Geometric shapes that are identical in size and shape are known as congruent figures. Congruent figures are those in which you may use a series of translations, rotations, and/or reflections to turn one figure into another.
What is rigid transformations?The separation between each pair of the geometric object's points is preserved during a rigorous change of the object. In other words, a rigid transformation maintains the object's size and shape. For instance, the rigid transformation of a triangle retains the angles and lengths of the triangle. Imagine a stiff shape distortion, similar to a cardboard shape.
There are isometric rotations, reflections, and translations. Accordingly, the size of the figure is unaffected by these adjustments. The figures are consistent if neither the size nor the form of the figure is altered.
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The area of a rectangle is 56.96 m²
If the length is 16, what is the width and perimeter?
Answer:
width is 3.56
Step-by-step explanation:
Area is = width x length
so Area/length
so 56.96/16=3.56
The width of the rectangle is 3.56 m and the perimeter is 39.12 m.
To find the width of the rectangle,
We need to use the formula for the area of a rectangle, which is:
Area = Length x Width
We know that the area of the rectangle is 56.96 m², and the length is 16 m. So,
We can substitute these values into the formula and solve for the width:
56.96 m² = 16 m x Width
Width = 56.96 m² / 16 m
Width = 3.56 m
Therefore, the width of the rectangle is 3.56 m.
To find the perimeter of the rectangle,
We need to use the formula:
Perimeter = 2 x Length + 2 x Width
We know that the length is 16 m and the width is 3.56 m,
So we can substitute these values into the formula and solve for the perimeter:
Perimeter = 2 x 16 m + 2 x 3.56 m
Perimeter = 32 m + 7.12 m
Perimeter = 39.12 m
Therefore, the perimeter of the rectangle is 39.12 m.
In conclusion, the width of the rectangle is 3.56 m and the perimeter is 39.12 m when the area is 56.96 m² and the length is 16 m.
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bowl a contains 2 red chips; bowl b contains two white chips and 1 red chip, and bowl c contains 1 red chip and 1 white chip. a bowl is selected at random, and one chip is taken at random from that bowl. if the selected chip is white, what is the probability that the chip belongs to bowl c?
Therefore the probability that the chip belongs to bowl c is 1/3.
What is the process of probability?Probabilities can be expressed as proportions with a 0–1 range or as percentages with a 0%–100% range. If an event has a probability of 1, it is very certain to occur; if it has a probability of 0, it has no chance of occurring. There are 45 chances out of 100 that an event will occur when its probability is 0.45 (45%).
Here,
A : 2 Red chips
B : 2 White chips
C: One Red and one White chip
P(selecting any bowl) = 1/3
1) We have to find P(W).
The selected chip can be white if it is either selected from Bowl B or Bowl C.
Symbolically this can be written as
P(W) = P(Bowl B and White chips) + P(Bowl A and White chips)
P(W) = [(1/3) × 1/1)] + [(1/3) × (1/2)]
P(W) = (1/3) + (1/6)
P(W) = 1/2
P(W) = 0.5
2) There is only one bowl with both of white and red chips and that bowl is bowl C. So it is possible the other chips in the bowl to red only if it has been selected from Bowl C.
So ,We need to find P(Bowl C | W).
P(Bowl C | W) = P(Bowl C and W)/P(W)
P(Bowl C | W) = (1/3) × (1/2)/(1/2)
P(Bowl C | W) = 1/3
Hence, the required probability is 1/3.
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What is the mode of 2 2 2 3 3 3 4 4 4 5 5 5 6 6 6?
The mode for a particular set of observations is 2,3,4,5,6 since it occurs the majority of the time.
What is mode?The mode formula is described in statistics as the formula for calculating the mode of a given collection of data. The value that occurs most frequently in a particular set is referred to as the mode, and the mode differs across grouped and ungrouped data sets. The mode may be calculated quite easily. Put all of the numbers in a given set in order, either lowest to highest or highest to lowest, and then count how many times each number appears in the set. The mode is the one that appears the most.
Here,
given set of observation:
2 2 2 3 3 3 4 4 4 5 5 5 6 6 6
Mode is the number which occurs the highest time.
So here 2,3,4,5,6 occurs the highest times(3 times).
So,2,3,4,5,6 is the mode.
The mode for given set of observation is 2,3,4,5,6 as it occurs most time.
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What is parallel to Y =- 5x 4?
The system of equations of line parallel to y = -5x + 4 is y = -5x + c where c is any arbitrary value of y-intercept.
The linear equation y = -5x + 4 is a straight line with slope -5 and y-intercept 4.
