Determine if a quadrilateral with the given vertices is an isosceles trapezoid. Show and explain all steps to prove or disprove.
A(-5,0) B(5,0) C(-3, 4) D(3, 4)

Answers

Answer 1

By satisfying all the four criteria, the quadrilateral with the vertices A(x, y) = (-5, 0), B(x, y) = (5, 0), C(x, y) = (-3, 4) and D(x, y) = (3, 4) is an isosceles trapezoid.

How to determine if a quadrilateral is an isosceles trapezoid

Based on vectorial expressions, an isosceles trapezoid satisfies the following properties:

(i) [tex]\overrightarrow{CD} = k \cdot \overrightarrow{AB}[/tex], for k ∈ [tex]\mathbb{R}[/tex]    

(ii) AB ≠ CD    

(iii) [tex]\overrightarrow{AC} \neq \overrightarrow {BD}[/tex]  

(iv) AC = BD

Now we proceed to prove each property:

Requisite I

(3 - (-3), 4 - 4) = (6, 0)

(5 - (-5), 0 - 0) = (10, 0)

(6, 0) = (5/3) · (10, 0)


Requisite II

AB = 6, CD = 10

AB ≠ CD

Requisite III

[tex]\overrightarrow{AC} = (2, 4)[/tex]

[tex]\overrightarrow{BD} = (-2, 4)[/tex]

[tex]\overrightarrow{AC} \neq \overrightarrow {BD}[/tex]

Requisite IV

[tex]AC = \sqrt{[-3-(-5)]^{2}+(4-0)^{2}}[/tex]

[tex]AC = \sqrt{2^{2}+4^{2}}[/tex]

[tex]AC = 2\sqrt{5}[/tex]

[tex]BD = \sqrt{(3-5)^{2}+(4-0)^{2}}[/tex]

[tex]BD = \sqrt{(-2)^{2}+4^{2}}[/tex]

[tex]BD = 2\sqrt{5}[/tex]

AC = BD

The figure with the entire quadrilateral is shown below. Therefore, the quadrilateral with the vertices A(x, y) = (-5, 0), B(x, y) = (5, 0), C(x, y) = (-3, 4) and D(x, y) = (3, 4) is an isosceles trapezoid.

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Determine If A Quadrilateral With The Given Vertices Is An Isosceles Trapezoid. Show And Explain All

Related Questions

An ice cream shop offers 6 different flavors of ice cream and 11
different toppings. How many choices are possible for a single
serving of ice cream with one topping?

Answers

Answer:

66

Step-by-step explanation:

Since these two events are independent, multiply the two probabilities together:

6*11 = 66 (choices)

distance on a street map is proportional to actual distance when the distance on the map is (1)/(2) cm, the actual distance is 3 km. shannas house is 16(1)/(2)km from the riding stables what is the distance on the map
a) 2 (3)/(4) cm
b) 5 (1)/(2) cm
C) 6cm
D) 11 cm

Answers

Answer:

b) 5 (1)/(2) cm

Step-by-step explanation:

CACHLATE THE SURFACE AREA, SHOW WORK!!! WILL GIVE BRAIN!!

Answers

Answer:

8 (i think)

Step-by-step explanation:

just use 1/2 x b x h

Answer:

Area of circle:

2^2 = 4

4 x 3.14 = 12.56

Area of two circles:

12.56 x 2 = 25.12

Now we find circumference:

2 x 3.14 x 2 = 12.56

Now we multiply it by height:

12.56 x 8 = 100.48

Let's add the given areas now:

100.48 + 25.12 = 125.6 cm2 is your answer.

ANSWER ASAP WILL GIVE BRAINLIEST NO LINKS
0.62
0.45
0.47
0.64​​

Answers

the answer would be 0.47

An art teacher had 16 pieces of blue chalk, 14 pieces of red chalk, and 10 pieces of
yellow chalk. She randomly gives a piece of chalk to each student in her class. What is
the probability that the first student will receive a piece of clue chalk?

Answers

Answer:

2/5 or 40%

Step-by-step explanation:

16/40 is blue and then simplify

HI PLS HELP ASAP ILL GIVE BRAINLIEST

Answers

Answer:

Monsoon

Step-by-step explanation:

Answer:

monsoon

I believe is the right answer

Where is Point C on the number line?

