Answer:
The marginal cost in this range is $0.50 per bouquet. This can be calculated by finding the difference in total cost of arranging 500 bouquets and 600 bouquets, which is $800, and dividing that by the difference in quantity of bouquets, which is 100. This gives a marginal cost of $0.50 per bouquet.
Two boys are comparing how fast they are growing Alex is 60 in tall and growing at a rate of 1/4 of an inch every month Leo is 48 in tall and growing at a rate of 1/2 of an inch every month where will they be at the same height
The boys will have same the height after 48 months.
What is an equation?An equation is a mathematical statement that shows that two mathematical expressions are equal.
Given that, two boys are increasing with the rate of 1/4 and 1/2 of an inch every month, they have height 60 in and 48 in, will need to find that when will they have equal height,
The height increased in x month of them is given by,
x/4 + 60 or x/2 + 48
Let they have equal height after y months,
y/4 + 60 = y/2 + 48
y/4 = 12
y = 48
Hence, the boys will have same the height after 48 months.
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PLEASE HELP ASAP‼️‼️ I just need the measurements for s and n
d of a transverse wave is 25 m/s, if the source produces a disturbance that has a frequency of 200 Hz, what is the wavelength of the wave?
The wavelength will be "0.125 m".
What are Frequency and Wavelength?The wavelength, as well as frequency, have an inverse relationship. It shows that whenever a short wavelength exists, a high frequency exists, and when a big wavelength exists, a lower frequency exists.
The distance of a single wave-particle travels after completing one oscillation would be its wavelength.
According to the given information,
Speed of transverse, s = 25 m/s
Frequency, f = 200 Hz
We know the formula,
→ Wavelength, λ = velocity/ frequency
By substituting the values, we ger
λ = 25/200
λ = 0.125
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1/2 minus (1/8+1/8) I need help can somebody give me advice on this
Answer: 38
Step-by-step explanation:
Subtract 1/8 from 1/2
12 - 18 is 38.
Steps for subtracting fractions
Find the least common denominator or LCM of the two denominators:
LCM of 2 and 8 is 8
Next, find the equivalent fraction of both fractional numbers with denominator 8
For the 1st fraction, since 2 × 4 = 8,
12 = 1 × 42 × 4 = 48
Likewise, for the 2nd fraction, since 8 × 1 = 8,
18 = 1 × 18 × 1 = 18
Subtract the two like fractions:
48 - 18 = 4 - 18 = 38
math trigonometry question
Hence, combine all the solutions we get,
[tex]x=\frac{\pi}{2} +2n\pi,x=\frac{3\pi}{2} +2\pi n ,[/tex][tex]x= sin^{-1} (\frac{1}{3} )+ 2\pi n ,x= sin^{-1 }(\frac{1}{3})+2\pi n[/tex].
What are trigonometric identities?Trigonometric identities are equalities which involves trigonometric functions which are true for every value of variables that occur on both sides of the identities.
Given,[tex]3\sin \left(2x\right) = 2\cos \left(x\right)[/tex]
[tex]3\sin \left(2x\right)-2\cos \left(x\right)=0[/tex]
Using trigonometric identities, [tex]sin2x= 2sinx cosx[/tex]
we get,[tex]-2\cos \left(x\right)+6\cos \left(x\right)\sin \left(x\right)=0[/tex]
Taking [tex]2cos(x)[/tex] as factor, we get,
⇒[tex]2cos(x)(3sin(x) -1)[/tex]
⇒[tex]2cos(x) = 0 , (3sin(x) -1)=0[/tex]
⇒[tex]cos (x)= 0[/tex] for x= [tex]x=\frac{\pi}{2} +2n\pi,\frac{3\pi}{2} +2\pi n[/tex] and
[tex](3sin(x) -1)=0 for x= sin^{-1} (\frac{1}{3} )+ 2\pi n , sin^{-1 }(\frac{1}{3})+2\pi n[/tex]
Hence, combine all the solutions we get,
[tex]x=\frac{\pi}{2} +2n\pi,x=\frac{3\pi}{2} +2\pi n ,[/tex][tex]x= sin^{-1} (\frac{1}{3} )+ 2\pi n ,x= sin^{-1 }(\frac{1}{3})+2\pi n[/tex].
