The length of segment YS within the square QRST is equal to 6.
How to determine the length of a line segment within a diagonal in a square
Squares are quadrilaterals with four sides of equal length and two diagonals of equal length, in that order, diagonals QS and RT are the diagonals of square QRST. Besides, we have the following information:
VY = 13, RV = 19
The length of segment YS can be found by means of the following formula:
RV = VY + YS
YS = RV - VY
YS = 19 - 13
YS = 6
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Can someone do all of this and explain each one
Answer: no exact answer
Step-by-step explanation:
In rhombus MATH, the coordinates of the endpoints of the diagonal MT are M(0,-1) and T(4,6). Write an equation of the line that contains diagonal AH. [Use of the set of axes below is optional.] Using the given information, explain how you know that your line contains diagonal AH.
The equation of the line that contains diagonal AH is y = -4/7 x + 51/14.
What is rhombus and some of its properties?
Rhombus is a parallelogram whose all sides are of equal lengths.
Its diagonals are perpendicular to each other and they cut each other in half( thus, they're perpendicular bisector of each other).
Its vertex angles are bisected by its diagonals.
The triangles on either side of the diagonals are isosceles and congruent.
Given;
The endpoints of the diagonal MT are M(0,-1) and T(4,6).
Now, The point that it passes through in this case is the midpoint of the diagonal MT. Using the midpoint formula you get
( (0+4)/2 , (-1+6)/2 ) = (2,2.5).
The slope of MT is (6--1)/(4-0) = 7/4.
We need this because the other diagonal must be perpendicular, which means that the slopes must be negative reciprocals. So the negative reciprocal of 7/4 is -4/7.
Now that we have the slope and the point, we can just use y=mx+b. We have an x and y value as well as the m....so we can substitute them in and calculate b.
2.5 = -4/7 (2) + b
5/2 = -8/7 + b
5/2 + 8/7 = b
35/14 + 16/14 = b
51/14 = b
Therefore, in the rhombus diagonal line has the equation will be y = -4/7 x + 51/14
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لله
+S
21
The picture shows the location of Cami's home, school, and library. Cami's home
2
miles from the library.
mile from the school and(
3
1 3/323
B 17
9
Cami's
Home
C 2/1/20
D 3-1
We
off
School
Cami walked from home to school, from school back home, and then from home
to the library. What is the total distance, in miles, that Cami walked?
A 1/23/2
Library
The total distance that Cami walked from home to school, then home, and then library, is 7. 46 miles
How to find the distance walked ?The distance walked by Cami, can be found to be :
= Distance from home to school + distance from school to home + distance from home to library
The distance in kilometers is:
= 5 + 5 + 2
= 12 kilometers
In miles, this is:
= 12 / 1. 60934 km per mile
= 7. 46 miles
In conclusion, the distance walked by Cami in miles, was 7. 46 miles.
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PLEASE HELLLP IM TAKING A QUIZ!!Cory is making popcorn. He knows that 3 identical scoops of unpopped
kernels produce 6 quarts of popcorn.
R
Which table most likely represents the total amount of popcorn, in quarts,
produced by x scoops of unpopped kernels?
Answer: C
Step-by-step explanation:
I am fairly certain this is the right answer. Good luck on your quiz!
Answer:C
Step-by-step explanation:
I remember this from class one time hope it helps:)
In ΔDEF, e = 9.2 cm, m m∠F=72° and m m∠D=61°. Find the length of f, to the nearest 10th of a centimeter.
The length of side f is 12.0 inches
How to determine the length of side fFrom the question, we have the following parameters that can be used in our computation:
In ΔDEF, e = 9.2 cm, m m∠F=72° and m m∠D=61°
The sum of angles in a triangle is 180 degrees
Using the above as a guide, we have the following:
E = 180 - 72 - 61
E = 47
Using the law of sines, we have
f/sin(F) = e/sin(E)
substitute the known values in the above equation, so, we have the following representation
f/sin(72) = 9.2/sin(47)
So, we have
f = sin(72) * 9.2/sin(47)
Evaluate
f = 12.0
Hence, the length is 12.0 inches
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What shape is this, why?
