Parallelogram ABCD has vertices: A(-3, 1), B(3, 3), C(4, 0), and D(-2, -2). In two or more complete sentences, explain how you can use the coordinates of the vertices to prove that parallelogram ABCD is a rectangle.

please help

Parallelogram ABCD Has Vertices: A(-3, 1), B(3, 3), C(4, 0), And D(-2, -2). In Two Or More Complete Sentences,

Answers

Answer 1

Step-by-step explanation:

via the distance formula (based on Pythagoras) I can prove that ABC is a right-angled triangle, and that ADC is fully congruent to ABC.

so, together these 2 triangles (joined at their Hypotenuses, the diagonal AC) build a rectangle.


Related Questions

Select the correct answer.
The speed of a ship is given by , where d is the distance the ship travels in 3 hours. If the ship travels 48 miles in 3 hours, what is the speed of the ship?
A.
12 miles per hour
B.
16 miles per hour
C.
45 miles per hour
D.
51 miles per hour

Answers

B 16 the boat is traveling 16 miles an hour

Select the correct answer.
Which value of x makes this equation true?
-12x2(x + 9) = 5(x + 4)
O A.
OB.
O C.
O D.

Answers

Answer:

B. -2

Step-by-step explanation:

-12x -2(x+9) = 5(x+4)

*ALWAYS REMEMBER YOUR BODMAS*

-12x -2x - 18 = 5x + 20

*group the like terms*

-14x - 5x = 20 + 18

-19x = 38

x = -2

The value of x that makes the equation true is: x = -2.

B. -2.

Here, we have to find the value of x that makes the equation true, we need to solve for x.

Let's solve the equation step by step:

-12x - 2(x + 9) = 5(x + 4)

Distribute the -2 and 5 on the right side of the equation:

-12x - 2x - 18 = 5x + 20

Combine like terms on both sides:

-14x - 18 = 5x + 20

Move the variable terms (5x) to one side of the equation and the constant terms to the other side.

Let's subtract 5x from both sides:

-14x - 5x - 18 = 5x - 5x + 20

-19x - 18 = 20

Move the constant term (-18) to the other side of the equation.

Let's add 18 to both sides:

-19x - 18 + 18 = 20 + 18

-19x = 38

Finally, divide both sides by -19 to isolate x:

x = 38 / -19

x = -2

So, the value of x that makes the equation true is: x = -2.

B. -2.

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Solve the equation for x.
√x-5 = x-11

Answers

Your answer would be 14

Answer:

√x-5 = x-11 = 9.

Step-by-step explanation:

Isolate the radical, then raise each side of the equation to the power of its index.

x = 9 Solve the equation for x.

help please
Find the sum or type
"impossible"
[3 -8] + [4 -5 -6]

Answers

The answer is negative 12

What is the expression for f(x) when we rewrite 36^x•6^(x-2) as 6^f(x)?
Answer: 3x-2

Answers

Using the given information, the expression for f(x) is 3x - 2

Writing an expression

From the question, we are to determine the the value of f(x)

The given expression is

36^x•6^(x-2)

That is

[tex]36^{x} \times 6^{x-2}[/tex]

This can be expressed as

[tex]6^{2x} \times 6^{x-2}[/tex]

Applying one of the laws of indices, we get

[tex]6^{2x+x-2}[/tex]

= [tex]6^{3x-2}[/tex]

Since the expression was rewritten as

[tex]6^{f(x)}[/tex]

By comparison,

f(x) = 3x - 2

Hence, the expression for f(x) is 3x - 2

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What is the scale factor of this dilation?

Answers:
A. 1/2
B.3/5
C.1 2/3
D.2

Answers

Answer:

3/5

Step-by-step explanation:

scale factor of ab to A'B'

AB:A'B'

5 : 3

in fraction the scale

factor is 3

5

heance a reduction.

hope it helps thank me later

#galadohannadivine29

#carry on learning

Which of the following angles are congruent?

Answers

Answer:

C

Step-by-step explanation:

if you rotate either of the triangles by 180 degrees, compare the angles and you will see that the answer is C

Given that the expression “p dollars for every q items” describes a unit price, which statement must be true?

Answers

The complete question is

"Given that the expression “p dollars for every q items” describes a unit price, which statement must be true?

p = 1

p = q

q = 1

pq = 1"

The statement that must be true would be from option D; pq = 1.

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.

Given that the expression “p dollars for every q item” describes a unit price,

So, the equation will be formed as

p x q = 1

pq = 1

Hence, the statement that must be true would be from option D; pq = 1.

