To rewrite an expression in equivalent form, you can use the distributive property, combine like terms, apply the commutative property, or use identities to simplify and rearrange the expression.
The distributive property states that multiplying a term and a sum of two or more terms is the same as multiplying each individual term and then adding the products together. It can be used to simplify expressions by breaking down larger terms into smaller ones. For example, 8(x + 2) can be rewritten as 8x + 16.Combining like terms is another way to rewrite expressions in equivalent form. This involves adding (or subtracting) two or more terms with the same variables. For example, 5x + 3x can be rewritten as 8x.The commutative property states that changing the order of two numbers or variables does not change their value. This can be used to rearrange expressions in equivalent forms. For example, 5x + 2y can be rewritten as 2y + 5x.Finally, identities are equations that are always true. They can be used to simplify and rearrange expressions in equivalent form. For example, (x + y)2 can be rewritten as x2 + 2xy + y2 using the identity (x + y)2 = x2 + 2xy + y2.
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Is reflection same as rotation 180 degrees?
Similar to the plane reflection, the line reflection is the inversion through a straight line. In reality, it goes through the same transformation as a 180-degree rotation.
What is reflection?A reflection is referred to as a flip in geometry.
A reflection is the shape's mirror image.
A line, called the line of reflection, will allow an image to reflect through it.
Every point in a figure is said to reflect the other figure when they are all equally spaced apart from one another. The line reflection is the inversion through a straight line, much as the plane reflection.
Actually, it undergoes the same change as a 180-degree rotation.
For this reflection, the rule would be written as RX-axis (x,y)→(x,y).
Rule of Notation: This notation rule tells you that image A has been reflected across the y-axis and the x-coordinates have been multiplied by -1.
It has the form by-axis A→B = axis (x,y)→(x,y).
Therefore, similar to the plane reflection, the line reflection is the inversion through a straight line. In reality, it goes through the same transformation as a 180-degree rotation.
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How do you know if a function is continuous or discontinuous?
A function is continuous if its graph is a single, unbroken line without any gaps. A function is discontinuous if its graph has breaks in it, or if it is undefined at certain points.
A function is continuous if its graph is a single, unbroken line without any gaps. This means that the function must have a defined value for every value of the independent variable. If the graph of the function is smooth, without any abrupt changes or jumps, then it is continuous. A function is discontinuous if its graph has breaks in it, or if it is undefined at certain points. This means that the function is not defined at certain values of the independent variable and hence, the graph is not a single, unbroken line. Discontinuities can arise from various sources, such as a function having an infinite value, a function having a zero value or a function having an undefined value. The graph of a discontinuous function typically has gaps or jumps, and it is not a single, unbroken line.
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What is the relationship between the base and height when you are finding the area of a triangle?
The base in term of the height of the triangle is written as ;b = 2A/h.
Define the term area of a triangle?A closed triangle has three sides. It is among the fundamental geometric shapes because it has three vertices and three sides.
Based on the length of its sides, a triangle can be labeled as equilateral, isoscles, or scalene.A two-dimensional shape's area is the space the shape takes up. By dividing the shape equal unit squares and counting them, since each unit square takes up one square unit space, the area may be obtained.Think about the ABC scalene triangle. Keep in mind that the height of a triangle must be perpendicular towards the base in order for its area to be expressed as being half that of a rectangle. Create a perpendicular hence from a vertex to the opposite side.Thus, the formula for the are area of the triangle is -
A = 1/2 bh
In which,
b = base of the triangle.
h = height of the triangle.
In term of the height.
b = 2A/h
Thus, the base in term of the height of the triangle is written as;b = 2A/h.
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What is the unit digit in 27 20 A 1 b5 C 12 D 20?
The correct option is A.Hence the given number follow the pattern of consective powers,so unit digit of given number will be 1.
What is unit digit?The unit digit is a number placed in the one's position.It is placed right most digit of the given number.The value of every digit in the number system by specifying the position of the particular digit in the number such as ones,tens,hundreds,thousands and so on.
How do we find unit digit of raised power?It is easy to identify the unit place of smaller number but when it comes to the raised to the power it becomes difficult to identify by simple observation.Then we use cyclicity chart.It is based on every digit in the number has its own repetitive pattern when raised to any specific power.
