Answer:
1/3 (Minimized) 2/6
Step-by-step explanation:
f(x) =(x - 5)/3 find the inverse function of this
The inverse function of f(x) = (x - 5)/3 is f^-1(x) = 3x + 5.
What is inverse function? How to calculate it? In mathematics, an inverse function is a function that undoes the work of another function. Specifically, if the function f applied to an input x gives a result of y, then the inverse function of f, denoted as f−1, applied to y gives the result x. In other words, the inverse of the function "f" applied to y will give us the input that we originally used to obtain y.To calculate an inverse function, one must first identify the original function. Then, one must switch the x and y variables, and solve for y. This is done by isolating the y in the equation and replacing it with the inverse function. For example, if the original equation is y = x + 4, then the inverse equation is x = y - 4.Once this is done, one can then determine the inverse function by taking the reciprocal of the function. This can be done by changing the sign of the exponent for any exponentiated terms and changing the sign of the coefficient for any multiplied terms. For example, if the function is y = x2 + 2x + 4, then the inverse function is y = (1/x2 + 2/x + 4)−1.In summary, to calculate an inverse function, one must first identify the original function, switch x and y, and solve for y, and then take the reciprocal of the expression.Solution:
To find the inverse of a function, we need to switch the x and y variables, and then solve for y.
Starting with f(x) = (x - 5)/3, we can switch the x and y variables to get y = (x - 5)/3.
We can then solve for x by multiplying both sides by 3, giving us 3y = x - 5.
We can then add 5 to both sides to get 3y + 5 = x, which is the inverse of our original function.
Therefore, the inverse of f(x) = (x - 5)/3 is f^-1(x) = 3x + 5.
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What is the area of triangle with base 12 cm and height is 9 cm *?
The area of the triangle is 54 square centimetres, which is calculated by multiplying the base (12 cm) and height (9 cm) and dividing by 2.
A = (12 cm * 9 cm) / 2
A = (108 cm²) / 2
A = 54 cm²
The area of a triangle is calculated by multiplying the base of the triangle and its height, and then dividing the result by 2. To calculate the area of the triangle with a base of 12 cm and a height of 9 cm, first the base and height must be multiplied together. 12 cm multiplied by 9 cm equals 108 cm². Then, the result of the multiplication, 108 cm², must be divided by 2. 108 cm² divided by 2 equals 54 cm². Therefore, the area of the triangle is 54 cm². To summarize, the area of a triangle is found by multiplying the base and height of the triangle, and then dividing the result by 2. In this case, the area of the triangle with a base of 12 cm and a height of 9 cm is 54 cm².
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A system of equations consisting of a linear equation and a quadratic equation has infinitely many solutions. Is this statement true?.
A system of equations consisting of a linear equation and a quadratic equation has infinitely many solutions is not true.
Linear equations are equations that graph as a line, while the quadratic equations are that graph as a parabola. Lines and parabolas in the xy-plane are convenient representations of linear and quadratic systems, respectively. One solution to the system is shown by each point where the line and parabola intersect. It is possible for a line and a parabola to intersect zero, one, or two times. This indicates that a linear and quadratic system may have zero, one, or two solutions.
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Help with this page??
(Ignore the drawings all over it)
((Picture is too small so the top question is written in here))
9. David makes $2 730.00/month. Calculate his monthly CPP and El contributions.
Hint: Find his annual gross pay first.
David's annual gross pay is $2 730.00 * 12 = $32 760.00.
What is the calculation for Davids monthly CPP and EI contribution?The current rate for Canada Pension Plan (CPP) contribution as of 2021 is 5.45% on the first $61 700 of pensionable earnings, and David's contribution would be 5.45% * $32 760 = $1 794.14.The current rate for Employment Insurance (EI) contribution as of 2021 is 1.62% on the first $54 000 of insurable earnings, and David's contribution would be 1.62% * $32 760 = $529.97.So, David's monthly CPP contribution would be $1 794.14 / 12 = $149.51, and his monthly EI contribution would be $529.97 / 12 = $44.17.To learn more about CPP refer:
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Clare ha $150 in her bank account. He buy for $200. What i clare' account balance now?
