Answers
As here we are given with an equilateral triangle, whose side is 3 cm, and we need to find the height and area of the equilateral triangle. So, for this let's recall that, the area of any equilateral triangle with side a is given by ;
[tex]{\boxed{\bf{Area_{(Equilateral\:\: Triangle)}=\dfrac{\sqrt{3}}{4}a^{2}}}}[/tex]So, if we substitute a = 3, in our Formula, it will yield to
[tex]{:\implies \quad \sf Area_{(Equilateral\:\:Triangle)}=\dfrac{\sqrt{3}}{4}(3)^{2}}[/tex]
[tex]{:\implies \quad \sf Area_{(Equilateral\:\:Triangle)}=\dfrac{\sqrt{3}}{4}(9)}[/tex]
[tex]{:\implies \quad \boxed{\bf{Area_{(Equilateral\:\:Triangle)}=\dfrac{9\sqrt{3}}{4}\:\:cm^{2}}}}[/tex]
Now, as we know that, for any triangle we also have a formula that is ;
[tex]{\boxed{\bf{Area_{(Triangle)}=\dfrac{1}{2}\times Base\times Height}}}[/tex]Now, Here as the triangle is equilateral, so it's base will just be same 3, and if we let height be H, so we will be having
[tex]{:\implies \quad \sf \dfrac{1}{2}\times 3\times H=\dfrac{9\sqrt{3}}{4}}[/tex]
[tex]{:\implies \quad \sf H=\dfrac{9\sqrt{3}}{4}\times \dfrac23}[/tex]
[tex]{:\implies \quad \boxed{\bf{Height=\dfrac{3\sqrt{3}}{2}\:\:cm}}}[/tex]
Related Questions
PLEASE HELP ASAP
are f(x)=4/x-2-1 and g(x)=3/x+2-2 inverses of each other?
Answers
Answer:
To find the inverse of:
[tex]f (x)=\dfrac{4}{x-2}-1[/tex]
Set the function to y:
[tex]\implies y=\dfrac{4}{x-2}-1[/tex]
Rearrange to make x the subject:
[tex]\implies y+1=\dfrac{4}{x-2}[/tex]
[tex]\implies (y+1)(x-2)=4[/tex]
[tex]\implies xy-2y+x-2=4[/tex]
[tex]\implies xy+x=2y+6[/tex]
[tex]\implies x(y+1)=2y+6[/tex]
[tex]\implies x=\dfrac{2y+6}{y+1}[/tex]
Swap x and y:
[tex]\implies y=\dfrac{2x+6}{x+1}[/tex]
Change y to the inverse of the function sign:
[tex]\implies f[/tex][tex]\:^{-1}(x)=\dfrac{2x+6}{x+1}[/tex]
Rewrite g(x) as a fraction:
[tex]g(x)=\dfrac{3}{x+2}-2[/tex]
[tex]\implies g(x)=\dfrac{3}{x+2}-\dfrac{2(x+2)}{x+2}[/tex]
[tex]\implies g(x)=\dfrac{3-2(x+2)}{x+2}[/tex]
[tex]\implies g(x)=\dfrac{3-2x-4}{x+2}[/tex]
[tex]\implies g(x)=-\dfrac{2x+1}{x+2}[/tex]
Therefore, as the inverse of f(x) ≠ g(x), the functions are NOT inverses of each other
Find the function with x-intercepts (-3, 0) and (5, 0), which also goes through the point (1, 8).
Answers
Answer:
y= -0.5x² + 1x + 7.5
Step-by-step explanation:
I graphed the points in Desmos and saw they looked liked a parabola the point (1,8) is in between -3 and 5 for the x-coordinate.
I put the values in a table. and had desmos do a regression
Answer:
f(x) = (-1/2)(x^2 + 8x - 15)
Step-by-step explanation:
Hope this helps
can someone help, please!?
Answers
Answer:
The answer is A. I have comfirmed it by having to maximize my screen and look at each dot carefully.
PLEASE HELP!!
A) 78
B) 145
C) 113
D) 102
Answers
Answer:
D
Step-by-step explanation:
the exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.
∠ BCD is an exterior angle of the triangle , then
∠ BCD = 35° + 67° = 102°
Identify similar pentagons.
Answers
Answer:
P, R
Step-by-step explanation:
If you dilate P, you can find out that P can be the same as R.
Store A sells 5 comics for $53.10. Store B sells 3 comics for $31.71. What is the difference in unit rate?
Answers
Answer:
Vendor 1 had a higher unit rate.
Step-by-step explanation:
If 2^2x = 2^3, what is the value of x?
