Can you justify that all sides and all angles are equal in a equilateral triangle?
Answers
If the given triangle has all three sides as congruent and the angles are same then the triangle is an equilateral triangle.
We will use the figure given below to prove the triangle as an equilateral triangle.
In the above figure,
Given, vertices of a triangle are A(X1, Y1), B(X2, Y2), and C(X3, Y3).
According to the properties of the equilateral triangle, the sides of an equilateral triangle should be equal in measure.
So, we use the distance formula:
d = √((x2 - x1)^2+(y2 - y1)^2 to verify if all three sides are congruent and equal to each other
If AB = BC = CA.
⇒ √((x(2) - x(1))^2 + (y(2) - y(1))^2) = √(x(3) - x(2))^2 + (y(3) - y(2))^2 = √(x(1) - x(3))^2+ (y(1) - y(3)) ^2
If the given triangle satisfies the above condition then the triangle is an equilateral triangle.
If the given triangle has all three sides as congruent then the triangles angles are also equal.
Hence, if the given triangle has all three sides as congruent and the angles are same then the triangle is an equilateral triangle.
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Related Questions
plz answer
correctly it is worth a lot of points
Answers
Answer:
75%
Step-by-step explanation:
Find area of the figure. PLEASE HELP!
Answers
Answer:
69
Step-by-step explanation:
Answer:
69 m²
Step-by-step explanation:
The figure is composed of 2 right triangles
The area (A) of a triangle is calculated as
A = [tex]\frac{1}{2}[/tex] bh ( b is the base and h the perpendicular height )
A of triangle on left is
A = [tex]\frac{1}{2}[/tex] × 9 × 10 = 45 m²
A of triangle on right is
A = [tex]\frac{1}{2}[/tex] × 8 × 6 = 24 m²
Total area = 45 + 24 = 69 m²
PLXS HELP NEED BY TODAY
Answers
Answer:
I believe its 17, this is a 90 degree angle, so 90-73=17
Step-by-step explanation:
x= 17°
Solve for x
3x+7=57 pleas hurry
Answers
Answer: x=50/3
Step-by-step explanation:
Answer:
16.6 ( the 6 is repeated) or 16 and 2/3
Step-by-step explanation:
Take the 7 away which equals 50 and then divide by 3..
Given f(x)=(0.5)^x, give the rule for g(x) if it is f(x) shifted to the left 1 unit, down 3 units, and reflected over the x-axis
Answers
Answer:
g(x) = -(0.5)^(x + 1) + 3
Step-by-step explanation:
First, let's define the transformations used in this case:
Horizontal shift (horizontal translation):
If we have a function f(x), a horizontal translation can be written as:
g(x) = f(x - N)
if N is positive, the translation is to the right
if N is negative, the translation s to the left.
Vertical shift (vertical translation):
If we have a function f(x), a vertical translation can be written as:
g(x) = f(x) + N
if N is positive, the translation is upwards
if N is negative, the translation is downwards.
Reflection over the x-axis.
If we have a function f(x), a reflection over the x-axis is written as:
g(x) = -f(x).
Now we have the function:
f(x) = (0.5)^x
Let's apply the transformations:
"shifted to the left 1 unit"
g(x) = f(x - (-1) ) = f(x + 1)
"shifted down 3 unts"
g(x) = f(x + 1) - 3
"reflected over the x-axis"
g(x) = -( f(x + 1) - 3 ) = -f(x + 1) + 3
now we can replace the function equation here and get:
g(x) = -f(x + 1) + 3 = -(0.5)^(x + 1) + 3
Identify the set as finite or infinite
{1 1/4, 1/16, 1/64,,,}
Answers
Answer:
??????
Step-by-step explanation:
What that does not make sence at all
A bottel holds z ounces of water a second bottel holds 16 onces witch is 8/5 times as much warter how much does the frist bottel hold
Answers
Answer:
The first bottle holds 10 ounces of water.
Step-by-step explanation:
The bottle holds z ounces.
The second bottle holds 16 ounces, which is 8/5 times the first, which is z.
How much water does the first bottle holds?
[tex]\frac{8z}{5} = 16[/tex]
[tex]8z = 16*5[/tex]
[tex]8z = 80[/tex]
[tex]z = \frac{80}{8}[/tex]
[tex]z = 10[/tex]
The first bottle holds 10 ounces of water.
Find 33⅓% of ⅘ of $4.50.
