Determine whether each quadrilateral is a parallelogram. Justify your answers.
And
Explain why the quadrilateral with the given vertices is a parallelogram. Use the indicated theorem.
Answers
The given quadrilaterals, 1 and 2, are parallelograms because the pair of opposite sides are parallel and the other pairs are congruent.
3. According to Theorem 7.9, quadrilateral ABCD is a parallelogram.
4. According to Theorem 7.12, quadrilateral PQRS is a parallelogram.
What is the proof for the parallelograms?3. Quadrilateral ABCD with vertices A(0,0), B(7,1), C(5,6), D(-2,5), and Theorem 7.9:
Theorem 7.9 states that if the opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram.
Using the distance formula, we can calculate the lengths of the sides of quadrilateral ABCD:
AB = √((7 - 0)² + (1 - 0)²) = √50
BC = √((5 - 7)² + (6 - 1)²) = √29
CD = √((-2 - 5)² + (5 - 6)²) =√50
DA = √((0 - (-2))² + (0 - 5)²) = √29
We can see that AB = CD and BC = DA, indicating that the opposite sides are congruent.
Quadrilateral PQRS with vertices P(-2,0), Q(3,1), R(4,4), S(-1,3), and Theorem 7.12:
Theorem 7.12 states that if both pairs of opposite sides of a quadrilateral are parallel and congruent, then the quadrilateral is a parallelogram.
Using the slope formula, we can calculate the slopes of the sides of quadrilateral PQRS:
Slope of PQ = (1 - 0) / (3 - (-2)) = 1/5
Slope of RS = (4 - 3) / (4 - (-1)) = 1/5
Slope of QR = (4 - 1) / (4 - 3) = 3
Slope of SP = (3 - 0) / (-1 - (-2)) = 3
The lengths of opposite sides can be calculated using the distance formula:
PQ = √((3 - (-2))² + (1 - 0)²) = √(25 + 1) = √26
RS = √((4 - 4)² + (4 - 1)²) = √(9) = 3
QR = √((4 - 3)² + (4 - 1)²) = √(1 + 9) = √10
SP = √((-1 - (-2))² + (3 - 0)²) = √(1 + 9) = √10
We can see that PQ = RS and QR = SP, indicate that the opposite sides are parallel and congruent.
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Related Questions
If you know the answer answer it with the explanation thank you.
Answers
The four numbers are 1, 5, 11, and 23.
Four numbers have a mean of 10 and the median is 8. Two of the numbers are 1 and 5. The other two numbers must be 11 and 23.
The mean of a set of numbers is calculated by adding all of the numbers and dividing by the number of numbers. In this case, the mean is 10, so the sum of the four numbers is 40. We already know that two of the numbers are 1 and 5, so the other two numbers must add up to 34.
The median of a set of numbers is the middle number when the numbers are arranged in ascending order. In this case, the median is 8, so the third number must be 8. This leaves the fourth number to be either 11 or 23.
If the fourth number is 11, then the mean of the four numbers will be 9.5, which is not correct. Therefore, the fourth number must be 23.
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tickets to a movie cost $10.50 for adults and $7.25 for students. you and a few friends purchased 8 tickets for $61.25. how many adult tickets and student tickets were purchased?
Answers
Answer:
1 adult ticket and 7 student tickets were purchased
Step-by-step explanation:
let a represent number of adult tickets purchased and s the number of student tickets purchased, then
a + s = 8 ( subtract s from both sides )
a = 8 - s → (1) ← based on total tickets purchased
10.5a + 7.25s = 61.25 → (2) ← based on cost of tickets
substitute a = 8 - s into (2)
10.5(8 - s) + 7.25s = 61.25
84 - 10.5s + 7.25s = 61.25
84 - 3.25s = 61.25 ( subtract 84 from both sides )
- 3.25s = - 22.75 ( divide both sides by - 3.25 )
s = 7
substitute s = 7 into (1)
a = 8 - 7 = 1
that is 1 adult ticket and 7 student tickets were purchased
A line passes through R(6, 9) and K(-6, 15)
a) What is the slope of RK?
b) Line VB is parallel to RK. What is the slope of VB?
c)Line WX is perpendicular to RK. What is the slope of WX?
