Which statement proves the given triangles are similar?

(√3 - i ) / (√3 + i ) × (√3 - i ) / (√3 - i ) = (√3 - i )² / ((√3)² - i ²)

… = ((√3)² - 2√3 i + i ²) / (3 - i ²)

… = (3 - 2√3 i - 1) / (3 - (-1))

… = (2 - 2√3 i ) / 4

… = 1/2 - √3/2 i

… = √((1/2)² + (-√3/2)²) exp(i arctan((-√3/2)/(1/2))

… = exp(i arctan(-√3))

… = exp(-i arctan(√3))

… = exp(-iπ/3)

By DeMoivre's theorem,

[(√3 - i ) / (√3 + i )]⁶ = exp(-6iπ/3) = exp(-2iπ) = 1

Answer:

C) 8

Step-by-step explanation:

Consecutive angles are equal to 180. So 22x+4+180. Solve that to get x=8. Hope I helped and post more questions :)

Answer:

-2,-3

Step-by-step explanation:

Answer:

Slope: -5/4

Step-by-step explanation:

Use slope (m) formula:

m = y2 - y1 / x2 - x1

m = 5 - 10 / 49 - 45

m = -5/4

Answer:

[tex]-\frac{5}{4}[/tex]

Step-by-step explanation:

Hi there!

Equation for the slope:

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex] where two given points are [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]

To find the slope of the line, plug in any two points given in the table. For example, we can use the points (49,5) and (53,0):

[tex]=\frac{5-0}{49-53}\\=\frac{5}{-4}[/tex]

Therefore, the slope of the line is [tex]-\frac{5}{4}[/tex].

I hope this helps!

Answer:

The radius is approximately 14 cm

Step-by-step explanation:

The circumference

C = 2 * pi *r

88 = 2 * pi *r

Divide by 2

44 = 3.14 *r

Divide by 3.14

44/3.14 = r

14.01273885=r

Answer:

Mean = 6.66

Median = 7

Mode = 7.68

Step-by-step explanation:

According to the Question,

Class interval   frequency

  56-63                    1

  48-55                   10

  40-47                   12

  32-39                    6

  24-31                     3

  16-23                     8

1). Mean = (Sum of all Observation) / (number of observation)

Mean = 40/6 = 6.66

2) For Median, If there are two number in the middle then you need to find their mean.  1  3   6   8  10  12  middle numbers are 6 and 8.

Median = (6+8) / 2 = 7

3) Mode = 3 × Median - 2 × Mean

Mode = 3×7 - 2×6.66

Mode = 7.68

Answer:

The right answer is a.

Step-by-step explanation:

PLEASE MARK ME AS A BRAINLIEST

Answer:

Exfoliation

Step-by-step explanation:

Changes in temperature cause rock to expand (with heat) and contract (with cold). As this happens over and over again, the structure of the rock weakens. Over time, it crumbles.

Rocky desert landscapes are particularly vulnerable to thermal stress. The outer layer of desert rocks undergo repeated stress as the temperature changes from day to night. Eventually, outer layers flake off in thin sheets, a process called exfoliation.

Step-by-step explanation:

we cannot see anything, and you did not describe anything. so, there is nothing to calculate.

Given:

A quadrilateral DEFG inscribed in a circle.

[tex]m\angle D=60^\circ, m\angle E=m^\circ, m\angle F=2k^\circ, m\angle G=60^\circ[/tex]

To find:

The value of variables [tex]m[/tex] and [tex]k[/tex].

Solution:

If a quadrilateral is inscribed in a circle then it is a cyclic quadrilateral. The opposite angles of a cyclic quadrilateral angle supplementary angles.

Quadrilateral DEFG inscribed in a circle. So, quadrilateral DEFG is a cyclic quadrilateral.

[tex]m\angle D+m\angle F=180^\circ[/tex]                [Supplementary angle]

[tex]60^\circ+2k^\circ=180^\circ[/tex]

[tex]2k^\circ=180^\circ-60^\circ[/tex]

[tex]2k^\circ=120^\circ[/tex]

Divide both sides by 2.