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What other areas of human or societal change have models that would fit an
exponential curve?

Answers

[tex]\large\bold{\underline{\underline{Answer:-}}}[/tex]

There are smooth exponential curves that control price performance, capacity, and bandwidth so it easy to predict the cost of something in the future. He said, "When people think about the future they think about it lineraly.

If anyone could help me, it would be greatly appreciated!

Answers

Answer: [tex]x=65^{\circ}, y=65^{\circ}, z=65^{\circ}[/tex]

Step-by-step explanation:

All radii of a circle are congruent, so by the base angles theorem

z = y = (180-50)/2 = 65.

Also, angles x and y are inscribed in the same arc, and they are thus congruent, meaning x = 65.

Can some help me with this, it’s urgent pls? It’s geometry

Answers

6. the name is circle x (due to the central point)
7. the diameter is segment WY
8. radius is 1/2 of the diameter so 1/2(15) = 7.5 meters
9. diameter is 2 times the radius so 2(4) = 8 cm
10. segment XW, segment XZ, segment XY
11. arc YW, arc WZ, arc ZY

The circle below is centered at the origin and has a radius of 7. What is its
equation?
A ²+2²=7
B. x²-y²=7
C. x²-²2²=49A
D. x² + y² = 49

Answers

Answer:

x² + y² = 49

Step-by-step explanation:

The equation for a circle is: x² + y² = r²

here, we know our circle's radius (r) to be 7

So, the equation for our circle is:                  {replace "r" with value}

x² + y² = 7²

which can be simplified to:

x² + y² = 49

hope this helps!! have a lovely day :)

If side c measures 32.3 units long, how long is side a?

Answers

Answer:

16.15

Step-by-step explanation:

sin(30) = a / c

a = c * sin(30)

a = 32.3 * 0.5

a = 16.15

Consider the systems of equations below. determine the number of real solutions for each system of equations. system a has real solutions. system b has real solutions. system c has real solutions.

Answers

System A has 2 real solutions, System B has 0 real solutions and System C has 1 real solution.

Given a system of equations for A is x²+y²=17 and y=-(1÷2)x, a system of equations for B is y=x²-7x10 and y=-6x+5 and a system of equations for C is y=-2x²+9 and 8x-y=-17.

For system A,

The two systems of equations are

x²+y²=17            ......(1)

y=-1÷2x             ......(2)

Substitute the value of equation (2) into equation (1) as

x²+(-x÷2)²=17

x²+(x²÷4)=17

Simplify the above equation by taking L.C.M. as

(4x²+x²)÷4=17

5x²=68

x²=68÷5

x=±3.688

Find the value of y by substituting the value of x in equation (2).

When x=3.688 then y is

y=-(1÷2)×3.688

y=-1.844

And When x=-3.688 then y is

y=-(1÷2)×(-3.688)

y=1.844

Thus, the points where the equations of system A intersect each other is (3.688,-1.844) and (-3.688,1.844)

So, the system of equations of A has 2 real solutions.

For system B,

The two systems of equations are

y=x²-7x+10            ......(3)

y=-6x+5                ......(4)

Substitute the value of equation (4) into equation (3) as

-6x+5=x²-7x+10

x²-7x+10+6x-5=0

x²-x+5=0

Simplify the above quadratic equation using the discriminant rule,

x=(-b±√(b²-4ac))÷(2a)

Here, a=1, b=-1 and c=5

Substitute the values in the discriminant rule as

x=(1±√(1-4\times 5\times 1))÷2

x=(1±√(-19))÷2

x=(1±√(19)i)÷2

Here, the value of x goes into the complex.

So, the system of equations of B has 0 real solutions.

For system C,

The two systems of equations are

y=-2x²+9            ......(5)

8x-y=-17            ......(6)

Substitute the value of equation (6) into equation (5) as

8x-(-2x²+9)=-17

8x+2x²-9+17=0

2x²+8x+8=0

Simplify the above quadratic equation using factorization method as

2x²+4x+4x+8=0

2x(x+2)+4(x+2)=0

(2x+4)(x+2)=0

x=-2,-2

Find the value of y by substituting the value of x in equation (5).

When x=-2 then y is

y=-2(-2)²+9

y=-8+9

y=1

Thus, the point where the equations of system C intersect each other is (-2,1)

So, the system of equations of C has 1 real solutions.