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Which is a quadratic function having a leading coefficient of 3 and a constant term of –12?
The required quadratic function having a leading coefficient of 3 and a constant term of –12 is f(x) = 3x^2 + bx - 12.
What is the equation?The equation is the relationship between variables and represented as y = ax + b is an example of a polynomial equation.
Here,
A quadratic function can be written in the general form:
f(x) = ax² + bx + c
where a, b, and c are constants.
Given a leading coefficient of 3 and a constant term of -12, we can write the quadratic function as,
f(x) = 3x² + bx - 12
Therefore, a quadratic function having a leading coefficient of 3 and a constant term of –12 is f(x) = 3x^2 + bx - 12.
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big augie's pizza now offers triangle shaped pizzas. how long must the sides fo the pizza be to the nearest inch equal the size of a round pizza with a 17 inch diameter?
Answer:
Step-by-step explanation:
The area of a round pizza with a 17 inch diameter is:
A = πr^2 = π(8.5)^2 ≈ 226.98 square inches
To find the length of the sides of a triangle with the same area, we can use the formula for the area of a triangle:
A = (1/2)bh
where b is the base of the triangle and h is the height.
Since the triangle is equilateral (i.e., all sides are equal), the base and height are the same. Let's call this length x. Then:
A = (1/2)bh = (1/2)x(x/2) = x^2/4
Setting this equal to the area of the round pizza, we get:
x^2/4 = 226.98
Multiplying both sides by 4, we get:
x^2 = 907.92
Taking the square root of both sides, we get:
x ≈ 30.13
So the sides of the equilateral triangle should be about 30.13 inches long to have the same area as a round pizza with a 17 inch diameter. Rounded to the nearest inch, the sides of the triangle should be 30 inches long.
Graphing quadratics find: y = - x^2 + 6x - 4
Axis of symmetry:
Vertex:
With process pls.
Answer:
Axis of Symmetry is 3 or x=5
vertex is (3,5)
Step-by-step explanation:
the vertex is either the highest or the lowest point on a quadratic function's graph, here (3,5) is the highest point, therefore it is the vertex.
Axis of symmetry is usually always the x value of the vertex, that is that in (3,5). 3 is the axis of symmetry. This is because along the line x=5 the graph shows perfect symmetry
please do say thanks.
2. Which of the following is a decreasing exponential function whose y-intercept is 20?
(1) y=20
20()*
(2) y=20
(3) y=-2x+20
-()*
(4) y=
+20
An exponential function of the form y = 20aˣ can be 20 at the y-intercept
when a = 1.
What is an exponential function?An exponential function in which the independent variable is the exponent.
An exponential function can be written in the form as, y = aˣ, where a is a constant and 'x' is the variable.
We know, the y-intercept is when the value of x = 0.
Therefore, An exponential function of the form y = 20aˣ can be 20 at y-intercept when a = 1.
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PLEASE HELP MEEE
find the lateral area of a cone with a radius of 7ft and a slant height of 13ft use 3.14 for and round to the nearest tenth ADD EXPLANATION!!!!
The lateral area of the cone with a radius of 7ft and a slant height of 13ft is 285.7 ft².
What is the lateral area of the cone?A cone is simply a 3-dimensional geometric shape with a flat base and a curved surface pointed towards the top.
The lateral area of a cone is expressed as;
A = π × r × l
Where r is radius and l is slant height.
Given the data in the question;
Radius r = 7ftSlant height h = 13ftLateral area A = ?Plug the given values into the above formula and solve for the lateral area of the cone.
A = π × r × l
A = 3.14 × 7ft × 13ft
A = 285.7 ft²
Therefore, the lateral area is 285.7 square feet.
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The quadrilateral is a trapezoid. What is the value of x? if the top is 21 and the bottom is 27 and x is in the middleA) 4B) 5C) 48D) 25
The value of x for The quadrilateral which is a trapezoid is if the top is 21 and the bottom is 27 is option 2 that is 5.
