Answers
Since both pairs of opposite sides of quadrilateral ABCD are parallel and equal, by definition, ABCD is a parallelogram.
Given that in quadrilateral ABCD, side AD is equal to side BC (AD = BC) and side AD is parallel to side BC (AD || BC), we can use these properties to prove that ABCD is a parallelogram.
Here is a step-by-step proof:
1. Definition of a parallelogram: A quadrilateral is a parallelogram if both pairs of opposite sides are parallel.
2. Given: AD = BC (opposite sides are equal) and AD || BC (opposite sides are parallel).
3. To Prove: AB || CD and AB = CD (the other pair of opposite sides are also parallel and equal).
4. Proof:
- Since AD = BC and AD || BC, we have one pair of opposite sides that are equal and parallel.
- In a quadrilateral, if one pair of opposite sides is equal and parallel, the quadrilateral is a parallelogram (This is a theorem in Euclidean geometry).
- Therefore, AB must be parallel to CD (AB || CD) because the opposite sides of a parallelogram are parallel by definition.
- Also, in a parallelogram, opposite sides are equal (another property of parallelograms), so we can conclude that AB = CD.
5. **Conclusion**: Since both pairs of opposite sides of quadrilateral ABCD are parallel and equal, by definition, ABCD is a parallelogram.
This logical sequence uses the properties of parallelograms and the given information to prove that ABCD must be a parallelogram.
Related Questions
#10 with explanation please
Answers
10. 4x = 1
x = 1/4
since there is no y if you graph x = 1/4 you would get a straight vertical line at x = 1/4
since it is a vertical line it is symmetric about the x axis ( it looks the same on both sides of the x axis)
Eight two-person teams are participating in a three-legged race. Find the number of orders in which all 8 teams can finish the race.
Answers
Therefore, the number of orders (combinations) of 2 people at a time from 8 is
₈C₂ = 8!/(2!6!)
= (8*7*6!)/(2*6!)
= (8*7)/2
= 56/2
= 28
Answer: 28
Answer:
thx for points man
Step-by-step explanation:
The total cost of a vacation to a rain forest includes a fee of $560 for the tour guide, plus $630 per person. The function y=560+630x/ x
models the average cost per person, in dollars, when x people go on the vacation.
What is the horizontal asymptote of the function?
y= ????
Answers
Answer: y= 630 is the horizontal asymptote for the given function.
Step-by-step explanation:
Horizontal asymptotes are horizontal lines that the graph of the function approaches as x tends to [tex]+\infty[/tex] or [tex]-\infty[/tex].
Thus, If there is a function f(x),
Then Its horizontal asymptote, y = [tex]\lim_{x\rightarrow \infty} f(x)[/tex]
Here the given function is, [tex]f(x) = \frac{560+630x}{x}[/tex]
Thus its horizontal asysmptote is, y = [tex]\lim_{x\rightarrow \infty} \frac{560+630x}{x}[/tex]
⇒ y = [tex]\lim_{x\rightarrow \infty}560/x+630[/tex]
⇒ y = 0+ 630
⇒ y= 630 is the horizontal asymptote of the given function f(x).
The horizontal asymptote of y = (630x + 560)/x is y = 630.
Linear functionA linear function is given by:
y = mx + b
where y, x are variables, m is the rate of change and b is the y intercept.
Given the total cost as y = 630x + 560.
For the function y = (630x + 560)/x, the horizontal asymptote is at:
y = 630x/ x = 630
The horizontal asymptote of y = (630x + 560)/x is y = 630.
Find out more on Linear function at: https://brainly.com/question/13763238
How are line graphs used to show how two variables are related?
Answers
The function h(x) = x2 + 14x + 41 represents a parabola. Part A: Rewrite the function in vertex form by completing the square. Show your work. (6 points) Part B: Determine the vertex and indicate whether it is a maximum or a minimum on the graph. How do you know? (2 points) Part C: Determine the axis of symmetry for h(x). (2 points)
Answers
Part A:
The first thing of completing the square is writing the
expression
as
which expands to
.
We have the first two terms exactly alike with the function
we start with:
and
but we need to add/subtract from the last term, 49, to
obtain 41.
