Find the area of equilateral triangle with side a. Please answer with completely simplified exact values. Answer: A = sq. Units
Solution :
It is given that the length of a side of a triangle is given by 'a'.
It is an equilateral triangle.
So the three sides will be of equal length and is a, a, a units.
Now the semi perimeter of the equilateral triangle is given by :
[tex]$S=\frac{a+a+a}{2}$[/tex]
[tex]$=\frac{3}{2}a$[/tex]
Therefore, using the Heron's formula, we can find the area of the equilateral triangle.
Area of the equilateral triangle is given by :
[tex]$A =\sqrt{S(S-a)(S-a)(S-a)}$[/tex]
[tex]$A =\sqrt{\frac{3a}{2}\left(\frac{3a}{2}-a\right)\left(\frac{3a}{2}-a\right)\left(\frac{3a}{2}-a\right)}$[/tex]
[tex]$A=\frac{\sqrt3}{4}a^2$[/tex] square units.
PLEASE HELP THANKS YOU
Radius
Diameter: 26 inches
Circunference :
Area:
Answer:
Radius is 13
Circumference = 26π
Area is 169π
Step-by-step explanation:
use the radius, circumference, and area formulas.
Radius is 13
Circumference = 26π
Area is 169π
substitute pi for 3.14, 3, etc if needed
In Triangle ABC. AB = 5, BC=8. and AC = 7. Name the largest angle of triangle ABC
i think its A
Step-by-step explanation:
Which of the following is the slope of a line that passes through the points (-5, 10) and (15, 2)
Answer:
(4) -2/5
Step-by-step explanation:
Rise/run
ERRE
What is the difference?
4y+6
y-5
2y+ 1
y-5
6y+7
y-5
2y+5
y-5
6y+ 7
-2y-10
2y+5
-2y-10
y-5
2y+ 1
y-5
6y+7
y-5
2y+5
y-5
6y+ 7
-2y-10
2y+5
-2y-10
what is the value ofny when -5 y-7/9
Work out the size of angle x.
х
79°
350
what angle is it I need 2 no cuz I cannot help u without the angle
Calculate the equation of the line through the points (-1, 1), (4.0), and (24,-4).
A y = 5x + 6
B y= 1/5x + 4/5
C y= -5x + 4
D y= -1/5x +4/5
Answer:
D
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (- 1, 1) and (x₂, y₂ ) = (24, - 4) ← 2 points on the line
m = [tex]\frac{-4-1}{24+1}[/tex] = [tex]\frac{-5}{25}[/tex] = - [tex]\frac{1}{5}[/tex] , then
y = - [tex]\frac{1}{5}[/tex] x + c ← is the partial equation
To find c substitute any of the 3 points into the partial equation
Using (4, 0 ) , then
0 = - [tex]\frac{4}{5}[/tex] + c ⇒ c = 0 + [tex]\frac{4}{5}[/tex] = [tex]\frac{4}{5}[/tex]
y = - [tex]\frac{1}{5}[/tex] x + [tex]\frac{4}{5}[/tex] → D
If a person walks 1/2 miles in 3/4 of an hour. What Is the unit rate?
Lines Line A E and Line G H are parallel in the image below. The image will be used to prove that the sum of the measures of the interior angles of Triangle C G H is 180°.
Lines A E and G H are parallel. Angles F and C are congruent.
Which statement would be included in the proof of why Measure of angle C + measure of angle G + measure of angle H = 180 degrees.?
Angles F and H are congruent.
Angles C and E are congruent.
Angles A and G are congruent.
Angles F and C are congruent.
Answer:
he corect f and c
Step-by-step explanation:
The answer would be F and C
Explanation: I got it right on the test I took.
Rita has 10 centimeters of
ribbon. She cuts the
ribbon into 8 equal pieces.
What is the length, in
centimeters, of each
piece of ribbon?