Answers

Answer:

i think 1.0

Step-by-step explanation:

Product and sum of 19 and -7

Answers

Answer:89

Step-by-step explanation:

Answer:

the answer is 89

Step-by-step explanation:

what is the median !!! help!! alegbra 2. marking brainliest

Answers

Answer:

The answer is 8.5

Step-by-step explanation:

Just list all the numbers and cross them out one by one.

Add up all of the numbers and divide by the number of numbers in the data set. The median is the central number of a data set. Arrange data points from smallest to largest and locate the central number. This is the median.

pls helpppp lol :/ I’d really appreciate it !!

Answers

Step-by-step explanation:

60+5x+5=180 (being angle of straight line)

5x+65=180

5x=180-65

5x=115

x=23

If triangle ABC is a right triangle AB is 21, BC is 42, and AC is 47, which of the following can be used to find the measure of Angle A? Select all that apply.
look at pic below for answer options:

Answers

Answer:

Sin(A) = 42/47

Cos(A)=21/47

Tan(A)=42/21=2

In ΔUVW, the measure of ∠W=90°, VW = 32 feet, and WU = 78 feet. Find the measure of ∠V to the nearest degree.

Answers

Answer: [tex]67.68^{\circ}[/tex]

Step-by-step explanation:

Given

[tex]\angle W=90^{\circ}[/tex]

[tex]VW=32\ ft[/tex]

[tex]WU=78\ ft[/tex]

from the figure, we can write

[tex]\Rightarrow \tan v=\dfrac{UW}{VW}\\\\\Rightarrow \tan v=\dfrac{78}{32}\\\\\Rightarrow \tan v=2.437\\\Rightarrow v=\tan^-1(2.437)\\\Rightarrow v=67.68^{\circ}[/tex]

A manufacturer tests a certain number of the headsets that are produced each day. If 280 units of that model are tested, and the manufacturer finds 273 headsets without any defects, what is the chance of finding a defective headset? Round your answer to the nearest tenth.

There is a
% chance of finding a defective headset.

Answers

Answer:

2.5

Step-by-step explanation:

273/280 = 97.5%

2.5% are defective

If 280 units of that model are tested, and the manufacturer finds 273 headsets without any defects, There is a 2.5% chance of finding a defective headset.

What is the unitary method?

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.

A manufacturer tests a certain number of the headsets that are produced each day.

If 280 units of that model are tested, and the manufacturer finds 273 headsets without any defects,

The chance of finding a non-defective headset

= 273/280

= 97.5%

The chance of finding a defective headset

= 100% - 97.5%

= 2.5% are defective

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solve this simultaneous equations 2x+3y =11
3x+5y = 18

Answers

Here is the answer no need to thank

whats 2+2?
Answer this question, its easy

Answers

4!!!!!!!!!!!!wahhhhh!

Answer:

it's 4 sooo easy for you and me

There are 1,000 balls in a container. All of the balls are the same size and shape. In the container, there are • 400 red balls; • 250 orange balls; • 100 green balls; and • 250 yellow balls. A student will pick one ball at random from the container. What are the probabilities that the student will pick a ball that is either red, orange, or green? Write the three different ways to represent this probability.

Answers

Answer:

I'm guessing you mean fraction decimal and percentage

The final answer is:

3/4

0.75

75%

Step-by-step explanation:

You have to add 400 + 250 + 100 and then you will get 750. Then you make 750 into a fraction, decimal, and percentage

Can I have brainliest? It would help me out, if not thanks anyways! Hope this helped and have a nice day!

The probability that the student will pick a ball that is either red, orange, or green is 0.75

What is Probability?

The probability that an event will occur is measured by the ratio of favorable examples to the total number of situations possible

Probability = number of desirable outcomes / total number of possible outcomes

The value of probability lies between 0 and 1

Given data ,

Let the probability that the student will pick a ball that is either red, orange, or green be P

Now , the total number of balls in the container = 1000 balls

And , probability that the student will pick a ball that is either red, orange, or green can be calculated as the sum of the probabilities of picking a red ball, an orange ball, or a green ball. That is,

P(Red or Orange or Green) = P(Red) + P(Orange) + P(Green)

The probability of picking a red ball is 400/1000 = 0.4

The probability of picking an orange ball is 250/1000 = 0.25

And the probability of picking a green ball is 100/1000 = 0.1.

Therefore , P (Red or Orange or Green) = 0.4 + 0.25 + 0.1 = 0.75

Hence , the probability is 0.75

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The radius of a cylindrical construction pipe is 3.5ft. If the pipe is 40ft long, what is its volume?

