a) The slope is 1
b) The equation of the tangent line is x-y=20.
What is slope?
Slope is calculated using the slope of a line formula, the ratio of "vertical change" to "horizontal change" between two different locations on a line is determined. The difference between the line's y and x coordinate changes is known as the slope of the line.Any two distinct places along the line can be used to determine the slope of any line.
a) To find the slope of the curve, the derivative of a function f(x) at the given point is a slope of the curve
Slope of the given curve y = x at the point P(25, 5) is the derivative f'(x) at P(25,5)
=>m = f'(x) = dy/dx
=>1
Since the derivative of x is 1
f'(x) at P(25, 5) is 1
= > Slope = 1
b) To find an equation of the tangent line at P (25,5) for the curve y = x.
The equation of tangent line in for the function f(x) at P ([tex]x_1,y_1[/tex]) is (y - [tex]y_1[/tex]) = m (x - [tex]x_1[/tex])
Given:
[tex]x_1[/tex] = 25 and [tex]y_1[/tex] = 5, f(x) =x and slope of tangent m = 1
The equation of the tangent line is (y - 19) = - 24(x - 2)
⇒ y - 5 = 1(x -25)
=> y=x-25+5
=> y=x-20
=> x-y=20
The equation of tangent is x-y=20.
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I need an answer to my math test i cant answer the question.
It is a proportionate relationship if the ratio remains not constant constant.
What kind of relationship is proportional?As an illustration of a proportionate relationship in real life, let's look at the following: There is a correlation between the number of gallons of gas we put in our car and the price we will have to pay when we fill up the tank. That is to say, the more gas we use, the more we will have to pay.
When two variables are correlated in a manner that their ratios are equal, this is known as a proportional relationship. The "constant of proportionality" is a term used to describe this constant.
Examining the ratios between the two variables will help you determine whether a relationship is proportional. It is a proportionate relationship if the ratio remains constant.
11 $24
36 $39
66 $79
85 $98
It is a proportionate relationship if the ratio remains not constant constant.
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If you double 7 you get
Answer:
49
Step-by-step explanation:
7x7 = 49
you can just square 7 in your calculator
the marks on a statistics midterm are normally distributed with a mean of 78 and a standard deviation of 6. what proportion of the class has a midterm grade of less than 75?
The proportion of the class with a midterm grade less than 75 is approximately 0.3085, or 30.85%. This means that 30.85% of the class is expected to have a midterm grade lower than 75.
We can use the cumulative distribution function (CDF) of the normal distribution to find the proportion of the class with a midterm grade less than 75.
The CDF of a normal distribution with mean μ and standard deviation σ evaluated at a point x is given by the formula:
CDF(x) = 0.5 * [1 + erf((x - μ) / (σ * √2))]
where erf is the error function.
For this problem, μ = 78 and σ = 6, and x = 75, so the CDF can be calculated as follows:
CDF(75) = 0.5 * [1 + erf((75 - 78) / (6 * √2))]
= 0.5 * [1 + erf(-0.3536)]
The value of erf(-0.3536) can be looked up in a table or calculated using a software package. The result is approximately -0.383.
CDF(75) = 0.5 * [1 + -0.383] = 0.5 * [0.617] = 0.3085
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Find an equation of a plane containing the line r=⟨−4,−3,4⟩+t⟨−4,4,−2⟩ which is parallel to the plane 2x+4y+4z=1
2x+4y+4z = 0 is an equation of a plane containing the line .
What's the plane's reply?
In geometry, a plane is a surface made up of all the lines that are parallel to one another and connect any two locations on it. The surface is level or flat, to put it another way.
A plane is defined uniquely through any of the following in a Euclidean space of any number of dimensions: with the aid of three non-collinear points.
Parallel line equation: 2x+4y+4z = d
Point ⟨−4,−3,4⟩ belong to this plane 2 * -4 + 4 * -3 + 4 * 4 = d; d = -4
So, this plane equation 2x+4y+4z = -4
Let check point when t = 1 we have point ⟨−4,4,−2⟩
We check now if it belong to plane: 2 * -4 + 4 *4 + 4 * -2 = 0, 0 = 0.