Answers
I hope this helps you :)
convertir 26 grados celsius a grados a grados fahrenheit
Answers
Answer:
Para transformar 26 °C a grados Fahrenheit tienes que multiplicar 26 x 9/5 y después sumarle 32. 1 °C son 33,8 °F.
Step-by-step explanation:
26 degrees Celsius is equal to 78.8 degrees Fahrenheit.
To convert 26 degrees Celsius to degrees Fahrenheit, you can use the following formula:
°F = (°C × 9/5) + 32
Plug in the value of celsius.
°F = (26 × 9/5) + 32
°F = (234/5) + 32
°F = 46.8 + 32
°F = 78.8
Therefore, 26 degrees Celsius is equal to 78.8 degrees Fahrenheit.
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Convert 26 degrees Celsius to degrees Fahrenheit?
Subtract the following polynomials in this equation.
Answers
Answer:
c
Step-by-step explanation:
it a c....................
Which list orders the numbers from least to greatest
Answers
least to greatest: -3, -2.4, -21/4, -1.5, -11/8
i need help i need help asap
Answers
Answer:
2(x-3)^2
Step-by-step explanation: simplify second expression and combine
Help please I need help
Answers
Answer:
12=4 3 4=2 2
Step-by-step explanation:
2. A physical fitness researcher devises a test of strength and finds that the results are normally distributed with a mean of 110 pounds and a standard deviation of 10.4 pounds. If a subject is randomly selected and measured, find the probability of a score between 110 and 128 pounds. (5
Answers
Answer:
Step-by-step explanation:
A physical fitness researcher devises a test of strength and finds that the results are normally distributed with a mean of 110 pounds and a standard deviation of 10.4 pounds. If a subject is randomly selected and measured, find the probability of a score between 110 and 128 pounds. (5
while shopping for clothes tracy spent $25 less than 3 times what curtis spent. Tracy spent $14. write and solve an equation to find how much curtis spent. Let x represent how much curtis spent.
Answers
3x-25=14
First, you'll add the 25 to the other side of the equation because its negative. 25+14 =39. then you'll divide these by 3. (because it says 3 times what curtis spent.)
39÷3=13. so the answer is 13. curtis spent 13 dollars shopping.
This image shows a square pyramid.
What is the surface area of this square pyramid?
32 ft²
64 ft²
128 ft²
136 ft²
Answers
Answer:
please provide the image! would love to help.
Step-by-step explanation:
Answer:
128
Step-by-step explanation:
I took the test
The value of almost everything you own assets such as a car computer oar house depreciates goes down overtime when an asset value decreases by a fixed amount each year the depreciation is called straight line depreciation suppose your truck has an initial value of $12,400 depreciates $820 per year write an equation illustrates this function if you plan to keep your truck for seven years and determine the value of the truck at the end of this. Period let v represent the dependent variable in T represent the independent variable
Answers
Answer:
A
Step-by-step explanation:
Trust
The correct equation is,
⇒ y = 12,400 - 820r
And, Amount for 7 years is, $6,660
What is Equation of line?The equation of line in point-slope form passing through the points
(x₁ , y₁) and (x₂, y₂) with slope m is defined as;
⇒ y - y₁ = m (x - x₁)
Where, m = (y₂ - y₁) / (x₂ - x₁)
We have to given that;
Here, your truck has an initial value of $12,400 depreciates $820 per year.
Let number of years = r
Hence, We get the correct equation is,.
⇒ y = 12,400 - 820r
So, For r = 7 years;
⇒ y = 12400 - 820 x 7
⇒ y = 12400 - 5740
⇒ y = $6,660
Thus, The correct equation is,
⇒ y = 12,400 - 820r
And, Amount for 7 years is, $6,660
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A rectangular landing pad measures 20' × 25' with a rectangular target on the pad measuring 6' × 8'. What is the geometric probability that a model rocket falling randomly on the pad will land in the target?
Answers
Answer:
9.6%
Step-by-step explanation:
The probability that a model rocket falling randomly on the pad will land in the target is 9.6% if the rectangular landing pad measures 20' × 25' with a rectangular target on the pad measuring 6' × 8'.
What is probability?It is defined as the ratio of the number of favourable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.
We have a rectangular landing pad measures 20' × 25' with a rectangular target on the pad measuring 6' × 8'.
To get the geometric probability, we must find the area of the rectangle.
