help please help ghelp

Given:

The vertices of a triangle are [tex](1,1),(-1,-1),(-\sqrt{3},\sqrt{3})[/tex].

To prove:

The given vertices are the vertices of an equilateral triangle.

Solution:

Distance formula:

[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

Let the vertices of the triangle are [tex]A(1,1),B(-1,-1),C(-\sqrt{3},\sqrt{3})[/tex]. Then, by using the distance formula, we get

[tex]AB=\sqrt{(-1-1)^2+(-1-1)^2}[/tex]

[tex]AB=\sqrt{(-2)^2+(-2)^2}[/tex]

[tex]AB=\sqrt{4+4}[/tex]

[tex]AB=\sqrt{8}[/tex]

Similarly,

[tex]BC=\sqrt{(-\sqrt{3}-(-1))^2+(\sqrt{3}-(-1))^2}[/tex]

[tex]BC=\sqrt{(1-\sqrt{3})^2+(1+\sqrt{3})^2}[/tex]

[tex]BC=\sqrt{(1)^2+(\sqrt{3})^2-2\sqrt{3}+(1)^2+(\sqrt{3})^2+2\sqrt{3}}[/tex]

[tex]BC=\sqrt{1+3+1+3}[/tex]

[tex]BC=\sqrt{8}[/tex]

And,

[tex]CA=\sqrt{(1-(-\sqrt{3}))^2+(1-\sqrt{3})^2}[/tex]

[tex]CA=\sqrt{(1+\sqrt{3}))^2+(1-\sqrt{3})^2}[/tex]

[tex]CA=\sqrt{(1)^2+(\sqrt{3})^2+2\sqrt{3}+(1)^2+(\sqrt{3})^2-2\sqrt{3}}[/tex]

[tex]CA=\sqrt{1+3+1+3}[/tex]

[tex]CA=\sqrt{8}[/tex]

Clearly, [tex]AB=BC=CA[/tex].

Since all sides of the given triangle are equal, therefore the given vertices are the vertices of an equilateral triangle.

Hence proved.

Answer:

the surface area of cylinder is 1733.28 inches²

hope it helps

have a nice day

Answer:

[tex]\frac{3}{10} , 0.48 , 0.73[/tex]

Step-by-step explanation:

In order to put this number in order from least to greatest, we have to turn them into fractions with the same denominator, so firstly we write down all of the decimals as fractions, and we will get...

[tex]0.48 = \frac{48}{100} \\\\0.73 = \frac{73}{100}[/tex]

Now, we need to find the smallest number that is divisible by 100 and by 10, and this number will be the least common denominator. The smallest number that is divisible by 100 and by 10 is 100, therefore 100 is the least common denominator. Now we have to make all of the fractions have the denominator of 100 and we do that in the following way...

[tex]\frac{48}{100}= \frac{48}{100}\\\\\frac{73}{100} = \frac{73}{100}\\\\\frac{3}{10} = \frac{(3)(10)}{(10)(10)} = \frac{30}{100}[/tex]

By looking at this we need to understand that...

[tex]\frac{30}{100}<\frac{48}{100}<\frac{73}{100}[/tex]

Therefore...

[tex]\frac{3}{10} < 0.48 < 0.73[/tex]

Answer:1) 32.  2).  3) 21.  4) 4

Step-by-step explanation: 1) 4*8=32m, 2) I don't know, 3) 6*7=42 for the area of a square but since a triangle half it so its 21, An the last is by 4 for example 4*10=40 but if doubled its 20*8 and that equals 160. and 160/40=4

Answer:Number 1

a. eleven thousand and twelve

b. four thousand three hundred and fifteen

c. twenty one thousnad and ten

Answer:Number 2

a.I one thousand

II one tousand

b.I hundreds

II cero

c.I ten thousands

II sixty thousand

Answer:

I believe the correct answer is 49.

Step-by-step explanation:

If this answer is incorrect let me know and I will fix it. I'm sorry in advance if it is wrong.

Answer:

42 crickets

Step-by-step explanation:

6 x 7= 42

Answer:

(5,3)

Step-by-step explanation:

1. Translation 5 units right, so the x-coordinates goes to 5.

2. Translation 5 units under, so the y-coordinates goes to 3.

So . the answer is (5, 3)

Answer:

If I understand this right, the answer is $48.00

Step-by-step explanation:

If they pay $1.50 three times a month just times $1.50 by 12 because there are 12 days in a month, then you get 16, then you times 16 by 3 and you get 48.

(I hope this is right lol)

Answer:

$54.00

Step-by-step explanation:

3 transactions × $1.50 per transaction = $4.50 per month

$4.50 × 12 months in a year = $54.00

Step-by-step explanation:

my answer is in the image above

p has to be greater than or equal to 8 root 2

Answer:

The 2 option :)

Step-by-step explanation:

The Chords : QL ,SM , Secant : NR , Tangents : a  and b , Diameter : QL, ,radii: PT , QT and TL therefore the Option A is the correct answer.

A circle is a round shaped figure , whose all points are in the same plane and at same distance from a single point known as center.

