Answer:
Step-by-step explanation:
The equation for a parabola is of the form y = ax^2 + bx + c, where a, b, and c are constants. The graph of a parabola is a U-shaped curve that is symmetrical about a line called the axis of symmetry.
In the equation (x-1)^2 = y+2, we can rewrite it as y = (x-1)^2 - 2. This is the standard form of a parabola with a = 1, b = 0, and c = -2.
The vertex of the parabola is the point on the graph where the parabola reaches its highest or lowest point. For a parabola in standard form, the vertex is always of the form (h,k), where h and k are the values of x and y, respectively, at the vertex. The vertex of this parabola is (1,-2).
The axis of symmetry of the parabola is a line that divides the parabola into two mirror images. For a parabola in standard form, the axis of symmetry is always the line x = h, where h is the value of x at the vertex. The axis of symmetry of this parabola is the line x = 1.
The directrix of a parabola is a line that is used to define the parabola. For a parabola in standard form, the directrix is always the line y = k + p, where k and p are constants and p is the distance from the vertex to the directrix. The directrix of this parabola is the line y = -2 + p, where p is the distance from the vertex to the directrix.
The focus of a parabola is a point on the axis of symmetry that is used to define the parabola. For a parabola in standard form, the focus is always the point F(h,k+p), where h and k are the values of x and y, respectively, at the vertex, and p is the distance from the vertex to the directrix. The focus of this parabola is F(1,-2+p), where p is the distance from the vertex to the directrix.
To sketch the graph of this parabola, we can start by plotting the vertex at (1,-2). Then we can draw the axis of symmetry, which is the line x = 1. Next, we can choose a value for p and draw the directrix y = -2 + p. Finally, we can use the vertex and focus to plot points on either side of the axis of symmetry, and connect these points to form the U-shaped curve of the parabola.
[asy]
unit size(1cm);
real p = 1.5;
pair F, V;
F = (1,-2+p);
V = (1,-2);
draw((-2,0)--(4,0));
draw((0,-4)--(0,4));
draw((-2,V.y)--(4,V.y),dashed);
draw((F.x,p)--(F.x,-4),dashed);
label("$x$", (4,0), E);
label("$y$", (0,4), N);
label("$y = (x - 1)^2 - 2$", (4,-3), E);
a dot("$F$", F, NW);
a dot("$V$", V, S);
label
What is the nature of the roots of the quadratic equation 5x^2 4x 1?
The nature of roots of quadratic equation 5x² = 4x - 1 is imaginary roots.
The standard form of a quadratic equation is:
ax² + bx + c = 0
The discriminant is defined as:
D = b² - 4ac
Using the value of discriminant, we can determine the nature of roots of a quadratic equation.
If:
D > 0, the quadratic equation has two distinct real roots or the roots are real and distinct.
D = 0, the quadratic equation has 1 real equal roots or the roots are unique
D < 0, the quadratic equation has complex conjugate roots or the roots are imaginary.
In this case, the quadratic equation is:
5x² = 4x - 1
transform it into the standard form:
5x² - 4x + 1 = 0
Calculate the discriminant:
D = (-4)² - 4 (5)(1)
= 16 - 20 = -4
Since D < 0, the roots are imaginary.
Your question is incomplete, but most probably your question was:
What is the nature of roots of quadratic equation 5x² = 4x - 1?
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The circle below has center H. Suppose that mLFEG=46°. Find the following.
From given circle, Measure of arc FG = 23πr/45 and ∠FHG = 92°.
The distance between the two locations along a segment of a curve is known as the arc length. Any portion of the circumference is an arc in a circle. The angle that an arc occupies at any given point is the angle created by the two line segments that connect that point to the arc's endpoints.
Length of an Arc = r, where is in radians, is the formula used to express the arc length of this arc OP.
The measure of ∠FHG = 2 × 46° [As Angle at center equals twice at circumference]
So, ∠FHG = 92°
Measure of the arc FG = 2πr(θ/360°)
FG = 2πr(92/360)
FG = 23πr/45
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The function w (t) = 29 + 0.0674t gives the estimated weight, in pounds, of a beaver t days
after June 1, where t < 90. Which of the following is the best interpretation of 29 in this context?