So, equation of plane 2x+4y+4z = 0
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2. review hipaa privacy standards and safeguards, identifying two administrative requirements used to protect patient privacy when using an ehr.
By using parabola techniques to back up data, healthcare organizations can ensure that patient information is protected and secure.
The Health Insurance Portability and Accountability Act (HIPAA) sets standards for the privacy and security of patient information, and these standards are critical for protecting patient privacy when using an electronic health record (EHR).
There are two key administrative requirements that help to protect patient privacy in EHRs: access controls and data backup and storage.
Access controls determine who can access a patient's information and what level of access they have.
Access controls ensure that only authorized individuals can access patient information and prevent unauthorized access or misuse of information.
Data backup and storage involves backing up all patient information and storing it in a secure location to ensure that it is protected from unauthorized access, theft, or loss.
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the symbol for _____ is rhoxy.
Rhoxy is the chemical symbol for Rhodium (Rh).
Rhodium is a transition metal found in group 9 of the periodic table, and its atomic number is 45. Its atomic mass is 102.90550 g/mol. Its atomic radius is 1.36 angstroms and its oxidation state is +3.
Rhoxy can be calculated by taking the atomic mass of Rhodium and converting it to moles. This is done by dividing the atomic mass of Rhodium by the molar mass constant, which is 1.00794 g/mol. This results in 0.1022 moles of Rhodium. The formula for moles of a substance is n = m/M, where n is the moles, m is the mass of the substance, and M is the molar mass constant.
To calculate the amount of Rhoxy, divide the moles of Rhodium by Avogadro’s number (6.02 x 10^23). This results in 1.68 x 10^-24 moles of Rhoxy. The formula for this calculation is n = n/N, where n is the moles of the substance, and N is Avogadro’s number.
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Complete question :
What is the symbol for Rhodium?
In Exercises 1 and 2, find the scale factor. Then list all palrs of congruent angles and
write the ratios of the corresponding side lengths in a statement of proportionality.
In Exercises 3 and 4, the polygons are similar. Find the value of x.
In exercises 1 and 2:
The scale factor is 4/3 and 2/3The congruent angles are: A = HB = IC = JW = SX = TY = UZ = VThe ratio of the correspoding side length: 4/3 and 2/3In exercise 3 and 4, the value of x is 6 and 9
Please refer to the attached picture below as the referrence
Exercise 1The scale factor of the two triangles can be calculated by comparing the smallest side of both triangle. We will use side AB on ABC and side HI on HIJ. The scale factor of the two triangles is:
AB = 36 = 4
HI 27 3
The congruent angles of the two triangles are
A = H
B = I
C = J
The ratio of corresponding side lengths are:
AB = 36 = 4
HI 27 3
BC = 42 = 4
IJ 31.5 3
CA = 59 = 4
JH 44.25 3
The ratio of corresponding side lenghts is 3/4
Exercise 2The scale factor of the two trapesium can be calculated by comparing the smallest side of both triangle. We will use side XY on WXYZ and side TU on STUV. The scale factor of the two triangles is:
XY = 4 = 2
TU 6 3
The congruent angles of the two triangles are
W = S
X = T
Y = U
Z = V
The ratio of corresponding side lengths are:
WX = 7 = 2
ST 10.5 3
XY = 4 = 2
TU 6 3
YZ = 7 = 2
UV 10.5 3
ZW = 10 = 2
VS 15 3
The ratio of corresponding side lenghts is 2/3
Exercise 3We can find the ratio of corresponding side lengths using the gvien data. We name the small parallelogram as A and the large one as B.
Side A = 2 = 1.5
Side B 8 x
2x = 12
x = 6
Exercise 4We can divide the poligons into 2 proportionally similar triangle. We name the small triangle as triangle C and the large one as triangle D.
Side C = 6 = x
Side D 10 15
6 = x
10 15
3 = x
5 15
45 = 5x
x = 9
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6.4 divided by 49.92
Answer:
1.4024390244 I hope that helps
The x-intercepts of a quadratic function are -3 and 5. What is the equation of its axis of symmetry?.
If the quadratic has x-intercepts of -3 and 5 the equation would be:
y=c(x+3)(x-5)
The axis of symmetry is an imaginary straight line that divides a shape into two identical parts, by creating one part as the mirror image of the other part.
