Quadrilateral ABCD has vertices A(- 3, 1), B(4, 2) B(4, 2), C(9, - 3) , and D(2, - 4) . aProve that quadrilateral ABCD is a rhombus b )Prove that ABCD is not a square .

Answers

Answer 1

9514 1404 393

Explanation:

The vectors representing the diagonals are ...

  AC = C - A = (9, -3) -(-3, 1) = (12, -4)

  BD = D - B = (2, -4) -(4, 2) = (-2, -6)

The dot-product of these vectors is the sum of the products of corresponding coordinates:

  (12)(-2) +(-4)(-6) = -24 +24 = 0

When the dot-product is zero, the vectors are perpendicular. These vectors are different lengths (BD = 1/2·AC), so they are not the diagonals of a square.

__

The midpoints of the diagonals will be in the same place if the quadrilateral is a rhombus.

  (A +C)/2 = (B +D)/2

We can simplify our effort a bit by multiplying by 2.

  A+C = B+D

  (9, -3) +(-3, 1) = (2, -4) +(4, 2)

  (6, -2) = (6, -2) . . . . . . . . . . . . . . . . yes, the midpoints are the same point

__

We have shown the diagonals of the quadrilateral are different lengths and perpendicular bisectors of each other, so the quadrilateral IS A RHOMBUS, NOT A SQUARE.


Related Questions

For each set of three measures, determine if they can be angle measures of a triangle.

Answers

Answer:

NO

NO

YES

NO

Step-by-step explanation:

The sum of the angles has to be equal to 180° because the sum of the angles in a triangle is 180°

The first one is already more that 180°, because you are adding 2 angles that are more than 100°

The sum of the second one is equivalent is 160°

The sum of the third one is equivalent to 180°

The sum of the fourth one is more than 180°

-Chetan K

guy pls help me!!!!!

Answers

Answer:

19

Step-by-step explanation:

6s-8= 106

6s = 114

s= 19

19

The angle that’s above is the same as this one so
( 6 • 19 ) - 8
I think so

someone help meh pleasee

Answers

The answer is  [tex]\mathsf {\frac{2}{9}}[/tex].

We are given the equation :

∛(8/729)∛8/∛7292/9

Answer:

[tex]\dfrac{2}{9}[/tex]

Step-by-step explanation:

Given expression:

[tex]\sqrt[3]{\dfrac{8}{729}}[/tex]

[tex]\textsf{Apply exponent rule} \quad \sqrt[n]{a}=a^{\frac{1}{n}}:[/tex]

[tex]\implies \left(\dfrac{8}{729}\right)^{\frac{1}{3}}[/tex]

[tex]\textsf{Apply exponent rule} \quad \left(\dfrac{a}{b}\right)^c=\dfrac{a^c}{b^c}:[/tex]

[tex]\implies \dfrac{8^{\frac{1}{3}}}{729^{\frac{1}{3}}}[/tex]

Rewrite 8 as (2 · 2 · 2) and rewrite 729 as (9 · 9 · 9):

[tex]\implies \dfrac{(2 \cdot 2 \cdot 2)^{\frac{1}{3}}}{(9 \cdot 9 \cdot 9)^{\frac{1}{3}}}[/tex]

[tex]\implies \dfrac{(2^3)^{\frac{1}{3}}}{(9^3)^{\frac{1}{3}}}[/tex]

[tex]\textsf{Apply exponent rule} \quad (a^b)^c=a^{bc}:[/tex]

[tex]\implies \dfrac{2^{(3 \cdot \frac{1}{3})}}{9^{(3 \cdot \frac{1}{3})}}[/tex]

[tex]\implies \dfrac{2^1}{9^1}[/tex]

[tex]\textsf{Apply exponent rule} \quad a^1=a:[/tex]

[tex]\implies \dfrac{2}{9}[/tex]

Learn more about exponent rules here:

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MAY SOMEONE PLZ HELP ME ON THESE :(((

Answers

Answer:

12) Domain: (-4, 1] Range: [-4, 0]

13) Domain: (-infinity, 1] Range: [0, infinity)

Function decreases from x = negative infinity to 0. (I'm assuming this is what the question is asking for!)

Minimum of y = 0 at x = 0

30 points reward just answer plsss​

Answers

D and then C because parentheses then multiply and divide then add and subtract
D and C. D because PEMDAS IS PARENTHESIS EXPONENTS MULITPLICATION DIVISON ADDITION AND SUBTRACTION. Sorry all caps

If each block sides are 1 cm long, what is the volume of this object?

Answers

4 cubic centimeters.

Brainliest would be great. Comment below if it helped!

