Answer:
2m+3r-2x-2y
Step-by-step explanation:
2m+3r=2m+3r
-2×x=-2x
-2×y=-2y
answer=2m+3r-2x-2y
Do rigid transformations make congruent figures?
Congruent figures are produced through rigid transformations. Congruent figures may always be connected to stiff transformations even though you could conceive of them as forms that "look precisely the same."
What is rigid transformation?Separation between each pair of points of a geometric object is maintained during exact modification of the object. In other words, exact transformations preserve the size and shape of objects. For example, a triangle rigid transformation preserves the triangle's angles and lengths. Imagine the distortion of a rigid shape similar to that of cardboard. The shape does not change even if it is slid left and right, rotated, and mirrored.
It was the opposite when I made a mold with putty. After that, you can twist and stretch things. However, these conversions are not exact. Stretching the shape changes the distance between each pair of points.
We may produce congruent shapes by applying rotations, reflections, and translations—three types of transformations. In reality, all congruent shape pairings may be matched to one another by combining one or more of these three transformations.
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Which expression is equivalent to 5y-3?
1/125y3
1/5y3
5/y3
125/y3
How do you graph 3 x?
The graph of y=3x is a straight line, it can be graphed by taking two points on the line.
What is a graph?
A diagram that depicts the relationship between two variables, usually measured along opposite axes in a pair, is used.
The equation we have is y=3x.
Since it is a linear equation, the graph will be a straight line.
A Line can be plotted with two points.
The two points on line y=3x are (0,0) and (1,3)
Because when x=0, y=0 and when x=1, y=3.
We have to plot the two points on the graph and join the points and extend the line segment.
This way we can graph y=3x.
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What are the 4 types of triangle?
Answer:
Scalene, isosceles and equilateral triangle are the types of triangles
Step-by-step explanation:
They differ from each other based on their side-length. If all the three sides are different in length, then its scalene triangle. If any two sides are equal in length, then it is an isosceles triangle.
How can we prove that at least one duplicate number must exist in Nums?
It is a straightforward application of the pigeonhole principle to demonstrate that there must be at least one duplication in nums. Here, each possible number in nums is a "pigeon," and each specific place where a pigeon can occur is a "pigeonhole."
How to determine whether there is at least one duplicate number in Nums:
Simple Method: The goal is to use nested loops and determine whether or not each element appears in the array more than once for each element.
If it's there, put it in a hash map. If not, keep examining the other components.Duplicate data might occasionally be helpful, but it can also make it more difficult to interpret your data.In order to identify and highlight duplicate data, use conditional formatting.In this manner, you can examine the duplicates and choose whether or not to delete them.Use the Remove Duplicates feature to permanently eliminate the duplicate data. To avoid inadvertently losing any information, it is a good idea to copy the original data to another worksheet before deleting the duplicates.Choose the cell range with the duplicate values you want to get rid of.then select Data > Remove Duplicates Check or uncheck the columns where you want to eliminate duplicates under Columns.Learn more about duplicate number Visit: brainly.com/question/15323323
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What is the value of x³ 3y²x² if x 3?
The value of x³ 3y²x² is 27y² when x is 3. This is because x³ is equal to 27, and multiplying it by 3y² and x² gives 27y².
The value of x³ 3y²x² when x is 3 can be calculated by first understanding how x³ is equal to 27. This is because when something is cubed, the value is three times itself. For example, if x is 2, then x³ is 2 x 2 x 2, which is 8. If x is 3, then x³ is 3 x 3 x 3, which is 27. Once this is understood, the value of x³ 3y²x² when x is 3 can be calculated by multiplying 27 (the value of x³ when x is 3) by 3y² and x². In this case, x² is also equal to 3, so the equation becomes 27 x 3y² x 3, which is equal to 27y². This means that the value of x³ 3y²x² when x is 3 is 27y².
x³ = 3 x 3 x 3 = 27
x³ 3y²x² = 27 x 3y² x 3 = 27y²
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You can work no more than 60 hours each week at your two jobs. Dog walking pays $7 per hour and your sales job at Computers & More, Inc. pays $12 per hour. You need to earn at least $450 each week to pay your bills.
Your friend solves the system of inequalities and tells you that a possible solution is
A possible solution to the system of inequalities is given as follows:
(20,35).