The shape is most specifically a trapezoid because it has a pair of parallel sides
How to determine the type of the shapeFrom the question, we have the following parameters that can be used in our computation:
The figure
From the figure, we have the following highlights:
The sides with lengths 21 and 24 are parallel sideThe other sides are non parallelUsing the above as a guide, we have the following:
The shape is most specifically a trapezoid
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What is the value of w in the solution to the following system of linear equations?.
The value of 'w' in the solution of the following system of linear equations is -[tex]\frac{1}{6}[/tex]
we can solve for a variable say 'v' then put the value of 'v' in the other equations and solve them for the value of 'w'
5v + 4w = 1
5v = 1 - 4w
v = [tex]\frac{1-4w}{5}[/tex]
now, when we put the value of 'v' in the second equation, we get:
3([tex]\frac{1-4w}{5}[/tex] ) - 6w = 2
3([tex]\frac{1-4w}{5}[/tex] ) = 2 + 6w
[tex]\frac{3-12w}{5}[/tex] = 2 + 6w
3 - 12w = 10 + 30w
-42w = 7
w = [tex]\frac{7}{-42}[/tex]
w = -[tex]\frac{1}{6}[/tex]
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The sum of two numbers is 17 and their product is 60 what are the two numbers?
Answer:
12 and 5
Step-by-step explanation:
12+5=17
12x5=60
Answer:
Step-by-step explanation:
5 12 step by step
1. In the figure below, a line intersects two parallel lines. Fill in the missing about how you might solve for the measurement help ASAP
Angle b is equal to 35°, angle a and angle e are each equal to 145°
What is an angle?An angle is formed when two lines intersect at a point. Types of angles are acute angle, obtuse angle and right angle. Vertical opposite angles are always congruent to each other. The sum of angles along a straight line is supplementary (add up to 180 degrees)
From the diagram:
b = 35° (vertical opposite angles are congruent)
a + b = 180° (sum of angles along a straight line)
a + 35 = 180
a = 145°
a = e = 145° (vertical opposite angles are congruent)
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When Cheryl's phone battery is 55% charged, she knows it will last for another 1.5 hours. If Cheryl's
phone battery loses its charge at a constant rate, how long, in hours, will it last when it is fully charged?
The battery will last 2.73 hours when it is fully charged
How to determine how long it will last when it is fully charged?The unit rate is the ratio of a certain number of units of one quantity to units of another quantity. Mathematically, the unit rate is one quantity divided by the other quantity
Since Cheryl's phone battery is 55% charged and it will last for another 1.5 hours. Thus, the rate will be:
rate = 1.5 hours/55% = 3/110 hour per %
When it is fully charged, that is 100%. Thus, it will take:
Time for 100% = (3/110) * 100% = 2 8/11 hours = 2.73 hours
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Solve the system of inequalities by graphing.
y < 3x+3
3x-y ≤ 4
The solution to the inequality are the region in the shaded area
How to determine the solution to the inequalityFrom the question, we have the following parameters that can be used in our computation:
y < 3x+3
3x-y ≤ 4
Represent properly
y < 3x + 3
3x - y ≤ 4
Next, we make a plot of the system to determine the solution
The shaded area in the plot represent the solution to the inequality
In this case, one of the coordinates in the shaded area has a coordinate of (0.2, 2)
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4. Calculate the surface area and volume of the composite figure below.
(+3 points each: +2 work; +1 correct answer)
1.5 yd
0.9 yd
2.4 yd
1.6 yd
1.3 yd
According to the information, it can be inferred that the total surface of the figure is 23.18yr². Additionally, the volume would be 7.8 yr³
How to calculate the volume and surface of the figure?To calculate the surface of the figure we must perform the following mathematical procedure.
We must find the surface of each of the faces that the figure has, we do this by multiplying base by height; in the case of triangles it is base times height divided in two.