So, the second step is to subtract -8 from the expression
The function in finalizing the square form is
Part B:
The vertex is acquired by equating the expression in the
bracket from part A to zero
It means the curve has a turning point at x = -7
This vertex is a minimum since the function will make a
U-shape.
A quadratic function
can either make U-shape or ∩-shape depends on the
value of the constant
that goes with
. When
is (+), the curve is U-shape. When
(-), the curve is ∩-shape
Part C:
The symmetry line of the curve will go through the vertex,
hence the symmetry line is
This function is shown in the diagram below
Answer:
Part A: The vertex form is h(x) = (x+7)^2 - 8 .
Part B: The vertex is a minimum. The vertex is (-7,-8).
Part C: The axis of symmetry is x=-7. (axis of symmetry is the x value of the vertex)
Step-by-step explanation:
This video will help you understand how I got the function into vertex form.
Search: How do you convert from standard form to vertex form of a quadratic Brian McLogan
This will help you find the vertex
Search: Finding the vertex of a parabola in standard form khan academy
The area of a triangle is ½ (b) (h), where the base and height are always two sides of the triangle.
a. True
b. False
Answers
The area of a triangle is ½ (b) (h), where the base and height are always two sides of the triangle.
Kieran’s wallet contains 7 bills: three $5 bills, two $10 bills, one $20 bill, and one $100 bill. if kieran pulls out two bills at random, what is the probability that he selects exactly two $5 bills?
Answers
Answer:
[tex]\bf\textbf{Probability of selecting exactly two $5 bill }=\frac{1}{7}[/tex]
Step-by-step explanation:
Total number of bills in the wallet = 7
Total number of $5 bills in the wallet = 3
Total number of $10 bills in the wallet = 2
Total number of $20 bill in the wallet = 1
Total number of $100 bill in the wallet = 1
We need to find the probability that he selects exactly two $5 bills.
Number of favorable outcomes = 3
[tex]\text{Probability of selecting one $5 bill }\frac{3}{7}[/tex]
[tex]\text{Probability of selecting second $5 bill }\frac{2}{6}[/tex]
[tex]\bf\textbf{Probability of selecting exactly two $5 bill = }\frac{3}{7}\times \frac{2}{6}=\frac{1}{7}[/tex]
Pleaseeeeeeeeeee help what is circle b
Answers
ne S is the blue line, where does it contact circle B?
it touches at Point K,
so that would be the tangency.
Answer Point K
need help: write the expression in a complete factored form: x²-9x+xy-9y
Answers
[tex]( x^{2} -9x)+(xy-9y)[/tex]
Now work on finding a common thing between the 2 groups:
[tex]x(x-9)+y(x-9)[/tex]
See, what you have in common there now is the (x-9) that you can factor out:
[tex](x-9)(x+y)[/tex]
And that is factored completely.
Find the median of the following set of data. $12.50, $13.23, $11.20, $14.50, $12.50, $13.23, $15.60, $15.75
Answers
It's 13.23
Answer:
The answer is 13.23
Step-by-step explanation:
In order to determine the median of the set of data, we have to know about median and how applicate it.
The median of a set of data is the middlemost number in the set. The median is also the number that is halfway into the set. To find the median, the data should first be arranged in order from least to greatest.
Also, if there is an even number of items in the data set, then the median is found by taking the mean (average) of the two middlemost numbers.
So, we arrange the set of data:
11.20
12.50
12.50
13.23
13.23
14.50
15.60
15.75
The data set is an even number.
The two middlemost numbers are: 13.23; 13.23.
So, the mean (average) is:
(13.23+13.23)/2=13.23
Finally, the median of the set of data is 13.23
Find the measures of an interior angle and an exterior angle of a regular polygon with 6 sides.
Answers
To find the measure of one angle, the formula is 360/n where n is the number of the sides of the polygon.
360/6 = 60°
The sum of all internal angles of a polygon can be find with the formula (n-2)*180° where n is the number of the sides. In this case 180(6-2) = 180*4 = 720°
To find one internal angle, follow this formula [180(n-2)] / n = [720/6] = 120°
Anyway, you can pick a vertex and from that vertex start to draw diagonals.
