Three vertices of parallelogram PQRS are show: Q(8, 5), R(5, 1), S(2, 5)
Place statements and reasons in the table to complete the proof that shows that parallelogram PQRS is a rhombus.

Answers

Answer 1

[tex]PQRS[/tex] is a rhombus since [tex]\overline{QR} \cong \overline{RS}[/tex] and [tex]m\angle R \neq 0^{\circ}[/tex], [tex]m\angle R \neq 90^{\circ}[/tex] and  [tex]m\angle R \neq 180^{\circ}[/tex]. [tex]\blacksquare[/tex]

How to demonstrate that a given figure represents a rhombus

In this question we must prove that a given parallelogram is a rhombus. A rhombus is quadrilateral with four sides of equal length and two pairs of angles of equal measure, different to each other. We must demonstrate that [tex]\overline {QR} \cong \overline {RS}[/tex] and [tex]m\angle R \neq 90^{\circ}[/tex] and [tex]m\angle R \neq 0^{\circ}[/tex] and [tex]m\angle R \neq 180^{\circ}[/tex] by geometric and algebraic definitions and theorems:

[tex]Q(x,y) = (8,5)[/tex], [tex]R(x,y) = (5,1)[/tex], [tex]S(x,y) = (2,5)[/tex]   Given[tex]QR = \sqrt{(5-8)^{2}+(1-5)^{2}} = 5[/tex]   Pythagorean theorem/Line segment length formula[tex]RS = \sqrt{(2-5)^{2}+(5-1)^{2}} = 5[/tex]   Pythagorean theorem/Line segment length formula[tex]QR = RS[/tex]   (2) and (3)[tex]\overrightarrow {QR} \,\bullet\,\overrightarrow{RS} = (-3)\cdot (-3) + (-4)\cdot (4) = -7[/tex]   Dot product[tex]\theta = \cos^{-1}\left(\frac{\overrightarrow{QR}\,\bullet\,\overrightarrow{RS}}{QR\cdot RS} \right) = \cos^{-1}\left(-\frac{7}{25} \right) \approx 106.260^{\circ}[/tex]   Dot product[tex]\overline{QR} \cong \overline {RS}[/tex]   (4) and (6)[tex]PQRS[/tex] is a rhombus.     (6) and (7)/Result

[tex]PQRS[/tex] is a rhombus since [tex]\overline{QR} \cong \overline{RS}[/tex] and [tex]m\angle R \neq 0^{\circ}[/tex], [tex]m\angle R \neq 90^{\circ}[/tex] and  [tex]m\angle R \neq 180^{\circ}[/tex]. [tex]\blacksquare[/tex]

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Related Questions

What is the length of 15,409,000 cubic yard in miles? (to
the nearest hundred)

Answers

Answer:

Step-by-step explanation:

The cube root of 15,409,000 = 248.84 yards.

There are 1760 yards in a mile

One edge of a cube = 248.84 / 1760 = .141386 miles.

So a cube would be .00283cubic miles. Your answer does not reach a hundredth place, I don't think.

A line passes through the point (-5,-2) and (0,2) write the equation in point-slope form

Answers

Answer:

y=4/5x+2

Step-by-step explanation:

Answer:

y=0.8x+2

Step-by-step explanation:

First, you would figure out the slope using the following equation: (y2-y1)/(x2-x1)=slope.

So, (2--2)/(0--5)= 4/5, or 0.8. This would be the slope.

Then, you would figure out b by putting a data point from the given ones. I chose (0, 2).

2=0.8(0) + b --> 2=0 + b --> 2=b

So, the final equation is y=0.8x+2

A=pir^2 solve for pi

Answers

Given problem;

   A = [tex]\pi[/tex]

   Solve for π;

To solve for π implies that we make it the subject of the expression.

So;

       A = π r²

      Now multiply both sides by [tex]\frac{1}{r^{2} }[/tex]

 So;

                A x [tex]\frac{1}{r^{2} }[/tex]   = [tex]\pi[/tex] x r² x [tex]\frac{1}{r^{2} }[/tex]

              r² cancels out from the right side and leaves only π;

                  π = [tex]\frac{A}{r^{2} }[/tex]

So    [tex]\pi = \frac{A}{r^{2} }[/tex]

Given the figure below find the values of x and z.