[tex]k^\circ=\dfrac{120^\circ}{2}[/tex]

[tex]k^\circ=60^\circ[/tex]

[tex]k=60[/tex]

Similarly,

[tex]m\angle E+m\angle G=180^\circ[/tex]

[tex]m^\circ+60^\circ=180^\circ[/tex]

[tex]m^\circ=180^\circ-60^\circ[/tex]

[tex]m^\circ=120^\circ[/tex]

[tex]m=120[/tex]

Therefore, the values of the variables are [tex]m=120[/tex] and [tex]k=60[/tex].

Answer:

0 or 1

Step-by-step explanation:

Given that Kelley  is tasked with having to use vertical line test to determine whether or not a curve is a function. Each vertical line that Kelly draws through her curve must intersect the curve at maximum one point only in order for thecurve to be a function

Answer is 0 or 1 point

Answer:

The quadrilateral is Rhombus

B=70°

Step-by-step explanation:

110+110+z+z=360

220+2z=360

2z=360-220

2z=140

z=140/2

Therefore, z=70

So Angle B=70

Since z= Angle B=Angle D

Answer:yes

Step-by-step explanation:66

The given statement  A U (B - C) = (A U B) - C is true.

A set is collection of well defined objects.

According to the given question we have to state whether A ∪ ( B - C ) = ( A ∪ B ) - C.

Lets consider we have three sets A, B and C and we also consider they intersect each other.

( B - C ) represents the elements which belongs to B but not in C.

∴ A ∪ ( B - C ) represents the no. of elements which belongs to the set B but not in C union the no. of elements which belongs to A.

AND

( A ∪ B ) - C represents no. of elements which belongs to A or B but not in C.

learn more about sets here :

https://brainly.com/question/8053622

#SPJ2

Answer:

silly question...I used technology to "cheat"

it is 11/23

34155 32775 33649 34485

72105 72105 72105 72105

Step-by-step explanation:

y - 6 = 0 ................ equation 1

x - 4 = 0 ................ equation 2

Answer:

Step-by-step explanation:

1.)1,2,3,4,5

mean=sum of all values/number of values

         =1+2+3+4+5/5

         =15/5

mean=3

Mode :

In the given data, no observation occurs more than once.

Hence the mode of the observations does not exist, means mode=0.

Median

1,2,3,4,5

Middle value is 3 so the median is 3.

2.)2,3,4,5,6,6

mean=sum of all values/number of values

         =2+3+4+5+6+6/6

         =26/6

mean =4.33

Mode

      is that value of the observation which occurs maximum number of times so here mode is 6.

Median

2,3,4,5,6,6

 4+5/2

9/2

median=4.5

3.)6,7,5,4,5,6,2,5

mean=sum of all values/number of values

         =6+7+5+4+5+6+2+5/8

        =40/8

mean =5

Mode

is that value of the observation which occurs maximum number of times so here mode is 5

Median

2,4,5,5,5,6,6,7

5+5/2

10/2

median=5

Answer:

Step-by-step explanation:

A + B = 750

A = 1.5 B

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

750-B = 1.5 B

750 = 1.5 B + B

750 = B(1.5 +1)

750 = B (2.5)

B = 300

A = 450

Answer:

12 times.

Step-by-step explanation:

That would be 40 * 0.3 = 12.

Answer:

Step-by-step explanation:

If a point (x, y) is rotated 90° counterclockwise about the origin, rule for the rotation will be,

(x, y) → (-y, x)

Therefore, coordinates of the image point after the rotation will be (-y, x).

Following this rule,

Image points of the quadrilateral will be,

A(3, 3) → A'(-3, 3)

R(5, 7) → R'(-7, 5)

M(7, 5) → M'(-5, 7)

Y(5, 1) → Y'(-1, 5)

By graphing the image points we can get the graph of the image quadrilateral A'R'M'Y'.