Hence, the system of equations for A is x²+y²=17 and y=-(1÷2)x having 2 real solution, a system of equations for B is y=x²-7x10 and y=-6x+5 having 0 real solution and a system of equations for C is y=-2x²+9 and 8x-y=-17 having 1 real solution.

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Let g be the piecewise defined function shown.

g(x)=
x + 4, −5 ≤ x ≤ −1
2 − x, −1 < x ≤ 5

Evaluate g at different values in its domain.

g(−4) =

g(−2) =

g(0) =

g(3) =

g(4) =

Answers

Answer:

g(4)= -2

g(-2)= 2

g(0)= 2

g(3)= -1

g(-4)= 0

Step-by-step explanation: See attachment, and don’t forget to check just in case ;)

Answer:

g(−4) = 0

g(−2) = 2

g(0) = 2

g(3) = -1

g(4) = -2

Step-by-step explanation:

Please Thank!

What value of a make the equation 14-a=19-12

Answers

[tex]14-a=19-12\\14-a=7\\a=14-7\\a=7[/tex]

Answer:

7

Step-by-step explanation:

14-a=19-12

14-a=7

14-7=a

7=a

Combine like terms

What is the approximate horizontal distance between Amelia and Brendon? Explain your reasoning

Answers

Answer:

60 ft

Step-by-step explanation:

using the sine ratio in the right triangle and the exact value

sin30° = [tex]\frac{1}{2}[/tex] , then

sin30° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{CD}{AD}[/tex] = [tex]\frac{30}{AD}[/tex] = [tex]\frac{1}{2}[/tex] ( cross- multiply )

AD = 60 ft

40. Se desea distribuir las bancas dentro de un salón de clases cada 1.5 m como
se muestra en la imagen, ¿de qué forma se puede saber el área requerida para
conservar la separación de las bancas?
1.5m

Answers

La forma adecuada para saber el área requerida para conservar la separación de las sillas es multiplicar (7.5) (4.5) opción B.

¿Cómo calcular el área requerida para mantener la separación?

Para identificar la operación necesaria para calcular el área requerida para ubicar las sillas con su respectiva separación de 1.5 metros es:

7.5 × 4.5 = 33.75

Esta expresión nos va a permitir calcular el área necesaria debido a que la separación entre sillas es 1.5 metros y tenemos 6 sillas a lo largo y 4 sillas a lo ancho, es decir:

1.5 × 5 = 7.5 distancia a lo largo1.5 × 3 = 4.5 distancia a lo ancho

Nota: Esta pregunta está incompleta porque falta la imagen y las opciones. Aquí está la información faltante:

Opciones:

A. Multiplicar (6)(4)

B. Multiplicar (7.5)(4.5)

C. Multiplicar (9)(6)

D. Multiplicar (9.5)(4.5)

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Which angles are vertical angles select two options

Answers

The pair of the vertically opposite angles are ∠ABC = ∠DBE and ∠CBD = ∠ABE Then the correct options are B and E.

The complete question is attached below.

What is Vertically opposite angle?

When two lines intersect, then their opposite angles are equal.

The diagram is given below.

∠ABC = ∠DBE

∠CBD = ∠ABE

Then the correct options are B and E.

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Figure B is a scaled copy of figure A.
What is the scale factor from figure A to figure B

Answers

Answer:

1/3

Step-by-step explanation:

We multiply 33(Figure A side) by 1 /3 to get 11(Figure B side).

Sienna is solving the quadratic equation by completing the square.

3x2 + 9x – 4 = 0

3x2 + 9x = 4

A(x2 + 3x) = 4

Answers

Answer:

See below

Step-by-step explanation:

3 (x^2 + 3x) = 4

3 ( x + 3/2)^2   = 4 + 27/4  

What is the solution for the system of x - y = -1 and 2x - 5y = -5 ?
Show your work.

Answers

Step-by-step explanation:

please mark me as brainlest

x - y = -1 multiply by 5

we get 5x -5y = -5

subtract the equations:

5x - 5y = -5

-

2x - 5y = -5

5x - 5y -(2x - 5y ) = - 5 - - 5

5x - 5y - 2x + 5y =0

3x = 0

x = 0

2(0) - 5y = -5

- 5y = -5

y = 1

Joanne has a pile of nickels and a pile of dimes. She counts her money and discovers that she has 30 nickels and 10 dimes. Let x represent the number of nickels and y represent the number of dimes. (HINT: Use the values of the coins.) How much money does Joanne have in total?

