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Answer:

Step-by-step explanation:

If the diagonals of the rectangle are congruent,

AC = BD

By using formula to calculate the distance between two points,

Distance between two points = [tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

Distance between A(0, -3) and C(2, 8),

AC = [tex]\sqrt{(8+3)^2+(2-0)^2}[/tex]

     = [tex]\sqrt{125}[/tex]

     = [tex]5\sqrt{5}[/tex]

Similarly, distance between two points B(-4, 0) and D(6, 5),

BD = [tex]\sqrt{(5-0)^2+(6+4)^2}[/tex]

     = [tex]\sqrt{125}[/tex]

     = [tex]5\sqrt{5}[/tex]

Therefore, both the diagonals are congruent.

Hence, given quadrilateral ABCD is a rectangle.

Answer:

Translate 4 units to the left and reflect over the x-axis

Step-by-step explanation: hope this helps :)

The composition of the transformations given in the figure is translate 4 units to the left and then reflect over the X axis.

Transformation of geometrical figures or points is the manipulation of a given figure to some other way.

Different types of transformations are Rotation, Reflection, Glide reflection, Translation and Dilation.

After translation, the original figure is shifted from a place to another place without affecting it's size.

After Reflection, figure is flipped. In other words, a figure becomes it's mirror image.

Consider the point P.

Before undergoing reflection, the figure must be above the X axis.

And the point P will be translated 4 units to the left.

After reflection, since the figure moved towards the other side of the X axis, the figure is reflected across the X axis.

Hence the missing parts are filled.

Learn more about Translation and Reflections here :

https://brainly.com/question/30270479

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Step-by-step explanation:

b= 140 ( alternate angle)

k = 130 ( veetically opposite angles)

may it help ub

Answers:

[tex]\csc(\theta) = \frac{7\sqrt{33}}{33}\\\\\sin(\theta) = \frac{\sqrt{33}}{7}\\\\\cot(\theta) = \frac{4\sqrt{33}}{33}\\\\[/tex]

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

Explanation:

Before we can find the trig ratios, we need to determine the length of the missing side. Apply the pythagorean theorem

[tex]a^2+b^2 = c^2\\\\4^2+b^2 = 7^2\\\\16+b^2 = 49\\\\b^2 = 49-16\\\\b^2 = 33\\\\b = \sqrt{33}[/tex]

The vertical side is [tex]\sqrt{33}[/tex] units long.

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

The side we just found is the opposite side to angle [tex]\theta[/tex] (greek letter theta)

The hypotenuse is 7 units long. The hypotenuse is always opposite the right angle.

Divide the hypotenuse over opposite to get the cosecant.

[tex]\csc(\theta) = \frac{\text{hypotenuse}}{\text{opposite}}\\\\\csc(\theta) = \frac{7}{\sqrt{33}}\\\\\csc(\theta) = \frac{7\sqrt{33}}{\sqrt{33}*\sqrt{33}}\\\\\csc(\theta) = \frac{7\sqrt{33}}{\sqrt{33*33}}\\\\\csc(\theta) = \frac{7\sqrt{33}}{\sqrt{33^2}}\\\\\csc(\theta) = \frac{7\sqrt{33}}{33}\\\\[/tex]

Note: In the third step, I multiplied top and bottom by sqrt(33) to rationalize the denominator.

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

Recall that sine is the reciprocal of cosecant, and vice versa.

So we'll use the same idea as before, but flip the original fraction.

[tex]\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}}\\\\\sin(\theta) = \frac{\sqrt{33}}{7}\\\\[/tex]

The denominator is already a rational number, so there's not much else to do here.

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

Cotangent is the ratio of adjacent over opposite

[tex]\cot(\theta) = \frac{\text{adjacent}}{\text{opposite}}\\\\\cot(\theta) = \frac{4}{\sqrt{33}}\\\\\cot(\theta) = \frac{4\sqrt{33}}{\sqrt{33}*\sqrt{33}}\\\\\cot(\theta) = \frac{4\sqrt{33}}{\sqrt{33*33}}\\\\\cot(\theta) = \frac{4\sqrt{33}}{\sqrt{33^2}}\\\\\cot(\theta) = \frac{4\sqrt{33}}{33}\\\\[/tex]

The steps are pretty much nearly identical as the section involving csc, except we're using the adjacent in place of the hypotenuse (so that means we use 4 in place of 7).

Answer:

8:21

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

2x + x = 3x

y - 3y = 2y

Answer:

85.7 ounces.

Step-by-step explanation:

428.5/5 = 85.7

Therefore, Ms. Emily put 85.7 ounces of pretzels into each bowl.