A secant is a segment that passes through 2 points on a circle, It is an infinite extension of a chord.

A tangent touches a circle at exactly one point and never enters the interior of the circle.

A chord is a line segment which connects two point on the circle.

A diameter is a chord that passes through the center of the circleThe radius is half of the diameter of the circle

Based on the above definitions

Chords : QL ,SM

Secant : NR

Tangents : a  and b

Diameter : QL

radii: PT , QT and TL

To know more about Circle

https://brainly.com/question/11833983

#SPJ2

Answer:

8 books were in each box

Step-by-step explanation:

According to the Question,

Assume X is the Number of Books In Each Box.

Algebraic Expression,

4X + 3 = 35

4X = 35 - 3

4X = 32  ⇔  X=8 books in Each Box.

Answer: 103 degrees

Step-by-step explanation: all angle of a regular triangle always add up to 180. so 62+15=77. and 180 - 77= 103

Answer:

A. 103 degrees

Step-by-step explanation:

In a triangle, the sum of angle measures is equal to 180 degrees, so by adding 62 & 15, & subtracting it from 180 you get the third angle measure of 103.

Answer:

not defined

Step-by-step explanation:

[tex] {x}^{2} = 56 - 2000 - 15637 \\ {x}^{2} = - 1758[/tex]

Answer:

P'=(0,3)

Step-by-step explanation:

P'=(-5+5, 7-4)

Answer:

8a) 3x

8b) 3 × x

8c) (2/3)x

8d) x/2

8e) 1/x

9a) 4x - 7

9b) x + 1/x

9c) 5(x + 2)

9d) x/(x + 4)

9e) (x/8) + x

Answer:

6,9,12

Step-by-step explanation:

A triangle cannot be considered a triangle unless the sum of the smaller two of the sides is greater than the larger side.

Answer:

(6, 9, 12)

Hope that this helps!

Step-by-step explanation:

- 1⅔ < -¼

__________________

Answer:

hypotenuse = 7.3

Step-by-step explanation:

the length two legs of the given triangle are 7 and 2 respectively.

using pythagoras theorem

a^2 + b^2 = c^2

7^2 + 2^2 = c^2

49 + 4 = c^2

53 = c^2

[tex]\sqrt{53}[/tex] = c

7.3 = c

Answer:

2355in³

Step-by-step explanation:

3.14(5)²×30=2355 in³

Answer:

Answer:94.2

Answer:94.2Step-by-step explanation:

Answer:94.2Step-by-step explanation:3.14(5)²×30

Answer:94.2Step-by-step explanation:3.14(5)²×303.14×25×30

Answer:94.2Step-by-step explanation:3.14(5)²×303.14×25×303.14×5×6

= 94.2

i am sorry if it is not correct

Answer:

u r ANS

Step-by-step explanation:

7/3 on number line

Mark above ANS as branliest

Answer:

8

Step-by-step explanation:

Given:

13 - 0.75w + 8x

where,

w = 12

x = 1/2

13 - 0.75w + 8x

Substitute the value of w and x into the equation

= 13 - 0.75(12) + 8(1/2)

= 13 - 9 + 8/2

= 13 - 9 + 4

= 8

Therefore,

13 - 0.75w + 8x = 8

Answer:

D

Step-by-step explanation:

point C is on the y with the value 2 so y=2 and x=z=0

For A)

arcsin(11/15)=angle of elevation

47.17=angle of elevation

For B)

tan(47.17)=11/x

11/tan(47.17)=x

10.2=x

Answer:

Gradient = -3

Step-by-step explanation:

The gradient of the graph = change in y/change in x

Change in y = the vertical distance = 3 units

Change in x = the run/horizontal distance = 1 unit

The line slopes downward, so it's a negative gradient.

Thus:

Gradient = 3/1 = -3

Answer:

"31st in the sequence"

87/3 = 29 ..   29 subtractions needed to get to zero

the 30th position in the sequence will be zero

the 31st is the first negative term

1 87

2 84

3 81

4 78

5 75

6 72

7 69

8 66

9 63

10 60

11 57

12 54

13 51

14 48

15 45

16 42

17 39

18 36

19 33

20 30

21 27

22 24

23 21

24 18

25 15

26 12

27 9

28 6

29 3

30 0

31 -3

Step-by-step explanation:

Answer:

32 ft³

Step-by-step explanation:

put r= 2 ft

V= 4/3x 3 X 2³

V= 32 ft³

I got this answer with help form Gauthmath App you can check out the app on Play Store and App store.

Answer:

d bro. pay attention at order of triangle's vertices

Answer:

Option : The product of the roots is - 4

Step-by-step explanation:

[tex]3x^2 + 9x - 12 = 0\\\\3x^2 + 12x - 3x - 12 = 0\\\\3x(x+4) -3(x+4) = 0\\\\(3x - 3) (x+ 4) = 0\\\\[/tex]

Therefore the roots are -4 and 1

The product of the roots are -4 x 1 = -4

Answer:

D

Step-by-step explanation:

3 - 7 = -4 and 3(3) + 2(-7) = -5, so D is the only choice that is correct for both inequalities.