Write a coordinate proof. Prove quadrilateral KLMN, having vertices K(–5, –4), L(0, 8), M(7, 4), and N(8, –4) is not a parallelogram.

Answers

Answer 1

Answer:

From the calculation,

KL = 13

NM = √65

Hence KL ≠ NM

Therefore, the quadrilateral KLMN is not a Parallelogram.

Step-by-step explanation:

K(–5, –4), L(0, 8), M(7, 4), and N(8, –4)

Where we have vertices, (x1, y1) , (x2, y2)

We use the formula

√(x2 - x1)² + (y2 - y1)²

Side KL = K(–5, –4), L(0, 8)

√(x2 - x1)² + (y2 - y1)²

√(0 - (-5))² + (8 - (-4))²

√ 5² + 12²

√25 + 144

= √169

= 13

Side KN = K(–5, –4), N(8, –4)

√(x2 - x1)² + (y2 - y1)²

√(8 -(-5))² + (-4 - (-4))²

√13² + 0²

√169

=13

Side MN = M(7, 4), N(8, –4)

√(x2 - x1)² + (y2 - y1)²

√(8 -7)² + (-4 - 4)²

√1² + (-8)²

√1 + 64

√65

Side LM = L(0, 8), M(7, 4),

√(x2 - x1)² + (y2 - y1)²

√(7-0)² + (4 - 8)²

√(49)² +(-4)²

√ 49 + 16

√65

We were asked in the above question to prove that the quadrilateral with the given vertices is not a Parallelogram.

One of the characteristics of a Parallelogram is that the opposite sides are parallel and congruent to one another. This means that, the opposite sides are similar .

For the Quadrilateral KLMN above to be a Parallelogram, this means

KL = NM

From the above calculation,

KL = 13

NM = √65

Hence KL ≠ NM

Therefore, the quadrilateral KLMN is not a Parallelogram.


Related Questions

Please Answer Now Identify the function’s vertical asymptotes. h(x)=x-4/x^2-4 x = 2 x = 4 x = -2, x = 2 x = -4, x = 4

Answers

Answer:

x = 2 and x = +2

Step-by-step explanation:

It's essential that you use parentheses to clarify what's happening here:

h(x)=x-4/x^2-4  =>  h(x)=(x-4) / (x^2-4)

We have vertical asymptotes at x values at which the denominator (x^2 - 4) is zero.  That would be x = 2 and x = +2.

Which set of algebra tiles represents the sentence below? Ada drove 2 fewer miles today than she drove yesterday. 2 boxes contain negative x and 1 box contains a plus sign. 1 box contains x and 2 boxes contain a minus sign. 1 box contains negative x and 2 boxes contain plus signs. 2 boxes contain x and 1 box contains a minus sign.

Answers

Answer:

The correct option is;

1 box contains x and 2 boxes contain minus sign

Step-by-step explanation:

Algebra tiles are used in teaching students algebraic concepts. The unit (small) tile represents the number one. The rectangular tile represents the variable x and the large square tile represents x²

The parameters given are;

Ada drove 2 fewer miles today than she drove yesterday, therefore;

Let X = number of miles Ada drove yesterday

We have number of miles Ada drove today = X - 2

Therefore, the correct option is 1 box contains x and 2 boxes contain minus sign

Answer:

its b

Step-by-step

i got it right on my test

Tanya wants to order 50 pizzas for a party. However, the pizza supplier can deliver only 45 pizzas on the given date. How will you describe the relationship between demand and supply of pizzas? A. Demand is equal to supply. B. Demand is greater than supply. C. Demand is less than supply.

Answers

Answer:

B

Step-by-step explanation:

The demand is 50 and the supply is 45. Since 50 > 45 the answer is that the demand is greater than the supply.