1)The estimated weight, in pounds, of the beaver 90 days after June 1
2)The estimated weight, in pounds, of the beaver on June 1
3)The estimated number of pounds by which the beaver's weight increased each day after June 1
4)The estimated number of pounds by which the beaver's weight increased in the 90 days after
June 1
Answer:
2) The estimated weight, in pounds, of the beaver on June 1.
Step-by-step explanation:
Given function:
[tex]w(t) = 29 + 0.0674t \quad t < 90[/tex]
where:
w = weight of a beaver (in pounds)t = time after June 1 (in days)When t = 0:
[tex]\begin{aligned}\implies w(0)&=29+0.0674(0)\\&=29+0\\&=29\end{aligned}[/tex]
Therefore, the constant of the equation (29) is the estimated weight of the beaver, in pounds, when t = 0.
As t = 0 is June 1:
29 is the estimated weight, in pounds, of the beaver on June 1.What is the slope of the line that contains the points (-3, -7/2) and (2, -4)
Answer: m = -1/10
Step-by-step explanation:
Use the slope formula to find the slope m.
m = −1/10
The Space Needle elevator can hold a maximum of 4,500 pounds. Twenty-five people need to use the elevator. Arian had some measures from the data set of how much each person weighed. Which measure would be most useful to determine if the people can safely use the elevator?
Answer choices
Mode
Mean
interquartile range
Median
The measure that would be most useful to determine if the people can safely use the elevator is B. Mean
How to illustrate the information?The most useful measure to determine if the people can safely use the elevator would be the mean weight of the people, as it would give an idea of the average weight of the group and if it is below 4,500 pounds.
The mode is the most common value in a set of data and does not give information about the weight of the entire group. The interquartile range is a measure of the spread of the middle 50% of the data and does not give information about the average.
In conclusion, the correct option is B.
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Find the distance AB:
A = (-2, 1) and B = (5, -4)
Simplify.
d = √(5− −2)² + (−4 − 1)²
A. √74
B. √24
C. √-16
The formula to calculate the distance:
d = √(x₂ - x₁)² + (y₂ - y₁)²
The points are:
(x₁,y₁) = -2, 1(x₂,y₂) = 5, -4We substitute and solve:
d = √(-5(-2))² + (-4-1)²
d = √7² + (-5)² = √49 + 25
d = √74 ====> Alternative "A"
Hape a and hape b are each made from five identical quare
The perimeter of hape a i 60 cm
work out the perimeter of hape b
50 cm is the required perimeter of shape B.
What is the perimeter?A closed path that covers, encircles, or outlines a one-dimensional length or a two-dimensional shape is called a perimeter.
A circle's or an ellipse's circumference is referred to as its perimeter.
There are numerous uses in real life for perimeter calculations.
We must sum up the lengths of the rectangle's four sides in order to get its perimeter.
So, according to the given figures:
Shape A's circumference is 60 cm.
Let x cm be the length of each square.
The total length of shape A's free bounds is equal to 12x.
Consequently, 12x = 60.
x = 5 cm
Currently, the length surfaces of form B equal 10x.
Shape B's perimeter equals 10x.
= 10(5)
= 50 cm
Therefore, 50 cm is the required perimeter of shape B.
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Correct question:
Shape A and Shape B are each made from 5 identical squares.
The perimeter of shape A is 60cm. Work out the perimeter of Shape B
Find (angle) Then classify the triangle by its angles.
M (angle) 1 =
Answer:
m∠1 = 110°obtuse triangleStep-by-step explanation:
You want to find the measure of the angle designated as ∠1, given the other two have measures of 40° and 30°. You also want the classification of the triangle based on its angles.
Angle sumThe sum of angles in a triangle is 180°.
40° +∠1 +30° = 180°
∠1 = 110° . . . . . . . . . . . . subtract 70°
Triangle classificationThe classification of a triangle as acute, right, or obtuse is based on the measure of its largest angle. If that angle is 90°, the triangle is a right triangle. If it is less, the triangle is acute; if it is more, the triangle is obtuse.
