each internal angle must be 60 degrees in length.
As a result, the triangle is not eqviangular.
(3) The triangle cannot be equilateral since the sides are not equal.
(4) We note that a^2 + b^2 = c^2.
The triangle is hence obtuse.
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In what quadrant does coordinate 2 3 lie?
The coordinate (2, 3) lies in the first quadrant of a Cartesian plane, which is the upper-right quadrant when the origin (0, 0) is the center.
The coordinate (2, 3) lies in a Cartesian plane, which is a two-dimensional plane with an origin (0, 0) at the center. There are four quadrants on the Cartesian plane. To find which quadrant the coordinate (2, 3) lies in, we must look at the signs of the x- and y-coordinates. The x-coordinate is 2, which is a positive number, and the y-coordinate is 3, which is also a positive number. This means that the coordinate (2, 3) lies in the first quadrant, which is the upper-right quadrant when the origin is the center. The other quadrants are numbered in a clockwise direction, starting with the first quadrant, which is the upper right. The second quadrant is the upper left, the third quadrant is the lower left, and the fourth quadrant is the lower right.
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In △OAB , points C and E lie on OA¯¯¯¯¯¯¯¯ , points D and F lie on OB¯¯¯¯¯¯¯¯ , and CD¯¯¯¯¯¯¯¯∥EF¯¯¯¯¯¯¯¯∥AB¯¯¯¯¯¯¯¯ . If OC=3 , EA=5 , OD=6 , and DB=14 , what is CE ?
Answer:
2
Step-by-step explanation:
I=$180
P=___
r=4.5%
t=3 years
what’s p?
Using the formula of Simple Interest, the value for the principal amount is obtained to be P = $1333.33.
What is Simple Interest?
Simple interest is a way to figure out how much interest will be charged on a sum of money at a specific rate and for a specific duration of time. Contrary to compound interest, where we add the interest of one year's principal to the next year's principal to compute interest, the principal amount under simple interest remains constant.
The value for Simple Interest is given as = $180
The value for rate is given as = 4.5%
The value for time is given as = 3 years
To find the value for Principal amount, follow the formula for Simple Interest -
SI = P R T/100
Where P is the principal amount, R is the rate and T is the time.
Substitute the values in the equation -
180 = (P × 4.5 × 3)/100
180 = 13.5P / 100
P = (180 × 100) / 13.5
P = 18000 / 13.5
P = 1333.33
Therefore, the value for principal amount is $1333.33.
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What are the 7 ways to classify a triangle?
Classifying Triangle by Sides or Angles: Equilateral triangle, Isosceles triangles, Scalene triangle, Right triangle, Obtuse triangle, Acute triangle, Equiangular triangle.
What are the seven ways to classify triangles ?A triangle is said to be equilateral or equiangular if each of its three sides is the same length. In the well-known Euclidean geometry, an equilateral triangle is also equiangular, meaning that each of its three internal angles is 60 degrees and congruent with the others.
A triangle having three acute angles is known as an acute triangle. A triangle having one obtuse angle and two acute angles is known as an obtuse triangle. No Euclidean triangle may contain more than one obtuse angle because in Euclidean geometry, a triangle's angles must add up to 180°.
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.
Obtuse-angled triangles or obtuse triangles are triangles with any one of its angles being an obtuse angle or more than 90°. Only 180° is equivalent to the internal angles of an acute triangle.
A scalene triangle is a triangle with three different side lengths and three different angle measurements. The total of all internal angles, however, is always equal to 180 degrees.
A triangle with two sides that have the same length is said to be isosceles. It can be stated as having exactly two equal-length sides or at least two equal-length sides, with the latter definition containing the equilateral triangle as an exception.
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Consider a circle whose equation is x2 + y2 – 2x – 8 = 0. Which statements are true? Select three options. The radius of the circle is 3 units. The center of the circle lies on the x-axis. The center of the circle lies on the y-axis. The standard form of the equation is (x – 1)² + y² = 3. The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.
Which example illustrates the commutative property of addition for polynomials?