The slope of parallel lines are equal. So any line with slope -5 is parallel to the line y = -5x + 4. So the equation of a line with slope -5 is
y = -5x + c
where c is a constant
c represent arbitrary value of y-intercept.
For example y = -5x + 2 is a straight line parallel to y = -5x + 4 but having value of y-intercept equal to 2.
--The question is incomplete, answering to the question below--
"What is parallel to y = -5x + 4?"
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In 2005, 13.1 out of every 50 employees at a company were women. If there are 46,043 total company employees, estimate the number of women.
What are the three 3 semantics models of parameter passing for subprograms?
The three semantics models of parameter passing for subprograms are: in mode, out mode, and inout mode
In this question we need to describe the three semantics models of parameter passing for subprograms.
The three semantics models of parameter passing for subprograms are:
1) in mode: They can receive data from corresponding actual parameters.
2) out mode: They can transmit data to the actual parameter.
3) inout mode: They can do both.
There are two conceptual models of how data transfers take places in parameter transmission: either an actual value is copied (to the caller, to the callee, or both ways), or an access path is transmitted.
Generally, the access path is a simple pointer or reference.
Therefore, in mode, out mode, and inout mode are 3 semantics models of parameter passing for subprograms
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How do you find the inverse of two variables?
To find the inverse of a function you just have to switch the x and the y and then solve for y.
Inverse Function
An inverse function or an anti function is defined as a function, which can reverse into another function. In simple words, if any function “f” takes x to y then, the inverse of “f” will take y to x. If the function is denoted by 'f' or 'F', then the inverse function is denoted by f^-1 or F^-1.
The inverse function returns the original value for which a function gave the output.
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What are the 7 whole numbers?
Answer:
There are an infinte amount of whole numbers
Step-by-step explanation:
7 examples are, 0, 3, 7 , 8 ,9 14, 39
Which expression can be used to find the sum of the polynomials 9 3x² 8x² 4x 5?
The expression which represents the sum of polynomials (9-3x²) and (-8x²+4x+5) is -11x² + 4x + 14
What is polynomial equation?
A polynomial equation is an algebraic equation that consists of variables and coefficients, which are often real numbers, and exponents which are non-negative integers. Polynomial equations can have one or more terms, and can involve addition, subtraction, multiplication, division, and exponentiation.
According to the given question:
The sum of polynomials can be calculated by combining like terms where there are multiple of the same variable.
= (9-3x²) + (-8x²+4x+5)
= 9 - 3x² - 8x² + 4x + 5
= -11x² + 4x + 14
Therefore, the expression which represents the sum of polynomials (9-3x²) and (-8x²+4x+5) is -11x² + 4x + 14
Complete question:
Which expression can be used to find the sum of the polynomials?
(9-3x²) and (-8x²+4x+5)
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my friend vreel purchased 22 rews and corazs for about $96 rews were $8 each and corazs were $3 each. write a systems of equations in standard form to model the relation ship between vreels rews (x) and conazs (y)
Answer:
Step-by-step explanation:
To model the relationship between Vreel's rews and corazs, we can set up a system of equations in standard form.
The standard form of a linear equation is Ax + By = C, where A, B, and C are constants and x and y are variables.
We know that Vreel purchased a total of 22 rews and corazs, and that the rews cost $8 each and the corazs cost $3 each. We can use this information to set up the following two equations:
The first equation represents the total cost of the rews: 8x + 0y = 96
The second equation represents the total number of rews and corazs that Vreel purchased: 1x + 1y = 22
Together, these two equations form a system of equations that can be used to model the relationship between Vreel's rews and corazs.
I hope this helps! Let me know if you have any other questions.
100 POINTS HELP PLEASE WILL GIVE BRAINLIEST
Answer:
D. Increase in assets
Step-by-step explanation:
The entry "Cash 750,000" is listed as a debit in the T-account because it is an increase in assets. In double-entry bookkeeping, a debit is used to record an increase in assets and a credit is used to record a decrease in assets. In this case, the business received cash in exchange for the airplane, which represents an increase in the business's assets. So the Cash account is debited and the Airplane account is credited.
you walk 45 m at an angle of 25 degrees s of e. then you walk 30 m north. what is the angle of the resultant vector?
So the angle of the resultant vector is approximately 53.13 degrees.
To find the angle of the resultant vector, you can use trigonometry to break the two vectors into their x and y components and then use the arctangent function to find the angle.
First, let's find the x and y components of the first vector (the one that travels 45 meters at an angle of 25 degrees south of east). To do this, we can use the trigonometric functions sine and cosine. The x component is equal to the distance traveled (45 meters) times the cosine of the angle (25 degrees), and the y component is equal to the distance traveled times the sine of the angle.