Answer:

85.7 ounces

Step-by-step explanation:

428.5 ounces ÷ 5=85.7 ounces

Answer:33

Step-by-step explanation:

trust

Answer:

[tex]{ \tt{7.1 \times {10}^{ - 3} }} \\ { \bf{negative \: means \: { \green{increase \: in \: decimal \: places}}}} \\ = { \tt{0.71 \times {10}^{ - 2} }} \\ = { \tt{0.071 \times {10}^{ - 1} }} \\ = { \tt{0.0071 \times {10}^{0} }} \\ { \boxed{ but \: {10}^{0} = 1}} \\ \therefore{ \tt{ = 0.0071 \times 1 = 0.0071}}[/tex]

Answer: (x+4)(x+6)

Explaination:

x^2 + 10x + 24

x^2 + 6x + 4x + 24

x(x+6) + 4(x+6)

(x+4)(x+6)

Solution: (x+4)(x+6)

Answer:

Answer:

R (3,-2) S(5,2) T(6,0)

Step-by-step explanation:

Answer: the answer is 2.25 kg

Step-by-step explanation:

Answer:

31793 cm^3

Step-by-step explanation:

Equation

Volume = [tex]\pi[/tex] * r^2 * h

Givens

d = 2*r

d  = 30

r = 15

h = 45

[tex]\pi[/tex] = 3.14

Solution

V = 3.14 * 15^2 * 45

V = 31793 rounded.

Answer:

(-1, 8)

the value of a is 8

Answer:

43 degrees

Step-by-step explanation:

Answer:

9.9 inches

Step-by-step explanation:

The area of a triangle is given by

A = 1/2 bh  where b is the length of the base and h is the length of the height

49 = 1/2 x*x

Multiply each side by 2

2*49 = x^2

98 = x^2

Take the square root of each side

sqrt(98) = sqrt(x^2)

9.899494937 =x

Rounding to the nearest tenth

9.9 =x

Answer:

Step-by-step explanation:

Tangents from the point outside the circle are equal

NL = JL  

NM + ML =JK + KL

2x - 7 + 9 = 8 + 10  

     2x + 2 = 18      {Subtract 2 from both sides}

           2x = 18 - 2

          2x  = 16   {Divide both sides by 2}

             x = 16/2

x = 8

MN = 2*8 - 7 = 16 - 7 = 9

MN = 9

Answer:

y = eˣ

Step-by-step explanation:

(Graphed via Desmos)

Answer:

y < 4 or y > 9

Step-by-step explanation:

The symbol < means less than, while the symbol > means greater than. So, the inequality y < 4 means that y is less than 4, and the inequality y > 9 means that y is greater than 9. When put together you have all real numbers y that are less than 4 or greater than 9.

Answer:

[tex] {x}^{2} - 9[/tex]

Step-by-step explanation:

[tex](x−3)(x+3)[/tex]

[tex]x(x+3)−3(x+3)[/tex]

[tex]x \times x+x \times 3−3x−3 \times 3[/tex]

[tex]x \times x−3 \times 3[/tex]

[tex] {x}^{2} - 9[/tex]

Answer:

(c) 84

hope this helps!!!!

Answer:

B) 27.2 m^2

Step-by-step explanation:

because to get the area of the parrelelogram, you use the formula (b)(h) or 6.8*4 to get 27.2.

Gọi số tấm thảm xưởng dệt dệt theo dự định là x ( tấm, x >0 )

⇒ số tấm thảm xưởng dệt dệt trong 1 ngày theo dự định x/30 (tấm)

xưởng dệt dệt đc số tấm thảm trong thực tế là x/20 (tấm)

⇒số tấm thảm xưởng dệt dệt trong 1 ngày thực tế là x+20/25 (tấm)

Vì năng suất tăng 25% nên số tấm thảm dệt được trong 1 ngày thực tế sẽ bằng 125% số tấm thảm dệt đc trong 1 ngày theo dự định nên ta có PT : x+20/25=125% * x/30

me lười làm khúc dưới quá nên tự xử nha.

Answer:

x = 31, x = 19

Step-by-step explanation:

[tex](x-25)^2=36\\\sqrt{(x-25)^2}=\sqrt{36}\\x-25=6 or -6\\\\x-25=6\\x=31\\\\x-25=-6\\x=19[/tex]

Respuesta:

Media = 6

Mediana = 6

Modo = 6

Desviación media = 1

Desviación estándar = 1.317

Explicación paso a paso:

Dados los datos:

5, 5, 8, 4, 6, 6, 7, 5, 6, 7, 4, 8, 6, 5, 6, 8

Datos reorganizados: 4, 4, 5, 5, 5, 5, 6, 6, 6, 6, 6, 7, 7, 8, 8, 8

La media: Σx / n = 96/16 = 6

El modo, = 6 (valor más alto que ocurre en los datos, valor de datos con la frecuencia más alta)

La mediana = 1/2 (n + 1) ésimo término

Mediana = 1/2 (17) término = 8.5 th término = (6 + 6) / 2 = 6

La desviación media = Σ (x - media) / n

Usando la calculadora, la desviación media = 1

La desviación estándar = √ (Σ (x - media) ² / n-1)

Desviación estándar = 1.317

Answer:

D

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

XYZ is congruent to DEF so:

X = D

Y = E

Z = F

Answer:

5x2+20x−15

Step-by-step explanation:

Answer:

[tex]1\frac{13}{23}[/tex]

Step-by-step explanation:

6² ÷ 23

36 ÷ 23

[tex]1\frac{13}{23}[/tex]