2.4 * 1.3 = 3.121.3 * 1.6 = 2.081.5 * 1.3 = 1.952.4 * 1.6 = 3.840.9 * 1.2 = 1.08Now we must multiply these values by the number of faces of this dimension:
3.12 * 1 = 3.122.08 * 2 = 4.161.95 * 2 = 3.93.84 * 2 = 7.681.08 * 4 = 4.32Then we add all the surfaces to have the total surface
3.12 + 4.16 + 3.9 + 7.68 + 4.32 = 23.18On the other hand, to find the volume of the figure we must multiply height by length by width; in the case of the triangle it is the same formula because it has a rectangular base.
2.4 * 1.3 * 1.6 = 4.9922.4 * 1.3 * 0.9 = 2.8084,992 + 2,808 = 7.8Learn more about yards in: https://brainly.com/question/28365360
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A certain model car has a keypad with 5 numbers on the door. To open the door, 5 numbers must be entered in the correct order and no number can be used more than once. What is the probability that someone could guess the correct code?
Answer:
Step-by-step explanation:
The probability that someone could guess the correct code for the car model with a keypad of 5 numbers is 1 in 120,000, or approximately 0.0000083.
To calculate this, we need to determine the total number of possible combinations of 5 numbers (without repetition) from a set of 5 numbers. This can be calculated as 5!/(5-5)! = 5! = 5x4x3x2x1 = 120.
So, the probability of guessing the correct code is 1/120 or 0.0000083. This means that the chances of guessing the correct code are very low and the car's security system is fairly secure.
We want to obtain a sample to estimate a population mean. Based on previous evidence, researchers believe the population standard deviation is approximately
. We would like to be 99.5% confident that the estimate is within 0.1 of the true population mean. How large of a sample size is required?
n=
Answer:
5,144,079
Step-by-step explanation:
[tex]\displaystyle CI=\mu\pm z\biggr(\frac{\sigma}{\sqrt{n}}\biggr)\\\\CI_{99.5\%}=\mu\pm2.807\biggr(\frac{80.8}{\sqrt{n}}\biggr)\\\\0.1=2.807\biggr(\frac{80.8}{\sqrt{n}}\biggr)\\\\0.1\sqrt{n}=226.8056\\\\\sqrt{n}=2268.056\\\\n=5144078.01914\\\\n=5144079[/tex]
Thus, you would need a sample size of 5,144,079 to be 99.5% confident that the true population mean is ±0.1 away from it with a population standard deviation of 80.8 (aka. our margin of error).
Linda and Rob charged a $67.44 restaurant bill on their credit card. They gave the card to the waitress, who accidentally transposed two digits and charged them $76.44. They did not notice this until they received their statement later that month. Their card has an 18% APR.
They plan to pay their monthly statement amount in full, but they need to deduct the amount they were overcharged, plus the finance charge that was based on the incorrect amount. If the overcharged amount was on their statement for 18 of the 31-day billing cycle, how much should they deduct from this monthly statement, including the amount they were overcharged?
Answer:
Step-by-step explanation:
a
A grade distribution for a particular math class is shown below.
Grade distribution
Quizzes,
30%
Homework
15%
Test, 30%
Classwork
25%
According to the circle graph, what must be true?
O Tests are weighed the most when determining a grade.
O
Homework is worth twice as much as quizzes.
More than half the grade is based on tests and quizzes combined.
If someone never does their classwork it is possible for them to earn an 80 % in the class.
The statement is true; Tests are weighed the most when determining a grade.
What is Graph?A graph contains data of which input maps to which output.
Analysis of this leads to the relations which were used to make it.
Given in the question that:
Grade distribution
Quizzes, 30%
Homework 15%
Test, 30%
Classwork 25%
The total giving 100%.
A particular student scored the following;
87.9% on exams, 77.8% quiz, 90% Home work and 100% on class participation
Calculating the percentages the student had for each
Exam total = 50 x 0.879 = 43.95% earned
Quiz = 30 x 0.778 = 23.34% earned
Home work = 15x 0.9 = 13.5% earned
Class participation = 5*1 = 5% earned
Total earned = 43.95+ 23.34 + 13.5+ 5 = 85.79%
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Jason decides to sell his band's CD. It required an investment of $3349 for computer hardware and it will cost $3.65 for materials for each disk. If each CD sells for $13.50, how
many must he sell to break even?