First, we have to define the axis of symmetry.
The point right in between the two x-intercepts of a quadratic equation is called axis of symmetry.
We have x-intercepts of -3 and 5
In ordered to find the axis of symmetry we have to find their middle intercept
To find the axis of symmetry:
-3+5/2=2/2=1
So the axis of symmetry is x = 1
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On a coordinate plane, line A B goes through (negative 4, 0) and (2, negative 3). Point C is at (negative 2, 2).
Which point on the x-axis lies on the line that passes through point C and is parallel to line AB?
The point on the x-axis that lies on the line passing through point C and parallel to line AB is (4, 0).
How to find the points that are parallelA line that is parallel to line AB and passes through point C has the same slope as line AB. The slope of line AB can be found using the formula:
m = (y2 - y1) / (x2 - x1),
where (x1, y1) and (x2, y2) are the coordinates of the two points on the line.
In this case, (x1, y1) = (negative 4, 0) and (x2, y2) = (2, negative 3).
Substituting these values into the formula, we get:
m = (-3 - 0) / (2 - -4) = -3 / 6 = -1/2
Since the slope of line AB is -1/2,
the slope of the line through point C and parallel to line AB is also -1/2.
A line with slope -1/2 and passing through (negative 2, 2) has the equation:
y - 2 = -1/2 (x - -2),
Rearranging this equation to solve for y, we get:
y = -1/2 x + 2
The x-axis has y-coordinate 0, so substituting 0 for y in the equation, we get:
0 = -1/2 x + 2
Solving for x, we get:
x = 4
hence the point is (4, 0)
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What are all the sides/angles?
Answer:
Clearly this figure is delusional loser bs
D = 93º
E = 43.5º
F = 43.5º
DF = 40
DE = 40
EF = 58
Step-by-step explanation:
Assuming angles F and E are the same angle, then:
8x - 24 = 40
8x = 40 + 24
8x = 64
x = 8
6x + 10 =
6 * 8 + 10 =
48 + 10 =
58
Cut the triangle in half:
58 / 2 = 29
sin x = 29 / 40 = 0.725 =~ 46.5º
D = 46.5 * 2
D = 93º
180 - 93 = 87º
87 / 2 = 43.5º
As a fundraiser for a debate club, the Pikesville High School debate club plans to sell
T-shirts that feature the school logo. The company producing the T-shirts will
charge the club $250 for the design and set-up costs, plus $10 per T-shirt. The club
members have decided to sell the T-shirts for $15 each.
How many shirts does the debate club need to sell in order to break even?
The number of shirts that the debate club need to sell on order to break even would be = 17 T-shirts.
How to calculate the number of T-shirts to be sold?The total amount of money that the company producing the T-shirts will charge the club = $250
The total charge contains the following:
The design,the set-up cost andThe cost for making each T-Shirt.The amount to sell each T-Shirt. = $15 each.
The number of T-shirts that can be sold = 250/15 = 16.6
That is approximately = 17 T-shirts.
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here is a rectangular prism.
work out the volume and round to 3 significant figures.
7.2cm,8.4cm,18cm
The volume is 1088.64 cm^2 of a rectangular prism with 7.2cm,8.4cm,18cm.
What is volume?
In mathematics, volume is the space taken by an object. Volume is a measure of three-dimensional space. It is often quantified numerically using SI derived units or by various imperial or US customary units. The definition of length is interrelated with volume.
here, we have,
a rectangular prism with 7.2cm,8.4cm,18cm
we know,
the volume is
V= l.b.w
here,
l= 7.2 cm
b= 8.4 cm
w= 18cm
i.e. V= 1088.64 cm^2
Hence, The volume is 1088.64 cm^2 of a rectangular prism with 7.2cm,8.4cm,18cm.
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Multiply (2x^2+6x-10)(x^2-2x+2).
A computer originally priced at $990, is reduced by 30%
Answer:
The answer is $297
Answer: The price of the PC is now $693.
Step-by-step explanation:
1. Find 30% of $990.
30% of $990 = $297
2. subtract.
$990 - $297 = $693
EASY 100 POINTS, WILL MARK BRAINLYEST TO FIRST ANSWER.
Data was collected on the amount of time that a random sample of 8 students spent studying for a test and the grades they earned on the test. A scatter plot and line of fit were created for the data.