Claire's current account balance would be -$50.
The amount that Clare has in his bank account initially = $150
The amount that he used from his bank account to buy the bike = $200
As we can see that the amount that Clare used to buy the bike is more than the amount that he has in his account, therefore his account balance becomes negative, that is:
$150 - $200 = -$50
Here, it means that Clare has to pay the bank the amount of $50 that he used more than the amount that he had in his account.
Therefore, Claire's account balance would be -$50.
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Write and solve an equation or a system of equations to help you solve the following problem.
A cable 84 meters long is cut into two pieces so that one piece is 18 meters longer than the other. What is the length of each piece of cable? (show your work)
The equation written is: x + 18 + x = 84
The lengths of each piece of the cable are: 33 meters and 51 meters.
How to Write an Equation?To write an equation, let the unknown quantity be represented as a variable, which would be used in creating an algebraic expression.
For example, we are given the following:
Length of a cable = 84 meters
The length of one the pieces that the cable is cut into is represented as x.
The second pieces = x + 18 meters.
The equation that would be created for this problem would be:
x + 18 + x = 84
Solve for x:
2x + 18 = 84
2x = 84 - 18
2x = 66
2x/2 = 66/2
x = 33
The length of one of the pieces = 33 meters
Length of the second piece = x + 18 = 33 + 18 = 51 meters.
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For how many different displays, starting at 10:00 AM and ending at 4:00 PM, during a particular day, will a digital clock show that the number of the hour is less than the number of the minute? [For example, at 2:15 the number of the hour is less than the number of the minute but at 2:01, the number of the hour is greater than the number of the minute]
A digital clock will show that the number of the hour is less than the number of the minute for 12 different displays, starting at 10:00 AM and ending at 4:00 PM.
What will the clock display?These displays are:
10:01 AM, 10:12 AM, 10:23 AM, 10:34 AM, 10:45 AM, 11:02 AM, 11:13 AM, 11:24 AM, 11:35 AM, 12:03 PM, 12:14 PM, and 12:25 PM.
For example, 10:01 AM and 11:23 AM.
From 10:00 AM to 12:59 PM, the hour will always be a single digit, so we can check the minutes to see if they are double digit.
From 10:00 AM to 10:59 AM, the minute has to be greater than the hour. So, we can pick the minutes starting from 01 to 59 and check whether the hour is less than the minute which gives us 12 such displays
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In a recent survey, the proportion of adults who indicated mystery as their favorite type of book was 0. 325. Two simulations will be conducted for the sampling distribution of a sample proportion from a population with a true proportion of 0. 325. Simulation a will consist of 1,500 trials with a sample size of 100. Simulation b will consist of 2,000 trials with a sample size of 50.
The option that describes the center and variability of simulation A and simulation B is The centers will roughly be equal, and the variability of simulation A will be less than the variability of simulation B. The correct answer is C.
Considering the details provided in the query,
The two simulations will be run with sampling proportions from a population with a true percentage of 0.325.
Simulacrum A:
100 samples were used.
Tests: 1500
Exercise B -
50 samples total.
2000 trials
Due to the relationship between simulations A and B, they are now nearly equal.
1500 x 100 is the overall sample size for Simulation A.
= 150000
The simulation B sample size is 2000 x 50.
= 100000
We can observe from the simulations A and B calculations above that when comparing the,
Sample Size = Comparison of Simulations A and B
Simulation B + Simulation = Variability
Your question is incomplete but most probably your full question was
In a recent survey, the proportion of adults who indicated mystery as their favorite type of book was 0.325. Two simulations will be conducted for the sampling distribution of a sample proportion from a population with a true proportion of 0.325. Simulation A will consist of 1,500 trials with a sample size of 100. Simulation B will consist of 2,000 trials with a sample size of 50. Which of the following describes the center and variability of simulation A and simulation B?