Answers

Answer:

Hello!!! Princess Sakura here ^^

Step-by-step explanation:

So first I would do...[tex]9x+39+12x-48=180[/tex] first because it'll give me the x value, so....

[tex]9x+39+12x-48=180\\21x-9=180\\21x=189\\x=9[/tex]

So now we know that the x equals 9 so we plug it in for (9x+39) because it's vertical to the other angle across from it and vertical angles are always congruent, so...

[tex]z=9(9)+39\\z=81+39\\z=120[/tex]

so now we know that x=9 and z=120.


Find the Highest Common Factor of 120 and 150.

Answers

Answer:

30

Step-by-step explanation:

120 divided by 30 is 4, and 150 divided by 30 is 5.

Answer: What is the greatest common factor of 120 and 150? The greatest common factor of 120 and 150 is 30, because 30 is the highest number that is divisible by both numbers.

the function f(x)=5(2)x represents number of bacteria, f(x), growing in a culture after x hours. How many bacteria are in the culture after 3 hours?

Answers

Answer:  40

=============================================

Explanation:

Assuming the function is f(x) = 5(2)^x, then we replace every x with 3. Then we use the order of operations PEMDAS to simplify. Or we can use a calculator to simplify in one step.

f(x) = 5(2)^x

f(3) = 5(2)^3

f(3) = 5(8)

f(3) = 40

WHAT DOES y= IxI mean

Answers

Answer:

it means the ratio of x

ex. |-5| = 5 and so on

|7|=7

Identify the written form of this number: 4,812,000. A. four hundred thousand, eight hundred twelve B. four thousand and eight hundred twelfths C. four million, eight hundred twelve thousand D. four billion, eight hundred twelve million Help please

Answers

Answer: C. four million, eight hundred and twelve thousand

Step-by-step explanation:

4,812,000.

When a figure consists of 7 numbers, it is regarded as millions. For example, 8,000,000 is right million on words.

4,812,000 will therefore be called four million, eight hundred and twelve thousand.

Nyali paid $62 for a bicycle. She sold it later for $46.

What was her percentage loss?

Answers

Answer:

25.8 %

Step-by-step explanation:

FIrst you need to find how much 1% of sixty two is worth (1.612) then find the difference between values ($16) then multiply these values together to find your answer

What's is the distance between (-2,7) and (-4,11)

Answers

Answer:

Step-by-step explanation:

The answer is in the picture above. Sorry for the previous mistake

Refer to the figure at the right. If
m22 = (a + 15)° and m23 = (a + 35)°, find the
value of a such that HĽ I HJ.

Answers

Answer:m∠1 = 145°

m∠2 = 35°

m∠3 = 35°

m∠4 = 145°

m∠5 = 145°

m∠6 = 35°

m∠7 = 35°

m∠8 = 145°

Step-by-step explanation:

The required value of a is 20°.

What are complementary angles?

In geometry, complementary angles are defined as two angles whose sum is 90 degrees. In other words, two angles that add up to 90 degrees are known as complementary angles.

Now it is given that,

m22 = (a + 15)° and m23 = (a + 35)°

Let m22 and m33 be the angle between HL and HJ.

And since HL is perpendicular to HJ therefore they are complement ot each other.

Thus,

m22 + m23 = 90°

⇒ (a + 15)° +  (a + 35)° = 90°

⇒ a° + 15° +  a° + 35° = 90°

⇒ 2a° +50° = 90°

⇒ 2a° = 90° - 50°

⇒ 2a° = 40°

⇒ a° = 40°/2

⇒ a° = 20°

Thus, the required value of a is 20°.

To learn more about complementary and supplementary angles:

brainly.com/question/17040049

#SPJ2

What is the mean of this set 18,21,20,14,17

Answers

Answer: 18

Step-by-step explanation:

Add them all up

18+21+20+14+17=90

Divide by 5 since that is how many numbers there are

90/5=18

Answer:

the mean is 18

Step-by-step explanation:

you add them all up and then divide by the number of numbers

18+21+20+14+17=90

90/5=18

hey diddle diddle the median is in the middle, you add and divide for the mean the mode is the one that appears the most and the range is the difference between.

Hope this helps!!

Study the number line shown. Match the question with the correct letter on the number line.

Answers

Answer:

C,B,D,A

Step-by-step explanation:

Start at 3(X)  and move based on the question

Determine whether the given lines are parallel, perpendicular or neither.