For example 2^5=32 ; Here 2 is the unit digit of given number.
Now we use cyclicity concept to find and get
Unit digit of 27^1=7(7^1=7)
Unit digit of 27^2=9(7^2=49)
Unit digit of 27^3=3(7^3=343)
Unit digit of 27^4=1(7^4=2401)
Hence for every four consective ,the unit digit will follow pattern of 7,9,3,1.
SO Unit digit of given number is 1.
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There were 17 unny day thi year, which wa 18 fewer than lat year. Two year ago , there were three time a many unny day a there were thi year. How many unny day were there in all three year?
The total number of sunny days for the three years is 103 days.
This year there were 17 sunny days.
There were 17 sunny days this year, 18 fewer than last year. This is to mean that, last year, sunny days were 18 days more than this year, Which can be found by;
18+17 = 35 sunny days
Sunny days two years ago were three times the sunny days this year which is;
3×17 = 51 sunny days
Therefore, the total number of sunny days for the three years is calculated by adding the total number of sunny days for the three years:
17 + 35 + 51 = 103 sunny days
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IF A:B = 5:6 and B:C = 7: 8 and C :D = 9:10, find the ratio
of A:B:C: D.
Answer:
A = 5 ; B = 6
B = 7 ; C = 8
C = 9 ; D = 10
convert C:D where C is equals to C in B:C
C = 144 ; D = 160
convert B:C where B is equals to B in B:C
C = 144 B = 126
convert A:B where B is equals to B in B:C
B = 126 A = 30
A = 30, B = 126, C = 144, D = 160
ratio
15:63:72:80Step-by-step explanation:
heart and star pls <3 brainliest will be appreciated <3(っ◔◡◔)っ -{ elyna s }-Which shape has 4 sets of parallel lines?
Answer:
Octagon
Step-by-step explanation:
An octagon has 4 sets of parallel lines and 8 sides.
we define a bow-tie quadrilateral as a quadrilateral where two sides cross each other. an example of a bow-tie quadrilateral is shown below. seven distinct points are chosen on a circle. we draw all chords that connect two of these points. four of these chords are selected at random. what is the probability that these four chosen chords form a bow-tie quadrilateral?
The probability of forming a bow-tie quadrilateral from four randomly chosen chords is approximately 6.25%.
This is because there are exactly 28 possible quadrilaterals that can be formed from the seven given points, and only one of those 28 quadrilaterals is a bow-tie quadrilateral. This means that the probability of forming a bow-tie quadrilateral is 1/28, which is equal to 0.0357, or 3.57%.
To explain further, when we draw all of the chords from the seven given points, we have 21 distinct chords. Out of these, 10 chords form triangles, leaving us with 11 chords that form quadrilaterals.
Since four of these chords are randomly chosen, the number of possible combinations of quadrilaterals that can be formed is equal to 11C4, or 495. Out of these 495 combinations, only one is a bow-tie quadrilateral. This means that the probability of forming a bow-tie quadrilateral is 1/495, or 0.002041, or 0.2041%.
Since 0.2041% is too small to be expressed as a whole number, it is rounded up to 6.25.
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How do you graph x is less than or equal to negative 2?
The graph of inequality x < −2 is as shown below.
In this question we need to graph x is less than or equal to negative 2.
i.e., we need to graph an inequality x < −2
First we draw a straight vertical line x = -2.
The graph of x = -2 is a straight line parallel to y-axis and intersects x-axis at (-2, 0)
We represent the graph of x = −2 by the dashed line.
The dashed line indicates that the line is the boundary of the inequality but not part of it. Shade in the left side of the line to indicate the inequality x<−2.
Therefore, the graph of x is less than or equal to negative 2 is as shown below.
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Hi my name is Bryce what is yours.
What value of b will cause the system to have an infinite number of solutions 6 3 3 6?
The value of b when the system has an infinite number of solutions is 12.
The Given equations are
y=6x-b ---(1)
6=3x+3y ----(2)
If the system has an infinite number of solutions, then equation 1 is equal to equation 2
If a pair of linear equations have unique or infinite solutions, then the system of equation is said to be a consistent pair of linear equations
Isolate variable y in equation 2
2=x+y
Multiply by 6 on both sides
y=6x-12 -----(3)
To find the value of b, equate equation 1 and equation 3
6x-b=6x-12
b=12
Thus the value of b=12.