Total outcomes = 20' × 25' = 500'
Total favourable outcomes = 6' × 8' = 48'
Probability = 48/500 = 0.096
= 0.096×100 = 9.6%
Thus, the probability that a model rocket falling randomly on the pad will land in the target is 9.6% if the rectangular landing pad measures 20' × 25' with a rectangular target on the pad measuring 6' × 8'.
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plz answer the question and explain how you got the answer
Answers
1,741.67 yards
Step-by-step explanation:
1 foot = 1/3 yards
5,225 divided by 3 is 1,741.67
10x5+4to the power of 2+(5+30 divided by 10
Answers
Answer:
10 * 5 + 4^2 + (5 + 30 ÷ 10)=74
Answer:
74
Step-by-step explanation:
HELPPPPPPPPPPPPPPPPP
Answers
Answer:
I think it's 160 square inches. Try L x W x H (length multiplied by width multiplied by height). So that would mean 4 x 5 = 20 x 8 = 160,
hope this helps!
Answer:
Step-by-step explanation:
Un albañil pone azulejos a una pared de 6 m de largo y 2,4 m de alto.Los azulejos son cuadrados de 20 cm de lado
Answers
Pregunta completa:
Un albañil pone azulejos a una pared de 6 m de largo y 2,4 m de alto. Los azulejos son cuadrados de 30 cm de lado. ¿Cuants, cajas tendra que comprar si en una caja hay 25 azulejos? Con procedimiento.
Respuesta:
160 tejas
7 cajas
Explicación paso a paso:
Dimensión de la pared = 6 m por 2,4 m
Área de la pared = 6 m * 2,4 m
Área de la pared = 14,4 m²
Longitud lateral, s de teja cuadrada = 30 cm = 0,3 m
Área de la loseta cuadrada = s² = 0.3² = 0.09m²
Número de baldosas cuadradas necesarias:
14,4 m² ÷ 0,09 m²
= 160 fichas cuadradas
Si hay 25 fichas en una caja;
Número de cajas a comprar:
160/25
= 6,4 ≈ 7 cajas
Please help algebra work
Answers
Answer:
I think it is J
Step-by-step explanation:
the x-2.... so on x axis on 2....and +5 is y intercept
Help please due td!!
Answers
the equation set up is “ 4x+13=105 “
do -13 on both sides which would then leave you with “ 4x=92 “. then you just divide 4x on both sides, giving you the answer of 23 :D
.............Option B)
pls help me! will give brainliest
Answers
Steps
X value to the left means add
X value to the right means subtract
Y value down means subtract
Y value up means add
Writing Linear Equations
Two less than five times a number x is equal to 13. Solve for x.
Answers
Answer:
x = 3
Step-by-step explanation:
5x - 2 = 13 (write the equation)
5x - 2 + 2 = 13 + 2 (isolate the variable)
5x = 15
5x/5 = 15/5 (simplify)
x = 3
Answer: x=3
Step-by-step explanation:
13=5x-2
13+2=5x
15=5x
x=15/5
x=3
For what value of a is - 4a zero of the polynomial p(x) = x ^ 2 - x - (2a + 2) ^ 2
Answers
Answer: [tex]a=\dfrac{1\pm \sqrt{13}}{6}[/tex]
Step-by-step explanation:
Given
Quadratic Equation is [tex]x^2-x-(2a+2)[/tex]
[tex]-4a[/tex] is the solution of the given equation
[tex]\therefore (-4a)^2-(-4a)-(2a+2)^2=0\\\Rightarrow 16a^2+4a-(4a^2+4+8a)=0\\\Rightarrow 12a^2-4a-4=0\\\Rightarrow 3a^2-a-1=0\\\\\Rightarrow a=\dfrac{1\pm \sqrt{1+12}}{2\times 3}=\dfrac{1\pm \sqrt{13}}{6}[/tex]
help me pls I would aprreciate it
Answers
Answer:
b
Step-by-step explanation:
Ashley started a savings account with Chase bank. She initially put in $200 in her account. If she was granted a .08% semi-annually, how much would she have in her account after a year?
Answers
account now equals 216
216 * .08 = 17.28
total after one year = $233.28
temperature in Moscow was 2 degrees Celsius then it dropped to 8 degrees Celsius below zero by how many degrees did the temperature drop
Answers
Answer:
10
Step-by-step explanation:
2--8
2+8
10
8 below zero is -8