196 CDs
340 CDs
339 CDs
195 CDs
Answer:
340 CDs
Step-by-step explanation:
To answer this question, we're dealing with three functions for one problem, namely the revenue function, the cost function, and the profit function.
The revenue function is R(q) = pq, where p is the price of a certain good and q is the quantity sold.
The cost function is C(q) = variable cost + fixed cost, where variable costs changes depending on the quantity of goods produced and fixed cost is a one-time cost for the producer (e.g., an investment, rent, etc.).
The profit function is P(q) = R(q) - C(q) and is simply the cost function subtracted from the revenue function.
The "break-even point" is the point at which profit = $0 and the point at which cost = revenue.
From the problem, we see that Jason invested $3349 (once) for his CDs and each disk requires $3.65 for the materials so our cost function is C(q) = 3.65q + 3349
Furthermore, we see that each disks sells for $13.50, so our revenue function is R(q) = 13.5q
Our profit function then is P(q) = 13.5q - (3.65q + 3349) = 13.5q - 3.65q - 3349 = 9.85q - 3349.
Thus, to find the break-even point, we set profit = 0 and solve for q:
[tex]0=9.85q-3349\\3349=9.85q\\340=q[/tex]
The graph below is the function f(x)
The value of lim x -> -1- f(x)= -1
What is the Limit of a function?The behavior of a function at a specific input is described by its limit, a crucial concept in calculus and analysis.
Hence,
As x approaches -1 from the left, the graph of f(x) leads you to the point (-1, 3), so the limit from the left is 3.
As x approaches -1 from the right, the graph leads to the point (-1, -3), so the limit from the right is -3.
The one-sided limits do not match, so the two-sided limit does not exist.
But f(x) is still defined at x = -1; this is indicated by the point (-1, -1). So f (-1) = -1.
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The graph below is the function f(x)
Find lim x -> -1- f(x)=
Solve this problem using Rational Zeroes Theorem (but explain it, please).
What are the real zeroes of the polynomial function:
f(x) = 4x^4 - 8x^3 - 19x^2 + 23x - 6?
The real zeroes of the polynomial function f(x) = 4x⁴ - 8x³ - 19x² + 23x - 6 are 1/2, 1, 3/2, and 2.
What do you mean by Polynomial?In mathematics, a polynomial is an expression consisting of variables and coefficients, which are combined using the operations of addition, subtraction, and multiplication. A polynomial can have one or more terms, where each term is the product of a coefficient and one or more variables raised to non-negative integer powers. For example, the polynomial 2x² - 3x + 1 has three terms: 2x², -3x, and 1.
For the given polynomial function, the constant term is -6 and the leading coefficient is 4. Therefore, the possible rational zeroes of the function are of the form p/q, where p is a factor of -6 and q is a factor of 4.
The factors of -6 are ±1, ±2, ±3, and ±6. The factors of 4 are ±1, ±2, and ±4. So the possible rational zeroes are:
±1/1, ±2/1, ±3/1, ±6/1, ±1/2, ±3/2
To determine which of these possible rational zeroes are actual zeroes, we can use synthetic division or long division to evaluate the function at each possible zero. Doing so, we find that the actual zeroes of the function are:
x = 1/2, x = 1, x = 3/2, x = 2
Therefore, the real zeroes of the polynomial function f(x) = 4x⁴ - 8x³ - 19x² + 23x - 6 are 1/2, 1, 3/2, and 2.
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Complete this sentence: The longest side of a triangle is always opposite the
• A. angle with the greatest measure
• B. second-longest side
• C. shortest side
• D. angle with the smallest measure
The longest side of a triangle is always opposite the,
A. angle with the greatest measure.
What is the way of classifying a triangle?If a² + b² < c² then it is an acute angle triangle.
If a² + b² = c² then it is a right-angle triangle.
If a² + b² ≥ c² then it is an obtuse angle triangle.
We know, The length of the largest side in a triangle is opposite to the largest angle.
The statement, The longest side of a triangle is always opposite the
angle with the greatest measure.
Because A longer angle will be more spread out and hence the opposite side will be longer too.
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A quilter created the following shape to use in a block for a new quilt.