Total Amount: $_____

Answers

$2.50

Step-by-step explanation:

10 dimes are 100 aka 1 dollar, and 30 nickels make 250

2 3/5t + 5 1/4t + 4t

Answers

Answer:

11 17/20t

Step-by-step explanation:

add the whole numbers first then add the numbers in fraction then there you get your answer.

Solve the following...
6x - 5 = -9x -9​

Answers

Answer:

6x - 5 = (-9x) - 9

6x + 9x = (-9) + 5

15x = (-4)

x = (-4/15)

[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]

[tex]\qquad \tt \rightarrow \:x = -\cfrac{4}{15} [/tex]

____________________________________

[tex] \large \tt Solution \: : [/tex]

[tex]\qquad \tt \rightarrow \: 6x - 5 = - 9x - 9[/tex]

[ add 9x and 5 on both sides ]

[tex]\qquad \tt \rightarrow \: 6x - 5 + 9x + 5 = - 9x - 9 + 9x + 5[/tex]

[tex]\qquad \tt \rightarrow \: 6x + 9x = - 9 + 5[/tex]

[tex]\qquad \tt \rightarrow \: 15x = - 4[/tex]

[tex]\qquad \tt \rightarrow \: x = - \cfrac{4}{15} [/tex]

Answered by : ❝ AǫᴜᴀWɪᴢ ❞

Simplify this radical.
[tex]\sqrt{84} \\\\1; 2\sqrt{21} \\2; 2\sqrt{42} \\3; 4\sqrt{21} \\or 4; 4\sqrt{42} \\[/tex]

Answers

The radical is 2√21.

What is radical?

The symbol that is used to denote square root or nth roots.

Given :

√84

= √2*2*21

=2√21

Hence, the radical is 2√21.

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please help me i need help quick

Answers

Answer:

x = -2

y = -6

Step-by-step explanation:

Equating the equations :

x - 4 = 4x + 23x = -6x = -2

y = -2 - 4y = -6
y=x-4y=4x+2

Equate both

x-4=4x+2-4-2=4x-x-6=3xx=-2

And

y=-2-4=-6

Graph attached

Determine whether each set of ordered pairs shown below is from a geometric sequence or from an arithmetic sequence.

{(-3, 7.5) , (-2, 10) , (-1, 12.5)}

Write the equation of the graph for the set of ordered pairs.

{(1, 150) , (2, 112.5) , (3, 84.375)}

Write the equation of the graph for the set of ordered pairs.

Answers

Using sequences concepts, it is found that:

The set of ordered pairs {(-3, 7.5) , (-2, 10) , (-1, 12.5)} is an arithmetic sequence with equation a(n) = 15 + 2.5d.The set of ordered pairs {(1, 150) , (2, 112.5) , (3, 84.375)} is a geometric sequence with [tex]a_n = 150(0.75)^{n-1}[/tex].

What is an arithmetic sequence?

In an arithmetic sequence, the difference between consecutive terms is always the same, called common difference d.

The nth term of an arithmetic sequence is given by:

[tex]a(n) = a(0) + nd[/tex]

The sequence {(-3, 7.5) , (-2, 10) , (-1, 12.5)} continues with points (0, 15), (1, 17.5), and so on, hence the first term and the common ratio are given, respectively, by:

a(0) = 15, d = 2.5.

Hence the equation is:

a(n) = 15 + 2.5n.

What is a geometric sequence?

A geometric sequence is a sequence in which the result of the division of consecutive terms is always the same, called common ratio q.

The nth term of a geometric sequence is given by:

[tex]a_n = a_1q^{n-1}[/tex]

For the sequence {(1, 150) , (2, 112.5) , (3, 84.375)}, the first term and the common ratio are given, respectively, by:

[tex]a_1 = 150, q = \frac{112.5}{150} = \frac{84.375}{112.5} = 0.75[/tex]

Hence the equation is given by:

[tex]a_n = 150(0.75)^{n-1}[/tex]

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Base area = 18 ft²
Volume=
11 ft
7

Answers

Answer:

nhddhdbndbd

Step-by-step explanation:

jh h benrheoek

a fence is 2m high by 33m long, if a gallon of paint is enough to paint 2.5m^2, how many gallons will be used to paint the entire fence?

Answers

The number of gallons of paint needed to paint the entire fence is 26.4 gallons.

Area of rectangle

Length = 33 mWidth = 2 m

Area = length × width

= 33 m × 2 m

= 66 square meter.

A gallon of paint = 2.5 m²

Number of gallons of paint needed = 66 square meter / 2.5 m²

= 26.4 gallons

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