In this case, the x component of the first vector is 45 meters * cos(25 degrees) = 39.74 meters. The y component of the first vector is 45 meters * sin(25 degrees) = 22.36 meters.
Now let's find the x and y components of the second vector (the one that travels 30 meters north). The x component of this vector is 0 meters (since it doesn't move in the east-west direction), and the y component is 30 meters (since it travels 30 meters in the north direction).
To find the resultant vector, we can add the x components and y components of the two vectors. The x component of the resultant vector is 39.74 meters + 0 meters = 39.74 meters, and the y component of the resultant vector is 22.36 meters + 30 meters = 52.36 meters.
To find the angle of the resultant vector, we can use the arctangent function (also known as the inverse tangent function). The angle is equal to the arctangent of the y component divided by the x component.
In this case, the angle is equal to arctan(52.36 meters / 39.74 meters) = arctan(1.318) = 53.13 degrees.
So the angle of the resultant vector is approximately 53.13 degrees.
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Find the x and y components of the initial vector first (the one that travels 45 meters at an angle of 25 degrees south of east). The trigonometric functions sine and cosine can be used to do this. The y component is equal to the distance traveled times the sine of the angle, and the x component is equal to the distance traveled times the cosine of the angle, or 45 meters times the cosine of the angle, or 25 degrees.
In this case, the x component of the first vector is 45 meters * cos(25 degrees) = 39.74 meters. The y component of the first vector is 45 meters * sin(25 degrees) = 22.36 meters.
The two vectors' x and y components can be added to determine the resultant vector. The resultant vector has two components: an x component of 39.74 meters plus 0 meters equals 39.74 meters, and a y component of 22.36 meters plus 30 meters equals 52.36 meters.
The arctangent function can be used to determine the angle of the resulting vector (also known as the inverse tangent function). The angle is determined by dividing the y component's arctangent by its x component.
In this case, the angle is equal to arctan(52.36 meters / 39.74 meters) = arctan(1.318) = 53.13 degrees.
So the angle of the resultant vector is approximately 53.13 degrees.
what is the greatest common factor for 32 and 81
(HURRYYY))
Answer:
9 :)))))))))))
a normal distribution of scores has a standard deviation of 10. find the z-score corresponding to a score that is 30 points below the mean.
The z-score 30 points below the mean is -3
The normal distribution of scores has a standard deviation(σ) of 10
Below the mean is (X-μ)=-30
The mean (average) of a data set is found by adding all numbers in the data set and then dividing by the number of values in the set.
Z=(X-μ)/σ
Z=-30/10
Z=-3
Therefore, the z-score is -3.
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How do you solve an inequality with 2 answers?
Answer:
Step-by-step explanation:
Example:
If you have the inequality 3<(x/9)+7
Begin with subtraction by subtracting 7 from both sides, rather than beginning with the parentheses x/9.
Do all processes to both sides of the inequality until you have solved for x.
Example: As mentioned in the previous step, you would begin by subtracting 7 from both sides.
So 3<(x/9)+7 becomes, -4<x/9
Now you would multiply both sides by 9 because the fraction x/9 is the same as x divided by 9, and the opposite of division is of course multiplication.
This process leaves you with the solution, -36<x, so x is greater than -36.
Remember that if your problem requires you to multiply or divide by a negative number, then you need to flip the inequality sign when you do so.
For example: If instead of multiplying by 9 in the previous problem you had to multiply by -9, you would get 36>x rather than 36<x.
Is an asymptote a continuous function?
An asymptote is a line that a curve approaches but never touches, so it is not part of the curve itself. As a result, an asymptote is not a function. However, the curve that approaches an asymptote may or may not be a continuous function.
A function is continuous if it is defined for all values in its domain and there are no breaks or jumps in the graph of the function.
For example, consider the function f(x) = 1/x. This function has a horizontal asymptote at y = 0, but it is not continuous at x = 0 because the value of the function is undefined at this point (division by zero is not allowed).
On the other hand, consider the function f(x) = ². This function has no asymptotes and is continuous for all values of x.
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What is the nature of the roots of x² − 3x 4 0?
The nature of the roots of the given equation x^2 - 3x - 4 = 0 is real and unequal.
The general form of a quadratic equation is ax^2 + bx +c = 0.
Comparing the given equation x^2 - 3x - 4 = 0 with the general form of quadratic equations, we get that:
a = 1, b = -3 and c = -4
If b^2 - 4ac > 0, then we say that the nature of the roots of the equation is real and unequal.