(2x^2 + 5x) = –(–2x2 – 5x)
(2x^2 + 5x) + 0 = (2x^2 + 5x)
(2x^2 + 5x) + (4x^2 – 4x) = 2x^2 + 5x + 4x^2 – 4x
(2x^2 + 5x) + (4x^2 – 4x) = (4x^2 – 4x) + (2x^2 + 5x)
D) The example (2x^2 + 5x) + (4x^2 - 4x) = (4x^2 - 4x) + (2x^2 + 5x) illustrates the commutative property of addition for polynomials.
The commutative property of addition for polynomials states that the order in which polynomials are added does not affect the result of the sum. In other words, it states that if we have two polynomials A and B, the result of adding A and B (A+B) will be the same as adding B and A (B+A).
For example, consider the polynomials (2x^2 + 5x) and (4x^2 - 4x). If we add these two polynomials in the order given, (2x^2 + 5x) + (4x^2 - 4x) = 6x^2 + x. Now, if we add these two polynomials in the reverse order, (4x^2 - 4x) + (2x^2 + 5x) = 6x^2 + x. We can see that the order of the polynomials does not affect the result of the sum, and thus it holds the commutative property of addition.
Option (2x^2 + 5x) + (4x^2 - 4x) = (4x^2 - 4x) + (2x^2 + 5x) illustrates the commutative property of addition for polynomials, because it shows that the order of the polynomials does not matter and it gives the same answer.
It is important to note that the other options does not illustrate the commutative property.
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Write two equations that represent the graph shown below- one equation using sine, and one equation using cosine.
Two equations that represent the graph shown below as sine function y = 0.909x−3 and as cosine function y = −0.416x −3.
What is sine function?The sine graph or sinusoidal graph is an up-down graph and repeats every 360 degrees i.e. at 2π.
The general form of a cosine function is:
y = a cosb (θ±c) ± d
Here, amplitude, a is = 1
For b, period is = π
2π/b = π
b = 2
c = 0
vertical shift = D = -3
Putting the value into formula
y = 1 cos2 (θ + 0) - 3
y = 1 ×−0.416(θ + 0) - 3
y = −0.416θ−3
y = −0.416x −3 (cosine function)
y = 1 sin2 (θ + 0) - 3
y = 1 ×0.909(θ + 0) - 3
y = 0.909θ−3
y = 0.909x−3 (sine function)
Thus, two equations that represent the graph shown below as sine function y = 0.909x−3 and as cosine function y = −0.416x −3.
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What is a dilation of a line?
A dilation of a line is a transformation that changes the size of the line but preserves its shape.
It is a type of similarity transformation. A dilation can either be a reduction, in which the line is made smaller, or an enlargement, in which the line is made larger. In both cases, the line's shape is preserved, but the size is changed.
The center of dilation, also known as the scale factor, is a fixed point around which a dilation takes place. The scale factor is a value that represents the amount of change in size, it can be greater than 1 for an enlargement or less than 1 for a reduction.
In geometry, a dilation is represented by a multiplication of the coordinates of a point by a scale factor. For example, a dilation of a line with a scale factor of 2 will result in the line being twice as long as the original line.
In conclusion, a dilation of a line is a transformation that changes the size of the line but preserves its shape. The center of dilation or scale factor is a fixed point around which a dilation takes place and is represented by a multiplication of the coordinates of a point by a scale factor.
It can be either an enlargement or a reduction depending on the scale factor value.
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Suppose that a water fountain produces a stream of water that follows the shape of a parabola. assigning the origin of a coordinate system to the point where the water stream emerges from the fountain, a measurement shows that the maximum height of the stream occurs at the point (6, 5). use symmetry to identify a third point and find a quadratic regression equation for the stream of water. a. y = negative 0.139 x squared 1.667 x b. y = negative 0.135 x squared 1.667 x c. y = 0.135 x squared 1.667 x d. y = 0.139 x squared 1.667 x
A quadratic regression equation for the stream of water is,
⇒ y = -0.139x² + 1.667x
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Here, The vertex = (6, 5)
Axis of symmetry is line, x = 6
And, A third point in the parabola is, (12, 0)
Hence, The quadratic regression equation for the stream of water is,
⇒ y = - a(x - 6)² + 5
= -a(x² - 12x + 36) + 5
= -ax² + 12ax - 36a + 5
Since the parabola passes through point (0, 0),
i.e. -36a + 5 = 0
⇒ a = 5/36
⇒ a = 0.139
Therefore, The equation is,
⇒ y = -0.139x² + 12(0.139)x
⇒ y = -0.139x² + 1.667x
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Answer:
Its A
Step-by-step explanation:
Interpret the number line diagram shown below, and write a statement about the temperature for Tuesday compared to Monday at 11:00 p.m.