Answers
The slope of line WX is 2.Since the slope of RK is -1/2, the slope of WX will be the negative reciprocal of -1/2, which means we flip the fraction and change its sign:
slope of WX = -1 / (-1/2) = 2.
a) To find the slope of the line RK, we can use the formula:
slope = (change in y) / (change in x)
Given the points R(6, 9) and K(-6, 15), we can calculate the change in y and change in x:
change in y = 15 - 9 = 6
change in x = -6 - 6 = -12
Plugging these values into the slope formula:
slope = (6) / (-12) = -1/2
Therefore, the slope of line RK is -1/2.
b) Since line VB is parallel to line RK, it will have the same slope as RK. Therefore, the slope of line VB is also -1/2.
c) To find the slope of line WX, which is perpendicular to RK, we can use the fact that the slopes of perpendicular lines are negative reciprocals of each other. Since the slope of RK is -1/2, the slope of WX will be the negative reciprocal of -1/2, which is 2.
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Choose the correct ordered pairs represented in the table. The following table gives per unit costs for furniture and shows selling prices. The numbers represent hundreds of dollars.
c 1 2 3 4 5
f(c)1 4 9 16 25
, , , ,
Answers
The correct ordered pairs represented in the table are (1, 1), (2, 4), (3, 9), (4, 16), and (5, 25).
The given table represents a function f(c) where c represents the quantity of furniture and f(c) represents the per unit cost in hundreds of dollars. We need to determine the correct ordered pairs based on the given information.
From the table, we can see that the values of c increase by 1 each time, starting from 1 and going up to 5. Similarly, the values of f(c) represent the square of the corresponding value of c. For example, f(1) = 1, f(2) = 4, f(3) = 9, and so on.
Based on this pattern, we can determine the correct ordered pairs:
(1, 1) corresponds to c = 1 and f(c) = 1
(2, 4) corresponds to c = 2 and f(c) = 4
(3, 9) corresponds to c = 3 and f(c) = 9
(4, 16) corresponds to c = 4 and f(c) = 16
(5, 25) corresponds to c = 5 and f(c) = 25
Therefore, the correct ordered pairs represented in the table are (1, 1), (2, 4), (3, 9), (4, 16), and (5, 25).
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I need the answer for this ones, please.
Answers
Answer:
Question 3) c.
Question 4) d.
Step-by-step explanation:
For the first question, it would be c., x is greater than and equal to -5. On the graph, there is a point at, (-5, -4). This restricts the graph from being all real numbers and the x value can't be less than -5. Since the point is a closed circle, it includes the point, so the domain will be -5, and everything greater than that value, making it C.
For the next question its asking for the range of the given graph. The range is based on y values. Domain is based on x values. There is a point at (-5, -4). Restrict the values of y to not be anything less than -4. And since the function continues and increases to positive infinity, the range would have to be y is greater than and equal to -4, making it d.
The measure of the largest scale of a triangle is 40o more than the measure of the smallest angle, and the measure of the remaining angle is 20o more than the measure of the smallest angle. Find the measure of each angle.
Answers
Answer:
40°, 60°, 80°
Step-by-step explanation:
You want the measures of the three angles of a triangle if the larger angles are 20° and 40° greater than the smallest.
Middle angleThe largest angle is 20° more than the middle angle, and the smallest is 20° less. Then the sum of the three angles is 3 times the middle angle, which must be 180°/3 = 60°.
The three angles are 40°, 60°, 80°.
__
Additional comment
If you need equations, you can designate the angles a, b, c, smallest to largest. Then c=a+40, and b=a+20. The sum is ...
(a) +(a +20) +(a +40) = 3a +60 = 180
Dividing by 3 tells you ...
a +20 = 60 . . . . . matches the value of b
a = 60 -20 = 40
c = 40 +40 = 80
If we were to write the equations in terms of b, we would have ...
(b -20) +b +(b +20) = 180
3b = 180
b = 60
This version gives a 1-step equation to solve instead of a 2-step equation, easier to do mentally.
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The measure of the Angles in the triangle are: the smallest angle is 40 degrees, the largest angle is 80 degrees, and the remaining angle is 60 degrees.
The measure of the smallest angle as x.
According to the given information, the largest angle is 40 degrees more than the smallest angle. Therefore, the measure of the largest angle is x + 40.
Similarly, the remaining angle is 20 degrees more than the smallest angle. So, the measure of the remaining angle is x + 20.