Which means that you work 20 hours dog walking and 35 hours on the sales job at Computers & More, Inc.
How to model the system of inequalities?The variables of the system of inequalities are given as follows:
Variable x: number of hours dog walking.Variable y: number of hours on the sales job at Computers & More, Inc.The number of hours is a countable amount, hence it cannot assume negative values, and the first two conditions are given as follows:
x ≥ 0.y ≥ 0.You can work no more than 60 hours each week at your two jobs, hence:
x + y ≤ 60.
You need to earn at least $450 each week to pay your bills, hence, considering the ratios:
7x + 12y ≥ 450.
Then the solution is obtained from the shaded region of the graph given at the end of the answer.
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| 3m-n | if m=-8, n=4, and p=-12
Answer:
-28
Step-by-step explanation:
need this done quickly pls
The simplest form of expression [tex]125\frac{2}{3}[/tex] is [tex]25[/tex].
Definition of exponent- Exponent means a quantity, describing the power to which base number is raised. In other words , Exponent refers to the number of times a number is used in a multiplication. The 4 types of exponents are: positive, negative, zero, and rational. Positive exponents tell you how many times to multiply a base by itself. Exponent is defined as the method of expressing large numbers in terms of powers.
Given :- expression: [tex]125^{\frac{2}{3} }[/tex]
Explanation:-In order to solve this expression , we use properties of exponents.
Hence , using the property - [tex]x^{m} x^{n}[/tex][tex]=x^{mn}[/tex]
and rewriting 125 as cube of 5
⇒[tex]125=5^{3}[/tex]
⇒[tex]5^({3)\frac{2}{3} }[/tex]
⇒[tex]5^{2}[/tex]
⇒[tex]25[/tex]
So, finally the simplest form of the given expression is 25.
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The distance between Eagle and lake and swallow lake on a mob is 9 cm the scale of the map is 14 m equals KM what is the actual distance between Eagle Lake and swallow lake?
The actual distance between Eagle Lake and swallow lake is 9/1400 km.
What is distance?
Distance is the measure of the amount of space between two points or objects. It can be measured in a variety of ways, including miles, kilometers, feet, and meters. Distance is an important concept in physics, mathematics, and many other scientific fields. In addition, distance is a key factor when considering the speed of objects or events. Distance can also be used to measure the time it takes for an object or event to travel from one point to another. Distance is a fundamental concept in understanding the physical universe, and it is essential for navigation, navigation systems, and communication.
The scale of the map is given as,
14 m = 1 Km
We know that, 1 m = 100 cm
So, 14 × 100 cm = 1 Km
1 cm = 1/1400 Km
So, 9 cm = 9 × 1/1400 km
= 9/1400 km.
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In the Diagram of parallelogram HIJK below, the diagonals HJ and IK are perpendicular, as shown. If HJ is 10 inches and IK is 24 inches long, then why must HK be 13 iches long?
The measure of the section HK of the parallelogram will be 13 inches.
What is a parallelogram?A parallelogram is a straightforward quadrilateral with two parallel sides. A parallelogram's opposite or facing sides are of equal length, and its opposite angles are of equal measure.
A diagonal in geometry is a line segment that connects two vertices of a polygon or polyhedron that are not on the same edge. Informally, any sloping line is referred to as a diagonal.
The length of the HK will be calculated as,
HK = √ ( 12² + 5²)
HK = √ ( 144 + 25 )
HK = √ (169 )
HK = 13 inches
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What is the equation of the line in slope intercept form calculator?
Slope-intercept form is often expressed using the formula y = mx + b, where m denotes the line's slope and b denotes the y-value of the line's y-intercept.
Define the slope of a line?The ratio of the change in the y coordinate to the slope of a line in mathematicsThe formula for the change in coordinate with respect to the changeAny three numbers that are proportionate to the line's direction cosines can be used to represent a line's direction ratios. In addition to direction ratios, direction numbers are also used.The steepness and direction of a line are frequently indicated by its slope.It is necessary to compute the ratio of the coordinate differences between the two points that make up the line. The result is a value that is determined by the line's slope. When compared to its, it exhibits.To learn more about Slope of Line refers to:
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Is 4096 a perfect cube if yes then what is the number whose cube is 4096?