Use the value 3.14 for π, and round your answer to the nearest whole number.

Be sure to include the correct unit in your answer.

Answers

Answer:

1539 ft^3

Step-by-step explanation:

3.5×3.5=12.25

12.25×3.14=38.465

38.465×40=1,538.6

1538.6 rounded to the nearest whole number is 1539.

5) A bag contains eight red
marbles and six blue
marbles. You randomly pick
a marble and return it to the
bag before picking another
marble. What is the
probabilty that the first
marble you picked was blue
and the second marble was
red? Record your answer as
a decimal to the
thousandths place (three
places past the decimal).

Answers

Answer:

P(B,R) = 24.490%

Step-by-step explanation:

P(B,R) = 6/14 x 8/14 which can be simplified to become 12/49 or 24.490%

95 - 3/4 what is the value of the expression

Answers

Answer:377 /4  = 94 and 1 / 4  =94.25

Step-by-step explanation:

Subtract

95 − 3 /4

 = 377 / 4

Convert integer to fraction

95 = 95 / 1

Find common denominator

95 over 1

 

− 3 over 4

= ( 95 × 4 ) over ( 1 × 4 )

 − ( 3 × 1 ) over ( 4 × 1 )

= 380 over 4

 − 3 over 4

4 is the least common multiple of denominators 1 and 4. Use it to convert to equivalent fractions with this common denominator.

Subtract

380 over 4

− 3 / 4

 

= ( 380 − 3 ) / 4

= 377 /4

Simplify

377 / 4

= 94 and 1 /494

Reduce fraction to lowest terms

1 is the greatest common divisor of 377 and 4. The result can't be further reduced.

Step 2 of 2: Simplify, sub-step b: Convert improper fraction to mixed number.

Convert improper fraction to mixed number

377 /4

= 94 1 /4

377 ÷ 4 = 94 remainder 1

By writing the whole number as a fraction, we will see that the solution is 377/4

How to solve the expression?

Here we want to take the difference between a whole number and a fraction:

95 - 3/4

To do this, we need to write the whole number as a fraction, to do it, we multiply and divide it by 4:

95 = (4/4)*95 = 380/4

Now we rewrite our expression as:

95 - 3/4 = 380/4 - 3/4 = 377/4

This is the solution of the expression.

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I WILL GIVE BRAINLIEST PLZZZ HELP AND NO LINKS!!!

What data are represented by the stem-and-leaf plot below?
Three rows of numbers are shown.
The key shows that 4 vertical line 1 means 41.
Row 1 is 3 vertical line 7 8 9
Row 2 is 4 vertical line 1 3 7
Row 3 is 5 vertical line 2 4
A. 37, 38, 39, 41, 43, 47, 52, 54
B. 73, 83, 93, 14, 34, 74, 25, 45
C. 7, 8, 9, 1, 3, 7, 2, 4
D. 37, 38, 39, 14, 34, 74, 25, 45

Answers

Answer:

The answer is C

Step-by-step explanation:

Answer:

C.) 7, 8, 9, 1, 3, 7, 2, 4

Step-by-step explanation:

A rectangle has an area of 54 square inches. The width of the rectangle is 9 inches.
What is the length of the rectangle?

A:6 inches

B:45 inches

C:3 inches

D:12 inches

Answers

Answer:

A: 6 inches

Step-by-step explanation:

Carl and his family are on a road trip. If they have traveled 1/3 of the total distance in the past 5 days, what fraction of the total distance did they travel per day?

Answers

Answer:

1/15

Step-by-step explanation:

if they did 1/3 of the trip in 5 days, that means it would 15 days to complete the trip ... better have some snacks

What is the distance between the following points?

Answers

Answer:

[tex]\sqrt{85}[/tex] or 9.21954

Step-by-step explanation:

Use the distance formula to determine the distance between the two points.

[tex]d = \sqrt{(x_{2} -x_{1})^{2} + (y_{2} - x_{1})^{2} }[/tex]

d = distance

[tex](x_{1}, y_{1})[/tex] = coordinates of the first point

[tex](x_{2}, y_{2})[/tex] = coordinates of the second point

Solve for x in the diagram below.

Answers

X = 20. 180 - 100 = 80, 80/4 = 20

Topic: Area of non shaded area.

PLEASE NO LINKS OR "Sorry i don't know this" or anything related to that.