Quadrilaterals called trapezoids have two parallel and two non-parallel sides. It also goes by the name Trapezium. A trapezoid is a closed, four-sided form or figure that has a perimeter and covers a specific area. It is a 2D figure rather than a 3D one. The bases of the trapezoid are the sides that are parallel to one another. Legs or lateral sides refer to the non-parallel sides. The height is the separation between the parallel sides.
From the given diagram, the expression below is true:
2(5x - 1) = 21 + 27
Expand
10x - 2 = 48
10x = 48 + 2
10x = 50
Divide both sides by 10
10x.10 = 50/10
x = 5
Hence the value of x is 5
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A boat travels about 8 kilometers per hour in
still water. If the boat is on a river that flows at a
constant speed of kilometers per hour, it can
travel at a 8 + r speed of kilometers per hour
downstream and 8 − r kilometers per hour
upstream. On the Chattahoochee river, the
boat can travel 4 kilometers upstream in the
same amount of time it takes to travel 12
kilometers downstream. What is the speed of the
river?
The speed of the river is given as follows:
4 kilometers per hour.
How to obtain the velocity of the river?The lowest speed that can be assumed by the boat is given as follows:
8 - r.
In which r is the speed of the river.
The lowest velocity is of 4 kilometers per hour, hence the speed of the river is obtained as follows:
8 - r = 4
r = 8 - 4
r = 4 kilometers per hour.
Then the maximum velocity is of:
8 + 4 = 12 kilometers per hour.
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what is the coefficient of x^4y^4 in the expansion of (x+y)8?
The coefficient of the term x⁴y⁴ as required to be determined in the task content is; Choice C; 70.
What is the coefficient of the term x⁴y⁴ in the given expansion.By observation, since the expansion is to the eighth power, it follows that the number of terms in the expansion would be 9.
On this note, the x⁴y⁴ term would be the 5th term whose coefficient would be; ⁸C⁴.
Therefore, the coefficient of the x⁴y⁴ as required would be; 70.
Ultimately, Choice C is correct.
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Exponential Growth and Exponential Decay
There are 30 bacterial cells on a petri dish. each hour the number of cells doubles. after 5 hours, how many cells are there
a) Identify if it is growth or decay.
b) Write an equation to model the situation
c) Answer the question.
a) This situation represents exponential growth, as the number of bacterial cells is doubling every hour.
b) Let N be the number of bacterial cells on the petri dish at time t in hours. The equation to model the situation is:
N = 30 x 2^t
This equation represents exponential growth, as the number of bacterial cells is doubling every hour. The initial number of bacterial cells is 30 (when t = 0), and the number of bacterial cells at any time t is given by multiplying the initial number by 2 raised to the power of t.
c) After 5 hours, the number of bacterial cells on the petri dish is:
N = 30 x 2⁵ = 30 x 32 = 960
So there are 960 bacterial cells on the petri dish after 5 hours.
The exponential growth and exponential decayThe math subject that is relevant to the case above is exponential growth and exponential decay. These are mathematical concepts that describe the behavior of quantities that increase or decrease at a constant percentage rate over time.
Exponential growth refers to a situation where a quantity grows at a constant percentage rate over time. In the case above, the number of bacterial cells doubles every hour, which is an example of exponential growth.
Exponential decay, on the other hand, refers to a situation where a quantity decreases at a constant percentage rate over time. An example of exponential decay could be the decay of a radioactive substance.
In summary, the case above involves the mathematical concept of exponential growth, which is a key concept in the field of mathematics and has important applications in fields such as biology, economics, and finance.
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The diagram below shows a rectangular prism made up of
inch cubes.
1. How many unit cubes whose dimensions are 3/5 inch fill up the rectangular prism?
_________
2. Find the total volume, in cubic inches, represented in the diagram.
_______ cubic inches
The number of unit cubes whose dimensions are 3/5 inch fill up the rectangular prism is (125/27)abc.