Find the y-intercept of the line of fit and explain its meaning in the context of the data.
5; for each additional hour a student studies, their grade is predicted to increase by 5% on the test
10; for each additional hour a student studies, their grade is predicted to increase by 10% on the test
60; a student who studies for 0 hours is predicted to earn 60% on the test
80; a student who studies for 0 hours is predicted to earn 80% on the test
Answer:
The y-intercept of the line of fit is 60, which means that a student who studies for 0 hours is predicted to earn 60% on the test. This indicates that there is a positive correlation between the amount of time a student spends studying and their grade on the test.
Step-by-step explanation:
Answer:
Give the guy brainliest he deserves it
Step-by-step explanation:
What is the slope of the function y = -2x-3y=−2x−3?
Answer:
The slope of the function y = -2x - 3 is -2. This is calculated by taking the coefficient of the x-term and making it the numerator of a fraction, and making the constant term the denominator.
Step-by-step explanation:
mark as brainliest
How do i do this and answer pls
two percent of the circuit boards manufactured by a particular company are defective. if circuit boards are randomly selected for testing, the probability it takes 10 circuit boards to be inspected before a defective board is found is
The probability that it takes 10 circuit boards to be inspected before a defective board is found is approximately 0.16777216%.
The probability that it takes 10 circuit boards to be inspected before a defective board is found can be calculated using the cumulative distribution function (CDF) of the geometric distribution. The CDF of the geometric distribution is given by the formula:
[tex]CDF(k) = (1 - p)^{k-1} * p[/tex],
where p is the probability of success (in this case, the probability of finding a defective circuit board) and k is the number of trials (in this case, the number of circuit boards inspected). Since the probability of finding a defective circuit board is 0.02, we can calculate the CDF as follows:
CDF(10) = [tex](1 - 0.02)^{10-1}[/tex] * 0.02 = 0.0016777216 = 0.16777216%.
This means that the probability that it takes 10 circuit boards to be inspected before a defective board is found is approximately 0.16777216%.
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Consider functions f and g.
f(x)
g(x)
Which expression is equal to f(x) + g(x)?
=
=
-3x² + 4x + 4
x (-7x - 7)
O A. -10x² 3x + 4
OB.
-3x²
3x
3
O C. -10x² + 4x - 3
4x² 3x + 4
O D.
-
-
-
-
A. -10x^2 - 3x +4 , is the expression is equal to f(x) + g(x).
What is equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign. In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal. For instance, 3x + 5 = 14 is an equation, in which 3x + 5 and 14 are two expressions separated by an 'equal' sign.
here, we have,
f(x)= -3x^2+4x+4
g(x)= x(-7x-7)
now,
f(x) + g(x)
=-3x^2+4x+4 +x(-7x-7)
= -10x^2 - 3x +4
Hence, A. -10x^2 - 3x +4 , is the expression is equal to f(x) + g(x).
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Identify which of the twelve basic functions fit the description given.
The six functions that are increasing on their entire domains
The six functions that are incresing on their domain are : identity, cubing, square root, exponential, natural log and logistic function.
What is Function ?Each element of X receives precisely one element of Y when a function from one set to the other is used. The sets X and Y are collectively referred to as the function's domain and codomain, respectively. Initially, functions represented the idealized relationship between two changing quantities.
The set of integers x for which a function has a valid definition is known as its domain. A closed interval is referred to as a function's domain if it is specified across the interval a≤ x ≤b.
The logistic function is a function that simulates the exponential expansion of a population while also taking into account variables like the carrying capacity of land and other considerations.
The inverse of an exponential function, the natural log is the logarithm to the base of the integer e. Natural logarithms are unique varieties of logarithms that are employed in the treatment of time and growth-related issues. The basis of logarithms and natural logs are exponential functions and logarithmic functions.
The six functions that are incresing on their domain are :
identity, cubing, square root, exponential, natural log and logistic.
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A ballet school wants to buy new slippers for students in a class. They collected the sizes and displayed them in a line plot.