A) The centers will roughly be equal, and the variabilities will roughly be equal.
B) The centers will roughly be equal, and the variability of simulation A will be greater than the variability of simulation B.
C) The centers will roughly be equal, and the variability of simulation A will be less than the variability of simulation B.
D) The center of simulation A will be greater than the center of simulation B, and the variability of simulation A will roughly be equal to the variability of simulation B.
E) The center of simulation A will be less than the center of simulation B, and the variability of simulation A will be greater than the variability of simulation B.
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Low tide, represented by the integer -1, is 1 foot below the average
water level. High tide is 5 feet higher than low tide.
a. What does 0 represent in this situation?
b. Write an integer that represents the average water level relative to high tide
Answer: a. In this situation, 0 likely represents sea level or the baseline from which water levels are measured.
b. To find the average water level relative to high tide, you need to take the average of high tide and low tide.
Since high tide is 5 feet higher than low tide, you can assume that low tide is 0 ft. Therefore, the high tide is 5 ft.
The average of two values is the sum of the values divided by the number of values. So average of 0ft and 5ft is (0+5)ft / 2 = 2.5 ft.
Therefore, an integer that represents the average water level relative to high tide would be 2.5 ft.
It's worth noting that relative to high tide means how much the average water level varies (higher or lower) from the high tide, so the answer was not an integer in this case.
Help please I need this answer very quick will be very appreciated
Answer:rotational
Step-by-step explanation:
it would not be a line because a line is a line and other make no sense
#8: Chris is employed as a waiter in an upscale restaurant. His restaurant pays him $5.75 per hour during which time he can serve two groups. The average tip per group is $8.75. Write an equation that outputs Chris' total income (1) based on the number of hours he works (h). please help me
Equation that represents Chris's total income I = ($5.75+$17.5)h , where X is the number of hours he works in a day.
What is equation?Equation is a mathematical statement that expresses the equality between two or more expressions.
Equation are different types such as equation with one variables and equation with two variables. The equation is used to determine the unknown values.
Chris salary $5.75 per hour.
During his work time he serves two groups.
The average tip per group = $8.75
Tips earned from two groups = $8.75 × 2 = $17.5
Then Chris total income in one hour = $5.75 + $8.75
Let Chris works h hours
Chris total income if he works total h hours in a day
I = ($5.75+$17.5) h
Hence, I = ($5.75+$17.5) h is the equation that determines Chris total income.
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What is a 3 2 image ratio?
A 3:2 image ratio refers to the proportion of the width to the height of an image or screen. It means that for every 3 units of width, there are 2 units of height.
The aspect ratio 3:2 is commonly used in digital photography, particularly for DSLR cameras and some mirrorless cameras.
In photography, the 3:2 aspect ratio is considered a standard format, it's the same as the traditional 35mm film frame, it's also the same as the aspect ratio of most modern digital cameras. It allows photographers to capture a wide range of scenes and subjects, and it's also a good option for cropping and printing photos.
For example, if an image's resolution is 3000x2000 pixels, it means that it has a 3:2 aspect ratio. The width of the image is 3000 pixels and the height is 2000 pixels, so 3000/2000 = 3/2
It's worth noting that the aspect ratio of 3:2 is a compromise between the wider aspect ratio of 16:9, used for video and some photography, and the taller aspect ratio of 4:3, used for more traditional photography.
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The data given represents the number of gallons of coffee sold per hour at two different coffee shops.
Coffee Ground
1.5 20 3.5
12 2 5
11 7 2.5
9.5 3 5
Wide Awake
2.5 10 4
18 4 3
3 6.5 15
6 5 2.5
Compare the data and use the correct measure of center to determine which shop typically sells the most amount of coffee per hour. Explain.