The total volume, in cubic inches, is represented in the diagram n cubic inches.
What is a cube?A cube is a three-dimensional object who has six faces.
Since each side of the unit cube has a length of 1 inch, the number of unit cubes that fill up the rectangular prism is equal to its volume in cubic inches. If the rectangular prism has dimensions a x b x c inches, then its volume is V = abc cubic inches.
Now, we need to find how many unit cubes whose dimensions are 3/5 inch fill up the rectangular prism. First convert the dimensions of the unit cube and the rectangular prism to a common unit, such as inches. Since 1 inch = 5/3 unit cubes, each side of the unit cube has a length (3/5) inch. Therefore, each side of the rectangular prism has dimensions (5a/3) x (5b/3) x (5c/3) unit cubes.
To find the number of unit cubes that fill up the rectangular prism, we can divide its volume (abc cubic inches) by the volume of each unit cube, which is (3/5)³ cubic inches. Thus, the number of unit cubes whose dimensions are 3/5 inch that fills up the rectangular prism is:
(abc) / [(3/5)³] = (125/27)abc
To find the total volume represented in the diagram, we need to add up the volumes of all the unit cubes shown in the diagram. Since we don't know the dimensions of the rectangular prism, we can't calculate its volume directly.
Therefore, the total volume represented in the diagram is n cubic inches.
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The graph of f(x) = |x| has been translated left 2 units and up 1 unit. If no other transformations of the function have occurred, which point lies on the new graph? (–4, 2) (–3, 1) ( –2, 5) ( –1, 2)
The point (- 1, 2) lies on the new graph.
What is Translation?A transformation that occurs when a figure is moved from one location to another location without changing its size or shape is called translation.
Given that;
The graph of f(x) = |x| has been translated left 2 units and up 1 unit.
Now, The function is,
⇒ f (x) = |x|
After translated 2 unit left we get;
⇒ f (x) = |x + 2|
And, After translated 1 unit down we get;
⇒ f (x) = |x + 2| + 1
Now, We can check all the given points as;
For point (- 1, 2);
Put x = -1 , f (x) = 2;
⇒ f (x) = |x + 2| + 1
⇒ 2 = |- 1 + 2| + 1
⇒ 2 = 1 + 1
⇒ 2 = 2
Thus, The point (- 1, 2) lies on the new graph.
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Click to show whether each function is linear or non-linear.
The linear equation is f(x) = 2^2 + x, while the other two functions are nonlinear functions
How to determine the function typesFrom the question, we have the following parameters that can be used in our computation:
The three equations
A linear equation is any equation that has a degree of 1
From the three equations, we can see that
Degree = 1
Degree = 2
Degree = 3
Hence, the linear function is f(x) = 2^2 + x
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Find the difference. use your answer in the simplest terms, using the slash ( / ) as the fraction bar.
7/8 - 5/7
urgent! (short answers please)
Answer: 9/56
Step-by-step explanation:
What is the percentage of data between 20 - 50?
The percentage of data between 20 and 50 is 25%
How to determine the percentage of dataThe boxplot in the complete question is added as an attachment
From the attached box plot, we have
From the given box plot it is clear that 20 is the median and 50 is the third quartile.
As a general rule:
There are 25% of data values between the median and the third quartile.
Hence, 25% of the data values are between 20 and 50.
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In AKLM, KL || NO. Given that MN=15, ML=48, and MO=20, find MK.
MK =
The length of MK is given as follows:
MK = 36.
What are similar triangles?Similar triangles are triangles that share these two features presented as follows:
Congruent angle measures.Proportional side lengths.The similar triangles for this problem are given as follows:
MNO and MKL.
Hence the proportional relationship for the side lengths is given as follows:
15/MK = 20/48
Applying cross multiplication, the length MK is given as follows:
20MK = 15 x 48
MK = 15 x 48/20
MK = 36.
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The residents of a city voted on whether to raise property taxes. the ratio of yes votes to no votes was 5to 6. if there were 10,604total votes, how many yes votes were there?
The number of yes votes would be 4,836.
