Answer: Yes, the quadrilateral ABCD is a trapezoid.
Step-by-step explanation: Given that the vertices of the quadrilateral ABCD are A(–4, –5), B(–3, 0), C(0, 2), and D(5, 1).
We are to determine whether ABCD is a trapezoid or not.
We know that a trapezoid is a quadrilateral with one pair of opposite sides parallel. Also, the slopes of two parallel lines are equal.
First, we will find the slopes of the sides AB, BC, CD and DA.
We have
[tex]\textup{Step 1: The slope of AB}=\dfrac{0+5}{-3+4}=\dfrac{5}{1}=5,\\\\\textup{Step 2: The slope of BC}=\dfrac{2-0}{0+3}=\dfrac{2}{3},\\\\\textup{Step 3: The slope of CD}=\dfrac{1-2}{5-0}=-\dfrac{1}{5},\\\\\textup{Step 4: The slope of DA}=\dfrac{-5-1}{-4-5}=\dfrac{2}{3}.[/tex]
Since the slopes of the sides BC and DA are equal, so BC an DA are the parallel sides of the quadrilateral ABCD.
Thus, the quadrilateral is a trapezoid because it has a pair of opposite sides parallel.
The quadrilateral is a trapezoid because it contains two opposite sides that are parallel, the quadrilateral is called a trapezoid.
What is a trapezoid?It is defined as the quadrilateral having four sides in which two sides are parallel to each other, it is a 2-dimensional geometry.
We have:
Quadrilateral ABCD with vertices A(–4, –5), B(–3, 0), C(0, 2), and D(5, 1)
To identify the quadrilateral is a trapezoid we must find the slopes of the lines AB, BC, Cd, and AD
For slope m the formula is given by:
[tex]\rm m = \frac{y_2-y_1}{x_2-x_1}[/tex]
For slope of AB:
[tex]=\rm \frac{0-(-5)}{-3-(-4)}[/tex]
[tex]=\rm \frac{0+5}{-3+4}[/tex]
= 5
For slope of BC:
[tex]=\rm \frac{2-0}{0-(-3)}[/tex]
[tex]=\rm \frac{2}{3}[/tex]
For slope of CD:
[tex]=\rm \frac{1-2}{5-0}[/tex]
= -1/5
For slope of AD:
[tex]=\rm \frac{-5-1}{-4-5}[/tex]
= 2/3
Because the slopes of the sides BC and DA are equivalent, BC and DA are the quadrilateral ABCD's parallel sides.
Thus, the quadrilateral is a trapezoid because it contains two opposite sides that are parallel, the quadrilateral is called a trapezoid.
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if you are flipping a coin what is the sample space
Answer:
Solution: {Heads, Tails}.
Step-by-step explanation:
Solution: {Heads, Tails}.
Sample space is a list of all the possible outcomes for the event. For flipping a coin the outcomes are {Heads, Tails}.
Margaret wants to call her friend overseas. There is a connection fee of $2 and a charge of $1.50 per minute. So the cost of the call is 2 + 1.5t dollars for t minutes.
How can you find the surface area of a composite solid made up of prisms
What is the circumference of a circle circumscribed around a rectangle with sides 10 cm and 24 cm?
For what value of xis the square of the binomial 3x+1 is 9 times greater than the square of the binomial x–2?
Final answer:
The value of x for which the square of the binomial 3x+1 is 9 times greater than the square of the binomial x−2 is obtained by equating (3x + 1)² to 9(x − 2)², which simplifies and solves to x = 5/6.
Explanation:
To find the value of x for which the square of the binomial 3x+1 is 9 times greater than the square of the binomial x−2, we need to formulate and solve an equation based on the given conditions:
(3x + 1)² = 9(x − 2)²
Expanding both sides gives us:
9x² + 6x + 1 = 9x² − 36x + 36
Now, by simplifying and solving for x, we find:
42x = 35
x = 35 / 42
x = 5 / 6
Therefore, the value of x is 5/6.