The sum of the angles in a triangle is always 180 degrees. Therefore, we can write the equation:
x + (x + 40) + (x + 20) = 180.
Simplifying the equation, we have:
3x + 60 = 180.
Subtracting 60 from both sides of the equation:
3x = 120.
Dividing both sides by 3:
x = 40.
Therefore, the measure of the smallest angle is 40 degrees.
Using this value, we can find the measures of the other two angles:
The largest angle is x + 40 = 40 + 40 = 80 degrees.
The remaining angle is x + 20 = 40 + 20 = 60 degrees.
the measure of the angles in the triangle are: the smallest angle is 40 degrees, the largest angle is 80 degrees, and the remaining angle is 60 degrees.
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11 of 3011 of 30 Questions
Question
A baker makes peanut butter cookies and chocolate chip cookies.
She needs 2 cups of flour and 34
cup of butter to make one batch of peanut butter cookies.
She needs 3 cups of flour and 1 cup of butter to make one batch of chocolate chip cookies.
If the baker has 26 cups of flour and 9 cups of butter, how many batches of each type of cookie can she make?
Answers
The baker can only make peanut butter cookies and cannot make any chocolate chip cookies with the given amount of ingredients.
Let's denote the number of batches of peanut butter cookies as "x" and the number of batches of chocolate chip cookies as "y."
From the given information, we can set up the following system of equations:
For the flour:
2x + 3y = 26
For the butter:
34x + y = 9
To solve this system of equations, we can use the substitution method or the elimination method. Let's use the elimination method:
Multiply the first equation by 17 (to make the coefficients of x in both equations the same):
34x + 51y = 442
Now we have the system of equations:
34x + y = 9
34x + 51y = 442
Subtract the first equation from the second equation:
34x + 51y - (34x + y) = 442 - 9
50y = 433
Divide both sides by 50:
y = 433/50
Since the number of batches of cookies cannot be fractional, we need to find a whole number solution for y. However, in this case, y is a fraction, indicating that the given amount of butter is not sufficient to make even one batch of chocolate chip cookies.
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Dot Plots and Histograms-Quiz-Level F
Briana is learning to play the guitar. At the end of each week, she records the number of days
she practiced. Her data is shown below.
2, 6, 4, 3, 0, 3, 4, 6, 5, 0, 4, 5, 7, 5, 6, 4, 5, 6
OFReady
Which dot plot displays the data distribution?
1
2
2
3
4
Number of Days
3
Number of Days
:
5
6
7
567
0
+
0
1
2
3
4
Number of Days
2
5
...
3
4
Number of Days
5 6
..
Answers
The dot plot that displays the data distribution is the dot plot on the lower left corner of the options with
Two dots at 0
One dot at 2
Two dots at 3
Four dots each at 4, 5, and 6
One dot at 7
A dot plot is a graphical presentation of data, on a number line, with the number of points of dot representing the frequency of data at each value on the number line.
The data can be presented as follows;
2, 6, 4, 3, 0, 3, 4, 6, 5, 0, 4, 5, 7, 5, 6, 4, 5, 6
The above data can be arranged in increasing order as follows; 0, 0, 2, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 6, 6, 6, 6, 7
Therefore, the frequencies of 0s is two, the frequencies of 4s, 5s and 6s are four each, and the frequency of 7 is one, which corresponds to the third graph or the graph in the bottom left corner of the figure.
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find the value of (32) 3/5
Answers
Answer:
19.2
Step-by-step explanation:
(32) 3/5
= 32 multiple 3/5
= 96/5 [ explanation: 32 multiple 3 = 96 ]
= 19.2 [ explanation: 96 divided by 5 = 19.2 ]
Hi can someone who is good at this please help I'm struggling here.
if there were 100 males and 200 females how many flies of each would have red eyes?
Answers
Answer:
The cross-over diagram is correct. The number of flies of each sex with red eyes will depend on the genotype of the parents.If a red-eyed male mates with a white-eyed female, all of the offspring will be female and have red eyes (XRXr).If a red-eyed male mates with a red-eyed female, half of the offspring will be male and have red eyes (XRY) and half will be female and have red eyes (XRXr).If a white-eyed male mates with a white-eyed female, all of the offspring will be white-eyed (XrXr).Therefore, if there are 100 males and 200 females, the number of flies of each sex with red eyes will be:Males: 50Females: 150I hope this helps!
proof of the converse of the
e theorem. As you read through the
to complete the statements on the
Complete the statements by choosing the correct
answer from the drop-down menu.
are being used to get the equation in
are being used to get the equation in
are being used to get the equation in
step 9.