The angle measure 110° is more than 90°, so this triangle is an obtuse triangle.
Six toilet rolls cost $1.99. Nine toilet rolls cost $2.69. Is cost directly proportional to number of toilet rolls? Explain your reason!
Answer:
not directly proportional
Step-by-step explanation:
if the cost is directly proportional to number of rolls , then the unit cost for both will be equal.
first
one roll costs $1.99 ÷ 6 = $0.33 ( to 2 decimal places )
second
one roll costs $2.69 ÷ 9 = $0.30 ( to 2 decimal places )
since the unit costs are different there is not a directly proportional relationship.
Answer:
No because to buy nine rolls would be $2.69 but to buy six and then three to make nine then it would be $2.985 which is more expensive.
Step-by-step explanation:
$1.99 divided by 2 = 0.995
$1.99 + 0.995 = $2.985
$2.985 > $2.69
Hope this helps!!! :)Plsssss help me in the photo
0.01 is not the way of expressing the relationship because it does not represent the correct ratio between 10 square and 100 square
What is ratio ?A ratio tells the relationship between two or more quantities by comparing their relative sizes.It is typically written as two or more numbers separated by a colon (:), such as 2:4, or expressed as a fraction, such as 2/4. The numbers in a ratio represent the relative amounts of the quantities being compared. A ratio can be used to compare any type of quantity, such as length, weight, or time.
A) 10 square is 1/10th of the area of 100 square. It can be represented as a fraction, where the numerator is the area of the smaller square (10) and the denominator is the area of the larger square (100). The fraction would be 1/10.
B) Another way of expressing the relationship is as a percentage, where the smaller area (10) is divided by the larger area (100), and the result is multiplied by 100 to get the percentage. So 10 square is 10% of 100 square.
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How many ways can the train be made up?
Answer:
16c9
Step-by-step explanation:
First, we will add up the number of different car possibilities. This is:
6 + 7 + 3 = 16.
Then, we need to take 9 of these 16 cars, giving us 16c9.
Hope this helped!
Answer:
4,151,347,200
Step-by-step explanation:
In describing the cost equation, Y = a + bX, "a" is:
- A) The dependent variable cost.
- B) The independent variable the level of activity.
- C) The total fixed cost.
- D) The variable cost per unit of activity.
Answer:
C) The total fixed cost.
What is the slope of 5x 2y =- 3?
The slope of 5x 2y =- 3 is -5/2.
To find the slope of the equation 5x 2y =- 3, we need to rearrange it into the slope-intercept form y = mx + b, where m is the slope and b is the y-intercept (the point where the line crosses the y-axis).
We start by rearranging the equation 5x 2y = -3 so that all the terms with y are on one side and all the terms with x are on the other side.
5x -2y = -3
Now, we divide both sides by -2 to isolate y.
-5x/2 = y + 3/2
Finally, we subtract 3/2 from both sides to get the equation in the slope-intercept form.
-5x/2 = y - 3/2
Therefore, the slope of the equation 5x 2y = -3 is -5/2.
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Alex, beverly and carl live on the ame traight road. Alex live 12 mile from berverly and carl 4 mie from berve,y, how far doe alex live from carl?
If we assume that Cal lives between Beverly and Alex: so the distance between the two of them is 11-4 = 7 miles.
What is the number line and why is it used?Number line is a line contain every real numbers which includes all rational and irrational number. Generally we use it for determining ranges of a set. Using number line we can understand range and domain of function easily. A number line is a picture representation of real numbers evenly laid out on a straight line.
How far is from 0 on a number line?The distance from zero of a positive number r is simply r. But if r is negative, then we make a positive number by multiplying by -1, in other words -r is the distance in that case.
There is a standard mathematical function that does this, called the modulus function.
And whether r is positive or negative we write it like this |r|
So for example |100|=100 and |-100|=100 as well.
Alex is 11 miles away, and Cal is 4 miles away, so the distance between the two of them is 11-4 = 7 miles.
