b) Show that the points (1,1), (-1,-1) and ( -root3, root 3 ) are the vertices of an equilateral triangle.
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.
Find the volume of this sphere.
Use 3 for 7.
3
V~ [?]ft
V = Tr3
( 2 ft
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.
Find RS. See image below
Step-by-step explanation:
since both cords are equal, so are arc length
4x + 18 = 7x - 51
3x - 21 = 0
x = 7
arc RS = 4(7) + 18
Pls help no files just type it in thank you
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
please put the math too I really need it ;)
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
[tex]x^{2} +2000+15637=56 \\\\what is X\\\\PLEASE HELP[/tex]
Answer:
not defined
Step-by-step explanation:
[tex] {x}^{2} = 56 - 2000 - 15637 \\ {x}^{2} = - 1758[/tex]
CAN SOMEONE HELP THANKS 14 POINTS
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!
Put these numbers in order from least to greatest.
0.48,0.73, and 3/10
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]
Identify each line or segment that intersects ⊙ T. HELP PLEASE!!!
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.
What is a Circle ?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
In ΔLMN, MN = 15, NL = 20, and LM = 6. Which list has the angles of ΔLMN in order from smallest to largest?
Answer:
m<N, m<L, m<M
Step-by-step explanation:
The angle that sees the longest side length has the bigger angle measurement
so the angles would be listed as following :
from smallest to largest :
m<N, m<L, m<M
please help me with this :)
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.
Find the volume of this cylinder.
_____ cubic inches
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
A(n) ______________ is the act of uniformly turning in a clockwise or counter-clockwise direction around a center point.
Answer Choices:
Dilation
Translation
Reflection
Rotation
What is the image point of (0, 8) after a translation right units and down 5 units?
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)
Which equation is a function of x?
Answer:
X=5
x=y2+9
x2=y
x2=y2+16
Step-by-step explanation:
If my answer is incorrect, pls correct me!
If you like my answer and explanation, mark me as brainliest!
For EASY BRAINLIEST!!!
Answer:
A.
B.
C.
D.
On both questions
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
Someone Helppp me please
Answer:
Step-by-step explanation:
diameter = 3.7
radius = diameter/2
=3.7/2
=1.85
area of circle = πr^2
=π*(1.85)^2
=3.4225π m^2
someone plz help me!!
Answer:
P'=(0,3)
Step-by-step explanation:
P'=(-5+5, 7-4)
Evaluate 13 - 0.75w+8x when w=12 and x= 1 over 2
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
Write an inequality to describe the relationship between -1 2/3 and-1/4
Step-by-step explanation:
- 1⅔ < -¼
__________________
Find the surface area and the volume of the composite figure
Answer:
See belowStep-by-step explanation:
Surface area of the figure:
S = 2(lw + lh + wh) + 1/2(4πr²) - πr² = 2(lw + lh + wh) + πr² S = 2(6*10 + 6*6 + 6*10) + 3.14*(6/2)² = 340.26 cm²Volume of the figure:
V = lwh + 1/2(4/3πr³) = lwh + 2/3πr³ V = 6*10*6 + 2/3*3.14*(6/2)³ = 416.52 cm³Answer:
> S = 340.26 cm²
> V = 416.52 cm³
Step-by-step explanation:
We need to find the surface area and the volume of the composite figure . The given figure is made up of a cuboid and a hemisphere . Let's Calculate them ,
Finding the Surface area :-
> S = 2(6*10 + 6*6 + 6*10) + 3.14*(6/2)
> S = 340.26 cm²
Volume of the figure:
> V = lbh + 1/2(4/3πr³)
> V = 6*10*6 + 2/3*3.14*(6/2)³
> V = 416.52 cm³
write the ordered triple of point C
A. (2,0,0)
B. (0,0,2)
C. (0,-2,0
D. (0,2,0)
Answer:
D
Step-by-step explanation:
point C is on the y with the value 2 so y=2 and x=z=0
Select the correct answer.
For which system of inequalities is (3,-7) a solution?
A.
x + y < -4
3x + 2y < -5
B.
x + y ≤ -4
3x + 2y < -5
C.
x + y < -4
3x + 2y ≤ -5
D.
x + y ≤ -4
3x + 2y ≤ -5
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.
pls answer
. its urgent pls
an
Answer:
a
Step-by-step explanation:
Answer:
option c
Step-by-step explanation:
[tex]\frac{-4}{3} * y = \frac{-3}{4}[/tex]
shift -4/3 to the right hand side . when it shifts to other side miltiplication changes to division
y = [tex]\frac{-3}{4} /\frac{-4}{3}[/tex]
now do reciprocal
y = [tex]\frac{-3}{4} *\frac{3}{-4}[/tex]
y = [tex]\frac{-9}{-16}[/tex]
minus and minus gets cancel
y = [tex]\frac{9}{16}[/tex]
y = [tex]\frac{(3)^2}{(4)^2}[/tex]
y = [tex](\frac{3}{4})^2[/tex]
which linear inequality is represented by the graph
Answer:
Step-by-step explanation:
2 1 -5 4 3 2 -11 2 4 5 X -2 ب ا -5 a Write down the gradient of the graph.
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
On a map of a town a school is located (-6, 3) and a movie theater is located (-6, -15) what is the distance from the school to the theater
Answer:The distance from the school to the theater = 18 units
Step-by-step explanation:
Distance between (a,b) and (c,d) = [tex]\sqrt{(d-b)^2+(c-a)^2}[/tex] units.
Given: On a map of a town a school is located (-6, 3) and a movie theater is located (-6, -15).
So, distance between (-6, 3) and(-6, -15) = [tex]\sqrt{(-6-(-6))^2+(-15-3)^2}[/tex]
[tex]=\sqrt{0^2+(-18)^2}\\\\=\sqrt{18^2}\\\\=18\ units[/tex]
Hence, the distance from the school to the theater = 18 units
Which statement about the equation 3x ^ 2 + 9x - 12 = 0 is true ? 1 . The product of the roots is -12 . 2 The product of the roots is -4 . 3 The sum of the roots is 3 . The sum of the roots is -9 .
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
sara is painting her house. to paint the second floor, she needs to lean her 15 foot ladder against her house to reach a point that is 11 feet above the ground
A) What is the angle of elevation that Sara's ladder will form with the ground?
B) How far from the base of the house should Sarah place the base of her ladder?
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
Q.No.1: A subset of {1,7,8 } is:
Step-by-step explanation:
you only need to provide an example ?
if your question here is complete, then the full set is
{1,7,8}
and these are all possible subsets (pick any one you like) :
{1}, {7}, {8}, {1,7}, {1,8}, {7,8}
and formally also
{}, {1,7,8}
the empty set is a subset of every set, and the whole set itself is also formally a subset.