Find the perimeter of an isosceles trapezoid whose two bases have lengths of 10cm and 16 cm and a side length of 5cm
The perimeter of the isosceles trapezoid is 36cm.
Explanation:An isosceles trapezoid is a quadrilateral with two parallel sides of unequal length. To find the perimeter of an isosceles trapezoid, we need to add the lengths of all its sides. In this case, the two bases have lengths of 10cm and 16 cm, and one of the side lengths is 5cm. Since the two bases are parallel, the other side length is also 5cm.
The perimeter is calculated by adding the lengths of the bases and the two side lengths: 10cm + 16cm + 5cm + 5cm = 36cm.
The diagonal of rectangle ABCD measures 2 inches in length What is the length of line segment AB?
Answer:
Step-by-step explanation:
B on edge
The Heller family is having a cookout. To be sure that they have enough food, they plan to have 0.5 pound of hamburger for each adult and 0.25 pound for each child. There will be 15 children at the cookout. If they buy 10 pounds of hamburger, what is the maximum number of adults they expect?
Answer:
12
Step-by-step explanation:
If A ⊂ B, then A ∩ B = A ∪ B.
The statement "If [tex]\( A \subset B \)[/tex], then [tex]\( A \cap B = A \cup B \)[/tex]" is not always true; it holds only if A = B.
The statement "If [tex]\( A \subset B \)[/tex], then [tex]\( A \cap B = A \cup B \)[/tex]" is not always true.
If [tex]\( A \subset B \)[/tex], it means that every element in set A is also in set B.
Now, consider the intersection of A and B [tex](\( A \cap B \))[/tex]. This intersection contains all elements that are common to both sets A and B.
On the other hand, the union of A and B [tex](\( A \cup B \))[/tex] contains all elements that are in either set A or set B, or both.
Since A is a subset of B, all elements in A are already in B, which means [tex]\( A \cap B = A \)[/tex]. However, [tex]\( A \cup B \)[/tex] would just be B, because all elements in A are also in B, so [tex]\( A \cup B \)[/tex] is simply B.
Therefore, the statement "If [tex]\( A \subset B \)[/tex], then [tex]\( A \cap B = A \cup B \)[/tex]" is not true in general; it is true only if A = B .
Find an equation of the plane. the plane through the point (3, −8, −2) and parallel to the plane 9x − y − z = 7
Final answer:
The equation of the plane parallel to the given plane 9x - y - z = 7 and passing through the point (3, -8, -2) is 9x - y - z = 37.
Explanation:
The question involves finding an equation for a plane that is parallel to a given plane and passes through a specific point. Since the planes are parallel, they will have the same normal vector, and thus the same coefficients for x, y, and z. The given plane's equation is 9x - y - z = 7, so the normal vector is (9, -1, -1). Our plane must also have this normal vector, meaning our plane's equation will have the form 9x - y - z = D, where D is a constant we need to find such that the plane passes through the point (3, -8, -2).
Substituting this point into the equation gives us 9(3) - (-8) - (-2) = D, which simplifies to 27 + 8 + 2 = D. Therefore, D = 37 and the equation of our plane is 9x - y - z = 37.
a rectangle that is 2 inches by 3 Inches has been scaled by factor of 7 suppose you want to scale the copy back to its original size what scale factor would you use?
This is about transformation of objects.
Scale factor back to original size = 1/7
We are told that the rectangle was scaled by a factor of 7.What this means is that if the length and width are x and y respectively, then the new scaled measurements will be;
7x and 7y.
Now,for us to scale back to the original size, all we need to do is to divide the new scale measurements by a factor of 7.This means the original size will be;
Length = 7x × 1/7
Width = 7y × 1/7
Thus,the scale factor will be 1/7 back to the original size.Read more at; https://brainly.com/question/17292295
The classroom encyclopedia set seems to fill a shelf that is 24 in long each book is 3/4 in thick how many books are in the classroom set
The diagonals BF and CE divide the hexagon ABCDEF into two equilateral triangles and a square. Find the perimeter of the hexagon if BF = 3 cm. Answer: P = cm
Answer: The perimeter of the hexagon is 18 cm.