Answer: 1.25
Step-by-step explanation:
because it is
By installing efficient water fixtures, the average American can reduce water use to about 45 gallons of water
Answer: 1,395 gallons
Step-by-step explanation:
There are 31 days in December.
If using this water fixture would reduce water usage to 45 gallons per day, the number of gallons to be used in December is:
= 45 * 31 days
= 1,395 gallons
Raj gave his mother a bouquet of 12 pink and white roses. There were 4 pink roses in the bouquet. Which ratio represents the number of white roses to the total number of roses in the bouquet? One-third One-half Two-thirds Three-fourths
Answer:
The answer would be 2/3 or C
Step-by-step explanation:
I got it
The graph of a sinusoidal function has a maximum point at (0,5)(0,5)left parenthesis, 0, comma, 5, right parenthesis and then has a minimum point at (2\pi,-5)(2π,−5)left parenthesis, 2, pi, comma, minus, 5, right parenthesis. Write the formula of the function, where xxx is entered in radians.
The graph and therefore, the sinusoidal function equation is a wave function graph and equation
The formula of the sinusoidal function can be written as follows;
[tex]y = \mathbf{5 \cdot sin\left (\dfrac{1}{2} \cdot \left (x + \dfrac{\pi}{2} \right)\right)}[/tex]
The process of deriving the equation of the sinusoidal function is as follows:
The given parameters of the sinusoidal function are;
The coordinate of the maximum point = (0, 5)
The coordinate of the minimum point = (2·π, -5)
Method:
The general form of the sinusoidal function is y = A·sin(B·(x - h)) + k
From the given coordinates of points on the graph of the sinusoidal wave, the values of A, B, h, and k can be calculated as follows
Solution:
y = A·sin(B·(x - h)) + k
Where;
A = Amplitude = (Maximum y-value - Minimum y-value)/2
∴ A = (5 - (-5))/2 = 5
A = 5
The period, T = 2·π/B = The time to complete a cycle = Time from maximum y-value to another maximum y-value
∴ The period, T = 2 × (The x-value at maximum y-value - The x-value at minimum y-value)
T = 2 × (0 - 2·π) = -4·π
Given that the period, T represent a scalar quantity, we have T = 4·π
∴ T = 4·π = 2·π/B
B = 2·π/4·π = 1/2
B = 1/2
From the given coordinates, at x = 0, f(x) is maximum, therefore, sin(B·(x - h)) = 1, which gives;
B·(x - h) = π/2
(1/2)·(0 - h) = π/2
h = -π/2
The vertical shift, k = (Maximum y-value + Minimum y-value)/2
∴ k = (5 + (-5))/2 = 0, there is no vertical shift
Therefore;
The equation of the sinusoidal function is y = 5·sin(1/2·(x - (-π/2)) + 0, from which the equation can be presented as follows;
[tex]y = \mathbf{ 5 \cdot sin\left (\dfrac{1}{2} \cdot \left (x + \dfrac{\pi}{2} \right)\right)}[/tex]
Learn more about sinusoidal functions here
https://brainly.com/question/22706973
Answer:
f(x)=5sin((1/2)x + (pi/2))
Step-by-step explanation:
Can I get some help with this question
If a⁵ = 3⁵, simplify (2a)⁷ ?
3⁷3⁸6⁶6⁷Answer :D option 6⁷ is the right answer.Explanation :Given :a⁵ = 3⁵To Find :(2a)⁷Solution :As, we have a⁵ = 3⁵
We know that if powers are equal then the base are also equal. In a⁵ = 3⁵, powers are equal on both sides so base will also be equal.
∴ a = 3
Now, we have to find (2a)⁷, so by substituting a = 3, we have :
⟹ (2a)⁷ = (2 × 3)⁷
⟹ (2a)⁷ = (6)⁷
⟹ (2a)⁷ = 6⁷
Therefore, correct answer is 6⁷.
Hence, correct option is D.