Help
Statement about the temperature for Tuesday compared to Monday at 11:00 p.m is temperature on Monday is 50⁰ F lesser than Tuesday
What is Number system?A number system is defined as a system of writing to express numbers.
In the given number line each unit is 10⁰ F
On Monday at 11:00 p.m. the temperature is 40⁰ F
Tuesday at 11:00 p.m. the temperature is -10⁰ F
The difference between two temperatures is 40⁰ F-( -10⁰)
40⁰ F+10⁰F
50⁰ F
The temperature on Monday is 50⁰ F lesser than Tuesday
Hence, statement about the temperature for Tuesday compared to Monday at 11:00 p.m is temperature on Monday is 50⁰ F lesser than Tuesday
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M=-3(-1,2) Write in slope intercept form, solve, graph
3x+y=-1 is the equation for slope as -3 and point as (-1,2).
What is equation?Algebraic expressions are used to express mathematical expressions, and algebraic expressions are used to express mathematical expressions. For example, 3x + 5 = 14 is an equation containing two expressions separated by a 'equal' sign. A mathematical statement made up of two expressions joined by an equal sign is known as an equation. 3x - 5 = 16 is an example of an equation. We get the value of the variable x as x = 7 after solving this equation. Linear equations are classified into three types: point-slope, standard, and slope-intercept.
Here,
slope=-3
point=(-1,2)
(y-y1)=m(x-x1)
y-2=-3(x+1)
y-2=-3x-3
3x+y=-1
The equation for slope as -3 and point as (-1,2) is 3x+y=-1.
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The value of which of these expressions is closest to e?
(¹+4)*
B. (1+²
OC. (¹+1)
OD. (1++)"
OA.
Therefore ,the solution of the given problem of expression comes out to be Option B is hence the appropriate choice.
What does expression mean?An algebraic expression must be checked by replacing each variable with a number and performing arithmetic operations. In the example above, the answer variable is identical to 6, since 6 + 6 = 12. If we know the values of the variables, we can replace them with those values and evaluate the expression.
Here,
Assumed: expressions
Finding the expression with a value that is closest to e
Solution:
e is worth 2.718, which equals (1 + 1/19).
(1 + 1/19)^19
=> (20/19)^19 = 2.65
=> (1+ 1/22)^22
= >(23/22)^22 = 2.659
=> (1 + 1/20)^20
= >(21/20)^20 = 2.653
=>(1 + 1/21)^21
= > (22/21)^21 = 2.656
As a result, the value of e is closest to the value of 2.659.
Option B is hence the appropriate choice.
Therefore ,the solution of the given problem of expression comes out to be Option B is hence the appropriate choice.
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A flower bed is in the shape of a rectangular prism. Its dimensions are 3 feet wide by 16 feet long by 6 inches deep.
a. How many cubic feet of topsoil do you need to fill the flower bed?
b. You can spread topsoil at a rate of 4 cubic feet per minute. How long will it take you
to spread all the topsoil?
How do you dilate a triangle by 2 with a compass?
Construct a dilate, with scale factor 2, of a triangle using only a ruler and compasses.
What is Dilation ?The center of dilation—the location from where the picture is shrunk or expanded—is necessary to build a dilation. A scale factor, or the quantity that controls how big or tiny the new picture will be, is also necessary. If the scale factor is more than 1, the new picture will be bigger than the original image, creating an enlargement. We see a decrease if the scale factor is less than 1, as the new picture will be smaller than the original image.
Step-1
Let's dilate triangle PQR by a scale factor of 2 with a center of dilation at point C.
Step-2
First, we will use a straightedge to connect the center of dilation C to each vertex. We are going to extend those lines across the whole page.
Step-3
Next, we'll place the point of the compass on the center of dilation C and the pencil on vertex Q and measure that distance.
Step-4
Now, without changing the size of the compass, we will move the point of the compass to vertex Q, and make a mark on the line that is extended through Q.