A six-sided figure with a large base of 13 inches. The side to the right of the base is 7 and one-half inches. The small side parallel to the base is 5.18 inches. There are two sides that form a point at a right angle. The smaller is 5 inches, and the larger is 6 inches.
What is the area of the shape for the quilt block?
sixty-three and three fourths in2
one hundred twelve and one half in2
one hundred twenty-seven and one half in2
225 in2
The total area of the quilt is: 112.5 square inches
How to determine the total area of the quilt?The six-sided figure is given, and we can deduce the following parameters from the question:
The shape is made of a triangle and a rectangle
The side lengths derived from the question are:
The triangle on top:
base: 5 inches and height: 5.18 inches
The rectangle at the bottom:
Base: 16 inches with a height of 7.5 inches
So, we have the total area of the figure to be
Area of figure = 1/2 * 5 * 6 + 13 * 7.5
Area of figure = 112.5
Based on the parameters, the total area is 112.5 square inches
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Click the bookings sheet tab and select cell f5. Calculate average revenue per passenger by dividing the fee by the number of passengers.
In this exercise we have to use the knowledge of excel to explain some functions that can be used, as:
In excel cell a division formula can be written as: =(A4+B4+C4+D4+E4)/5
If you track your daily earnings in an Excel spreadsheet, you can use the same spreadsheet to estimate your forecasted earnings for any period of time. You can use Excel's AVERAGE function to find out your average daily income. Multiply your average daily sales by the number of days specified to estimate how much profit you could make over time.
In mathematics, the average of a list of data represents the central value of the set of data. Mathematically defined as the ratio of the sum of all data and the number of items in the list. In statistics, the mean of a particular set of numerical data is also called the mean. For example, the average of 2, 3, 4 is (2+3+4)/3 = 9/3 =3. So here 3 is the center value of 2, 3, and 4. So the meaning of average is to find the average of a group of numbers.
mean = sum of values / number of values
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(1 point) Find an equation of a line perpendicular to 2 = 10 and passing through the point (3,2). The line is
An equation for a line perpendicular to the line 2 = 10 can be found by finding the slope of that line and then finding the slope of the perpendicular line. The slope of the line 2 = 10 is 0, so the slope of the perpendicular line would be undefined.
The equation of a line with slope m passing through the point (x1, y1) can be written in the form:
y - y1 = m(x - x1)
Since the slope of the line is undefined, the equation of the line would be in the form:
x - x1 = constant
To find the equation of the line that passes through the point (3, 2), we substitute the values into the equation:
x - 3 = constant
So the equation of the line that is perpendicular to the line 2 = 10 and passes through the point (3, 2) is:
x - 3 = constant
or simply:
x = 3.
1.6.3 Quiz: Graphs of Polynomial Functions
Question 8 of 10
How many zeros does the graphed polynomial function have?
A. 3
B. 1
OC. 4
D. 2
2
-10
-15-
8
0
19
The zeros of the given polynomial function are 3
Zeros of a polynomial:Zero of a polynomial are numerical values at which the polynomial will equal zero. In other words, zeros of a polynomial are numerical values of the variable which give zero when we plug into the polynomial.
For example, for a polynomial p(x) the zeros are the value of 'x' which satisfies p(x) = 0. This means by identifying the x-intercepts, we may determine the polynomial's zeros.
In the case of a graph, we can determine the zeros of a polynomial by observing the points at which the graph line will cut the x-axis. In simple words, we can say that the x-coordinates of the points where the graph meets the x-axis are the zeros of the polynomial.
Here we have a graph
In the given graph the polynomial function meets the x-axis three times at three different points.
Therefore,
The zeros of the given polynomial function are 3
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solve for x, 11, 31°
The value of x is 21.4.
What is right-angle triangle?
A right triangle, also known as a right-angled triangle, right-perpendicular triangle, orthogonal triangle, or formerly rectangle triangle, is a triangle with one right angle, or two perpendicular sides. The foundation of trigonometry is the relationship between the sides and other angles of the right triangle.
The height of the right-angle triangle is 11. The hypotenuse of the right-angle triangle is x. The measure of the angle opposite to height is 31°.
The sine of an angle is the ratio of height to the hypotenuse.