Answer:

The volume for this object is 4.

Step-by-step explanation:

For each block, we need to multiply using the volume formula which is

Length x Width x Height

So, if the side lengths for all these blocks are 1. That means we would do 1x1x1 for every block. Since there are 4 blocks that means our equation for the whole object would be 1+1+1+1 or simply 1x4. And we all know the answer to our equation 1 x 4 is 4.

, Hope this helps :)

Have a great day!!

What’s the answer???????

Answers

Answer:

77

Step-by-step explanation:HOPE YOU ADD JRVERANO2010

Question 20 of 40
Anna thinks of a number. She subtracts 5 from the number, multiplies the
result by 2, and then adds 6. The number she ends up with is 14. What
number did Anna start with?
If you work backward to solve this problem, what do you do first?
A. Divide 14 by 2
OB. Add 5 to 14
C. Subtract 5 from 14
D. Subtract 6 from 14
What’s the first steps when doing it backwards ?

Answers

Answer:

2(x-5)+6=14 is your starting equation, and then we solve:

2(x-5)+6=14

2(x-5)/2 +6=14/2

x-5+6=7

the first step is to divide by 2, so A :)))

Camille's science class is making slime from cornstarch and glue. Camille is helping pass out materials. She gives each student 4 ounces of cornstarch from a 5-pound bucket. If Camille's class has a total of 18 students, how many ounces of cornstarch will she have left?

Answers

Answer:

8 ounces

Step-by-step explanation:

16oz/lb

16*5= 80oz of cornstarch in bucket

4oz * 18students = 72oz

80-72= 8 oz remaining

The amount of cornstarch left is 8 ounce.

What is Multiplication?

To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.

Given that;

Each student get = 4 ounce of cornstarch

Total number of student = 18 students

And, Total amount of cornstarch = 5 pound

Here,

Since, Amount of total cornstarch to student = Each student get × Total number of student

⇒ Amount of total cornstarch to student = 4 × 18

⇒ Amount of total cornstarch to student = 72 ounce

Since, 1 pound = 16 ounces

So, We get;

⇒ Total amount of cornstarch = 5 × 16

⇒ Total amount of cornstarch = 80 ounces

Thus, Amount of cornstarch left = 80 - 72

⇒ Amount of cornstarch left = 8 ounces

Learn more about the multiplication visit:

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#SPJ5

If f(x)=2x^2-4, find f(0) and f(-3)

Answers

Answer:

1st problem. x= √2, -√2 or Decimal form x= 1.41421356...

2nd problem.  x= √2/2 , -√2/2 or Decimal form X= 0.70710678...

Kwami had two large sheets of paper. He cut each piece of paper in half, then he cut the smaller pieces of paper in half two more times.

Answers

Answer:

14

Step-by-step explanation:

i hope i not fail this test someone help

Answers

Answer:

the answer to your question is pie

Answer:

A: is irrational number

B: is rational number

C: is irrational number

D: as a natural or whole number, including 9, can also be written as a fraction p1 they are all rational number. hence 9 is a rational number

so D is the the answer

whoever solves correctly gets brainliest The number of miles will be x. Next, we’ll have the inequality 8x+2<=10 then we will solve the inequality 8x+2-2<=10-2 and simplify 8x<=8. divide 8 both sides x<=1


4. Graph the solution to your inequality on a number line or describe, in words, how to graph the inequality on a number line.

Answers

Answer:

Step-by-step explanation:

Need help asp pls pls pls

Answers

Answer:

D.

Step-by-step explanation:

u should times each num in brakect 5 times

exp:

-2×-2×-2×-2×-2=-32

Will give brainliest!!! Describe the life of peasants in the middle ages. Make sure to include the labor they were put through and how the women were treated. 8-10 complete sentences pleaseeee.

Answers

explain in a different way I can't understand what your saying?

Which of the following shapes is not a parallelogram? Trapezoid Square Rectangle

Answers

Answer: Trapezoid

Step-by-step explanation: A parallelogram is a shape that has two pairs of parallel sides, two pairs of equal opposite angles, two pairs of equal and parallel sides. Hope this helps!! :))

Answer:it's trapezoid i got a 100%

Step-by-step explanation:

answer po plss plss plss

Answers

Answer:

additive identity property (a)

Step-by-step explanation:

the answer to this question would be A, i’ve done this before.

If BAC = ADB = 90. The value of x is

Answers

I’m extremely sorry, I am stumped

write at least 5 arithmetic sequence and determine the common difference

Answers

An arithmetic sequence is a sequence where we use addition or subtraction to get to the next term.