Step-by-step explanation: As given in the question, hexagon is shown in the attached figure.
The diagonals g and h divides the hexagon into two two equilateral triangles and one square .
Also, length of diagonal g = 3 cm.
We are to find the perimeter of hexagon.
We know that all the sides of a square are equal, so we have
length of b = length of h = length of e = length of g = 3 cm.
Since the two triangles are equilateral, so all their sides will be equal.
That is, length of a = length of f = length of g =length of c =length of d = length of h = 3 cm.
We know that the perimeter of a polygon is equal to the sum of the lengths of its sides.
Therefore, the perimeter of hexagon is given by
P = a + b + c + d + e + f = 3 + 3 + 3 + 3 + 3 + 3 = 18 cm.
Thus, the perimeter of the hexagon is 18 cm.
what is the rate of decay, as a percent, for the following function n(x)=7(0.067)^x
Answer: The rate of decay is 93.3%.
Step-by-step explanation:
Since we have given that
The exponential function is given by
[tex]n(x)=7(0.067)^x[/tex]
As we know the general equation of exponential function that is given by
[tex]n(x)=a(1-b)^x[/tex]
Here, a denotes the initial value
1-b denotes the rate of decay.
So, On comparing both the equations, we get that
[tex]1-b=0.067\\\\b=1-0.067\\\\b=0.933=0.933\times 100=93.3\%[/tex]
Hence, the rate of decay is 93.3%.
C=
5\9
(F−32)
The equation above shows how temperature F, measured in degrees Fahrenheit, relates to a temperature C, measured in degrees Celsius. Based on the equation, which of the following must be true?
I.) A temperature increase of 1 degree Fahrenheit is equivalent to a temperature increase of 5\9 degree Celsius.
II.) A temperature increase of 1 degree Celsius is equivalent to a temperature increase of 1.8 degrees Fahrenheit.
III.) A temperature increase of 5\9 degree Fahrenheit is equivalent to a temperature increase of 1 degree Celsius.
A) I only
B) II only
C) III only
D) I and II only
Mowing the lawn is one of Jeremy's jobs at home. But, Jeremy's dad offered to help him this week. His dad drew the following diagram of the lawn and told Jeremy to choose one of the parts to mow. If Jeremy wants to mow the rectangle with the smaller area, which one should he choose?
Let's find out the area of the two parts separately to see which part is smaller.
Area of rectangle is given by Length * Width
Area of Part 1
Width of Part 1 is 16'
Length of Part 1 is 16-12 = 4'
So area of Part 1 is 16*4 = 64' square
Area of Part 2
Width of Part 2 is 8'
Length of Part 2 is 8'
So area of Part 2 is 8*8 = 64' square
So area of both the parts is same . Hence Jeremy may choose any of the parts.
Hope it helps ..!!
in 3/4 identify the role of 3. Then explain how to read tbis number
Answer:
The 3 is the numerator, To read the number is "three-fourths"
Step-by-step explanation:
I hope this helps!
The equation below shows the total volume (V), in cubic units, of 4 identical boxes with each side equal to s units:
V = 4s3
If s = 2.5 units, what is the value of V?
25 cubic units
30 cubic units
62.50 cubic units
156.25 cubic units
HELP FAST
Answer:
62.50
Step-by-step explanation: im smart
Find the equation of the plane through the point p=(5,5,4)p=(5,5,4) and parallel to the plane 5x+2y−z=−6.
Can you please help me out ??
Which measurement statement is correct?