Answers

Answer:B) 150

Step-by-step explanation:

Area of rec= L×W

= 10×30= 300

Area of shaded area= 1/2 Base× Height

1/2×10×15=75

75×2 = 150

Area of unshaded part= 300-150= 150

Answer:

150 Square Units

Step-by-step explanation:

(Sorry if I become confusing)

The base of the triangles is 10 units.

The height of the triangles is 15 units.

The formula I used was A=[tex]\frac{1}{2}bh[/tex]

b=base and h=height A=area

A=[tex]\frac{1}{2}(10)(15)[/tex]

A=[tex]\frac{1}{2}(10)(15)[/tex]=75

A=75

Multiply by two to get the area for both triangles.

75·2=150

Is algebra.
PLEASE HELP NO LINKS OR FILES.
I don't want links.
I don't want links.
I don't want links.
I don't want links.

Answers

Answer: the answer is b

Step-by-step explanation:

B) 14x^2+37x+5
hope this helps!

The functions ) and g(x) are shown on the graph.
Rx) = x2
What is g(x)?
g(x) (2, 12)

Answers

Given:

The graphs of f(x) and g(x).

The function f(x) is given by:

[tex]f(x)=x^2[/tex]

The graph of g(x) passes through the point (2,12).

To find:

The function g(x).

Solution:

From the given graph it is clear that the vertex of both function f(x) and g(x) is at (0,0). It means the graph of f(x) is not translated. It means the graph of f(x) is only vertically stretched to get the graph of g(x). So,

[tex]g(x)=kf(x)[/tex]

Where, k is the stretch factor.

[tex]g(x)=kx^2[/tex]               ...(i)

The graph of g(x) passes through the point (2,12). Putting [tex]x=2, g(x)=12[/tex], we get

[tex]12=k(2)^2[/tex]

[tex]12=k(4)[/tex]

[tex]\dfrac{12}{4}=k[/tex]

[tex]3=k[/tex]

Putting [tex]k=3[/tex] in (i), we get

[tex]g(x)=3x^2[/tex]

Therefore, the correct option is A.

Which transformation produces another triangle that has the same area as the one shown?
A clockwise rotation of 180' about the origin, then a
dilation by scale factor 2
3
2
A reflection in the line y = -2, then a translation of
2 units right.
1
Р
-4 -3
-2
11
Z
-10
-1
Q4%
A clockwise rotation of 90 about the origin, then a
dilation by scale factor 4.
-2
R
-3
A dilation by scale factor then a translation of
4 units up.

Answers

Answer:

A reflection in the line y = -2, then a translation 2 units right.

Step-by-step explanation:

Transformation is the movement of a point from its initial location to a new location. Types of transformation are rotation, reflection, translation and dilation.

Rigid transformation are transformation that preserves the shape and size of the object. Rotation, reflection, translation are rigid transformation whereas dilation is not a rigid transformation.

Any transformation regarding dilation changes the side length of the object and hence the area.

From the question, only one option is right. The rest options are not right because they involve dilation. The correct option is:

A reflection in the line y = -2, then a translation 2 units right.

12. A right trapezoid is shown below. The measurements shown are in centimeters. Find the area of the
trapezoid to the nearest square centimeter. Show your work.

•16
•11
•^89

Can someone help me with this one? I know it doesn’t have a picture, but that’s because it wouldn’t let me show the whole problem!

Answers

1201.5 ft^2

the formula to find the area of a trapezoid is b1+b2/2xh
so plug in your numbers
16+11/2x89
therefore your answer is 1201.5 ft^2

Find the perimeter of the parallelogram *
10 inches
5 inches
8 inches

Answers

Step-by-step explanation:

We know that in a parallelogram

Opposite sides are of equal lengthThe sides are,

[tex]\\ \:\:\:\:\sf {:}\dashrightarrow 5in,10in,10in,5in[/tex]

we know,

[tex]\boxed{\sf Perimeter=Sum\:of\:all\:sides}[/tex]

[tex]\\ \:\:\:\:\sf {:}\dashrightarrow Perimeter_{(Parallelogram)}=5+5+10+10[/tex]

[tex]\\ \:\:\:\:\sf {:}\dashrightarrow Perimeter_{(Parallelogram)}=10+20[/tex]

[tex]\\ \:\:\:\:\sf {:}\dashrightarrow {\underline{\boxed{\bf Perimeter_{(Parallelogram)}=30inches}}}[/tex]

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