Answer:

b

Step-by-step explanation:

Zaheer, a boy of height 1.5m was watching the entire programme. Initially he observed the top of theflagpoleat an angle of elevation 300 . When he moved 10 m towards the flag post the angle of elevation of the top of the flagpole increased to 450. What is the height of the flag pole?

Answers

Answer:

[tex]h = 15.163\ meters[/tex]

Step-by-step explanation:

(Assuming the correct angles are 30° and 45°)

We can use the tangent relation of the angle of elevation to find two equations, then we can use these equations to find the height of the pole.

Let's call the initial distance of the boy to the pole 'x'.

Then, with an angle of elevation of 30°, the opposite side to this angle is the height of the pole (let's call this 'h') minus the height of the boy, and the adjacent side to the angle is the distance x:

[tex]tan(30) = (h - 1.5) / x[/tex]

Then, with an angle of elevation of 45°, the opposite side to this angle is still the height of the pole minus the height of the boy, and the adjacent side to the angle is the distance x minus 10:

[tex]tan(45) = (h - 1.5) / (x - 10)[/tex]

So rewriting both equations using the tangents values, we have that:

[tex]0.5774 = (h - 1.5) / x[/tex]

[tex]1 = (h - 1.5) / (x - 10) \rightarrow (h - 1.5) = (x - 10)[/tex]

From the first equation, we have that:

[tex]x = (h - 1.5) / 0.5774[/tex]

Using this value of x in the second equation, we have that:

[tex]h - 1.5 = \frac{ (h - 1.5) }{0.5774} - 10[/tex]

[tex]h + 8.5 = \frac{ (h - 1.5) }{0.5774}[/tex]

[tex]0.5774h + 4.9079 = h - 1.5[/tex]

[tex]0.4226h = 6.4079[/tex]

[tex]h = 15.163\ meters[/tex]

pleaseee help! i need the answer for x (look at picture)

Answers

Answer:

180 - 133

Step-by-step explanation:

Answer:

x = 47 degrees

Step-by-step explanation:

Solve for X:

x + 133 = 180

180 - 133 = 47

x = 47

Please please help me. I'll give you the BRAINLIEST if correct! Given the equation A=250(1.1)^t, you can determine that the interest is compounded annually and the interest rate is 10%. Suppose the interest rate were to change to being compounded quarterly. Rewrite the equation to find the new interest rate that would keep A and P the same. What is the approximate new interest rate? Convert your answer to a percentage, round it to the nearest tenth, and enter it in the space provided, like this: 42.53%

Answers

Answer:

A=250(1+2.5)^4/12

Step-by-step explanation:

A=250(1+0.1)^t

compounded  quarterly : divide the annual by 4 : 0.1/4=0.025 or 2.5%

2.5% every  3 month (quarterly), t=4/12 (quarterly)

the equation will be :

A=P(1+r/n)^t (p is the principal),r is the rate, n is the number of compounding , t is the time.

i hope it works, just try it

A=250(1+2.5)^4/12

Answer:

hi skkedklsk sn1. soosis

The ratio of adults to children at a cricket match is 7:3.
There 150 people at the match.
How many children attended the cricket match? ​

Answers

Step-by-step explanation:

Ratio of adults to children= 7:3

Total no. Of people at the cricket match:150

To find the value of the ratios, 7x+3x=150 ; 10x=150 ; x=150/10:15

So, 7:3 is 7(15) adults to 3(15) children,

Total no. Of adults: 105

Total no. Of children: 45

So, as per the question, the no. Of children that attended the cricket match is 45

Write 3x 1/2 in radical form

Answers

Answer:

3x^1/2 in radical form is

[tex] \sqrt{3x} [/tex]

Hope this helps you

5/8 divided by 4/5 plssss

Answers

Answer:

The correct answer is 25/32

Step-by-step explanation:

Let's recall that the division of two fractions is the same as multiplying the first fraction by the inverse or reciprocal of the second fraction. We get the reciprocal of a fraction by interchanging its numerator and denominator.