Answers:
Wide Awake, with a median value of 4.5 gallons
Wide Awake, with a mean value of about 4.5 gallons
Coffee Ground, with a mean value of about 5 gallons
Coffee Ground, with a median value of 5 gallons
The correct measure of center to determine which shop typically sells the most amount of coffee per hour will be C. Coffee Ground, with a mean value of about 5 gallons.
How to explain the measure of center?The mean is calculated by adding all the data points together and dividing by the number of data points.
When comparing the mean values of the two shops, Coffee Ground has a higher value of 5 gallons compared to Wide Awake's mean value of about 4.5 gallons. This indicates that Coffee Ground typically sells more coffee per hour on average.
The correct option is C.
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PLEASE HELP!!! TO THE PERSON WHO GIVES ME THE RIGHT ANSWER I WILL GIVE BRAINLIEST!!! PLEASE HELP.
Each of 36 students at a school play bought either a cup of orange juice or a sandwich. A cup of orange juice costs $1 and a sandwich costs $3. The total amount collected was $76. How many students bought orange juice, and how many bought a sandwich?
Let x represent the number of students who bought a cup of orange juice and y represent the number of students who bought a sandwich. Then the problem can be represented by this system of equations:
x + 3y = 76
x + y = 36
Answer the questions to solve the problem.
1. Explain what you should do with the two equations to eliminate one of the variables. (2 points)
2. Find the value of y. (3 points)
3. Find the value of x. (2 points)
4. Interpret the solution and check the values in the system. (3 points)
Answer:
see explanation
Step-by-step explanation:
given the system of equations
x + 3y = 76 → (1)
x + y = 36 → (2)
1
subtracting (2) from (1) term by term will eliminate x
(x - x) + (3y - y) = 76 - 36
0 + 2y = 40
2y = 40 ( divide both sides by 2 )
y = 20
3
substitute y = 20 into either of the 2 equations and solve for x
substituting into (2)
x + 20 = 36 ( subtract 20 from both sides )
x = 16
4
that is 16 students bought orange juice and 20 bought a sandwich
As a check
substitute the values for x and y into the equations and if both sides are equal then they are the solution
(1) : 16 + 3(20) = 16 + 60 = 76 ← True
(2) : 16 + 20 = 36 ← True
since both equations are true, then
x = 16 and y = 20 are the solutions to the system
Determine the lope, x-intercept and y-intercept of the line given by the equation 2x3y=6
For the given equation of the line 2x + 3y = 6 , the slope = -2 /3,
the x-intercept = 3 and the y-intercept = 2.
As given in the question,
Given equation of the line is :
2x + 3y = 6
Standard equation of the line with slope 'm' and y -intercept = c
y = mx + c
Convert the given equation into standard form we get,
2x + 3y = 6
⇒ y = (-2/3)x + 6/3
⇒y = (-2/3)x + 2
Slope of the line = -2/3
y - intercept when x = 0
y = 2
x - intercept when y = 0
x = 3
Therefore, for the given equation of the line the slope , x- intercept ,and y-intercept is equal to (-2/3) , 3 , and 2 respectively.
The above question is incomplete, the complete question is:
Determine the slope, x-intercept and y-intercept of the line given by the equation 2x + 3y = 6?
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The perimeter of a rectangle is 212 centimeters. Find the length and width if the length is an even integer and the width is 5 times the next consecutive even integer.
The length and width of the rectangle are 16 cm and 90 cm respectively
What is the Perimeter of a Rectangle?The perimeter P of a rectangle is given by the formula, P=2 ( L + W) , where L is the length and W is the width of the rectangle.