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What is Circumcentre and Orthocentre?
Step-by-step explanation:
circumcentre:
In geometry, the circumscribed circle or circumcircle of a polygon is a circle that passes through all the vertices of the polygon. The center of this circle is called the circumcenter and its radius is called the circumradius. Not every polygon has a circumscribed circle.
othocentre:
The orthocenter is the intersection point of three altitudes drawn from the vertices of a triangle to the opposite sides. A centroid is the intersection point of the lines drawn from the midpoints of each side of the triangle to the opposite vertex.
In the diagram below, Ois circumscribed about quadrilateral ABCD. What is
the value of x?
D
A
72⁰
3x⁰
с
B
OA. 36
OB. 105
OC. 24
OD. 96
As per the quadrilateral ABCD, the value of x will be equal to 36°.
What is a Polygon?A polygon is described in geometry as a compact, two-dimensional shape having three or more straight lines. Poly, which means "many," and gon, which means "angle," make up the Greek word "Polygon." Polygons of several kinds can be seen all around us.
As per the given diagram in the question,
The given angles are:
∠ A = 72°
∠ C = 3x
For a cyclic quadrilateral,
∠ A + ∠ C = 180°
72 + 3x = 180
3x = 180 - 72
3x = 108
x = 108/3
x = 36°
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How do you find 2 mean?
Using the mean formula, we will add the two values and divide the result by 2 to determine the mean of the two values.
What is mean?The average of a group of variables is referred to as the mean in mathematics and statistics.
There are several methods for calculating the mean, including simple arithmetic means (adding the numbers together and dividing the result by the number of observations), geometric means, and harmonic means.
So, to find the mean of 2 values:
Mean formula: Sum of the terms / Number of terms
Now, using the formula, to obtain the mean of 2 values, we will get the sum of the 2 given values and divide it by 2.
Therefore, using the mean formula, we will add the two values and divide the result by 2 to determine the mean of the two values.
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Correct question:
How do you find mean of 2 values?
The graph shows the the number of mistakes made on an exam. How many students made four or more mistakes?
In the figure, a∥b and m∠3 = 34°.
What is the m∠7?
Enter your answer in the box. |__|
Therefore, In the figure, a∥b angle m∠7 = 34° .
What is angle ?An angle is a figure in Euclidean geometry made up of two rays that share a vertex, or common terminus, and are referred to as the sides of the angle. Angles of two rays lie in the plane containing the rays. Angles can also result from the intersection of two planes. Dihedral angles are the name given to them.
Here,
Given that a and b are parallel lines,
∠3 and ∠7 are corresponding angles and congruent
m∠3 = 34°
thus ,m∠7 =m∠3 = 34°
so, m∠7 = 34°
Therefore, In the figure, a∥b m∠7 = 34° .
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Evaluate each expression.
The final answers are a) 12 b)3/28 c) 2
What is the reciprocal of a number?In Maths, reciprocal is simply defined as the inverse of a value or a number. If n is a real number, then its reciprocal will be 1/n. It means that we have to convert the number to the upside-down form. For example, the reciprocal of 9 is 1 divided by 9, i.e. 1/9
Given here a) 4÷1/3 = 4×3
=12
b) 3/8÷7/2 = 2×3/8×7
= 3/28
c) 3¹/₂ ÷7/4 = 7/2÷7/4
= 2
Hence the answers are 12, 3/28 , 2
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What is the value of the expression? −2^6−(6)^2
Answer:
-100
Step-by-step explanation:
To solve -2^6 - 6^2, we can evaluate each term separately.
2^6 = 64
6^2 = 36
-2^6 - 6^2 = -64 - 36 = -100
Answer the geometry question
Answer:
52 degrees
Step-by-step explanation:
The 3 angles of a triangle add up to 180 degrees
To find angle C, use 180 - B - A = C
180 - 85 - 43 = 52
The first term in an arithmetic sequences is 5. The third term in the sequences is -1. The tenth term in the sequences is -22. Write the explicit form that would be used to find the nth term in the sequence. Show the steps you took to write the simplified explicit form.
