The maximum number of miles she can drive is $111.388.
What is Unitary method?The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.
Step-by-step explanation:
The rental company charges $19.95
and, 18 cents for each mile driven.
So,
$40 - $19.95 = $20.05
Thus, the maximum number of miles she can drive
=$20.05 / by 0.18
= 111.388
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Joe ordered a large cake for his brothers. He gave 1 out of 12 of the cake to David, 5 out of 12 of the cake to John, and 2 out of 12 of the cake to Ali. He ate the remaining cake himself. What fraction of the whole cake did Joe eat?
Answer: 4/12 or 1/3
Step-by-step explanation:
A whole cake is 12/12.
He gave away 1/12, 5/12, and 2/12s of the cake
1+5+2 = 8
So he gave out 8/12s of the cake, which means he has 4/12 left, or 1/3 if you want simplest form.
Hope this helps.
what is the rule of the reflection?
The rule of reflection in the image shown is: (x, -y).
What is Reflection?Reflection is a transformation which creates a new image by flipping over a line of reflection. The new image is congruent to the original image after reflection. The rule of reflection over an x-axis is given as, (x, -y).
In the image given we can see that rotating triangle LMN over the x-axis gave us:
M(-5, 4) → M'(-5, -4)
L(-4, 2) → L'(-4, -2)
N(-2, 3) → N'(-2, -3)
Therefore, the rule of reflection is: (x, -y).
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Give the outcomes for each of the following events.
MN= cm
Help me please!! Stuck on this thanks:)
Answer:
3π
Step-by-step explanation:
arc length = radius x central angle in radians
π = radius x π/3
radius = 3π
since OMN is an equilateral triangle, radius = MN
thus MN = 3π
please help me answer this!!
The value of x from the given expression is 5/6
Expansion of equation
Given the expression to expand expressed as:
15 = 3/5(6x + 20)
We are to determine the value of x
15(5) = 3(6x + 20)
Expand
75 = 18x +60
Collect like terms
18x = 75 - 60
18x = 15
x = 15/18
x = 5/6
Hence the value of x from the given expression is 5/6
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A pen and a ruler cost $2.10. 2 such pens and 3 such rulers cost $4.90. Find the cost of one ruler.
The cost of one ruler is $0.70
Applications of simultaneous equationsFrom the question, we are to determine the cost of one ruler
Let x represent the cost of a ruler
and
y represent the cost of a pen
From the given information, we can write that
y + x = $2.10 ----------- (1)
2y + 3x = $4.90 ----- (2)
From equation (1),
y + x = $2.10
Then,
y = $2.10 - x
Substitute this into equation (2)
2y + 3x = $4.90
2($2.10 - x) + 3x = $4.90
$4.20 - 2x + 3x = $4.90
$4.20 +x = $4.90
x = $4.90 - $4.20
x = $0.70
Hence, the cost of one ruler is $0.70
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Which could be used to evaluate the expression negative 6 (4 and two-thirds)? (negative 6) (4) (negative 6) (two-thirds) (negative 6) (4) times (negative 6) (two-thirds) (negative 6 4) (negative 6 two-thirds) (negative 6 4) times (negative 6 two-thirds)
Hence, the required expression is (Negative 6) (4) + (negative 6) (two-thirds).
What is an expression?expression is a combination of numbers, variables, and functions (such as addition, subtraction, multiplication or division etc.). This math operation can be addition, subtraction, multiplication, or division. The structure of an expression is: Expression is (Number/Variable, Math Operator, Number/Variable)
How to solve?LHS,
(-6)([tex]\frac{14}{3}[/tex]) = -28
RHS,
(-6)()[tex]4+\frac{2}{3}[/tex]) = -28
LHS=RHS
Hence, the required expression is (Negative 6) (4) + (negative 6) (two-thirds).
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Which statements about the local maximums and minimums for the given function are true? Choose three options.
Over the interval [1, 3], the local minimum is 0
Over the interval [2, 4], the local minimum is –8.
Over the interval [3, 5], the local minimum is –8.