Upon saying that, we have:

5/8 ÷ 4/5 =

5/8 * 5/4 = (We use the inverse and not it is a multiplication)

25/32

The correct answer is 25/32

You have a wire that is 50 cm long. You wish to cut it into two pieces. One piece will be bent into the shape of a square. The other piece will be bent into the shape of a circle. Let A represent the total area of the square and the circle. What is the circumference of the circle when A is a minimum

Answers

Answer:

88.6647727273 cm²

Step-by-step explanation :

The perimeter of the square =(50/2)

                                               = 25 cm

∴ Side of the square = (25/4)

                                    = 6.25 cm

∴ Area of of the square = (6.25)²

                                        = 39.0625 cm²

The circumference of the circle =(50/2)

                                            = 25 cm

∴ 2πr = 25

⇒ r = 25/(22/7)(2)

Area of the circle = (22/7) { 25/(22/7)2} {25/(22/7)2}

                             = (25×25×7) / (2×2×22)

                             = 4365/88

                             = 49.6022727273 cm²

∴ Total area of the circle and the square =(49.6022727273+39.0625000000)

= 88.6647727273 cm²

Hope it helped

If yes mark BRAINLIEST!

which of the following represents the factorization of the trinomial below? x^2+9x-22

Answers

Answer:

(x+11)(x-2)

Step-by-step explanation:

To factorise: x^2+9x-22

You must first divide the centre term in such a way that the sum of the 2 values will be divisible by x squared and minus 22 respectively.

So x^2+9x-22 = x^2 -2x + 11x - 22.

Now factorize x^2 - 2x and 11x-22 individually.

x^2 - 2x = x(x-2)

11x - 22 = 11(x-2)

Since these both have the same value in the brackets, use 5at one of the brackets and the other is the combination of them together:

(x+11)(x-2)

Hope this helps

Answer: (x + 11)(x - 2)

Step-by-step explanation: Since the constant term is negative, it can be factored as a positive times a negative.

Before we do that however, an x will go in the first position

of each binomial because x² breaks down into x · x.

Remember, the factors of the constant term

must add to the coefficient of the middle term.

So let's list out the factors of -22.

Factors of -22

+22 · -1

-22 · +1

+11 · -2

-11 · +2

Looking at the list above, that pair

of factors that add 9 is +11 and -2.

So our answer therefore is (x + 11)(x - 2).

Note that if you wrote your answer

as (x - 2)(x + 11), it means the same thing.

(-38)÷ ------- =not defined.fill in the blanks
please fill the answer

Answers

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▹ Answer

▹ Step-by-Step Explanation

The answer is because anything divided by infinity is not defined.

Hope this helps!

- CloutAnswers ❁

Brainliest is greatly appreciated!

━━━━━━━☆☆━━━━━━━

pleaseee help me w dis asap!!

Answers

Answer:

x=2 f(x)=5-x

o≤x≤3  f(x)=x

2<x<3 f(x)=1

3<x≤5  f(x)=5-x

Step-by-step explanation:

The domain of 8(x) =
8
is:
4-
6-x
A. {x:**3}
B. {x:x*3 and 2 *6}
C. {x:**0}
D. {x:x*6}
E. {x:x*4 and *6}

Answers

A 34_46_37_3÷56×34÷77+34

What is the slope of a line that is perpendicular to the line whose equation is y=45x−3 A. −45 B. −54 C. 54 D. 45

Answers

Answer:

  B.  -5/4

Step-by-step explanation:

We're going to assume that you don't mean

  y = 45x -3

which has a perpendicular line with a slope of -1/45.

Rather, we're going to assume that you mean

  y = 4/5x -3

so that the slope of the perpendicular line is -5/4.

__

Similarly, we're going to assume that the answer choices are supposed to represent fractions, so that the above slope matches choice B.