Perimeter P = 2 ( Length + Width )
Given data ,
Let the perimeter of the rectangle be P = 212 cm
Now , the equation will be
The length of the rectangle be = L
And , length is an even integer and the width is 5 times the next consecutive even integer
So , the width of the rectangle W = 5 ( L + 2 )
Substituting the values in the equation , we get
Perimeter of rectangle P = 2 ( Length + Width )
212 = 2 ( L + 5 ( L + 2 ) )
On simplifying the equation , we get
106 = L + 5L + 10
6L = 96
Divide by 6 on both sides of the equation , we get
L = 16 cm
So , W = 5 ( L + 2 )
W = 5 x 18
W = 90 cm
Hence , the length and width of rectangle is 16 and 90 respectively
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Y = 5x + 2
2y - 4 = 10x
please help need a solution
Answer:
Infinitely many solutions.
Step-by-step explanation:
y=5x+2
2y-4=10x
----------------
2(5x+2)-4=10x
10x+4-4=10x
10x=10x
What are the 4 triangle classifications by angle measure?
The 4 types of triangle with respect to angle measurement :
Acute Triangle
Obtuse Triangle
Right triangle
Equivalent triangle
What are the four types of triangles by angle measurement ?A triangle is said to be equilateral if each of its three sides is the same length. In the well-known Euclidean geometry, an equilateral triangle is also equiangular, meaning that each of its three internal angles is 60 degrees and congruent with the others.
A triangle having three acute angles is known as an acute triangle. A triangle having one obtuse angle and two acute angles is known as an obtuse triangle. No Euclidean triangle may contain more than one obtuse angle because in Euclidean geometry, a triangle's angles must add up to 180°.
A right triangle, also known as a right-angled triangle, right-perpendicular triangle, orthogonal triangle, or previously rectangled triangle, is a triangle with one right angle, or two perpendicular sides. The foundation of trigonometry is the relationship between the sides and various angles of the right triangle.
Obtuse-angled triangles or obtuse triangles are triangles with any one of its angles being an obtuse angle or more than 90°. Only 180° is equivalent to the internal angles of an acute triangle.
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There are four different triangles for measuring angles:
sharp triangle
Sharp triangle
correct triangle
comparable triangle
What are the four different kinds of triangles according to angle?If all three sides of a triangle are the same length, the triangle is equilateral. Equiangular triangles are equilateral triangles in well-known Euclidean geometry. His three internal angles, which are all 60 degrees, are therefore consistent with one another.
An acute triangle is a triangle having three acute angles. Obtuse triangles are those with one obtuse angle and two acute angles. Euclidean geometry mandates that the total of all the angles of a triangle be 180°, hence a triangle cannot have more than one obtuse angle.
A right triangle, also known as a right triangle, right triangle, right triangle, right triangle, right triangle, or formerly right triangle, is a triangle with one or two right sides. The basis of trigonometry is the relationship between the sides of a right triangle and different angles.
An obtuse or obtuse triangle is a triangle with one of its angles obtuse or greater than 90°. An acute triangle has only 180° interior angles.
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What are the three types of solution and differentiate each type of solution?
Solutions can be divided into supersaturated, unsaturated, and saturated solutions based on how well the solute dissolves in the solvent.
A homogeneous mixture with the major ingredients solute and solvent is referred to as a solution.
Solutions can be divided into supersaturated, unsaturated, and saturated solutions based on how well the solute dissolves in the solvent.
Supersaturated solution: The excess solute will crystallize quickly in a supersaturated solution because it contains a lot of solute at a temperature where it will be decreased.
Unsaturated solution: When a solvent can dissolve any more solute at a specific temperature, the solution is said to be unsaturated.
Saturated solution: A saturated solution is one in which a solvent can no longer dissolve any more solute at a particular temperature.
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Ben like to go in the covered dome when he feel overexcited. The dome cover an area of 1 2/3 quare meter, which i 5/840 of the total playground area what i the total
The total playground area is 280 square meter, if the dome cover an area of 1+2/3 = 5/3 square meter.
The area covered by the dome = 5/3 square meter
The area covered by the dome is 5/840 times of the total playground area.