The explicit form that would be used to find the nth term in the sequence is aₙ = 2 + 3n
What is arithmetic sequence?
The difference between each consecutive term in an arithmetic sequence is constant.
An explicit formula for an arithmetic sequence is a = d(n - 1) + c, where d is the common difference between consecutive terms.
According to the given question:
The first term in an arithmetic sequence is 5 that is a = 5
Now, the third term in the sequences is -1
a₃ = a + 2d
By substituting the value of a and a₃ we can find d for the arithmetic sequence.
-1 = 5 + 2d
2d = -6
d = -3
So, the explicit form that would be used to find the nth term in the sequence is
aₙ = 5 - (n - 1)(-3)
Simplifying further to get
aₙ = 2 + 3n
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#11: During a basketball game the Dragons made 12 three
pointers and 11 foul shots (1 point each) and the rest of their
points came from two point baskets.
Determine the equation, slope and y-intercept for a function
that outputs the total points the Dragons scored (p) based on
the number of 2-point baskets made (b).
Slope:
Y-Intercept:
Equation (in slope-intercept form):
Answer:
Slope: 2
Y-Intercept: 47
Equation (in slope-intercept form): p = 2b + 47.
Step-by-step explanation:
To determine the equation, slope, and y-intercept for a function that outputs the total points the Dragons scored based on the number of 2-point baskets made, you will need to use the information given about the number of 3-pointers, foul shots, and 2-point baskets made.
First, let's define p as the total number of points the Dragons scored and b as the number of 2-point baskets made.
We know that the Dragons scored a total of 12 three-pointers * 3 points per 3-pointer + 11 foul shots * 1 point per foul shot = 47 points from 3-pointers and foul shots.
Therefore, the total number of points the Dragons scored can be expressed as:
p = 47 points + 2 points per 2-point basket * b 2-point baskets
This equation is in slope-intercept form, with the slope being 2 points per 2-point basket and the y-intercept being 39 points.
The equation in slope-intercept form is:
p = 2b + 47
Therefore, the slope of the function is 2, the y-intercept is 39, and the equation is p = 2b + 47.
What are the 2 types of functions give examples?
The two types of functions are linear and non linear functions.
A linear function is a function that can be written in the form f(x) = mx + b, where m and b are constants. This type of function has a constant rate of change, meaning the output will always increase or decrease the same amount for a given change in the input. For example, if the input increases by 3, the output will increase by 6. An example of a linear function is f(x) = 3x + 5. This function will always increase by 3 for each increase in the input, and will always have a y-intercept of 5.
A non-linear function is a function that cannot be written in the form f(x) = mx + b. This type of function has a variable rate of change, meaning the output will increase and decrease at different rates for different changes in the input. An example of a non-linear function is f(x) = x2 - 4x + 5. This function will increase and decrease at different rates for different changes in the input, and will always have a y-intercept of 5.
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What is the slope of the line y =- 3x 1 3?
The slope of the line y =3x(1 ,3) is 3.
Describe slope.The ratio of how much y grows as x grows by a certain amount is known as a line's slope. The slope of a line indicates how steep it is, or how much y rises as x rises. Anywhere along the line, the slope remains constant (the same). In math, we frequently want to quantify the steepness. Slopes B and C are clearly higher than slope A. While slope A is just four units high, they are both seven units high. Therefore, it would seem that height and steepness are related.
Given
Equation
y = 3x (1,3)
Using slope intercept form,
y = mx + b
m = slope
m = 3
The slope of the line y =3x(1 ,3) is 3.
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List the sample space for rolling a fair eight-sided die.
Answer: The sample space of rolling an eight-sided die would be (1, 2, 3, 4, 5, 6, 7, 8)
Step-by-step explanation: Sample space is defined as a set of all possible outcomes. In an eight-sided die, there are eight faces and hence, we have the probability of getting any number within 1 to 8.
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Answer:
D
Step-by-step explanation:
105% of what number is 21?
How do you prove that a triangle is similar by SSS?
"If in two triangles, sides of one triangle are proportionate to (i.e., in the same ratio of) the sides of the other triangle, then their corresponding angles are equal and consequently the two triangles are comparable," asserts the Side-Side-Side (SSS) criteria.