Yes, 4096 is a perfect cube. The number whose cube is 4096 is 16. To find the cube root of a number, you can use the following formula:
cube root of a number = ∛a
For example, to find the cube root of 4096, you would calculate:
∛4096 = 16
This means that 16 is the number whose cube is 4096. You can verify this by calculating 16 x 16 x 16, which is equal to 4096.
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What is the equation in the slope intercept form of a line passing through the given points 1 and 1 and 3 and 7?
The equation of line in slope intercept form of line passing through the points (1,1) and (3,7) is y = 3x - 2 .
The Slope Intercept form of equation of line is denoted as y = mx + c , where m is the slope and c is y intercept .
the required line passes through the points (1,1) and (3,7) ,
So , the slope(m) is = (7-1)/(3-1) = 6/2 = 3 .
putting the value in slope intercept form , we get ;
1 = 3(1) + c ;
1 = 3 + c ;
c = 1 - 3 ;
c = -2 .
the equation of line will become ⇒ y = 3x - 2 .
Therefore , the equation of the line in slope intercept form is y = 3x - 2 .
The given question is incomplete , the complete question is
What is the equation in the slope intercept form of a line passing through the given points (1,1) and (3,7) ?
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Are all equilateral triangles congruent Yes No?
All equilateral triangles are NOT congruent.
Only those equilateral triangles whose sides have the same length will be congruent.
Those whose sides have different lengths will not be congruent.
By the criteria of congruence:Side Angle Side: Two triangles are congruent if two sides of one triangle have the same measure as the two sides of the other, the angle being equilateral if they have the same (60º)Side Side Side: Two triangles are congruent if all three sides of one have the same length as the other.Angle Side Angle: Two triangles are congruent if two of their angles and the side between the two angles are equal in the other triangle.Is x 3 a factor of the polynomial x³ 3x² 4x 12?
Yes, x +3 is a factor of polynomial X³ +3x² -4x -12
Polynomial:
In mathematics, a polynomial is an expression which includes indeterminates (also called variables) and coefficients, that entails handiest the operations of addition, subtraction, multiplication, and effective-integer powers of variables. An instance of a polynomial of a single indeterminate x is x² − 4x + 7. An example with 3 indeterminates is
x³ + 2xyz² − yz + 1.
Polynomials appear in lots of areas of arithmetic and technological know-how. For example, they're used to form polynomial equations, which encode a wide range of issues, from elementary word troubles to complicated clinical issues; they may be used to outline polynomial functions, which seem in settings ranging from basic chemistry and physics to economics and social science; they're utilized in calculus and numerical analysis to approximate other features. In advanced mathematics, polynomials are used to construct polynomial rings and algebraic varieties, which can be primary concepts in algebra and algebraic geometry.
Factor out the greatest common factor from each group.
Group the first two terms and the last two terms.
(x³ + 3x²)− 4x− 12
Factor out the greatest common factor (GCF) from each group.
x²(x+3)−4(x+3)
Factor the polynomial by factoring out the greatest common factor,
x+3.(x+3)(x2−4)
Rewrite
4 as 2².
(x+3)(x²−2²)
Since both terms are perfect squares, factor using the difference of squares formula,
a²−b²=(a+ b)(a−b)
where
a = x and b = 2.
(x+3)[(x+2)(x-2)]
Remove unnecessary parentheses.
(x+3)(x+2)(x−2)
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eric is randomly drawing cards from a deck of 52. he first draws a red card, places it back in the deck, shuffles the deck, and then draws another card. what is the probability of drawing a red card, placing it back in the deck, and drawing another red card? answer choices are in the form of a percentage, rounded to the nearest whole number. 4% 22% 25% 13% save
b. The probability of drawing a red card, placing it back in the deck, and drawing another red card is approximately 22%.
This is because there are 26 red cards in a standard deck of 52 cards, out of which half (13) are red. So, when Eric draws a red card and puts it back in the deck, the probability of drawing another red card is 13/52, which is approximately 25%.
However, since the deck is shuffled after the first draw, this probability is slightly reduced to 22%. Thus, the probability of drawing a red card, placing it back in the deck, and drawing another red card is approximately 22%.
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What is the nature of the roots of the quadratic equation if the value of its discriminant is negative?
when the discriminant is negative, that is, less than 0, then the roots are imaginary.