Step-5
Notice that since we measured the distance from C to Q and then used that same distance to mark the line, we have now created a new point that is twice the distance from C that Q was.
We now repeat the process for each of the other vertices of the triangle.
Step-6
These marks represent the vertices of our dilated image. We often use the same letters with an apostrophe to show that it is the corresponding vertex.
Step-7
Finally, we use the straightedge to connect all of the new vertices.
Now,See how triangle P ′ Q ′ R ′ is tw ce the size of the original triangle.
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How do polynomial identities apply to complex numbers?
Polynomial identities can be applied to complex numbers in the same way they are applied to real numbers, by replacing the real numbers in the polynomial with complex numbers and following the same algebraic rules and procedures.
What is a complex number?
A complex number is a number that can be written in the form a + bi, where a and b are real numbers and i is the imaginary unit, which is defined as the square root of -1.
Polynomial identities are equations that are always true for any values of the variables, regardless of whether the variables represent real numbers or complex numbers. Complex numbers can be represented in the form of a + bi, where a and b are real numbers and i is the imaginary unit.
For example, the identity[tex](x + y)^2 = x^2 + 2xy + y^2[/tex] is true for any real numbers x and y, and it also applies to complex numbers a + bi and c + di. The identity becomes [tex](a + bi + c + di)^2 = (a + c)^2 + 2(a + c)(bi + di) + (bi + di)^2[/tex]
Another example is the identity [tex](a+bi)^2 = a^2 + 2abi - b^2[/tex] which is always true for any complex number a+bi. This identity applies to any complex number and can be used to simplify polynomials involving complex numbers.
Hence, polynomial identities can be applied to complex numbers in the same way they are applied to real numbers, by replacing the real numbers in the polynomial with complex numbers and following the same algebraic rules and procedures.
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The egg displayed is composed of 4 arcs from 4 sectors.
• The arc AC has centre B.
• The arc BD has centre A.
• The arc AB has centre O.
• The arc CD has centre E.
• The radius of the central circle is 1cm.
• OE and OB form a right angle.
Calculate the perimeter of the egg.
The perimeter of the egg comprising of arcs AB, AC, BD, and CD is π·(6-√2)/2 centimeters
What is the perimeter of a plane figure?The perimeter of a figure is the length of the boundary line of a plane occupied by the figure.
The perimeter of the egg can be found by finding the sum of the lengths of the arcs that together form a composite figure of the perimeter of the egg
The length of arc AC centered at point B is found as follows;
The angle at the center B is the base angle of the isosceles right triangle
The acute angle of an isosceles right triangle is 45°, therefore, the angle at B = 45°
The radius of the arc AC, AB = AO + OB = BC
AO and OB are the radii of the circle with center O
AO = OB = 1 cm
AB = 1 + 1 = 2 = BC
The length of AC = (45/360)× 2×π×2 = π/2
AC = π/2
The radii and angle at the center of arc BD are also 2 cm and 45°
The length of arc BD is therefore, (45/360) × 2 × π × 2 = π/2
BD = π/2
The angle at the center of arc CD = ∠CED
∠CED ≅ ∠AEB (Vertical angle postulate)
∠AEB = ∠AEO + ∠BEO = 45° + 45° = 90°
∠CED = ∠AEB (Definition of congruency)
∠CED = ∠AEB = 90°
The radius of the arc CD, CE = ED = BC - EB
EB = √(1² + 1²) = √2
CE = 2 - √2
Length of arc CD = (90°/360°) × 2 × π × (2 - √2)) = π × (2 - √2))/2
CD = π·(2 - √2)/2
The radius of the arc AB = 1 cm
Angle at the center of arc AB = 180°
Length of arc AB = π × 1 = π
AB = π
The perimeter of the egg = AC + CD + BC + AB
Therefore;
The perimeter of the egg = π/2 + π × (2 - √2))/2 + π/2 + π = π·(6 - √2)/2
The perimeter of the egg is π·(6 - √2)/2 cm
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A cylinder with a height of 9cm. And a width of 10cm. Find the exact volume.
A. 90pi cm^3
B. 45pi cm^3
C. 900pi cm^3
D. 225pi cm^3
Answer:
The correct answer is D. 225pi cm^3.