Let the total area of the playground = A
5/3 = 5/840 × A
A = (5 × 840)/(3 × 5)
A = 280 square meter
--The given question is incomplete, the complete question is " Ben like to go in the covered dome, when he feels overexcited. The dome covers an area of 5/3 square meter, which is 5/840 of the total playground area. What is the total playground's area?"--
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What is ¾ divided by 2?
3/4 divided by 2 in the fraction is equal to 3/8.
A fraction is used to represent the portion of the whole quantity. Also, we know that every integer is a rational number and any whole number can be written in the form of n/1, where n is any whole number.
On the given data, we need to use the concept of the division of fractions.
3/4 ÷ 2
=3/4 × 1/2 [ Reciprocal of 2 is 1/2]
=3/8
Therefore, 3/4 divided by 2 in the fraction is equal to 3/8.
Once you have your final fraction, just divide the numerator by the denominator to get your answer in decimal form: 3/8=0.375
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Select all the correct locations on the table. Consider the following expression. 7 1/5 . 49 7/5 Select "equivalent" or "not equivalent" to indicate whether the expression above is equivalent or not equivalent to the values or expressions in the last column.
The first and second expressions are equal. The second expression is not synonymous. The third expression is interchangeable. The fourth expression is incorrect.
What is expression?An expression or mathematical expression is a finite collection of symbols that is well-formed according to context-dependent norms. In mathematics, an expression is a phrase that has at least two numbers or variables and at least one arithmetic operation. Addition, subtraction, multiplication, or division are all examples of math operations. A number, a variable, or a combination of numbers, variables, and operation symbols constitutes an expression. An equation consists of two expressions joined by an equal sign. Example of a word: the sum of 8 and 3. Example of a word: The product of 8 and 3 equals 11. 8 + 3 is an expression.
Here,
According to image,
First expression is equivalent. Second expression is not equivalent. Third expression is equivalent. Forth expression is not equivalent.
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Find the measures of x and y
X
Y
The right angle, 99, 171, and 159 are four of the angles. It follows that the x and y angles, which are also equal, must both equal 201/2.
what is angle ?A place where two lines converge creates an angle. They are quantified in degrees and are denoted by the symbol °. Four essential types are reflex, acute, right, and obtuse angles. A circle has 360 degrees. One terminal exists when two rays (half-lines) are merged form an angle. The rays are referred to as the angle's sides, occasionally as its legs, and occasionally as its arms, while the latter is referred to as the angle's vertex. The place where all points of an angle converge is known as the vertex.
given
A polygon's internal angle measurements are equal to (n-2) * 180, where n is the number of sides.
Therefore, 4 * 180 = 720 is the total of the internal angles of this 6-sided object.
The remaining two equal angles are 720 - 90 - 99 - 171 - 159 = 201 .
The right angle, 99, 171, and 159 are four of the angles. It follows that the x and y angles, which are also equal, must both equal 201/2.
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Help!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
the answer is 45°
Step-by-step explanation:
because they mirror eachother
Answer:
Step-by-step explanation:
I'm not sure but I think that is 45
i need helppppp
plweeeeeade
Answer:
9/4
Step-by-step explanation:
Use the process of elimination. Divide each number's numerator by its denominator; if the outcome repeats itself, it isn't a terminating decimal. Therefore, when you divide 9/4, it equals 2.25, which is a terminating decimal.
Are these similar?
Anything helps thank you!
The angles are congruent and the ratios of sides are equal, then the polygons are similar.
What is the similarity of polygons?
The similarity of polygons refers to the relationship between two or more polygons in which the corresponding angles are congruent (equal in measure) and the corresponding side lengths are in proportion.
We have,
Polygon 1:
Opposite Sides 24 = 24, 12=12,
Angles = 90°
Polygon 1:
Opposite Sides 16 = 16, 8=8,
Angles = 90°
This means that if two polygons are similar, their corresponding angles will have the same measure, and their corresponding side lengths will be in the same ratio. In other words, the ratio of any pair of corresponding sides of similar polygons will be the same.