Therefore, b^2 - 4ac = (-3) ^ 2 - 4 x 1 x (-4) = 25 >0
Hence, we conclude that the nature of the roots of the given equation is real and unequal.
The question is incomplete, the complete question is:
What is the nature of the roots of x² − 3x - 4 = 0?
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Describe the graph of the proportional relationship represented by the equation y = 7.5x.
The graph of the equation y = 7.5x shows the proportional relationship.
What is an equation?An equation is a combination of different variables, in which two mathematical expressions are equal to each other.
The given equation is,
y = 7.5x.
The graph of the equation y = 7.5x is shown below.
At x = 1, the value of y = 7.5,
At x = 2, the value of y = 7.5 x 2 = 15
At x = 3, the value of y = 7.5 x 3 = 22.5
And so on.
The value of y multiplied by 7.5 by increasing value of x by 1.
Thus, the graph of the equation y = 7.5x shows the proportional relationship.
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Which of the following is a solution of the equation 2x y 10 *?
The solution of the given equation 2x + y = 10 is equal to option b. x = 2 and y = 6.
As given in the question,
Given equation is equal to :
2x + y = 10
Simplify and Check which given option represent the solution of the equation :
a. x = 9
2(9) + y = 10
⇒y = -8
Incorrect option.
b. x = 2
2(2) + y = 10
⇒y = 6
Correct option.
c. x = 1
2(1) + y =10
⇒y = 8
Incorrect option
d. x =4
2(4) + y = 10
⇒y = 2
Incorrect option
Therefore, for the given equation 2x + y = 10 , option b . x = 2 and y = 6 is the correct answer.
The given question is incomplete , the complete question is :
Which of the following is a solution of the equation 2x + y = 10?
a. x = 9 and y = 3
b. x = 2 and y = 6
c. x = 1 and y = 7
d. x = 4 and y = 3
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Can I claim sickness benefit on Universal Credit?
Yes, you can claim sickness benefits on universal credit.
Here we have to find out if it is possible to claim the sickness benefit on Universal credit.
In order to find that, we must know the definition of universal credit,
The term universal credit refers to a payment to help with your living costs.
Here we have to know that as per the definition of universal credit here you can self-certify for up to the first 7 days of your claim by notifying Universal Credit that you have a health condition that prevents you from working. Then on the 8th day, your condition persists and if you have not already done so, then you will definitely need to submit medical evidence in order to claim for benefit.
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Which is a quadratic equation in FACTORED FORM?
A
f(x)=2x2+5x−12f(x)=2x^2+5x-12f(x)=2x
2
+5x−12
B
f(x)=2x+5f(x)=2x+5f(x)=2x+5
C
f(x)=2(x+5)2−12f(x)=2(x+5)^2-12f(x)=2(x+5)
2
−12
D
f(x)=2(x+5)(x−12)f(x)=2(x+5)(x-12)f(x)=2(x+5)(x−12)
Answer:
Step-by-step explanation: it is b
Determine the equation of the circle with center (0, -5) containing the point
(-√109,-6).
x^2 + y^2 - 10y + (-85) is equation of the circle with center (0, -5) containing the point (-√109,-6).
How do you find the equation of a circle?To find the equation of a circle with a given center and containing a given point, we can use the distance formula. The distance formula is given by:
d = √((x2 - x1)^2 + (y2 - y1)^2)
where (x1, y1) is the center of the circle and (x2, y2) is the point on the circle. In this case, the center of the circle is (0, -5) and the point on the circle is (-√109, -6). Plugging these values into the distance formula, we get:
d = √((-√109 - 0)^2 + (-6 - (-5))^2)
d = √((-√109)^2 + (-1)^2)
d = √(109 + 1)
d = √110
Since the point (-√109, -6) is on the circle, the distance from the center of the circle to this point is the radius of the circle. Therefore, the radius of the circle is √110.
The equation of a circle with center (h, k) and radius r is given by:
(x - h)^2 + (y - k)^2 = r^2
In this case, the center of the circle is (0, -5) and the radius is √110, so the equation of the circle is:
(x - 0)^2 + (y - (-5))^2 = (√110)^2
x^2 + y^2 - 10y + 25 = 110
x^2 + y^2 - 10y + (-85) = 0
This is the equation of the circle with center (0, -5) and containing the point (-√109, -6).