To find the volume of a cylinder, you use the formula:
V = πr^2h
Where V is the volume, π is pi, r is the radius of the base, and h is the height of the cylinder.
In this case, the height is 9cm, and the width is 10cm. To find the radius, we divide the width by 2:
r = 10cm / 2 = 5cm
Now we can plug in the values into the formula:
V = πr^2h
V = π(5cm)^2(9cm)
V = π(25cm^2)(9cm)
V = 225π cm^3
So the volume of the cylinder is 225π cm^3
Step-by-step explanation:
Answer: D) 225pi cm^3.
Step-by-step explanation:
(05.06 LC) DO CORRECTLY
Which graph best represents a constant function? (5 points)
Constant functions have graph that are horizontal lines in the plane and are linear functions. Graph 3 is the correct answer.
What is a constant function?One of the simplest forms of real-valued functions is a constant function, which is used to express a quantity that remains constant across time. Constant functions have graphs that are horizontal lines in the plane and are linear functions. The x-value serves as the function's domain, which is depicted on the x-axis, and the y-axis serves as its range, which is indicated by the symbol f(x).
We know that the constant functions remain constant, that is they do not change their value. Constant functions have graphs that are horizontal lines in the plane and are linear functions.
Hence, graph 3 is the correct answer.
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Which statements about the line that passes through (−2, 0) and (2, −4) aretrue? Select all correct statements. The slope of the line is 1. The line intersects the y-axis at (0, −2). The equation of the line is y = −x − 2 The line intersects the x-axis at (−2,
The correct options for the line are-
B. The line intersects the y-axis at (0, −2).C. The equation of the line is y = −x − 2.D. The line intersects the x-axis at (−2, 0).Define the equation of the line?The formula for a straight line reads y=mx+c where c is the height from which the line intersects the y-axis, often known as the y-intercept, and m is the gradient.Coordinate are: (−2, 0) and (2, −4)
Slope m = y2 - y1 / x2 - x1
m = (-4 + 0)/(2 + 2)
m = -4/4 = -1
Slope is -1 , option A incorrect.
For the y-intercept
Use point (-2, 0) and slope m = -1
0 = -1(-2) + b
b = -2
As, y-intercept is -2.
Option B correct.
Find equation of the line.
y = mx+ b
y = -x + (-2)
y = -x - 2
Thus, equation of the line is y = −x − 2.
Option C is also correct.
Find the x-intercept.
if y = 0
0 = -x - 2
x = -2
Thus, line intersects the x-axis at (−2, 0).
The option D is also correct.
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The complete question is-
Which statements about the line that passes through (−2, 0) and (2, −4) are true? Select all that apply.
A. The slope of the line is 1.
B. The line intersects the y-axis at (0, −2).
C. The equation of the line is y = −x − 2.
D. The line intersects the x-axis at (−2, 0).
Does 8 15 17 form a right triangle?
Yes, 8, 15, 17 is a Pythagorean Triple and sides of a right triangle.
What is meant by Pythagorean?
The Pythagorean theorem, sometimes known as Pythagoras' theorem, is a basic relationship between a right triangle's three sides in Euclidean geometry.According to this rule, the areas of the squares on the other two sides add up to the area of the square whose side is the hypotenuse, or the side across from the right angle.Pythagoras, a Greek philosopher who was born around 570 BC, is remembered by the theorem's name.The theorem has likely been proved the most times of any mathematical theorem using a variety of techniques.The proofs are numerous, some of which go back thousands of years, and include both geometric and algebraic proofs.To learn more about Pythagorean refer to
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Yes, 8, 15, and 17 are triples of Pythagoras, and the sides are right triangles.
What is Pythagoras?The Pythagorean theorem, also known as the Pythagorean theorem, is the fundamental relationship between the three sides of a right triangle in Euclidean geometry.
According to this rule, the area of a square with two other sides is the area of the square whose side is the opposite side of the hypotenuse, or right angle.
The name of this phrase evokes the Greek philosopher Pythagoras, who lived around 570 BC. was born. This theorem has probably been proven most frequently of all mathematical theorems using various techniques.
There are numerous proofs, some dating back thousands of years, involving both geometric and algebraic proofs.
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