For example, two triangles are similar if the ratio of their corresponding sides is the same, and their corresponding angles are equal. Similarly, two quadrilaterals are similar if the ratio of their corresponding sides is the same and their corresponding angles are equal.
It's important to note that similarity is a stronger relationship than congruence, because in congruence all the sides and angles must have the same measure, while in similarity only the angles and ratios of sides are the same.
Additionally, the similarity of a polygon can be determined by measuring the angles of the polygon, and comparing the ratios of the corresponding sides.
If the angles are congruent and the ratios are equal, then the polygons are similar.
Hence, the angles are congruent and the ratios of sides are equal, then the polygons are similar.
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Can somebody PLEASE help me? It’s due today.
Click on the image to see the answers.
Answer:
I don't care for the points
Step-by-step explanation:
The answer is the last one
My water bottle was fully filled then I drank 40% of it. In this situation "y" is the amount of water remaining and " x" is the amount of water that I had at the start. Mark all the equations that represent the situation
Step-by-step explanation:
1.y = x * (1-0.4)
2.y = x - 0.4x
3.x = y / (1-0.4)
4.x = y + 0.4y
The equation 1 and 2 correctly represent the situation. In the first equation, we are multiplying the initial amount of water (x) with (1-0.4) which is the percentage of the water that is remaining after drinking 40% of it. In the second equation, we are subtracting 0.4x from x, which is equivalent to multiplying x by (1-0.4).
The equation 3 and 4 are not correct, as they are trying to calculate the initial amount of water from the remaining amount, but it's not possible to know the initial amount once it has been consumed.
You have 0.6X amount water remaining.
The amount of water remaining in the water bottle is X minus 40%. This means that if you had X amount of water at start you now have 60% of X left. That is, you have 0.6X amount of water remaining.
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The table gives a partial set of values of a polynomial h(x), which has a leading coefficient of 1.
x –2 0 1 2 3
h(x) 0 –12 0 8 0
If every x-intercept of h(x) is shown in the table and has a multiplicity of one, what is the equation of the polynomial function?
h(x) = x3 – 2x2 – 5x + 6
h(x) = x3 – 6x2 + 11x – 6
h(x) = x3 + 2x2 – 5x – 6
h(x) = x4 + 14x3 + 19x2 – 66x – 72
The equation of the polynomial function is (a) h(x) = x^3 - 2x^2 - 5x - 6
How to determine the equation of the polynomial function?From the question, we have the following parameters that can be used in our computation:
x –2 0 1 2 3
h(x) 0 –12 0 8 0
The x-intercepts are where y = 0
So, we have
x = -2, x = 1 and x = 3
The multiplicity is 1
So, we have
h(x) = (x + 2)(x - 1)(x - 3)
Expand
= (x + 2)(x^2 - 4x + 3)
This gives
= x(x^2 - 4x + 3) + 2(x^2 - 4x + 3)
So, we have
= x^3 - 4x^2 + 3x + 2x^2 - 8x + 6
Evaluate the like terms
= x^3 - 2x^2 - 5x - 6
So the equation is h(x) = x^3 - 2x^2 - 5x - 6
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What are the 4 physical properties of solutions?
The 4 physical properties of solutions are:
1) Concentration
2) Solubility
3) Viscosity
4) Transparency
PHYSICAL PROPERTIES OF SOLUTIONIn chemistry, a solution is a homogeneous mixture of two or more substances. The four common physical properties of solutions are:
1) Concentration: The amount of solute present in a given amount of solvent, typically measured in molarity, molality, or mass percentage.
2) Solubility: The maximum amount of solute that can be dissolved in a given amount of solvent at a specific temperature and pressure.
3) Viscosity: The resistance of a fluid to flow, which can be affected by the presence of a solute.
4) Transparency or Opacity: The property of a solution by which it allows light to pass through it or not.
These are the 4 common physical properties of solutions, but there are many other physical properties that can be used to describe solutions depending on the context.
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