There will be some triangles, the sum of all internal angles of a triangle is 180°. In a polygon, the sum of all internal angles equals to the sum of all internal angles of all the triangles.
Hope I'm clear.
The interior angle of a regular hexagon is 120 degrees, and the exterior angle is 60 degrees.
Explanation:To find the measures of an interior angle and an exterior angle of a regular polygon with 6 sides, we will use the fact that the sum of interior angles of a polygon is given by (n-2)×180°, where 'n' is the number of sides of the polygon. Thus, a regular hexagon will have its interior angles sum to (6-2)×180° = 720°. Since all interior angles in a regular polygon are equal, each interior angle will be 720° ÷ 6 = 120°. The exterior angle of a regular polygon is calculated as 360° ÷ n. Therefore, an exterior angle of a regular hexagon will be 360° ÷ 6 = 60°.
So, the interior angle of a regular hexagon is 120°, and the exterior angle is 60°.
Line GJ is tangent to point A at point G.
If AG = 9 and GJ = 12, find AJ.
Answers
AJ = square root (81 + 144)
AJ = square root (225)
AJ = 15
answer
15
Quadrilateral ABCD is an Isosceles Trapezoid. Which angle is congruent to Angle C?
Answers
The base angles C and D are congruent because this is an isosceles trapezoid. In addition, angle A = angle B because this is another pair of base angles (imagine rotating the figure 180 degrees to make segment AB the base)
Answer:
The reason why any angles coming out from D and C are congruents is because of the geometry coungruence's concept of 2 items having the same pattern, shape or form and size as the mirror image of the other.
2 angles would be congruent by being the same angle in degrees or radians.
Thereby any angle coming out from C as vertex would be congruent with any other vertex point angle mirroring the resulting figure shaped by the radiants or degrees of such angle.
Step-by-step explanation:
A rectangle is 3 times as long as it is wide. The perimeter is 60cm. Find the dimensions of the rectangle.
Answers
length = 3x
2(x + 3x) = 60
4x = 60/2
4x = 30
x = 30/4
x = 7.5 cm ← width
length = 3x = 3 * 7.5 = 22.5 cm
A small class has 10 students, 5 of whom are girls and 5 of whom are boys. The teacher is going to choose two of the students at random. What is the probability that the first student chosen will be a girl and the second will be a boy? Write your answer as a fraction in simplest form.
Answers
P(1st pick is a girl) = 5/10 which reduces to 1/2
P(2nd pick is a boy) = 5/9
P (both) = 1/2 * 5/9 = 5/18 <=
Answer:
The required probability is 5/18.
Step-by-step explanation:
Total number of total students = 10
Number of girls = 5
Number of boys = 5
Formula for probability:
[tex]Probability=\frac{\text{Favorable outcome}}{\text{Total outcome}}[/tex]
The probability that the first student chosen will be a girl = [tex]\frac{5}{10}=\frac{1}{2}[/tex]
After selecting 1 student, the total number of student is
[tex]10-1=9[/tex]
The probability that the second student chosen will be a boy = [tex]\frac{5}{9}[/tex]
The probability that the first student chosen will be a girl and the second will be a boy is
[tex]P=\frac{1}{2}\times \frac{5}{9}[/tex]
[tex]P=\frac{5}{18}[/tex]
Therefore the required probability is 5/18.
The lines 2x - 3y = 1 and 2x + 3y = 2 are intersecting. true or false
Answers
-3y = -2x + 1
y = 2/3x - 1/3...slope = 2/3, y int = -1/3
2x + 3y = 2
3y = -2x + 2
y = -2/3x + 2/3...slope = -2/3, y int = 2/3
different slopes, different y int's....means 1 solution...so yes, they intersect
TRUE
Answer:
the given statement is true.
Step-by-step explanation:
The given lines are
2x - 3y = 1 and 2x + 3y = 2
Write these equations in slope intercept form of a line y = mx +b
For the first equation
[tex]2x-3y=1\\\\3y=2x-1\\\\y=\frac{2}{3}x-\frac{1}{3}[/tex]
For the first equation
[tex]2x+3y=2\\\\3y=-2x+2\\\\y=-\frac{2}{3}x+\frac{2}{3}[/tex]
The slope and y-intercepts of first line are 2/3 and -1/3 respectively.