Over the interval [1, 4], the local maximum is 0.
Over the interval [3, 5], the local maximum is 0.
The statements about the local maximums and minimums for the given function which are true include:
Over the interval [2, 4], the local minimum is –8.Over the interval [3, 5], the local minimum is –8.Over the interval [1, 4], the local maximum is 0.What is Function?This is defined as the mathematical entities which assign unique outputs to given inputs and defines a relationship between the two variables.
According the the graph: over the interval [2, 4], the local minimum is –8 because the given minimum point is (3.4, -8) and over the interval [3, 5], the local minimum is –8.
Over the interval [1, 4], the local maximum is 0 and over the interval [3, 5], there is no maximum point hence why it is false.
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What is the smallest natural number in which its digits are only 1's and 2's and which is divisible by 3 and 8?
Look at the multiples of lcm(3, 8) = 24, each of which are divisible by both 3 and 8. Naturally, the number we're looking for must have at least two digits.
The last/ones digit of a number [tex]n[/tex] can be computed by evaluating [tex]n \pmod{10}[/tex]. Suppose the ones digit is 1. Then
[tex]n \equiv 24k \equiv 20k + 4k \equiv 4k \equiv 1 \pmod{10}[/tex]
but this has no solution since no multiple of 4 ends in 1. So our number ends with a 2.
If our number has two digits, then in order for it to be divisible by 3, the first digit must be 1, since 1 + 2 = 3. But 12 is not divisible by 24.
If our number has three digits, then it's either 111 (with digital sum 1 + 1 + 1 = 3) or 222 (digital sum 2 + 2 + 2 = 6), since no other triplet of 1s and 2s sums to a multiple of 3. But 111 = 3×37 and 222 = 2×111, so neither are divisible by 24.
Now suppose [tex]n[/tex] has four digits. Also suppose that the tens digit is 2. Then our number must be 1122 to uphold divisibility by 3, but 1122 = 2×3×11×17 is not divisible by 8. So the tens digit must be 1. This in turn leaves two remaining candidates, 1212 and 2112. We have 1212 = 12×(100 + 1) not divisible by 8, so our number must be [tex]\boxed{n=2112}[/tex]. And it is, since 2112 = 24×88.
Pina has two equations that she found to be valuable models for her research. She thinks that if she can find the solution of the two graphs, she will be able to identify a key point to her studies. What can Pina expect in terms of solutions of these two graphs?
-3x + y = 10
y = 3x − 6
parallel lines
infinite solutions
both parallel lines and no solution
no solution
The Institute of Education Sciences measures the high school dropout rate as the percentage of 16- through 24-year-olds who are not enrolled in school and have not earned a high school credential. Last year, the high school dropout rate was 8.1%. A polling company recently took a survey of 1,000 people between the ages of 16 and 24 and found that 6.5% of them are high school dropouts. The polling company would like to determine whether the dropout rate has decreased. When testing whether the dropout rate has decreased, the appropriate hypotheses are
The appropriate hypothesis which is used to test the dropout rate are [tex]H_{0}:p > =0.081\\[/tex] and [tex]H_{1}: p < 0.081[/tex].
Given Drop out rate through 24 year old who are not enrolled is 8.1%, sample size=1000 and we have to find the hypothesis to test the drop out rate of the school.
The variable which needs to be studied is X=Number of individuals with age between 16 and 24 years old that are high school dropouts.
The parameter of interest is the proportion to high school drop outs is p.
Sample proportion=[tex]p^{1}[/tex]=0.065
The hypothesis can be formed as under:
[tex]H_{0}:p > =0.081[/tex] (null hypothesis)
[tex]H_{1}:p < 0.081[/tex] ( alternate hypothesis)
Null hypothesis is a hypothesis which is tested for its validity and alternate hypothesis is hypothesis which is opposite of null hypothesis means if null hypothesis is rejected then the alternate hypothesis will be true.