The discriminant in a quadratic equation is equal to:
b^2 - 4*a*c, where b is the coefficient of the degree 1 variable, a is the coefficient of the degree 2 variable and c is the constant term. There can be 3 possibilities regarding the discriminant of a quadratic equation:
Case 1: When b^2 - 4*a*c = 0
In this case, the roots of the equation are equal and real.
Case 2: When b^2 - 4*a*c > 0
In this case, the roots of the equation are real.
Case 3: When b^2 - 4*a*c < 0
In this case, the roots of the equation are imaginary.
So, when the discriminant is negative, that is, less than 0, then the roots are imaginary.
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What additional information do you need to prove ∆ ABC ≅ ∆ def by the ASA postulate?
There are some postulates, such as Side-Side-Side, Side-Angle-Side, Angle-Side-Angle, and Angle-Angle-Side, that can be applied to demonstrate the congruence of triangles.
The Angle-Side-Angle (ASA) postulate asserts that two triangles are congruent if two angles and the included side of one triangle are congruent with two angles and the included side of another triangle.
The basic components, primarily the three angles as well as the three sides of a triangle, must be equal to the corresponding angles and sides of the other triangle for two triangles to be congruent.
To demonstrate that the triangle ABC is congruent, we must show that two of its angles and one of its sides are congruent.
If the lengths of the matching sides and angles of two triangles match, the triangles are said to be congruent. In maths, congruence relates to the similarity of two figures in terms of their size and shape. The mirror image of one shape is the same as the other if two shapes are congruent.
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Can someone help me with Questions 1 and 2 on this assignment? I am not really understanding them. I would deeply appreciate it!
Add 5 to 2 = 2 will make 7 = 7 a true statement and adding 5 to 2 ≠ 3 to make 7 ≠ 8 will make a true statement.
What is a number system?The number system is a way to represent or express numbers.
A decimal number is a very common number that we use frequently.
Any of the multiple sets of symbols and the guidelines for utilizing them to represent numbers are included in the Number System.
(1)
As per the given,
2 = 2
Add 5 on both sides of the above equation,
2 + 5 = 2 + 5
7 = 7 (True)
(2)
As per the given
2 ≠ 3
Add 5 on both sides of the above equation,
2 + 5 ≠ 3 + 5
7 ≠ 8 (True)
Hence "It is correct that if you add 5 to 2 = 2, you will get 7 = 7, and if you add 5 to 2 ≠ 3, you will get 7 ≠ 8".
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easy points, please answer a proper answer though
For an investment of $26,245, a quarterly statement reports that the account balance is $26,192. The statement also reports that for the same quarter, the rate of return on the investment was - 0.02%. Given the information regarding the investment's quarterly activity, is the reported rate of return reasonable? Use complete sentences to explain your answer.
The return rate is unreasonably low. This is so since the investment is $26,245 and the account balance is $26,292 according to the quarterly statement. It is obvious that the investment has increased. Furthermore, the actual rate of return is 0.18% (($26,292-$26,244)/ $26,292)*100).
What does return on investment mean?
The percentage change in an investment's value is represented by the annual rate of return. For instance, if you estimate a 10% annual rate of return, you're anticipating that your investment's value would rise by 10% annually.
What exactly does compounding mean?
Compounding is the method through which interest is added to both the principle balance already in place and the interest that has already been paid. Thus, compounding can be thought of as interest on interest, with the result that returns on interest are magnified over time, or the so-called "magic of compounding."
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A rectangular frame is placed around a water color painting. the width of the frame is consistent around the painting. the dimensions of the painting are 24 inches by 18 inches. what is the width of the frame if the area of the frame is 400 square inches?
If the frame has a 400 square inch surface area, its breadth is 5 inches.
Let's call the width of the frame w.
The total width of the painting and the frame is 24 inches + 2w inches since there is a frame of width w on both sides of the painting.
Similarly, the total height of the painting and the frame is 18 inches + 2w inches, since there is a frame of width w on both the top and bottom of the painting.
The area of the frame is the difference between the area of the rectangular frame and the area of the painting. The area of the rectangular frame is (24 inches + 2w inches) * (18 inches + 2w inches) = 432 inches + 72w inches + 36w inches + 4w^2 inches. The area of the painting is 24 inches * 18 inches = 432 inches.