The slope and y-intercepts of second line are -2/3 and 2/3 respectively.
Since, the slopes and y-intercepts of these lines are different.
Hence, these lines are intersecting.
Therefore, the given statement is true.
A standard die is rolled. P(A)= the probability of rolling a three
P(B)= the probability of rolling a even number
What is P(A or B)
Answers
P(A)= 1/6 since 3 is one possibility out of 6
P(B)= 1/2 since there are 3 numbers that mke this true out of 6 and 3/6= 1/2
P(A or B)= 1/6+1/2
P(A or B)= 2/3
Final answer: 2/3
Find the 13th term of the sequence 8, -16, 32, -64, ...
A. 32768
B. -16384
C. -65536
D. None of these
Answers
8
-16
32
-64
128
-256
512
-1024
2048
-4096
8192
-16384
32768
Answer is A
a(n)=ar^(n-1), a=initial term, r=common ratio, n=term number.
The common ratio,r, is -16/8=32/-16=-64/32=-2, and the first term, a, is 8
So the rule for this sequence is:
a(n)=8(-2)^(n-1), so the 13th term is:
a(13)=8(-2^12)
a(13)=32768
PLEASE HELP!!!!!!!!!!!!! GEOMETRY
Answers
so answer is C. -7
The green line has a slope of 1/7, the opposite reciprocal is -7/1 or
-7.
LETTER C
a country's population in 1995 was 175 million. In 2000 it was 181 million. Estimate the population in 2020 using exponential growth formula. Round you answer to the nearest million
Answers
The formula is
P=Ae^rt
P 181 million
A 175 million
E constant
R rate of growth?
T time 2,000−1,995=5 years
Solve the formula for r
R=(log (p/A)÷log (e))÷t
R=(log(181÷175)÷log(e))÷5
R=0.0067
Now find the population in 2020
P=Ae^rt
P?
A 175 million
R 0.0067
T time 2,020−1,995=25 years
P=175×e^(0.0067×25)
P=207 million. .....answer
The population of a town in 2000 was 430. The population is increasing at a rate of 0.9% every year. What will be the projected population of the town in 2010? Round your answer to the nearest whole number.
options are 440,450,460,470
Answers
P=Ae^rt
P ?
A 430
R 0.9/100=0.009
T time 2010-2000=10 years
E constant
P=430×e^(0.009×10)
p=470
Help! question down below!
Answers
they would be similar since they have the same angles, but different length sides
they are different sizes
the sides are different lengths
congruent, means same size and shape
the only answer that applies is A
Which is the graph of f(x)=3/2(1/3)^x
Answers
Answer:
Graph B
Step-by-step explanation:
Given is a function as
[tex]f(x) = \frac{3}{2} (\frac{1}{3} )^x[/tex]
There are 4 graphs given.
Out of the 4 options we have to select one which suits this graph
Let us study about f graph
X intercept is at infinity.
Or y=0 is asymptote for this curve
y intercept is when x =0
i.e. y intercept =3/2 (1) = 3/2
Only A and B satisfy this value of y intercept
Out of A and B we have to select one option
When x=1, we get
f(1) = 3/2 (1/3) = 1.5
This is satisfied only by Graph B.
Hence answer is graph B.
When x tends to -infinity y
Molly hikes 1/6 mile every day.
To hike a total of 11/6 miles, she would have to hike for____ days. To hike a total of 1/3 of a mile, she would have to hike for____ days.
Answers
she hikes 1/6 a day, to get 11/6 , she would have to hike 11 days
to hike 1/3 of a mile
1/3 / 1/6 = 1/3 * 6/1 = 6/3 = 2
so she would have to hike 2 days
Answer:
11 days and 2 days
Step-by-step explanation:
Molly hikes every day = [tex]\frac{1}{6}[/tex] miles
She would take days to hike total [tex]\frac{11}{6}[/tex] miles = [tex]\frac{\frac{11}{6} }{\frac{1}{6} }[/tex]
= [tex]\frac{11}{6}[/tex] × [tex]\frac{6}{1}[/tex] = 11 days.