[tex]Z_{H_{0} }=(p^{1}-p)/\sqrt{p*(1-p)/n}[/tex]
=[tex]0.065-0.081/\sqrt{(0.081*0.0919)/1000}[/tex]
=-1.85
Hence the appropriate hypothesis are [tex]H_{0}:p > =0.081[/tex] and [tex]H_{1}:p < 0.081[/tex].
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2 dogs, 4 horses 1 giraffe and a duck are lying on the bed. 3 chickens are flying over a chair. How many legs are on the ground?.
Answer:
8+16+2= 24 legs on ground
Step-by-step explanation:
The circumference of a sphere was measured to be 76 cm with a possible error of 0.5 cm. (a) Use differentials to estimate the maximum error in the calculated surface area. (Round your answer to the nearest integer.) cm2 What is the relative error
The maximum error in the calculated surface area is 24.19cm² and the relative error is 0.0132.
Given that the circumference of a sphere is 76cm and error is 0.5cm.
The formula of the surface area of a sphere is A=4πr².
Differentiate both sides with respect to r and get
dA÷dr=2×4πr
dA÷dr=8πr
dA=8πr×dr
The circumference of a sphere is C=2πr.
From above the find the value of r is
r=C÷(2π)
By using the error in circumference relation to error in radius by:
Differentiate both sides with respect to r as
dr÷dr=dC÷(2πdr)
1=dC÷(2πdr)
dr=dC÷(2π)
The maximum error in surface area is simplified as:
Substitute the value of dr in dA as
dA=8πr×(dC÷(2π))
Cancel π from both numerator and denominator and simplify it
dA=4rdC
Substitute the value of r=C÷(2π) in above and get
dA=4dC×(C÷2π)
dA=(2CdC)÷π
Here, C=76cm and dC=0.5cm.
Substitute this in above as
dA=(2×76×0.5)÷π
dA=76÷π
dA=24.19cm².
Find relative error as the relative error is between the value of the Area and the maximum error, therefore:
[tex]\begin{aligned}\frac{dA}{A}&=\frac{8\pi rdr}{4\pi r^2}\\ \frac{dA}{A}&=\frac{2dr}{r}\end[/tex]
As above its found that r=C÷(2π) and r=dC÷(2π).
Substitute this in the above
[tex]\begin{aligned}\frac{dA}{A}&=\frac{\frac{2dC}{2\pi}}{\frac{C}{2\pi}}\\ &=\frac{2dC}{C}\\ &=\frac{2\times 0.5}{76}\\ &=0.0132\end[/tex]
Hence, the maximum error in the calculated surface area with the circumference of a sphere was measured to be 76 cm with a possible error of 0.5 cm is 24.19cm² and the relative error is 0.0132.
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For the following exercises, find (f ∘ g)(x) and (g ∘ f)(x) for each pair of functions.
35. f(x) = 3x + 2, g(x) = 5 − 6x
Answer:
The value of [tex]$(f \circ g)(x)$[/tex] is 17-18x and [tex]$(g \circ f)(x)$[/tex] is -7-18x.
Step-by-step explanation:
It is given in the question functions f(x) as 3x+2 and g(x)=5-6x.
It is required to find [tex]$(f \circ g)(x)$[/tex] and [tex]$(g \circ f)(x)$[/tex].
To find [tex]$(f \circ g)(x)$[/tex], substitute g(x) for x in f(x) and simplify the expression.
To find [tex]$(g \circ f)(x)$[/tex], substitute f(x) for x in g(x) and simplify the expression.
Step 1 of 2
Substitute g(x) for x in f(x) and simplify the expression.
[tex]$$\begin{aligned}&(f \circ g)(x)=f(5-6 x) \\&(f \circ g)(x)=3(5-6 x)+2 \\&(f \circ g)(x)=15-18 x+2 \\&(f \circ g)(x)=17-18 x\end{aligned}$$[/tex]
Step 2 of 2
Substitute f(x) for x in g(x) and simplify the expression.