In step 14, "similar argument" means to draw segment
and follow the same logic in steps 3-12.
step 6.
step 8.
Answers
The converse of the parallelogram angle theorem is proved.
How to explain the informationThe term parallelogram is defined as a quadrilateral whose two pairs of sides are parallel to each and the four angles at the vertices are not equal to the right angle and then the quadrilateral.
Here we are given that LM ≅ ON and LO ≅ MN
Here we have also know that ∠LNO and ∠NLM are alternative and interior angles
Then according to the reflexive property, it can be written as
=> LN ≅ LN
Then as per the SSS similarity the given triangle is written as,
ΔLNO ≅ ΔNLM
Here we have also it can be written as ∠OLN ≅ ∠MNL and ∠LNO ≅ ∠NLM
Then it can be written as LM || ON and LO || MN
Then the LMNO is a parallelogram
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[2.4-(0.3-3.21)·2+0.44÷(-2)]÷2/5 pls help me asap I litteraly have no idea how to do this
Answers
0.3-3.21= -2.91
-2.91 * 2= -5.82
2.4 - 5.82= -3.42
-3.42 + 0.44= -2.98
-2.98 / -2= 1.49
1.49 / 2= 0.745
0.745 / 5= 0.149
Select the reason that best
supports Statement 2 in the
given proof.
A. Division Property of Equality
B. Subtraction Property of Equality
C. Linear Pair Postulate
D. Transitive Property
Answers
The reason that best supports Statement 2 in the given proof is
C. Linear Pair Postulate
What is linear pair postulate?The Linear Pair Postulate, also known as the Linear Pair Axiom, is a fundamental concept in geometry related to angles and their relationships. It states the following:
If two angles form a linear pair, then they are supplementary.
In the proof the angles are linear pair hence their sum id supplementary
∠ 1 + ∠ 2 = 180 degrees
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B= {X:X es un número entero comprendido entre -1 y 1}
Answers
The set B is the set of integers between -1 and 1, which includes -1, 0, and 1.
The set B can be defined as follows:
B = {x: x is an integer between -1 and 1}
This means that B is a set that contains all the integers x that satisfy the condition of being between -1 and 1. In other words, B includes the integers -1, 0, and 1. These are the only integers that fall within the specified range.
To represent this set in roster notation, we can write:
B = {-1, 0, 1}
In set-builder notation, we can express B as:
B = {x | x ∈ ℤ, -1 ≤ x ≤ 1}
This notation indicates that B consists of all the integers x such that x belongs to the set of integers (ℤ) and x is greater than or equal to -1 and less than or equal to 1.
In summary, the set B is the set of integers between -1 and 1, which includes -1, 0, and 1.
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anyone can solve this?
[tex] \sqrt[4] {a}^{3 \:} to \: power[/tex]
Answers
The value of the expression [tex]\sqrt[4]{a}^3[/tex] when evaluated is [tex]a^\frac34[/tex]
How to evaluate the expressionFrom the question, we have the following parameters that can be used in our computation:
[tex]\sqrt[4]{a}^3[/tex]
Consider an expression expressed as xⁿ
The expression can be expanded as
xⁿ = x * x * x .... in n places
Using the above as a guide, we have the following:
[tex]\sqrt[4]{a}^3 = \sqrt[4]{a} * \sqrt[4]{a} * \sqrt[4]{a}[/tex]
Apply the exponent rule of indices
[tex]\sqrt[4]{a}^3 = a^\frac14 * a^\frac14 * a^\frac14[/tex]
Apply the power rule of indices
[tex]\sqrt[4]{a}^3 = a^\frac34[/tex]
Hence, the expression [tex]\sqrt[4]{a}^3[/tex] when evaluated is [tex]a^\frac34[/tex]
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2.2 2.1.4 a Given that A and B are complementary angles and 7 cos A-3 = 0. Determine WITHOUT the use of a calculator, the value of: 7 cos B-3 tan A. (4)