Answer:

I got my answer on Khan Academy:

Answer:

[tex]{ \tt{let \: that \: unknown\: side \: be \: x}} \\ { \boxed{ \tt{perimeter = (8 \times side)}}} \\ 41.6 = (3.2 \times 2) + (5.9 \times 5) + x \\ x = 5.7 \:in \\ { \bf{answer : 5.7 \: inches}} \\ \\ { \underline{ \blue{ \tt{becker \: jnr}}}}[/tex]

Answer:

Always a parabola or U Shaped

U shaped or by rotating U it will be like intersect symbol.. You can see it in attached file

Answer:

In mathematics, a cubic function is a function of the form f(x)=ax^3+bx^2+cx+d where the coefficients a, b, c, and d are real numbers, and the variable x takes real values, and a ≠ 0. In other words, it is both a polynomial function of degree three, and a real function.

Answer:

Undefined

Step-by-step explanation:

Lim x - - > 1(1 /In(2-x) + 1/(x-1))

To find the limit as x tends to 1

Substitute x = 1 into the function ;

(1 / In(2 - 1) + 1 / (1 - 1))

(1 / In 1) + (1 / 0)

1 / 0 + 1 / 0

Undefined

Answer:

The solution of the system is  (5, -7)

Step-by-step explanation:

Here we have the system:

y = (-1/5)*x - 6

y = -2*x + 3

We know that this system is graphed below, and the question is incomplete, but I assume that we want to find the solution to this system. If you can see the graph, the solution is just the point where both graphs intersect, but we can find the solution analytically.

We know that:

y = (-1/5)*x - 6

y = -2*x + 3

Then, we can write:

y =  (-1/5)*x - 6 = y =  -2*x + 3

This leads to:

(-1/5)*x - 6  = -2*x + 3

Now we can solve this for x.

(-1/5)*x + 2*x = 3 + 6

(-1/5)*x + (10/5)*x = 9

(9/5)*x = 9

x = (5/9)*9 = 5

x = 5

now that we know the value of x, we can input this in one of the two equations above to find the correspondent value of y, we will get:

y = -2*x + 3 = -2*5 + 3

y = -10 + 3 = -7

y = -7

Then the solution is:

x = 5 and y = -7, or (5, -7)

Answer:

Is the question original or you simply made it.

Answer:

270 coins

n + p

Step-by-step explanation:

Given that :

Number of nickels = 140

Number of pennies = 130

The total numbers coins had:

Number of Nickel + number of pennies

140 + 130 = 270 coins

If Number of nickels = n ; number of pennies = p

The total number of coins :

Number of Nickel + number of pennies

n + p

Answer:yo we talking the same test

Step-by-step explanation:

Insta= santiagorez

Answer:

Radius , r = 5 units

Step-by-step explanation:

The standard form of a circle's equation:

  [tex](x-a)^2 + (y -b)^2 = r^2 \ , \ where \ (a , b) \ is \ the \ centre\ and\ r \ is \ the \ radius.[/tex]

Given equation :

  [tex]x^2 - 2x + y^ 2- 4y = 20\\\\[/tex]

Find radius .

Convert the given equation into standard form.

[tex](x - 1)^2 = x^ 2 - 2x + 1 \\\\(y - 2) ^2 = y^ 2 - 4y + 4\\\\[/tex]

Now add both equations :

  [tex](x - 1)^2 + (y - 2)^2 = r^2[/tex]

[tex](x ^ 2 - 2x + 1) + (y^2 - 4y + 4 ) = r^2\\\\(x^2 -2x + y^2 - 4y ) + 1 + 4 = r^2\\\\20 + 1 + 4 = r^2[/tex]          [tex][ \ given : \ x^2 - 2x + y^ 2 - 4y = 20 \ ][/tex]

[tex]25 = r^2 \\\\5 = r[/tex]

Answer:

2

Step-by-step explanation:

5-3=2 it's simple really

Answer:

5-3=2

Hope This Helps!!!

Answer:

the answer for that is 61.

Step-by-step explanation:

Answer:

second option

Step-by-step explanation:

[tex]shaded~area\\(x-1)^2+y^2<25\\and\\(x+4)^2+y^2<16[/tex]

Answer:

A

Step-by-step explanation:

edge

not sure if this is the right question so i dont know if we're thinking about the same question...