To hike a total [tex]\frac{1}{3}[/tex] of a mile she would have to hike = [tex]\frac{\frac{1}{3} }{\frac{1}{6} }[/tex]
[tex]\frac{1}{3}[/tex] × [tex]\frac{6}{1}[/tex] = 2 days
To hike a total of [tex]\frac{11}{6}[/tex], she would have to hike for 11 days. To hike a total of [tex]\frac{1}{3}[/tex] of a mile, she would have to hike for 2 days
If 400 bricks, each measuring 81" by 31", are required to build a wall 42 feet high, how long is the wall?
Answers
81 x 31 = 2 511 (area of a brick)
2511 x 400 = 1 004 400 (area of the wall)
Convert 1 004 400" to ft. [1ft. = 12"]
1 004 400 / 12 = 83 700 ft.
Now this is what we have.
-Hight 42 ft.
-Length X ft.
-Area 83 700ft.
Algebra time.
42 x X = 83 700 (to get X you would devide 83 700 by 42)
83 700 / 42 = 1 992.85ft. (X = 1 992.85ft.)
So the length of the wall would be 1992.85ft.
The height of the wall is 166.07 ft.
What is the 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.
Given that, 400 bricks, each measuring 81" by 31", are required to build a wall 42 feet high.
Here, Area of a one brick 81"×31"
6.75×2.58=17.44 ft²
Total area of 400 bricks = 400×17.44=6975 ft²
Total brick area divided by 42' height of wall
=6975÷42=166.07 ft
Therefore, the height of the wall is 166.07 ft.
To learn more about the unitary method visit:
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If c is a real number and if 2+i is a solution of the equation x^2-4x+c, what is the value of c
Answers
so if a+bi is a root then a-bi is also a root
if 2+i is a root then 2-i is also a root
so, the factored form of a quadratic equation with roots r1 and r2 is
(x-r1)(x-r2)
so
2+i and 2-i
(x-(2+i))(x-(2-i))
(x-2-i)(x-2+i)
expanding we get
x²-4x+5
so c=5
What is the value of the rational expression 2x-1/x+5 when x = 0?
Answers
2(0) - 1
= ---------------
0 + 5
- 1
= ----------
5
answer
-1/5
The value of the rational expression of equation is A = -1/5
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
A = ( 2x - 1 ) / ( x + 5 )
when x = 0
Substituting the values in the equation , we get
A = ( 2 ( 0 ) -1 ) / ( 0 + 5 )
On simplifying , we get
A = -1/5
Hence , the equation is solved and A = -1/5 when x = 0
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Identify the polynomial written in ascending order. 8x3+ 2x2− 6x − 11 2x2− 11 + 8x3− 6x −6x + 8x3− 11 + 2x2 −11 − 6x + 2x2+ 8x3
Answers
The answer is -11 - 6x + 2x^2 + 8x^3 <==
Paul and Scott were solving the same problem. Who is wrong? Explain their error.
Paul Scott
__________________
log 3x=9 log 3x=9
3^x=9 x=3^9
3^x=3^2 x=19,683
x=2
Answers
x=3⁹
x=19 683
3 ^x = 9. 3^x = 3^2, x = 2 . If we have log˙(x) a = b then: a = x^b, Paul wrote it in a form: b = x^a. Scott was right. He wrote: 3^9 = x and as a result he had: x = 19,683.
So Paul is Wrong
Which shows the graph of the solution set of 3y – 2x > –18? Mark this and return
Answers
First, you disregard the inequality to graph the equation. Find the x- and y-intercepts, plot them, and connect these two dots by extending infinitely from both sides.
x-intercept: let y = 0
0 - 2x = -18
x = 9
y-intercept: let x = 0
3y- 0 = -18
y = -6.
The graph is shown in the picture. Next, you test the inequality by choosing a random data point that does not coincide with any of the data points passed by the line. Suppose, we choose the origin (0,0)
3y- 2x > -18
3(0) - 2(0) > -18
0 > 18
The inequality is true for (0,0), Thus, the shaded region must include this point. All of the region to the left bounded by the line is a solution. Note that the data points are hollow because they are not part of the solution because of the inequality '>'. If it were ≥, then those points would be solid.