_____

If the slope of a line is m, the slope of the perpendicular line is -1/m. The reciprocal of a fraction is the fraction that has numerator and denominator swapped. -1/(4/5) = -5/4.

rearrange w= 3(2a+b) -4 to make a the subject

Answers

Answer:

a = - 1/2b + 1/6w + 2/3

Step-by-step explanation:

w= 3(2a+b) - 4

Add 4 on both sides.

w + 4 = 3(2a+b)

Divide 3 into both sides.

w/3 + 4/3 = 2a+b

Subtract b on both sides.

w/3 + 4/3 - b = 2a

Divide 2 into both parts.

w/3/2 + 4/3/2 - b/2 = a

a = w/6 + 4/6 - b/2

a = 1/6w + 2/3 - 1/2b

Answer:

a=(w-3b+4)/6

Step-by-step explanation:

w= 3(2a+b) -4

w=6a+3b-4

6a= w-3b+4

a=(w-3b+4)/6

Which of the system(s) below works best to solve by elimination? Why? System 1 : 3m+n=71 2m-n=30
System 2 : 4x+y=1 y=-2x+9
System 3 : 5x+4y=15 5x + 11y=22

Answers

Answer:

first option is easiest since it involves just adding both equations term by term.

3m+n=71

2m-n=30

Step-by-step explanation:

The first system looks like the easiest one, because the two equations are listed already in standard form, and the variable "n" appears as positive "n" in the first equation, and as its opposite "-n" in the second equation. Therefore the elimination method works directly by adding both equations term by term (thus cancelling out completely one of the variables in the resultant/combined equation.

Please answer this fast in 2 minutes

Answers

Answer: (4,10)

Step-by-step explanation:

This is the answer because you would have to plug in everything into the midpoint formula and then solve for x2 and y2. Hope this helps! :)

Answer:

(4,10)

Step-by-step explanation:

Juan y Luis deben pagar su deuda de suma 4500, si el triple de lo que debe Juan menos, lo que debe Luis asciende a 3500 ¿cuánto es la deuda de cada uno?

Answers

Answer:

donda esta laletcha

Step-by-step explanation:

hola

6.
(a) Pens cost 36 cents each.
Pencils cost 12 cents each.
(i) Write an expression for the cost of y pens.

Answers

Pens = 36y

Pencils 12y

This is because the cost of pens is 36 times however many pens you buy

The Sam Egeos for pencils except it’s 12 cents.

I don’t understand what this question says, please help :(

Answers

Answer:

a(15) = 131

Step-by-step explanation:

Explicit Arithmetic Sequence Formula: an = a1 + d(n - 1)

We are given a1 and d, so plug them in:

an = 5 + 9(n - 1)

To find the 15th term, plug 15 in for n:

a(15) = 5 + 9(15 - 1)

a(15) = 5 + 9(14)

a(15) = 5 + 126

a(15) = 131

Answer:

Step-by-step explanation:

d = 9 ----> d is common difference

[tex]a_{1} = 5\\\\[/tex] ----> first term

In arithmetic sequence, the difference between two terms is constant.

to find nth term,

[tex]a_{n} = a_{1} + (n-1)d\\\\a_{15} = 5 + 14*9\\\\ = 5 + 126\\= 131[/tex]

find 1st, 2nd, 3rd, 4th and 10th nTh term. rule is 3n+4

Answers

Answer:

When n is 1

3n+4

=3*1+4

=3+4

=7

When n is 2

3n+4

=3*2+4

=6+4

=10

When n is 3

3n+4

=3*3+4

=9+4

=13

When n is 4

3n +4

=3*4+4

=12+4

=16

When n is 10

3n+4

=3*10+4

=30+4

34

Two lines AB and CD intersect at O. If ∠AOC + ∠COB + ∠BOD = 270°Find the measures of ∠AOC, ∠COB, ∠BOD, ∠DOA.

Answers

Answer:

  all are 90°

Step-by-step explanation:

Vertical angles are congruent, and linear angles are supplementary, so we have ...