A horizontal number line starting at 3.5 with tick marks every 0.5 units up to 8. The following values are labeled: the value of 4 has one dot, the value of 4.5 has two dots, the value of 5 has two dots, the value of 6 has one dot, the value of 6.5 has two dots, the value of 7 has one dot, and the value of 8 has one dot. The image is titled Ballet Shoe Sizes.
What is the range, and what does it mean in terms of this data set?
The range is 4.5, and it means that the data varies by a value of 4.5.
The range is 3.5, and it means that it is the value that occurs the most.
The range is 4.0, and it means that the data varies by a value of 4.0.
The range is 4.0, and it means that it is the value that is the smallest.
The range is 4.5, and it means that the data varies by a value of 4.5.
What is the data set?A data set is a structured group of data. As we are all aware, data is a grouping of information that has been gathered by observations, measurements, research, or analysis. Facts, figures, names, and even simple descriptions of objects could be included in it.
The range is the difference between the largest and smallest values in a data set.
In this case, the largest value is 8 and the smallest value is 3.5,
so the range is 8 - 3.5 = 4.5.
This means that the ballet shoe sizes in this class vary by 4.5, with the largest size being 8 and the smallest size being 3.5.
Hence, The range is 4.5, and it means that the data varies by a value of 4.5.
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How do you simplify 6 1/2 div 2 1/3?
After simplifing [tex]6\frac{1}{2} \ and \ 2\frac{1}{3}[/tex] after dividing the value is [tex]2\frac{11}{14}[/tex]
What are Fractions ?Any number of equal parts is represented by a fraction, which also represents a portion of a whole. A fraction, such as one-half, eight-fifths, or three-quarters, indicates how many components of a particular size there are when stated in ordinary English.
A mixed fraction is one that is represented by both its quotient and remainder. A mixed fraction is, for instance, 2 1/3, where 2 is the quotient and 1 is the remainder. An amalgam of a whole number and a legal fraction is a mixed fraction.
The numerator of an improper fraction is bigger than the denominator. For instance, 2/3 is a valid fraction since its denominator is bigger than its numerator, but 3/2 is an improper fraction.
The mixed fractions are
[tex]6\frac{1}{2} \ and \ 2\frac{1}{3}[/tex]
The improper fractions are :
13/2 and 7/3
Dividing 13/2 by 7/3 we get the value :
(13/2)/(7/3) = 13/2 * 3/7 = 39/14 = [tex]2\frac{11}{14}[/tex]
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rite a linear cost function for the following situation. identify all variables used. a ski resort charges a snowboard rental fee of $40 plus $6.25 per hour.
The cost function is C(t) = $46.25.
Companies frequently utilize the cost curve to reduce costs and increase production efficiency. A cost function is a function of input prices and output quantity whose value represents the cost of producing that output given those input prices.
The evaluation of marginal costs and sunk costs are only two examples of the many potential uses for this cost curve.
Given that,
Rental fee = $40
Additional fees= $6.25 per hour
So, cost function is $40+$6.25= $46.25
Thus, The cost function is C(t) = $46.25.
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The region bounded by y=6-x^2 and y=2 is revolved about the x-axis. What is the volume of the solid obtained?
The region bounded by y=6-x^2 and y=2 is revolved about the x-axis has the volume as 384pi/5.
What is volume?The area that any three-dimensional solid occupies is known as its volume. These solids can take the form of a cube, cuboid, cone, cylinder, or sphere.
Various forms have various volumes. We have examined the numerous three-dimensional solids and shapes, such as cubes, cuboids, cylinders, cones, etc., in three-dimensional geometry.
The intersection points of y = 6−x^2 and y = 2 are given by the equation 6 − x^2 = 2, i.e., x^2 = 4, so x = −2 and x = 2.
The integration can be written as:
[tex]\int\limits^2_{-2} {\ \pi (y_t^2 - y_b^2) } \, dx \\\\\int\limits^2_{-2} {\ \pi((6 - x^2)^2 - 4)} \, dx \\\\\int\limits^2_{-2} {\ \pi (x^4 - 12x^2 + 32)^2} \, dx\\ \\= \pi [\frac{x^5}{5} - 4x^3 + 32x ]_{-2}^2\\\\= \frac{384 \pi}{5}[/tex]
Hence, the region bounded by y=6-x^2 and y=2 is revolved about the x-axis has the volume as 384pi/5.