If we assume that Cal lives on the opposite side of Beverly from Alex:
Alex is 11 miles away from Beverly, and Cal is 4 miles away from Beverly in the opposite direction from Alex, so the distance between Alex and Cal is 11 + 4 = 15 miles.
The easiest way to see this is by creating a number line.
(for the first possible solution) If you put Beverly as a point, let's call it 0, then we would put Alex at 11 and Cal at 4, and the distance between them is 7.
(for the second possible solution) If you put Beverly as a point, 0, then we would put Alex at 11 and Cal at -4, and the distance between them is 15.
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45 PTS no need to explain.
Answer:
B. SAS-----------------------------------
The two triangles have 2 sides marked as congruent and the included angles are congruent as vertical angles:
AC ≅ EC,BC ≅ DC,∠ACB ≅ ∠ECDThis gives us SAS congruence postulate.
The matching choice is B.
Which of the following is equivalent to 5 a) ²/3 + 2/1/1/0 4 b) 1/2 x 1/1/20 c) / x4 d) / x4 ÷ 4 ? Show your thinking.
what is the equation of a line that is parallel to 4x+3y=12 AND passes through the point (3,4) ?
Answer:
Step-by-step explanation:
Given Line equation is 4x+3y=12 and point (3,4)
Given condition two line are parallel
Parallel means two straight lines having same slope.
From the above condition we can use "point-slope" equation.
[tex]y-y_{1} =m(x-x_{1} )[/tex]
From the given line equation we can find slope easily.
We can rewrite the line equation as [tex]y=-\frac{4}{3} x+4[/tex]
We can compare the above equation as y=mx+b
slope [tex]m=-\frac{4}{3}[/tex] and point [tex](x_{1} ,y_{1} )[/tex]=(3,4) submit in slope-point equation.
Becareful while submit point in the slope point equation.
Note:(Many students do mistakes while submitting point.
[tex]y-4=-\frac{4}{3}(x-3)[/tex]
solve and get the answer
Equation of line is 4x+3y=24
Is 5 an algebraic term?
5 is not an algebraic expression.
Since it is obvious that 5 is a constant, even if constants constitute a component of the algebraic equation, they do not finish it. A variable and an operator are also necessary for an expression to qualify as an algebraic expression. Any unknown term, such as x, y, or z, can be a variable, and the operators + and - can be used. Terms with no associated variables are known as constants. A variable and an operator are also necessary for an expression to qualify as an algebraic expression.
It follows that 5 cannot be an algebraic expression.
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A state trooper used a radar gun to measure the speed (in miles per hour) of all the cars that drove past her stretch of highway in a twenty minute period. She separated the results by whether the cars were traveling northbound or southbound. The histograms show the speed of each car that she recorded.
Which statement is an appropriate inference based on the median of each data set?
Question 4 options:
1.)The northbound cars were generally faster because the median for the northbound cars is less than the median for the southbound cars.
2.)The northbound cars were generally faster because the median for the northbound cars is greater than the median for the southbound cars.
3.)The southbound cars were generally faster because the median for the northbound cars is less than the median for the southbound cars.
4.)The southbound cars were generally faster because the median for the northbound cars is greater than the median for the southbound cars.
Answer:
2.
Step-by-step explanation:
There are more boxes towards the highest numbers which means that the medians for northbound cars are generally high while the medians for southbound cars are located more on the smaller numbers representing the speed.
Tyrell is traveling to Chicago, Illinois. He takes a cab service from the airport to his hotel. The table shows the linear relationship between the number of miles the cab travels, x, and the total fee, y.
Cab Fare
Number of Miles Total Fee
2 $17.00
5 $21.50
7 $24.50
10 $29.00
15 $36.50
What does the y-intercept mean in this situation?
When the cab travels 0 miles, the total fee will be $14.00.
When the cab travels 0 miles, the total fee will be $1.50.
For every additional mile the cab travels, the total fee increases by $14.00.
For every additional mile the cab travels, the total fee increases by $1.50.
The y-intercept in this situation means A. When the cab travels 0 miles, the total fee will be $14.00.
What is the y-intercept?The formula to find the y-intercept is y = f(x), where x = 0, and then solve for y.