In the figure, [tex] \angle[/tex] AOB = [tex] \frac{1}{2} [/tex][tex] \angle[/tex] BOC and [tex] \angle[/tex] BOC = [tex] \frac{2}{3} [/tex][tex] \angle[/tex] COD . Show that [tex] \angle[/tex] COD = [tex] \frac{1}{2} \angle[/tex] AOD mentioning necessary axioms.
~Thanks in advance !
Answer:
See Below.
Step-by-step explanation:
Statements: Reasons:
[tex]1)\text{ }\angle AOD=180[/tex] Straight Angle Theorem
[tex]2)\text{ } \angle AOB+\angle BOC+\angle COD=\angle AOD[/tex] Angle Addition
[tex]3)\text{ } \angle AOB+\angle BOC+\angle COD=180[/tex] Substitution
[tex]\displaystyle 4)\text{ } \angle AOB=\frac{1}{2}\angle BOC[/tex] Given
[tex]\displaystyle 5)\text{ } \angle BOC=\frac{2}{3}\angle COD[/tex] Given
[tex]\displaystyle 6)\text{ } \frac{1}{2}\angle BOC+\frac{2}{3}\angle COD+\angle COD=180[/tex] Substitution
[tex]\displaystyle 7)\text{ } \frac{1}{2}\Big(\frac{2}{3}\angle COD\Big)+\frac{2}{3}\angle COD+\angle COD=180[/tex] Substitution
[tex]\displaystyle 8)\text{ } \frac{1}{3}\angle COD+\frac{2}{3}\angle COD+\angle COD=180[/tex] Multiplication
[tex]\displaystyle 9)\text{ } 2\angle COD=180[/tex] Addition
[tex]10)\text{ } \angle COD=90[/tex] Division Property of Equality
[tex]\displaystyle 11)\text{ } \frac{1}{2}\angle AOD=90[/tex] Division Property of Equality
[tex]\displaystyle 12)\text{ } \angle COD=\frac{1}{2}\angle AOD[/tex] Substitution
Answer:
this is your answer. good luck.
A float in a parade may use as many as a florist sells 7 in years. If is the number of a florist sells in 1 year, write an algebraic expression to represent the number of a float in the parade may use.
Answer:
um
Step-by-step explanation:
Solve for x 4 + 2.1x = 22.9
Rudy and Tracy want to plant some orange trees. They clear a rectangular piece of land with a length of g + 10 and a width of 35. What is the perimeter, if g = 15
True or False: A millisecond is a millionth of a second.
Answer:
False
Step-by-step explanation:
a millisecond (ms or msec) is one thousandth of a second
Answer:
False
Explanation:
A millisecond is a thousandth of a second. A millionth of a second is called a microsecond.
uhhhhhhh i dont understand tis
Answers:
f) hard working. Think of "industry" or "industrial" to help remember.b) state of disorder. Mayhem is effectively chaos.e) expressions of sorrow. For example, you would give lamentations at a funeral.i) gridlock or standstill. Example: "Congress is at an impasse on passing a new spending bill". You can think of it like saying "it's not possible to pass or get through".a) A long angry rant or speech. I'm not sure what trick you can use to remember this, but the term "harangue" sounds negative which seems to be fitting with the angry rant/speech.c) Overly concerned about small details. Usually you might hear it used in a way where someone mentions "not to be pedantic", they basically mean "not to nitpick at the fine details". h) Terrible; extremely poor. Someone who is abominable has bad morals or values as a person. For instance, a murderer is someone who is abominable.d) Characterized as having too high of an opinion of oneself. Someone with a big ego only thinks about themself and no one else. The tern narcissism also applies.g) The effects of something. Specifically, repercussions are referred to as unintended consequences of an action. j) The act of surrendering. I don't know of a useful trick to help remember this term.Which quadratic equation?
Answer:
step 1. plug in (-3, 0).
step 2. y = x^2 + x - 6 works and the others dont.
step 3. plug in (-2, -4), (-1, -6), (0, -6), (1, -4), (2, 0)
step 4. All points work in the equation x^2 + x - 6.