  ∠AOC + ∠COB + ∠BOD = 270°

  180° + ∠BOD = 270°

  ∠BOD = 90°

Since the lines cross at right angles, all of the angles are 90°.

There are eight marbles in a bag. Four marbles are blue (B), two marbles are red (R) and two marbles are green (G) Steve takes a marble at random from the bag. What is the probability that Steve will take a blue marble.

Answers

Answer:

1/2

Step-by-step explanation:

There are 8 marbles in total and 4 are blue, so 4/8 are blue. Then simplify 4/8 and you will get 1/2.

Answer:

1/2 or 50%

Step-by-step explanation:

Blue= 4, Red= 2, Green= 2

Total marbles= 8

P(B)= 4/8= 1/2 or 50%

(x4- 4x2 + 5x - 1) = (x + 2)
Solve using remainder Therom

Answers

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Lets do this step by step.

Simplify: [tex](4x2 - 2x) - (-5x2 - 8x).[/tex]

~~~~~~~~~~~~~~~~~~~~~~~~~

Solution:

[tex](4x2 - 2x) - (-5x2 - 8x)= 4x2 - 2x + 5x2 + 8x.= 4x2 + 5x2 - 2x + 8x.= 9x2 + 6x.= 3x(3x + 2).[/tex]

~~~~~~~~~~~~~~~~~~~~~~~~

Answer: [tex]3x(3x + 2)[/tex]

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Hope this helped you.

Could you maybe give brainliest..?

❀*May*❀

The hypotenuse of a right triangle is 9[tex]\sqrt{2}[/tex] cm, and the shorter leg is 9 cm. Find the length of the other leg.

Answers

Answer:

9 cm

Step-by-step explanation:

If you were to imagine this right triangle, you would find it to be a 45 - 45 - 90 triangle. Perhaps the " shorter leg " piece of information was present to trick you, considering that the legs are congruent by converse to base angle theorem.

How is this triangle a 45 - 45 - 90? In such a triangle, the legs can be posed as x cm, as the base angles are congruent ( 45 and 45 ), thus the legs of the triangle are congruent as well. The hypotenuse would be x√2, and as we can see -

If legs = x, Hypotenuse = x√2 = 9√2

Thus, the length of the other leg is 9 centimeters ( 9 cm )

Hope that helps!

The length of the base of a right-angled triangle ABC is 6 centimeters and the length of the hypotenuse is 10 centimeters. Find the area of the triangle.

Answers

Answer:

24

Step-by-step explanation:

Ok, so we see that we have 6 as a leg of the right triangle and 10 as the hypotenuse.  As we look closer, we can tell that this makes the Pythagorean triple 6, 8, 10.  6, 8, 10 is just the Pythagorean triple 3, 4, 5 but it is multiplied by 2.  So now that we know both the legs of this right triangle, we can use the area of a triangle formula (bh)/2.  6*8=48 and 48/2 = 24 which gives us our answer.

HELP PLZZZZZZZZZZZ!!!!!!!

Answers

Answer:

A) 21/20

Step-by-step explanation:

Tangent = Opposite/Adjacent

21/20

Tan= Opposite/ adjacent

what is the simplified value of 1/3 divied by 2/3

Answers

Answer:

1/2 or 0.5

Step-by-step explanation:

1/3 divided by 2/3

1/3 times 3/2

3/6

1/2, or 0.5

Answer:

1/2

Step-by-step explanation:

1/3 ÷2/3= 1/3×3/2( this is because fractions cannot be divided and the reciprocal of the fraction by which 1/3 had to be divided has to be taken which makes 2/3 as 3/2 and division as multiplication)

so, 1/3×3/2 gives 3/6, when simplified, gives 1/2.

On line A, each time x increases by 1 y increases by A) .5 B) 1 C) 1.5 D) 2

Answers

Answer:

b

Step-by-step explanation:

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