[tex]$$\begin{aligned}&(g \circ f)(x)=g(3 x+2) \\&(g \circ f)(x)=5-6(3 x+2) \\&(g \circ f)(x)=5-18 x-12 \\&(g \circ f)(x)=-7-18 x\end{aligned}$$[/tex]
Describe the transformations necessary to transform the blue graph of f(x) into the red graph of g(x)
Transformation is a process that involves either increasing, or decreasing the size of a given object, or changing its orientation to produce an image.
The required transformations are:
i. For graph a - translation.
ii. For graph b - dilation.
Rigid transformation involves a change in the orientation of a given object or resizing of a given object to produce an image. The types of transformation are reflection, translation, rotation, and dilation.
i. Reflection is a type of transformation that requires flipping a given object about a reference point or line.
ii. Translation is a type of transformation that involves moving an object in a particular direction without a change in its size and orientation.
iii. Rotation is a type of transformation that involves turning an object at a given angle about a reference point.
iv. Dilation is a type of transformation that require increasing or decreasing the size of the object using a given factor.
Therefore the necessary transformation to transform the blue graph of f(x) into the red graph of g(x) is:
a. For graph a is translation.
b. For graph b is dilaton.
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According to the fundamental theorem of algebra, how many roots exist for the polynomial function? (9x 7)(4x 1)(3x 4) = 0
3 roots are exist, since the polynomial is of third degree.
According to statement
This follows immediately from the zero product property: if ab=0, then either a=0 or b=0. We have3 roots are exist, since the polynomial is of third degree.
(9x+ 7)(4x +1)(3x+ 4) = 0
from which it follows that each of which admits only one solution.
AND
using the fundamental theorem of algebra, expanding we have a polynomial that is of third degree:
(9x+ 7)(4x +1)(3x+ 4) = 0
108x^3 + 255 x^2 +169x + 28 =0
The theorem states that a polynomial will have up to n distinct roots. In this case, it follows that there are exactly 3, since the solutions to the system above are all distinct.
So, 3 roots are exist, since the polynomial is of third degree.
DISCLAIMER : The question was incomplete. Please find the full content below.
QUESTION
According to the Fundamental Theorem of Algebra, how many roots exist for the polynomial function? (9x + 7)(4x + 1)(3x + 4) = 0 1 root 3 roots 4 roots 9 roots
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The question is already stated on the picture.
The central angle is 77 degrees mate.
Consider parallelogram PQRS, where PQ ≅ RS and QR ≅ PS. Construct diagonal PR and diagonal QS. By the SSS criterion, ΔPQR ≅ ΔRSP and ΔPQS ≅ ΔRSQ. Therefore, ∠QPS ≅ ∠SRQ and ∠PQR ≅ ∠RSP since corresponding angles of congruent triangles are congruent.
What statement is proven by the given steps?
A.
A quadrilateral with congruent consecutive angles is a parallelogram.
B.
Consecutive angles of a parallelogram are congruent.
C.
Opposite angles of a parallelogram are congruent.
D.
A quadrilateral with congruent opposite angles is a parallelogram.
The correct answer would be option(C) opposite angles of a parallelogram are congruent.
What is Parallelogram?A parallelogram defined as a special type of quadrilateral which has both pairs of opposite sides parallel and equal.
Given that PQRS is a parallelogram.
PQ ≅ RS
QR ≅ PS
By the SSS criterion, ΔPQR ≅ ΔRSP and ΔPQS ≅ ΔRSQ.
Therefore, ∠QPS ≅ ∠SRQ and ∠PQR ≅ ∠RSP since corresponding angles of congruent triangles are congruent.
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Answer:
"B"
Step-by-step explanation:
sabbir arrived at dhaka train station at 9 30 pm write this time using the 24hr clock
Okay so a 24hr clock is very simple. We usually turn to "PM" when its 12:00 (day time).
In the 24hr clock we do not, we don't use PM or AM but its crucial to know when converting a standard clock time to military time (aka. 24hr).
9:30 PM in 24hr clock is 12:00 + 9:30 because 9:30 is past that first 12 hours.
So in 24hr clock time it is 21:30. You can also count backwards from midnight to figure it out, for example 12:00 AM (midnight), minus 9:30 is 2:30. Therefore 24:00-2:30=21:30.