Therefore, the area of the frame is 432 inches + 72w inches + 36w inches + 4w^2 inches - 432 inches
= 72w inches + 36w inches + [tex]4w^2[/tex] inches = 400 inches.
Combining like terms, we get [tex]4w^2[/tex] inches + 108w inches = 400 inches.
Dividing both sides by 4, we get [tex]4w^2[/tex] inches + 27w inches = 100 inches.
We can use the quadratic formula to solve this equation in the quadratic form:
w = [tex]\frac{(-b +/- sqrt(b^2 - 4ac))}{2a}[/tex]
= [tex]\frac{(-27 +/- sqrt(27^2 - 4 * 1 * 100))}{2*1} \\[/tex]
= [tex]\frac{(-27 +/- sqrt(729 - 400))}{2}[/tex]
= [tex]\frac{(-27 +/- sqrt(329)) }{2}[/tex]
= [tex]\frac{(-27 +/- sqrt(289))}{2}[/tex]
The solutions are w =[tex]\frac{ (-27 + 17)}{2}[/tex] = -5 inches and w = [tex]\frac{(-27 - 17)}{2}[/tex] = -22 inches.
Since the width of the frame must be positive, the correct solution is w = -5 inches. The frame is five inches wide.
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What is the quotient t?
x-1 is the quotient when [tex]x^2-2x+1[/tex] is divided by x-1
if we equate x-1=0
=> x=1
after putting the value of x=1 in the equation [tex]x^2-2x+1[/tex] to find the remainder.
so the value of [tex]x^2-2x+1[/tex] when x=1
=>1 -2*1 +1
=>0
so the value is 0 which means that x-1 completely divides the given equation [tex]x^2-2x+1[/tex]
since the given equation is quadratic equation and one factor is linear so other factor which is quotient also need to be linear.
let the quotient after division is ax+b
and according to rule of division
[tex]x^2-2x+1[/tex] = (x-1)*(ax+b)
as remainder is 0
so (x-1)*(ax+b) = a[tex]x^2[/tex] +(b-a)x -b
comparing a[tex]x^2[/tex] +(b-a)x -b with [tex]x^2-2x+1[/tex]
we observe that a=1 ,b=-1
so the quotient of the above divsion is x-1
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Complete question:
what is the quotient when [tex]x^2-2x+1[/tex] is divided by x-1
How do you compare growth rate of a function?
Step 1: Given the functions f(x) and g(x) , compute the limit limx→∞f(x)g(x) lim x → ∞ f ( x ) g ( x ) .
Step 2: If the limit in Step 1 is a finite constant a≠0 a ≠ 0 , then the growth rate of f(x) is a times the growth rate of g(x) at sufficiently large x .
Now, According to the question:
Steps on How to Compare the Rates of Change of Two Functions Using Limits
Step 1: Given the functions f(x) and g(x), compute the limit
limx→∞f(x)/g(x).
Step 2: If the limit in Step 1 is a finite constant a≠0, then the growth rate of f(x) is a times the growth rate of g(x) at sufficiently large x. If the limit in Step 1 is ∞, then the growth rate of f(x) is greater than the growth rate of g(x). If the limit in Step 1 is 0, then the growth rate of g(x) is greater than the growth rate of f(x).
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Why is the square root of 4 only 2 and not 2?
The fact that four identical unit objects arranged in a square formation would produce a square with length 2, rather than length -2, provides the logical basis for the fact that the "principal" square root of 4 is 2 rather than -2.
What is the square root?
The factor that can be multiplied by itself to obtain a given number is known as the square root. The square root is represented by The opposite of squaring a number is finding its square root.
According to the given question:
The value of root 4 exactly corresponds to 2. However, we can say that there are always two roots for any given number, and that the roots can be either positive or negative. Consequently, the value of root 4 is 2, or +2 and -2 (positive 2 and negative 2).
Hence ,the square root of 4 only 2 and not - 2.
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How do you solve for x and y in two equations?
We can solve for x and y in two equations by using the Elimination method for the simultaneous linear equations.
The Elimination approach results in the reduction of one problem to a single-variable equation when two simultaneous linear equations are solved. Following this, the answer is the same as when one line was vertical or parallel. The Gaussian elimination method is the name given to this approach.