Take a look at the triangles below.
- We can see that all three pairs of the sides of these triangles are congruent. - This is also known as "side-side-side" or "SSS." According to the SSS criteria for triangle congruence, two triangles are congruent if they have three pairs of congruent sides.
SSS Congruence Rule Theorem
When one triangle's three sides are identical to the corresponding three sides of another triangle, two triangles are said to be congruent.
The aforementioned theorem will now be proven.
Given: [tex]\triangle A B C[/tex] and [tex]\triangle P Q R[/tex] such that AB=PQ, BC=QR and AC=PR.
To prove: [tex]\triangle A B C \cong \triangle PQR[/tex]
Construction: Let BC be the longest side of [tex]\triangle A B C[/tex] and so QR is the longest side of [tex]\triangle P Q R.[/tex]
Draw PS so that [tex]\angle R Q S=\angle C B A[/tex] and [tex]\angle Q R S=\angle B C A[/tex].
Join SQ and SR.
In [tex]\triangle ABC[/tex] and [tex]\triangle SQR[/tex],
BC=QR Given
[tex]\angle C B A=\angle R Q S[/tex] By construction
[tex]\angle B C A=\angle Q R S[/tex] By construction
[tex]\triangle A B C \cong \triangle SQR[/tex] By ASA congruence
[tex]\angle A=\angle S[/tex] By CPCTC
AB=SQ By CPCTC
AC=SR
Now, AB=PQ and AB=SQ => PQ=SQ
Similarly, AC=PR and AC=SR => PR=SR
Hence, [tex]\triangle ABC \cong \triangle PQR,[/tex]
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find the area of the largest rectangle that can be inscribed in the ellipse x2 a2 + y2 b2 = 1
The area of the largest rectangle that can be inscribed in the ellipse is 2ab
The term ellipse in math is a circle that has been stretched in one direction to give it an oval shape
Here we have given the following equation x²/a² + y²/b² = 1
Now, we have to find the area of the largest rectangle that can be inscribed in the ellipse
Here we all know that the Area of rectangle = 4xy
That can be written as A = 4xy
Now, we have to differentiate the given expression then we get,
=> dA/dx = 4xdy/dx + 4y ----------------------(1)
Here we have given an equation x²/a² + y²/b² = 1
Now, we have to differentiate this one also, then we get,
=> 2x/a² + 2y(dy/dx)/b² = 0
If we equate both of the equation then we get the value as.
=> dy/dx = - xb²/a²y
Now, substitute the values on equation (1), then we get,
=> dA/dx = 4x( - xb²/a²y) + 4y
Equate the expression with 0, then we get the value of
=> a²y² = b²x²
=> x²/a² = y²/b²
When we simplify this one then we get the value of x as (a/√2) and y as b/√2
Therefore, the Area is calculated as,
=> 4xy = 4(a/√2)(b/√2) = 2ab
So, the value 2ab is the area of the greatest rectangle that can be inscribed in an ellipse x²/a² + y²/b² = 1
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2/9x18
Please show step by step example
tell whether the lines for each pair of equations are parallel perpendicular or neither y= -1/5x + 6 and -2x+10y=5
NEED HALP ASAP!!
Answer:
neither coz m1=-1/5 and m2=1/5
m1 is not equal to m2 [not parallel]
m1× m2 is not equal to -1.[not perpendicular]
A triangle has two sides of length 8.3 and 3.4. What compound inequality describes the possible lengths for the third side, x?
Using Pythagoras theorem the compound inequality for the possible length is 7.6 ≤ x ≤ 9
Pythagoras TheoremPythagoras theorem states that “In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides“. The sides of this triangle have been named Perpendicular, Base and Hypotenuse. Here, the hypotenuse is the longest side, as it is opposite to the angle 90°.
To find the possible value for the third side, we have to use Pythagoras formula which is given as;
x² = y² + z²
In the first scenario, we would assume the third side is the hypothenuse
x² = 8.3² + 3.4²
x = 9
In the second scenario, we would assume the third side is one of the legs of the triangle and the formula will change to
8.3² = y² + 3.4²
y² = 8.3² - 3.4²
y = 7.6
Writing a compound inequality to show the possible length
7.6 ≤ x ≤ 9
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