A. There are 2 cups in a pint
B. There are pints in a cup
C. There are 4 quarts in a pint
D. There are 4 pints in quart
Eric's father Works two part-time jobs one in the morning and one in the afternoon and works a total of 40 hours each 5-day work week. if his schedule is the same each day, and he works 3 hours each morning, how many hours does Eric's father work each afternoon
The number of hours does Eric's father work each afternoon is 5 hours.
Given that,
A total of 40 hours each 5-day work week. And, his schedule is the same each day, and he works 3 hours each morning.Based on the above information, the calculation is as follows:
[tex]= (40 - (3\times 5)) / div 5\\\\= (40 - 15) \div 5\\\\= 25 \div 5[/tex]
= 5
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Which statements are true regarding the regular dodecagon? Check all that apply.
The smallest angle of rotational symmetry for the dodecagon is 30°.
The dodecagon has a rotational symmetry of 180°.
The order of rotational symmetry for the dodecagon is 10.
The dodecagon has a rotational symmetry of 135°.
The angles of rotational symmetry for the dodecagon are multiples of 30°.
The statements that can be inferred to be true regarding the regular dodecagon include:
The smallest angle of rotational symmetry for the dodecagon is 30°.The dodecagon has a rotational symmetry of 180°.The angles of rotational symmetry for the dodecagon are multiples of 30°.A dodecagon simply means a twelve-sided star polygon that encloses space. It can be regular when all the interior angles and sides are equal.
It should be noted that the smallest angle of rotational symmetry for the dodecagon is 30° and it has a rotational symmetry of 180.
Read more about angles on:
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for a rectangular solid with length 12 in width 2 in in height 15 in state the appropriate formula for volume and also find the volume
In a rhombus MPKN with an obtuse angle K the diagonals intersect each other at point E. The measure of one of the angles of a ∆PKE is equal 16°. Find the measures of all angles of ∆PKE and ΔPMN.
Answer:
m∠KEP = 90°
m∠EKP = 74°
m∠EPK = 16°
m∠N PM= 16°
m∠MNP = 16
m∠M = 148°
Step-by-step explanation:
If you do RSM those are the answers
which number produces an irrational number when multiplied by 0.5
a cube has a width of 20 ft what is the surface area of the cube
The surface area of the cube is 2,400 square feet.
To find the surface area of a cube, one must use the formula:
[tex]\[ \text{Surface Area} = 6 \times (\text{side length})^2 \][/tex]
Given that the width of the cube is 20 feet, we can assume that all sides of the cube are equal, since a cube has all sides of equal length. Therefore, the side length of the cube is 20 feet.
Now, we can substitute the side length into the formula:
[tex]\[ \text{Surface Area} = 6 \times (20 \text{ ft})^2 \] \[ \text{Surface Area} = 6 \times 400 \text{ ft}^2 \] \[ \text{Surface Area} = 2,400 \text{ ft}^2 \][/tex]
Thus, the surface area of the cube is 2,400 square feet.
Most sample surveys use random digit dialing equipment to call residential telephone numbers at random. the telephone polling firm zogby international reports that the probability that a call reaches a live person is 0.15. calls are independent. (a) a polling firm places 7 calls. what is the probability that none of them reaches a person?
The probability that none of the 7 calls reaches a person is approximately 0.1967.
Explanation:To find the probability that none of the 7 calls reaches a person, we need to calculate the probability that each individual call does not reach a person and then multiply those probabilities together.
The probability that a call reaches a live person is 0.15, so the probability that a call does not reach a live person is 1 - 0.15 = 0.85.
Therefore, the probability that none of the 7 calls reaches a person is 0.857 ≈ 0.1967.
Enrique charges $5 for every 1/5 hour he spends walking dogs.in the morning he walks buttons for 2/5 hour bruno for 1/5 hour and pepper for 3/5 hour. Monday thru friday. On saturdays he takes mimi diva and coco to the dog park for 4/5 of an hour. On wendsday this week it rained and pepper wanted to stay out for only 1/5 hour. How many hours did enrique spend with the dogs this week. Explain your method
I really neeed help!! 20 points!!,