Solution:
Given,
The ratio of yes votes to no votes is 5:6. So, assuming the actual values of yes votes and no votes be 5x and 6x respectively. We can frame an equation as follows,
5x + 6x = 10,640
=> 11x = 10,640
=> x = 967.27272727
So, the number of yes votes would come out to be,
5*967.272727 = 4836.3636
Since the answer can not be a fractional integer,
therefore, we will round it up to 4,836.
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does this table represent a proportional relationship
Yes, the table represents the proportional relationship.
What is proportional relationship?The proportional relationship between the variables {x} and {y} is such that -
y/x = K {constant}
y = Kx
y₁/x₁ = y₂/x₂ = k
A proportional relationship is represented by a straight line {where K is the slope}. It is concluded from the fact that the equation of the straight line passing through origin is of the form y = mx.
Given is a table as shown in the image.
For a direct or proportional variation -
y₁/x₁ = y₂/x₂ = k {k is constant parameter}
1/2 = 2/4 = k {constant}
1/2 = 1/2 = k {constant}
Therefore, yes, the table represents the proportional relationship.
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The graph of a piecewise-defined function is shown below.
On the interval
the function is given by the rule , and on the interval the function is given by the rule .
The graph of a piecewise-defined function y=c is a horizontal line reaching height c from the x-axis.
Explain about the piecewise-defined function?A piecewise function is arithmetic that is constructed from bits of various functions across various time intervals.
To determine which of the above intervals (as well as inequalities) -
the data user belongs to before evaluating a piecewise function at each given input.Simply substitute the provided input there in function specification for that specific period after that.Keep in mind that the function is represented by the line y=1 and is from -∞ to 0, or the left side.
Similar to that, the function is y=-1 from 0 to ∞ (doesn't include) .
Hence, the rule provides the function:
y=1, for x≤0,
y=-1, for x>0.
Thus, the graph of a function y=c is a horizontal line reaching height c from the x-axis.
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The complete question is-
The graph of a piecewise-defined function is shown below.
Check the correct option-
On the interval (x≤0, x≤1, x<1, x<0) the function is given by the rule (x= - 1, y= - 1, y=1, x=1), and on the interval (x≥0, x>1, x≥1, x>0) the function is given by the rule (y= - 1, x= - 1, y= 1, x= 1).
Andrea has 6 hours to spend training for an upcoming race. She completes her training by running full speed the distance of the race and walking back the same
distance to cool down. If she runs at a speed of 8 mph and walks back at a speed of 2 mph, how long should she plan to spend walking back?
Andrea has 6 hours to spend training for an upcoming race. She completes her training by running full speed the distance of the race and walking back the same distance to cool down. If she runs at a speed of 8 mph and walks back at a speed of 2 mph, she will spend 72 minutes walking back.
What is Time?This is referred to as the measured period during which an action, process, or condition exists or continues .
'x' rill represent the amount of time spent running in hours, then 3-x represents the time spent walking in hours.
Distance = Speed × time
Distance = 8x
Speed = 2mph
Time = (6-x)hours
Substitute the values
8x = 2 (6-x)
8x = 12 - 2x
10x = 12
x = 12/10 = 6/5
6/5 × 60 = 72minutes.
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Lelah has budgeted $135
for new clothes. She decides to buy a pair of shoes that cost $35.25,
and then she buys some $18.25
shirts.
Which inequality represents this situation, where s
is the number of shirts she can buy?
The inequality that this situation, where s is the number of shirts she can buy is S>81.5.
What is a solution set to an inequality or an equation?If the equation or inequality contains variable terms, then there might be some values of those variables for which that equation or inequality might be true. Such values are called solution to that equation or inequality. Set of such values is called solution set to the considered equation or inequality.
We are given that;
Budget of lelah for clothes= $135
For shoes= $35.25
For shirts= $18.25
Now,
S+$18.25+35.25>135
S>135-18.25-35.25
S>135-53.5
S>81.5
Therefore, the inequality will be S>81.5.
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which terms are used to describe events that have no outcomes in common?