The equation for a linear relationship is y = mx + b, where x is the independent variable, y is the dependent variable, m is the slope of the line, and b is the y-intercept.
Cab Fare
Number of Miles Total Fee
2 $17.00
5 $21.50
7 $24.50
10 $29.00
15 $36.50
Difference between 7 and 5 = 2
Difference between $24.50 and $21.50 = $3
Variable cost per mile (Slope) = Rise/Run
= $1.50 ($3/2)
y = mx + b
y-intercept, b = 24.50 - 7(1.5)
= 14
= $14.00
Thus, the y-intercept in this situation means Option A while the slope shows that for every additional mile, the total fee increases by $1.50.
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Answer:
The y-intercept in this situation means A. When the cab travels 0 miles, the total fee will be $14.00.
Step-by-step explanation:
What is a 9 sided shape called?
A 9-sided shape is called a nonagon.
Therefore the answer is nonagon.
A nonagon is a polygon with nine sides and nine angles. A nonagon can be regular or irregular, depending on the lengths of its sides and angles. A regular nonagon has equal sides and angles, while an irregular nonagon has sides and angles of different lengths.
Nonagons are two-dimensional shapes, and they can be described by their number of sides, angles, and vertices. They are considered a type of polygon, which is a closed geometric figure that is made up of straight lines. In addition to nonagons, there are other types of polygons such as triangles, quadrilaterals, pentagons, hexagons, heptagons, and so on.
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Write the place value and value of each digit of the decimals 6905.327 also write its name and expanded form
Answer:
6000.000 + 900.000 + 0 + 5 + 3/10 + 2/100 + 7/1000
six thousand nine hundred and five ones point(.) three tenths two hundredths and seven thousandths
Step-by-step explanation:
right!!!
if i drank x ounces of juice and someone drank 1/3 more than that what is your equation.
Answer:
y = x + 1/3
Step-by-step explanation:
We know
You drank x ounces of juice and someone drank 1/3 more than what you think
Let's y represent the total, we have the equation
y = x + 1/3
Answer: 4/3x (or 1/3 + x, since your wording's pretty odd)
Step-by-step explanation:
i can't tell if the one-third you're referring to is a third of how many ounces of juice you drank (meaning it will change if you drank 1, 2, 3 oz of juice and so on) or if it's always going to be a third of an ounce more than the amount of oz of juice you drank (in which case it'd be 1/3 + x). anyway just choose whichever answer you're looking for :3
How many minutes will a bus take to cover 5 km travelling at 9 km/h?
Answer:
the bus will take approximately 33.33 minutes to cover 5km at a speed of 9 km/h.
Step-by-step explanation:
To find out how many minutes it will take for a bus to cover 5km at a speed of 9km/h, we need to use the formula:
time = distance / speed
In this case, the distance is 5 km, and the speed is 9 km/h. To convert the speed to km/min we can divide 9 by 60.
9 km/h = 0.15 km/min (by dividing 9 by 60)
Now we can substitute the distance and speed into the formula:
time = 5 km / 0.15 km/min = 33.33 min
So, the bus will take approximately 33.33 minutes to cover 5km at a speed of 9 km/h.
It's important to note that in this problem km/h is the speed and the distance is given in km, so you need to convert it to km/min in order to find the time. Also the time you get will be in minutes.
How do you write log2 in exponential form?
To change logarithmic form to exponential form, spot the logarithmic equation's base and move the base to another side to the equal sign. Moving the base will make the current number or variable into the exponent.
Do not move something but the base: the other numbers or value will not change sides, and the word "log" will be release.
Log Rules:
1. the first rule is logb(mn) = logb(m) + logb(n)
2. the second rule is logb(m/n) = logb(m) – logb(n)
3. the third rule is: log b (mn) = n · logb(m)
1. Multiplication can be turned outside the log into addition and vice versa can be turned.
2. Division can be spin outside the log into a subtraction, and vice versa.
3. An exponent can be proceeded as a multiplier outward on all within a log, and vice versa.
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A triangle has 2 sides of length 2 and 18 what compound inequality describes the possible lengths for the third side length
I'm pretty sure the answer is 72 :))
Ashley is selling handmade jewelry to earn money for camp. Bracelets sell for $7.62 and
necklaces sell for $15.67, and she needs to make at least $450 in revenue to cover the cost
of camp.