We can understand the above method through an example:
Equation 1: 4x + 6y = 8
Equation 2: 3x + 4y = 5
Step 1: In order to ensure that the two equations have the same leading coefficient, multiply each equation by a reasonable value. Equation 1 may be easily solved by multiplying it by 3, the x coefficient from Equation 2, and Equation 2 by 4, the x coefficient from Equation 1.
Therefore the equations become,
12x + 18y = 24
12x + 16y = 10
Step 2: Subtract equation 2 from equation 1
We get 2y = 14
From the above equation, we get the value of y as 7
Step 3: We will substitute the value of y in one of the initial equations
Substituting the value of y in equation (1) 4x + 6y = 8
4x + 6(7) = 8
4x + 42 = 8
4x = 34
x = [tex]\frac{34}{4}[/tex]
x = [tex]\frac{17}{2}[/tex]
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Henrik buys 40 collectible cards per month. Kharif sells 20 cards from his collection of 180 each month. When will Henrik have more cards than Kharif? Show your work.
Henrik will exceed Kharif in the number of cards in the 4th month because in the 4th month Henrik has a total of 160 cards and Kharif has only 100 cards left.
What are arithmetic Operations?The four fundamental operations of arithmetic are addition, subtraction, multiplication, and division of two or even more items.
Included in them is the study of integers, especially the order of operations, which is important for all other areas of mathematics, notably algebra, data management, and geometry.
As per the data given in the question,
Total cards brought by Henrik per month = 40
Total cards sold by Kharif per month = 20
Total collection of Cards of Kharif = 180
Then,
Let's check after 3 months how many cards both have right now.
Henrik = 3 × 40 = 120
Kharif = 180 - (3 × 20) = 120
It means that after 3 months both are having the same number of cards.
Now, let's check for 4th month,
Henrik = 4 × 40 = 160
Kharif = 180 - (4 × 20) = 100
It means in the fourth month, Henrik will have more cards than Kharif.
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How do you describe the nature of the roots of 3x² 4x 5 0?
The nature of the roots of the given quadratic equation 3x²+ 4x - 5 = 0 are real and distinct.
As given in the question,
Given quadratic equation is written as:
3x²+ 4x - 5 = 0
Standard form of quadratic equation is :
ax² + bx + c = 0
And nature of the roots depends on the value of discriminant 'D' .
D = b² - 4ac
here b = 4 , a = 3 , and c = -5
Discriminant 'D' = 4² - 4(3)(-5)
⇒ D = 16 + 60
⇒ D = 76 > 0
When the value of discriminant 'D' > 0 then nature of the roots are real and distinct.
Therefore, the nature of the roots of the given equation is real and distinct.
The above question is incomplete ,the complete question is :
How do you describe the nature of the roots of 3x²+ 4x - 5 = 0?
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What is the solution to the system of equations y =- 3x 2 5x 2y 15?
The solution for the system of equations is (-19,55).
As given the equations in the question
y = –3x – 2
Simplify the above
y + 3x = -2
5x + 2y = 15
Multiply y + 3x = -2 by 2 and subtracted from 5x + 2y = 15.
2y - 2y + 5x -6x = 15 + 4
-x = 19
x = -19
Putting the value of x in the equation y + 3x = -2.
y + 3 × - 19 = -2
y - 57 = -2
y = -2 + 57
y = 55
Therefore the solution for a system of equations is (-19,55).
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PLS HELP FAST I WILL MARK THE FIRST BRAINLIEST
In science class, Alex estimates the volume of a sample to be 42 mL. The actual volume of the sample is 38 mL. Find the percent error of Alex’s estimate. Round your answer to the nearest tenth.
Group of answer choices
1.9%
2.1%
9.5%
10.5%
SHOW YOUR WORK PLS
The percent error of Alex’s estimate will be 10.5% which is the correct answer would be an option (D).
How to calculate the percent error?To find the percent error of Alex's estimate, we need to first calculate the difference between the estimated value and the actual value.
In this case, the difference is 42 mL - 38 mL = 4 mL.
Now we can divide the difference by the actual value and multiply by 100% to find the percent error.
As per the given question, the percent error is :
⇒ (4 mL / 38 mL) x 100%
⇒ 10.5%.
Therefore, the answer is 10.5%.
Learn more about the percent error here :
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