The term used to describe events that have no outcomes in common is called "Mutually Exclusive."
Probability is a measure of how likely an event is to occur. The probability of an event ranges from 0 to 1, where 0 means that an event will not occur, and 1 means that an event will certainly occur.
In Mutually Exclusive events, the probability of both events happening at the same time is 0, which means that the outcome of one event completely eliminates the possibility of the outcome of the other event. The probability of getting heads and tails at the same time is 0, as it is impossible for the coin to show both heads and tails at the same time.
In mathematical terms, Mutually Exclusive events are represented by
=> P(A) + P(B) = P(A or B),
where P(A) represents the probability of event A, P(B) represents the probability of event B, and P(A or B) represents the probability of either event A or B occurring.
To summarize, Mutually Exclusive events are events that have no outcomes in common and have a probability of 0 of occurring simultaneously.
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Alonzo borrowed money from a credit union for 2 years and was charged simple interest at an annual rate of 8%. The total interest that he paid was $1120.
How much money did he borrow?
If necessary, refAssignmener to the list of financial formulas.
$1
I need help quick
The money borrowed by Alonzo at a simple interest rate of 8% for a time period of 2 years is $7000.
What is simple interest?
In the fields of finance and economics, interest is the payment made at a set rate by a borrower or deposit-taking financial institution to a lender or depositor in excess of the principal amount (the amount borrowed). It is not the same as a fee that the borrower might pay to the lender or another entity.
Borrowers must pay lenders simple interest as a fee in exchange for a loan. For simple interest calculation, compounding interest is excluded from the calculation and just the original principal is used. Simple interest applies to all loans, not just specific ones. Additionally, it refers to the kind of interest that banks give their customers on their savings accounts.
Given,
Time period = 2 years
Rate of interest = 8%
The simple interest paid at the end of 2 years = $ 1120
The money borrowed or the principal amount is
Simple interest = (Principal amount * rate * time)
1120 = P * 0.08 * 2
P = 1120/0.16 = $7000
Therefore the money borrowed by Alonzo at a simple interest rate of 8% for a time period of 2 years is $7000.
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if milk cost 0,58 per gallon how much would 3 1/2 cost
I am stuck on both of these questions.
1. Draw a vertical y-axis on the left-hand side of your graph and label it. Then draw a horizontal
x-axis at the bottom of your graph. Then label the coordinates of each corner of the sign on your graph. Draw a line on your graph. What is the slope of line a?
2. What is the equation of line a?
I think this is the graph I need to use I am not sure.
PLEASE HELP. ASAP ALMOST DUE?????
A linear function is demonstrated by the line a.
Line a has a slope of one.
Y = x + 2 is the equation for the line a.
How do you calculate a line's slope?
Following points on line a (x,y) = (0,2) and are available in the figure (2,4)
Calculating the slope (m) involves using:
m= y^2-y^1/x^2-x^1
This results
m= 4-2/2-0
Analyze m = 1
Consequently, the line's slope is 1.
The formula for line aThe formula for this is y = m(x - x1) + y1.
We thus have:
y = (x - 0) + 2
y = x + 2: Compare the difference and the result.
Consequently, y = x + 2 is the equation for the line a.
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Which quadrilateral has diagonals that are alwaysperpendicular bisectors of each other?1) square 2) rectangle 3) trapezoid4) parallelogram
The quadrilateral with diagonals that are always perpendicular bisectors of each other is a square. Correct option is 1.
In a square, the diagonals bisect each other at right angles, which means they intersect at a 90-degree angle. Moreover, since a square has four congruent sides and four right angles, the diagonals are also congruent. Thus, each diagonal is a perpendicular bisector of the other diagonal, splitting it into two equal segments.
In contrast, a rectangle has diagonals that bisect each other, but they are not always perpendicular. A trapezoid has only one pair of opposite sides that are parallel, and its diagonals do not bisect each other.
A parallelogram has opposite sides that are parallel, but its diagonals do not necessarily bisect each other or intersect at a right angle.
Therefore, the correct answer is a 1 (square).
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