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if there is a 40% chance that it will rain today and a 40% chance that it will rain tomorrow, what is the probability that it rains at least one of the days? (give your answer as a percentage.)
The probability that it rains at least one of the days is 40%.
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 probability is equal to the variety of possible outcomes. the total number of outcomes that could occur. For instance, there is only one way to receive a head and there are a total of two possible outcomes, hence the probability of flipping a coin and getting heads is 1 in 2. (a head or tail). P(heads) = 12 is what we write.Given data :
Let D1 = the event that it will rain on today
D2 = the event that it will rain on tomorrow.
P(D1) = 40% = 0.4
P(D2) = 40% = 0.4
The general probability formula can be expressed as: Probability = Number of Favorable Outcomes / Total Number of Outcomes. or. P(A) = f / N.
P(D1) + P(D2) / 2 = 0.4 + 0.4 = 0.8 / 2 = 0.4 = 40%
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.
feature scaling using techniques like mean normalization can make gradient descent converge faster true false
The statement is True. Mean normalization scales data to have a mean of 0, which allows the gradient descent algorithm to more quickly identify the optimum point.
Mean normalization is a feature scaling technique used to speed up the learning process of gradient descent algorithms. It works by mapping the values of a dataset to a range of [-1, 1], or [0, 1], by subtracting the mean from each data point and dividing by the standard deviation. This scaling process helps to reduce the impact of the outliers and normalize the data, allowing the gradient descent algorithm to more quickly converge on the optimal solution. This results in faster and more accurate models.
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At times, the relationship between a dependent and an independent variable is expressed as a logarithmic equation: Given a positive constant € and the two equations below, what is the relationship between X and Y? Equation 1: Log(c) = X/2 Equation 2: Log(c^2) = Y
The relationship between x and y is that x is equal to twice the value of y.
The relationship between x and y can be expressed as a logarithmic equation. The first equation states that Log(c) = X/2, where c is a constant. The second equation states that Log(c^2) = Y. We can solve for the relationship using the two equations given. For equation 1, we can isolate X on one side of the equation to get X = 2*Log(c). For equation 2, we can isolate Y on one side of the equation to get Y = Log(c^2). Plugging the expression for X into equation 2, we get Y = Log(c^2) = Log(c)*2 = 2*Log(c) = X. Therefore, the relationship between X and Y is X = Y.To calculate the relationship between x and y, we can use the power law equation, which states that c^(x/2) = c^y. This can be rewritten as x/2 = y, so we can conclude that the relationship between x and y is x = 2y. Therefore, the relationship between x and y is that x is equal to twice the value of y.
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Given ab is congruent to Ed. Ab is parallel to de, c is the midpoint of ae prove triangle abc is congruent to triangle edc
Side-Angle-Side postulate states that if two sides and the angle joining them of a triangle are congruent to the corresponding sides of another triangle, then the triangles are congruent.
therefore triangle ABC congruent triangle EDC
The corresponding sides of both triangles are congruent.
The corresponding angles have the same measure. That is, they are congruent.
First draw two triangle: ABC and CDE that meet the questions criteria.
triangle ABC and CDE
C is the midpoint of BD and AE
By using definition of midpoint AC congruent CE ; BC congruent CD
With the help of definition of vertical angles we can say angle BCA congruent angle DCE
Side-Angle-Side postulate states that if two sides and the angle joining them of a triangle are congruent to the corresponding sides of another triangle, then the triangles are congruent.
therefore triangle ABC congruent triangle EDC
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Notice that not all intervals in the frequency distribution are equal in width. Why do you think that unequal width intervals were used
Frequency distributions can show absolute or relative frequencies, such as percentages or proportions.
What is meant by frequency distribution?Organizing and presenting frequency counts in a way that makes them easier to understand is done through frequency distributions, which are visual displays. Absolute or relative frequencies, such as percentages or proportions, can be displayed in frequency distributions.
The number of people in each category on the measuring scale is arranged by tabulation or graphic representation in a frequency distribution. The full data set can be simply viewed by the researcher thanks to this.
An ordered tabulation of how many people fall into each group on a scale of measurement is known as a frequency distribution. Both a table and a graph can be used to arrange a frequency distribution, although both display the same two components: 1.
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