A graduated cylinder that is 24 cm tall can hold 1 L of water.
a. What is the radius of the cylinder? (round to the nearest hundredth)
b. What is the height of the 500 ml mark?
c. The 250 ml mark?
Recall that 1 liter (L) is equal to 1000 milliliters (ml).
Due soon, please I don't understand.
Answer:
LOL i belive its 200 because i did this exact same thing yesterday for homework and got it right, if its not then i dont know what to say.
Step-by-step explanation:
Find exact value. tan (sin-1 5/8)
Answer:
The chicken closed the road.
And then he crawled up the spot
and come over the duck
If a circle has a radius of 18 feet, what is its circumference (to the nearest whole foot)?
Step-by-step explanation:
[tex]2\pi \times r = 2\pi \times 18 = 113.09 = 113 \: {feet}^{2} [/tex]
What is the MAD of these numbers 1,1,4,5,5,5,6,7,7,10,10?
Please give an explanation
Answer:
2.2314
Step-by-step explanation:
To find the mean absolute deviation of the data, start by finding the mean of the data set.
1+1+4+5+5+5+6+7+7+10+10= 61
61÷11= 5.5-2.5= 2.2
Example:
Find the MAD of 2,4,6,8
Step 1 :
Find the mean of the data :
(2+4+6+8) / 4 = 20/4 = 5
Step 2 :
Find the distance between each data and mean.
Distance between 2 and 5 is 3
Distance between 4 and 5 is 1
Distance between 6 and 5 is 1
Distance between 8 and 5 is 3
Step 3 :
Add all the distances :
3+1+1+3 = 8
Step 4 :
Divide it by the number of data :
8 / 4 = 2
John is planning on building a shelf in the shape of a right triangle. He wants the shelf to be 99 inches at its widest and 4040 inches long. He believes the diagonal will be 41 inches. Is he accurate?
Given:
Shape of the shelf is a right triangle.
Width of the shelf = 9 inches
Length of the shelf = 40 inches
He believes the diagonal will be 41 inches.
To find:
Whether he is accurate or not.
Solution:
According to the Pythagoras theorem,
[tex]Hypotenuse^2=Perpendicular^2+Base^2[/tex]
Using Pythagoras theorem, find the length of the diagonal.
[tex]Diagonal^2=Width^2+length^2[/tex]
[tex]Diagonal^2=(9)^2+(40)^2[/tex]
[tex]Diagonal^2=81+1600[/tex]
[tex]Diagonal^2=1681[/tex]
Taking square root on both sides.
[tex]Diagonal=\pm \sqrt{1681}[/tex]
But side cannot be negative.
[tex]Diagonal=41[/tex]
Therefore, the length of the diagonal is 41 inches. So, John is accurate.
Translate this sentence into an equation. 99 is the product of Chrissy's age and 9 Use the variable c to represent Chrissy's age.
Answer:
[tex]9c=99\\[/tex]
Step-by-step explanation:
Product means multipulcation
So it must be 9c = 99
Answer:
99=c×9
Step-by-step explanation:
Chrissy =c
99=c×9
that will be your answer because you have been told to write an equation not to solve.
I really need this pls
Answer:
[tex]\displaystyle m=-1[/tex]
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
Reading a Cartesian planeCoordinates (x, y)Slope Formula: [tex]\displaystyle m=\frac{y_2-y_1}{x_2-x_1}[/tex]Step-by-step explanation:
Step 1: Define
Find points from graph.
Point (2, 0)
Point (0, 2)
Step 2: Find slope m
Simply plug in the 2 coordinates into the slope formula to find slope m
Substitute in points [Slope Formula]: [tex]\displaystyle m=\frac{2-0}{0-2}[/tex][Fraction] Subtract: [tex]\displaystyle m=\frac{2}{-2}[/tex][Fraction] Divide: [tex]\displaystyle m=-1[/tex]