Examples:

1, 3, 5, 7, 9...

Common Difference: Add 2

2, 6, 10, 14, 18, 22..

Common Difference: Add 4

100, 90, 80, 70, 60, 50..

Common Difference: Subtract 10.

25, 30, 35, 40, 45..

Common Difference: Add 5

1, 10, 19, 28, 37..

Common Difference: Add 9

Hope it helps!

[tex]ANSWERED:\\GraceRosalia[/tex]


1. Translate the following sentence into an equation and solve. The
product of five and the sum of a number x and three is twelve .?

Answers

Answer:

5*(x+3) = 12

Step-by-step explanation:

Product means multiply

Sum means add

Is means equals

product of five and the sum of a number x and three is twelve

5*(x+3) = 12

A line passes through the points (-6, 8) and ( 3, 7). What is the equation of the line in Slope-Intercept Form?​

Answers

Step-by-step explanation:

y=−x+2

Explanation:

Alright, so this is a two-part question. First we need to find the slope, then we need to find the y-intercept. Finally we plug all this into the slope intercept equation y=mx+b

The slope is commonly referred to as m=riserun this can also be expressed as m=y2−y1x2−x1 by using the change in y and the change in x.

m=5−8−3−(−6)

m=−33

m=−1

Alright, now lets find the y-intercept by using that slope. If we plug that slope into the base formula we get y=−x+b. Since we already know one point, lets put (−3,5) into that equation and solve for b.

5=−(−3)+b

5−3=3+b−3

2=b

Now is if plug out b into out equation, we get a finally answer of y=−x+2

Even though we're done, lets check it by putting in the other point.

8=−(−6)+2

8−6=6+2−6

2=2

The sum of three times a number and seven is equal to the difference of the number and fifteen. Find the number. Round your answer to the nearest integer, if necessary.

Answers

Answer:

2

Step-by-step explanation:

Let the number be x

3x + 7=15-x

4x = 8

x=2

In the equation 3x + 2x + 7 = 6x, what are the like terms?

Answers

Answer:

3x , 2x and 6x are like terms!!

Answer:

The like terms are 3x. 2x. 6x because they both have the x statement

Step-by-step explanation:

Josh was driving on a road that had a 30 mi/h speed limit posted. A deer jumped out from the side of the road, causing him to slam on the brakes. His tires left 71 ft skid marks. The road had a drag factor of 0.78. His brakes were operating at 95% efficiency. Should Josh get a ticket for speeding?

Answers

Answer no

Step-by-step explanation:

please mark brainlyest

pls help i give brainless

Answers

Answer:

1. 11 AM

2. 10:30 AM

Step-by-step explanation:

Answer:

Number 5 she started at 11:00 am

number 6 she started at 10:30 am

Step-by-step explanation:

:)

Algebra 2 ............​

Answers

The equation of the line through the point (-4, 7) and with a slope of -5/2 is y = -5/2x - 3

The equation of a line in slope intercept form is expressed as:

[tex]y-y_0 = m(x-x_0)[/tex]

m is the slope

(x0, y0) is the point on the line.

Given the following parameters:

m = -5/2 and (x0, y0) =(-4, 7)

Substitute the given coordinates into the formula above;

y  - 7 = -5/2(x + 4)

2(y-7) = -5(x+4)

2y-14 = -5x - 20

2y = -5x - 20  + 14

2y = -5x - 6

y = -5/2x - 3

Hence the equation of the line through the point (-4, 7) and with a slope of -5/2 is y = -5/2x - 3

Learn more here: https://brainly.com/question/17003809

help me again plz thank you i make sure who answer this i will give five stars and a thx botton

Answers

Answer:

15,296

Step-by-step explanation:

Hope this helps!


Help plz.. it’s due tonight

Answers

The answer is y=5.3 because when you subtract 2.8 from 8.1 you get 5.3

multiple 6 to become 9

Answers

the answer would be 3

Help me, please!! I have other math questions up if you guys could help with that too!

Find the value of x and y.

Answers

Answer:

x=25, y=19

Step-by-step explanation:

130+2x=180

x=25

54+2x+4y=180

y=19

Answer:

x = 25 , y = 19

Step-by-step explanation:

130° and 2x° are adjacent angles on a straight line and sum to 180° , so

130 + 2x = 180 ( subtract 130 from both sides )

2x = 50 ( divide both sides by 2 )

x = 25

--------------------------------------------------------------

The exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.

130° is an exterior angle of the triangle , then

54 + 4y = 130 ( subtract 54 from both sides )

4y = 76 ( divide both sides by 4 )

y = 19

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