2x + 3y = 1
3x – 2y = 1

Answers

Answer:

Hello!!! Princess Sakura here ^^

Step-by-step explanation:

These two equations are perpendicular it's pretty tough to figure it out with the only the equations like last time but if you graph it's more easier because it's visual.

So the equations solved for y is...

[tex]y=-\frac{2}{3} x+\frac{1}{3}[/tex]

[tex]y=\frac{3}{2}x-\frac{1}{2}[/tex]

Question Progress
Factorise 3x^2+ 5x = 12

Answers

Answer:

(3x-4)(x+3) = 0

x = -3, 4/3

Step-by-step explanation:

3x^2 + 5x = 12

3x^2 + 5x - 12 = 0

(3x-4)(x+3) = 0

x = -3, 4/3

Explain in detail what happens to the particles before, during, and after sublimation.

Answers

Answer:

The process in which a solid changes directly to a gas is called sublimation. It occurs when the particles of a solid absorb enough energy to completely overcome the force of attraction between them. Solid carbon dioxide changes directly to the gaseous state. ...

Step-by-step explanation:

Determine the slope from the following order pairs:
(0,3) (3,-1)

Answers

use slope formula
y^2-y^1/x^2-x^1

the answer is -4/3

What is the solution to 4.1 x 6.5 + 7.6 + 2

Answers

Answer:

36.25

Step-by-step explanation:

2y + x + 7 = 0
how do i solve with substitution?

Answers

Answer:

x+2y=-7

Step-by-step explanation:

2y + x =-7

x+2y=-7

When solving for x, set y to 0. When solving for y, set x to zero. You can just isolate the variables from there.

please help for a cookie ​

Answers

Answer:

B

Step-by-step explanation:

what is mensuration and give three common shapes and their diagrams​

Answers

Maths > Mensuration

Mensuration

Suppose you want to put a boundary around your garden or field. For that, you need to find out the length of the boundary. Also, what if you want to find out the area and volume of different geometrical shapes. So this is something we are going to see in his chapter. So let us study the topic mensuration and mensuration formulas in detail.

Cylinder

Circles

Polygons

Rectangles and Squares

Trapezium, Parallelogram and Rhombus

Area and Perimeter

Cube and Cuboid

Question. Explain the use of mensuration in daily life?

Answer. The uses of mensuration in real life are many. Some of these uses are as follows:

Measurement of agricultural fields, and site areas for the purpose of purchase/selling transactions.

Measurement of volumes for packaging solid food items, milk, and liquids.

Measurements of surface areas for the purpose of estimating the painting of houses etc.

Question. What is meant by mensuration?

Answer. Mensuration refers to the branch of mathematics which involves the study of various geometrical shapes. Furthermore, it deals with the areas and Volume of such geometrical figures. So, this subject is all about the process of measurement.

Question. Explain what is the volume in mensuration?

Maths > Mensuration

Mensuration

Suppose you want to put a boundary around your garden or field. For that, you need to find out the length of the boundary. Also, what if you want to find out the area and volume of different geometrical shapes. So this is something we are going to see in his chapter. So let us study the topic mensuration and mensuration formulas in detail.

Cylinder

Circles

Polygons

Rectangles and Squares

Trapezium, Parallelogram and Rhombus

Area and Perimeter

Cube and Cuboid

Question. Explain the use of mensuration in daily life?

Answer. The uses of mensuration in real life are many. Some of these uses are as follows:

Measurement of agricultural fields, and site areas for the purpose of purchase/selling transactions.

Measurement of volumes for packaging solid food items, milk, and liquids.

Measurements of surface areas for the purpose of estimating the painting of houses etc.

Question. What is meant by mensuration?

Answer. Mensuration refers to the branch of mathematics which involves the study of various geometrical shapes. Furthermore, it deals with the areas and Volume of such geometrical figures. So, this subject is all about the process of measurement.

Question. Explain what is the volume in mensuration?

Answer. Any solid occupies some region in space. Furthermore, the magnitude of this region is known as the volume of the solid. A standard unit of volume happens to be the cubic centimetre.

Question. What do we understand by mensuration formula?

Answer. A mensuration formula helps in computing the length-related properties of an object. This computation takes place on the basis of known lengths, areas, etc. Beyer (1987) came forward with a collection of mensuration formulas for the various plane and geometric figures. properties of an object. This computation takes place on the basis of known lengths, areas, etc. Beyer (1987) came forward with a collection of mensuration formulas for the various plane and geometric figures.