Therefore,
sin 31° = height/hypotenuse
sin 31° = 11/x
Multiply x with both sides:
x sin 31° = 11
Divide sin 31° with both sides:
x = 11/ sin 31°
x = 21.35
x ≈ 21.4 units
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Sarah has 275 red beads and 3 times as many blue beads. She uses a total of 156 beads to make a bracelet. How many beads are left?
Answer: 994 beads
Step-by-step explanation:
Red Beads = 275
Blue Beads = 825 (275 x 3)
825 + 275 = 1100 beads (total)
1100 - 156 = 994 beads
What is the percent increase from 2000 of 5.53 and 2010 of 22.5 . Round to nearest tenth of a percent
There was a 305.1% increase in the value from 2000 to 2010.
What is Percent?
To compute a percentage, divide the value by the entire amount and multiply the result by 100.
To calculate the percent increase, we need to determine the difference between the two values and divide it by the original value, then multiply by 100 to express it as a percentage.
For the year 2000:
Percent increase = (22.5 - 5.53) / 5.53 * 100 = 305.05%
And rounded to the nearest tenth of a percent, this would be 305.1%.
So, There was a 305.1% increase in the value from 2000 to 2010.
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1. The size of the Chinese economy is predicted to surpass the size of the US economy at the some point in the next 40 years (Here you can see this is an old example; sometimes its fun to look at those to see what people thought back then). The size of an economy is measured by its gross domestic product (GDP). Projections of the GDPs of China and the United States (in trillions of dollars) are as follows, where t = 0 corresponds to the year 2000: YChina (t) = 1.35 * 1.076t YUSA (t) = 10.4 * 1.024 (a) Is this an example of discrete or continuous growth? Explain. (b) What is the interpretation of the parameters (1.35, 1.076) and (10.4, 1.024) in the two functions? (c) Find the projected level of GDP for each country for the years 2011, 2025 and 2047.
a. This is an example of continuous growth, as the functions for the GDPs of both countries are given as continuous functions of time.
(b) In the function for China's GDP, the parameter 1.35 represents the initial level of GDP in the year 2000, and the parameter 1.076 represents the annual rate of growth of GDP. In the function for the US's GDP, the parameter 10.4 represents the initial level of GDP in the year 2000, and the parameter 1.024 represents the annual rate of growth of GDP.
How to calculate the projected valueIt should be noted that on order to calculate the projected level of GDP for each country for the years 2011, 2025 and 2047, we can substitute the corresponding values of t into the functions for YChina and YUSA:
For China:
YChina(11) = 1.35 * 1.076^11 ≈ 4.65 trillion dollars
YChina(25) = 1.35 * 1.076^25 ≈ 30.83 trillion dollars
YChina(47) = 1.35 * 1.076^47 ≈ 516.97 trillion dollars
For the US:
YUSA(11) = 10.4 * 1.024^11 ≈ 15.63 trillion dollars
YUSA(25) = 10.4 * 1.024^25 ≈ 30.19 trillion dollars
YUSA(47) = 10.4 * 1.024^47 ≈ 57.17 trillion dollars
So according to these projections, China's GDP has already surpassed the US's GDP as of 2025 and is expected to continue to grow at a much faster rate than the US's GDP in the future.
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Help me with this Quadratic Functions graph it
If f(r)=√, which equation describes the graphed function?
The equation that describes the graphed function is given as follows:
A. y = f(-x + 3).
What is a translation?A translation happens when either a figure or a function are moved horizontally or vertically.
The four translation rules for functions are given as follows:
Left a units: f(x + a).Right a units: f(x - a).Up a units: f(x) + a.Down a units: f(x) - a.The parent function for this problem is given as follows:
[tex]y = \sqrt{x}[/tex]
The function was reflected over the y-axis, hence it is given as follows:
[tex]y = \sqrt{-x}[/tex]
Then it was moved 3 units right, hence the definition is given as follows:
[tex]y = \sqrt{-(x - 3)}[/tex]
[tex]y = \sqrt{-x + 3}[/tex]
Hence:
y = f(-x + 3), as x was replaced by -x + 3.
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