Hopefully it helps, heart will help me alot too!
Answer:
21:30
Step-by-step explanation:
The 24hour clock uses 0:00 for midnite. 1am through noon are just 1:00 - 12:00. But the pm hours continue counting up, 13 - 23.
For example, 1pm is 13:00 and 2pm is 14:00.
To change to 24 hour clock, for pm hours, ADD 12.
So for your problem, 9:30 is:
9:30 + 12
= 21:30
Find the length of the midsegment .
A.15
B.44
C.22
D.13
Answer: 22
Step-by-step explanation:
Using the triangle midsegment theorem,
[tex]2(5x+2)=3x+32\\\\10x+4=3x+32\\\\7x+4=32\\\\7x=28\\\\x=4[/tex]
So, the length of the midsegment is 5(4) + 2 = 22
What is the probability that a two-digit number selected at random has a tens digit less than its units digit
The probability that a two-digit number selected at random has a tens digit less than its units digit is 0.2667 (4/15).
[tex]A=24B=90\\\\P=A/B\\\\P=24/90\\p=4/15[/tex]
There are 90 two-digit numbers (99-9). Of these, six numbers are divisible by 15 (15, 30, 45, 60, 75, 90). This is also divisible by 5. Therefore, the preferred case is 30-6 = 24. Therefore, the required probability is 24/90 = 4/15.
The probability of an event can be calculated by simply dividing the number of favorable results by the total number of possible results using a probabilistic expression. Whenever you are uncertain about the outcome of an event, you can talk about the probability of a particular outcome, that is, its potential.
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Pauley graphs the change in temperature of a glass of hot tea over time. he sees that the function appears to decrease quickly at first, then decrease more slowly as time passes. which best describes this function?
Non-linear graph best describes this function.
Why nonlinear?
As described in the question, Pauley graphs the change in temperature of a glass of hot tea over time. He sees that the function appears to decrease quickly at first, then decrease more slowly as time passes. It is linear because the graph decreases over time. It is linear because there is both an independent and a dependent variable but it doesn't satisfies one condition of being linear. Thus, It's Nonlinear because linear functions are increasing functions. It is nonlinear because linear functions increase or decrease at the same rate.
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Answer:
B
Step-by-step explanation:
I need answer fast!!
3. Write the rule that describes the second transformation. (5 points)
The rule that describes the second transformation is; Rotated at 90° clockwise
How to Interpret Transformations?From the given diagram we can see that;
The transformation from Rectangle ABCD to A'B'C'D' follows the transformation sequence of;
Shift 1 unit downwards then translate 5 units to the right.
However, for the transformation of A'B'C'D' to A"B"C"D", we see that the transformation is; Rotated at 90° clockwise
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What is the area of a rectangle with side lengths of 6/8 meter and 4/10 meter?
Enter your answer as a fraction in simplest form by filling in the boxes.
$$
m²
A parallelogram in which adjacent sides are perpendicular to each other is called a rectangle. The area of a rectangle with side lengths of 6/8 meter and 4/10 meter is 0.3 meters².
What is a rectangle?A parallelogram in which adjacent sides are perpendicular to each other is called a rectangle. A rectangle is always a parallelogram and a quadrilateral but the reverse statement may or may not be true.
The area of a rectangle with side lengths of 6/8 meter and 4/10 meter is,
Area of rectangle = 6/8 meter × 4/10 meter
= 24 / 80 meters²
= 6 /20 meters²
= 0.3 meters²
Hence, The area of a rectangle with side lengths of 6/8 meter and 4/10 meter is 0.3 meters².
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If the expression (2+ 3+ 2i) is a factor of a polynomial, which expression below
must also be a factor?
A: -(x+3+2i)
B: (x-3-2i)
C:(x-3+2i)
D:(x+3-2i)
Step-by-step explanation:
180 250 300 H.C.F by division method
Select the correct answer from each drop-down menu.