-254 minus -254 equals ?

Answers

Answer:

0

Step-by-step explanation:

They both cancel eachother out.

On Monday, Jayla raised $ 30 and Carlos raised $ 50. After that, Jayla raised $ 12 per day and Carlos raised $ 7 per day. After how many days will they have raised the same amount? They will raise the same amount after days. (Only type in the number for your final answer)

Answers

Answer:

4 days

Step-by-step explanation:

For Jayla:

[tex]Base\ Amount = \$30[/tex]

[tex]Additional = \$12[/tex] daily

For Carlos:

[tex]Base\ Amount = \$50[/tex]

[tex]Additional = \$7[/tex] daily

Represent the number of days with d

Jayla's expression can be represented using:

[tex]30 + 12*d[/tex]

Carlos' can be represented as:

[tex]50 + 7 * d[/tex]

Equate both expressions:

[tex]50 + 7 * d = 30 + 12 * d[/tex]

[tex]50 + 7d = 30 + 12d[/tex]

Collect Like Terms

[tex]12d - 7d = 50 - 30[/tex]

[tex]5d = 20[/tex]

Solve for d

[tex]d = 20/5[/tex]

[tex]d = 4[/tex]

De divided by f if d= -24 e= -4 f= 8

Answers

The answer is 12 in this problem

Given the values in the table on the left come from
a continuous function, which intervals must
contain an x-intercept? Select two options.
-0.8 -3.2 < x < -2.4
2.4 < x < 3.2
1.6 < x < 2.4
DONE

Answers

Answer:

B and d

Step-by-step explanation:

Edge 2020

Answer:

-3.2 and 1.6

Step-by-step explanation:

At an amusement park, Robin bought a t-shirt for $13 and 8 tickets for rides. She spent a
total of $32 Write an equation and determine how much each ticket cost.

Answers

Answer:

$2.37

Step-by-step explanation:

if you 13 from 32 and then divide that by 8 you get 2 dollars and 37 cents

Answer:

2.37

Step-by-step explanation:

32-13=19

19/8=2.37

The amount of available disk space on a digital video recorder changed from 81% to 9% after recording 12 episodes of a show. Each episode requires the same amount of disk space. Which statement is true? The change in available disk space is 6% per episode. The change in available disk space is −6% per episode. The change in available disk space is 7.5% per episode. The change in available disk space is −7.5% per episode.

Answers

Answer:

The change in available disk space is −6% per episode

Step-by-step explanation:

Given that :

Available disk space changed from 81% to 9% after recording 12 episodes of a show

Each episode requires the same amount of disk space

Change in disk space =

Final % = 9%

Initial percentage = 81%

Change = final value - initial value :

(9 - 81)% = -72%

72% reduction in disk space

Space taken up per episode :

Reduction in space / number of episodes

= -72% / 12

=- 6%

Can someone pls help me solve this? I just don’t get it, please help please

Answers

Answer:

conveyor 1 10/2=5/1

conveyor 2 -8/2=-4/1

conveyor 1 is steeper

Step-by-step explanation:

conveyor 1 goes up 5 ft for every foot it runs where

conveyor 2 goes down 4 ft for every foot it runs

Find the value of b for the triangle using the Pythagorean Theorem.

Answers

Step-by-step explanation:

Hey there!

Given;

The given figure is a Right angled triangle, taking reference angle as angle B.

Hypotenuse= AB=5

Base= CB= 4

Perpendicular= AC=b

Using Pythagorean theorem.

[tex] {h}^{2} = {p}^{2} + {b}^{2} [/tex]

[tex]p = \sqrt{ {h}^{2} - {b}^{2} } [/tex]

Put all values.

[tex]b = \sqrt{ {5}^{2} - {4}^{2} } [/tex]

[tex]b = \sqrt{25 - 16} [/tex]

[tex]b = \sqrt{9} [/tex]

Therefore, the value of b is 3.

Hope it helps...

Shyann won 40 halloween candies playing the toss at her school's carnival. Later she gave three to each of her friends. She only has remaining. How many friends does she have?

Answers

Answer:

alot

Step-by-step explanation:

i cant understand this

Answer:

13

Step-by-step explanation:

13 times 3 = 39

40-39=1

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