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Amelia has a summer job mowing the lawn and trimming hedges for a neighbor. The number of minutes that amelia spends mowing the lawn is 10 minutes longer than three times the number of minutes it takes to trim the hedges. It takes Amelia a total of 120 minutes to complete both tasks
Using system of linear equations, Amelia spent 92.5 minutes mowing the lawn and 27.5 minutes trimming the hedges
System of Linear EquationSystem of linear equations is the set of two or more linear equations involving the same variables. A linear equation can be defined as the equations of the first order, whereby the highest power of the variable in the equation is one.
To solve this problem, we have to write a system of linear equation;
Let;
x = number of minute spent mowing lawny = number of minute trimming the hedgesWe can represent the problem with two set of equations as;
x + y = 120 ...eq(i)
x = 3y + 10 ...eq(ii)
From equation 1
x + y = 120
x = 120 - y ..eq(iii)
Put eq(iii) into eq(ii)
120 - y = 3y + 10
collect like terms
120 - 10 = 3y + y
110 = 4y
y = 110 / 4
y = 27.5 minutes
Put y = 27.5 in equ(i)
x + 27.5 = 120
x = 120 - 27.5
x = 92.5 minutes
She spent 92.5 minutes mowing the lawn and 27.5 minutes trimming the hedges.
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What's the numerator for the following rational
expression? 2/f+4/f=?/f
The numerator for the rational expression is 6
How to find the numerator for the rational expression?Let us assume the value of numerator to be x
[tex]\frac{2}{f} +\frac{4}{f} = \frac{x}{f}[/tex]
Since these are fractions with same denominators (like fractions),
[tex]= > \frac{2}{f} +\frac{4}{f} \\\\ = \frac{2 +4}{f}\\\\= \frac{6}{f}[/tex]
x = 6
The numerator for the rational expression is 6
What are fractions?Fractions are used to depict the components of a whole or group of items. Two components make up a fraction. The numerator is the number that appears at the top of the line.It indicates how many equally sized pieces of the entire thing or collection were removed. The denominator is the quantity listed below the line. The total number of identical objects in a collection or the total number of equal sections that the whole is divided into are both displayed.The number of parts we take makes up a fraction when the whole is divided into equal parts.Fractions with same denominators are called like fractions.To learn more about fractions, refer:
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A number, .f, rounded to 1 d.p. is 49.2
Another number, g,
rounded to 1 d.p. is 7.8
What are the lower and upper bounds of
f - g?
Answer:
3
Step-by-step explanation:
The lower bound of f-g is 41.31 .
The upper bound of f-g is 41.49 .
Given,
A number 'f' rounded to 1 decimal point is Number = 49.2
A number 'g' rounded to 1 decimal point is Number = 7.8
Now,
The range of f rounded to 1 decimal point is [49.15 , 49.24].
The range of g rounded to 1 decimal point is [7.75 , 7.84].
So,
Lower bound of f-g = 49.15 - 7.84
Lower bound of f-g = 41.31
Next,
Upper bound of f-g = 49.24 - 7.75
Upper bound of f-g = 41.49
Therefore the lower bound of f - g is 41.31 and upper bound of f - g is 41.49.
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Can 55 years old get SSS?
No They can not because you need to be at least 62 years old
A proportional relationship is shown here:
x = 0, 1.4, 2.8, 4.2, 5.6
y = 0, 1, 2, 3, 4
What is the slope of the line that represents this relationship?
Graph the line that represents this relationship.
Answer:
y=1.4x
Step-by-step explanation:
Find the relationship.
1.4/1=1.4
2.8/2=2.8
and so on so we know it is 1.4
so y=1.4x
Each interior angle of a regular polygon is 120°.
Find the value of each exterior angle of the polygon.
Answer:
exterior angle = 180° - 120°
= 60°
Answer:
60 degrees
Step-by-step explanation:
180-120=60
You plan projects revenue of $5,000, $8,000, and $10,000, in years 1 through 3. Expenses are projected to be $9,000 for each of years 1 through 3. If your only funding need is the gap between revenue and expenses, which is the best estimate of your maximum cumulative funding need?
The best estimate of your maximum cumulative funding needed, based on the projected revenue and the expenses is $ 4, 000.
How to find the maximum cumulative funding needed ?The maximum cumulative funding needed would be the amount that would be total gap between revenue and expenses in the three years that the plan will be in effect.
In year 1, the gap is :
= 5, 000 - 9, 000
= $ - 4, 000
In year 2, the gap is:
= 8, 000 - 9, 000
= $ - 1, 000
In year 3, the gap is:
= 10,000 - 9, 000
= $ 1, 000
The cumulative funding needed is :
= ( -4,000 + - 1, 000 ) + 1, 000
= - $4, 000
You have a maximum cumulative funding needed of $ 4, 000.
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What SAS stand for in math?