Trapezoid PQRS
4650
be inscribed in a circle because the
Reset
115⁰
Next
65°
Based on the inscribed quadrilateral conjecture: trapezoid QPRS can be inscribed in a circle because its opposite angles are supplementary.
What is the Inscribed Quadrilateral Conjecture?The inscribed quadrilateral conjecture states that the opposite angle of any inscribed quadrilateral are supplementary to each other. That is, they have a sum of 180 degrees.
From the diagram given, the opposite angles in the trapezoid, 115 + 65 = 180 degrees.
Therefore, we can conclude that: trapezoid QPRS can be inscribed in a circle because its opposite angles are supplementary.
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Eric was rock climbing. At one point, he stopped and climbed straight down 2\dfrac{1}{2}2
2
1
2, start fraction, 1, divided by, 2, end fraction meters. Then he climbed straight up 6\dfrac{3}{4}6
4
3
6, start fraction, 3, divided by, 4, end fraction meters. Eric was wondering what his change in elevation was after these two moves.
Which of the following equations matches the situation above?
The equation that matches the given situation is [tex]-2\frac{1}{2}+6\frac{3}{4}=?[/tex] . So, after two moves, Eric's elevation changed [tex]4\frac{1}{4}[/tex] meters above.
We know that in mathematics, subtraction means removing something from a group or a number of things. What is left in the group gets smaller when we subtract. The minuend is the first element we use. The subtrahend is the part that is being removed. The difference is the portion that remains after subtraction.
Assume that "negative" means climbing down and "positive" means climbing up. We must locate the elevation change in this area.
Given that Eric climbed straight down [tex]2\frac{1}{2}[/tex] meters. So we can write [tex]-2\frac{1}{2}[/tex].
Again Eric climbed straight up [tex]6\frac{3}{4}[/tex] meters. So, we can write [tex]6\frac{3}{4}[/tex].
Then the change = [tex]-2\frac{1}{2}+6\frac{3}{4}[/tex]
=[tex]-\frac{(2*2+1)}{2}+\frac{6*4+3}{4}[/tex]
=[tex]-\frac{5}{2} +\frac{27}{4}[/tex]
=[tex]\frac{-(5*2)+27}{4}[/tex]
=[tex]\frac{-10+27}{4}[/tex]
=[tex]\frac{17}{4}[/tex]
=[tex]\frac{4*4+1}{4}[/tex]
=[tex]4\frac{1}{4}[/tex]
Therefore, the equation that matches the given situation is [tex]-2\frac{1}{2}+6\frac{3}{4}=?[/tex] . So, after two moves, Eric's elevation changed [tex]4\frac{1}{4}[/tex] meters above.
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Question is on the picture:)
Answer:
Z = 90 degrees
Step-by-step explanation:
Reason is a diameter subtends angle of 90 degrees on the circumference
A measure of the strength of the relationship between two variables is referred to as the.
A statistical indicator of the strength of the association between the relative movements of two variables is the correlation coefficient.
To gauge how strongly two variables are related to one another, correlation coefficients are used.
A statistical indicator of the strength of the association between the relative movements of two variables is the correlation coefficient. The values are in the -1.0 to 1.0 range. There was a measurement error in the correlation if the estimated value was larger than 1.0 or lower than -1.0. Perfect negative correlation is shown by a correlation of -1.0, and perfect positive correlation is shown by a correlation of 1.0. A correlation of 0.0 indicates that there is no linear link between the two variables' movements. Finance and investing can benefit from the usage of correlation statistics.
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statements and reasons please
The lines YZ and WZ are equivalent because the diagonal bisects the parallelogram into two parts of which are equal.
What are the properties of a parallelogram?Properties of a parallelogram include;
Opposite sides are equalOpposite angels are equalThe angles are supplementary to each other The diagonals of a parallelogram bisect each otherFrom the figure, we have that lines YZ and WZ are equivalent because the diagonal bisects the parallelogram to two four of which they are of equal lengths.
Thus, the lines YZ and WZ are equivalent because the diagonal bisects the parallelogram into two parts of which are equal.
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