Write the inequality in standard form that describes this situation. Use the given numbers and
the following variables.
X
= the number of bracelets
V
= the number of necklaces
Equation for the sentence's inequality are $7.62 and necklaces are $15.67, which means that 7.62x + 15.67y >= 450.
what is inequality ?An inequality in mathematics is a relationship between two expressions or values that is not equal. Thus, imbalance leads to inequality. An inequality creates the link between two values that are not equal in mathematics. Egality is distinct from inequality. When two values are not equal, most commonly use the not equal symbol (). Different inequalities are used to contrast values, no matter how small or large. Many simple inequalities can be resolved by modifying the two sides until the variables are all that remain. But a number of things contribute to inequality: Negative values on both sides are divided or added. Trade off the left and right.
given
let X = the number of bracelets
let Y = the number of necklaces
The inequality equation = 7.62x + 15.67y >= 450
Equation for the sentence's inequality She needs to generate at least $450 in revenue because bracelets are $7.62 and necklaces are $15.67, which means that 7.62x + 15.67y >= 450.
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what is 13 divided by 12
Answer:
1.0833333333333333333333333333333333 (repeats)
Step-by-step explanation:
use a calculator
find each value:
X=
Y=
GH=
GJ=
FE=
GE=
The values for figure is x = 2, y = 9,
GH = 8, GJ = 7,
FE = 3, GE = 7.
What is quadrilateral?A closed quadrilateral has four sides, four vertices, and four angles. It is a form of polygon. In order to create it, four non-collinear points are joined. Quadrilaterals always have a total internal angle of 360 degrees.
The Latin words quadra, which means four, and latus, which means sides, are combined to form the English word quadrilateral. A quadrilateral does not always have to have equal lengths on each of its four sides.
Given figure shows
GH parallel to EG
GH = EG
GH = 3y - 19
EG = 8
3y - 19 = 8
3y = 27
y = 9
GH = 3y - 19 = 3(9) - 19 = 8
and GJ parallel to JE
GJ = JE
GJ = 3x + 1
JE = 5x - 3
3x + 1 = 5x - 3
5x - 3x = 1 + 3
2x = 4
x = 2
values are,
GJ = 3x + 1 = 3(2) + 1 = 7
JE = 5x - 3 = 5(2) - 3 = 7
FE = 6x - y
substitute values,
x = 2, y = 9
FE = 6x - y = 6(2) - 9 = 12 - 9 = 3
Hence x = 2, y = 9
GH = 8, GJ = 7,
FE = 3, GE = 7.
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Nancy Stone has a small company and has negotiated a special rate for rental cars when she and other employees take business trips. The maximum charge is $45. 00 per day plus $0. 40 per mile. Discounts apply when renting for longer periods of time or during off-peak seasons
A linear inequality that models the total cost of the daily rental c(m) as a function of the total miles driven, m is c(m) ≤ 45 + 0.4 m.
What is linear inequality?
In mathematics, an inequality involving a linear function is referred to as a linear inequality. One of the inequality symbols is found in a linear inequality. In graph form, it displays the non-equal data.
Given:
Nancy Stone has a small company and has negotiated a special rate for rental cars when she and other employees take business trips.
The maximum charge is $45. 00 per day plus $0. 40 per mile.
A linear inequality involves a linear function. It contains one of the symbols of inequality. It exactly looks like a linear equation, with the inequality sign replacing the equality sign.
According to the statement Nancy has negotiated a special rate and the maximum charge is $45.00 per day with the addition of $ 0.40 per mile.
So,
a linear inequality that models the total cost of the daily rental as a function of the total miles driven, m is:
c(m) ≤ 45 + 0.4m
Hence, a linear inequality that models the total cost of the daily rental c(m) as a function of the total miles driven, m is c(m) ≤ 45 + 0.4 m.
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