A 2/3
B 3/2
C 2
D 3
Answers
divide 2 on both sides
x= 3/2
Each of the teams in a mixed volleyball league consists of 5 men and 5 women. there are 9 men and 10 women, including julia, who are trying out for a team. how many possible teams would include julia?
Answers
There are 9 men and 10 women, including Julia, who are trying out for a team. so there are 31,752 possible teams that would include Julia.
What is the combination?Each of the different groups or selections can be formed by taking some or all of a number of objects, irrespective of their arrangments is called a combination.
Each of the teams in a mixed volleyball league consists of 5 men and 5 women.
There are 9 men and 10 women, including Julia, who are trying out for a team.
The number of combinations for men
= (9 × 8 × 7 × 6 × 5)/(1 × 2 × 3 × 4 × 5)
=126.
The number of combinations for women
= (10 × 9 × 8 × 7 × 6)/(1 × 2 × 3 × 4 × 5)
=252.
The number of the possible team would include Julia
(126 × 252) = 31,752.
Learn more about combinations;
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May someone please help I will give 30 points to who can answer fully, no download scam link either
Answers
We can write equations by rewriting the important phrases of information using variables. These variables make the equation look neater and it is faster to write a letter instead of constantly repeating 'cost of student tickets', for example.
The important pieces of information lies in the second last sentence of this question.
the tickets of your friend, her mom and her little sister costs a total of $23the tickets of 2 adults and 3 students costs a total of $39Now, let's rewrite them into equations.
Given
x= cost of adult tickets
y= cost of student tickets
Assuming that your friend and her little sister are students, the two equations are:
x +2y= 23 -----(1)2x +3y= 39 -----(2)To convert these equations into slope-intercept form, move all the terms that are not y to the right-hand side of the equation before dividing both sides by the coefficient of y. This is to ensure that the coefficient of y is 1 and that your equation is in y= mx +c, where m is the slope and c is the y-intercept.
From equation (1):
x +2y= 23
2y= -x +23
Divide both sides by 2:
[tex]\bf{y = - \frac{1}{2} x + \frac{23}{2} }[/tex]
From equation (2):
2x +3y= 39
3y= -2x +39
Divide both sides by 3:
[tex]\bf{y= - \frac{2}{3} x + 13}[/tex]
The solution to the system of equations is the point at which the two lines intercept on the graph. I have attached the graph as an image.
The solution is (9, 7).
The x coordinate is the cost of an adult ticket, while the y coordinate is the cost of a student ticket. This means that adult tickets cost $9 and student/ child tickets cost $7.
What is the average rate of change for this quadratic function for the interval from x = 2 to x = 4? O A. -12 B. 12 C. -6 O D. 6
Answers
D. 6.
We have been given graph of a function. We are asked to find the average rate of change of our given function for the interval from [tex]x=-4[/tex] to [tex]x=-2[/tex].
We will use formula [tex]Average[/tex] [tex]rate[/tex] [tex]of[/tex] [tex]change[/tex] [tex]=\frac{f(b)-f(a)}{b-a}[/tex] to solve our given problem.
[tex]Average[/tex] [tex]rate[/tex] [tex]of[/tex] [tex]change[/tex] [tex]=\frac{f(-2)-f(-4)}{-2--4}[/tex]
[tex]Average[/tex] [tex]rate[/tex] [tex]of[/tex] [tex]change[/tex] [tex]=\frac{6--6}{-2+4}[/tex]
[tex]Average[/tex] [tex]rate[/tex] [tex]of[/tex] [tex]change[/tex] [tex]=\frac{6+6}{2}[/tex]
[tex]Average[/tex] [tex]rate[/tex] [tex]of[/tex] [tex]change[/tex] [tex]=\frac{12}{2}[/tex]
[tex]Average[/tex] [tex]rate[/tex] [tex]of[/tex] [tex]change[/tex] [tex]=6[/tex]
Therefore, the average rate of change for our given function on given interval would be 6 and option B is the correct choice.
Answer:
6
Step-by-step explanation:
because i am in credit recovery and i had a test on it
PLEASE HELP!!! 30 POINTS!!!
Answers
Answer:
D. 16
Step-by-step explanation:
16 because 4 * 2 * 2= 16 there are 4 shirts and 2 pants so that is 8 combos and then two pairs of shoes so 16 combos. hope that helps.
Answer:
16 or 48
Step-by-step explanation:
i dont think this is the correct answer
radius
name 2 chords
diameter
center
central angle
intercepted Arc for Angle EFG
Answers
a
45°
I’m very confused on this please help me:)
Answers
Answer:
45 degrees
Step-by-step explanation:
Since this angle is a right angle (1/4 of a full circle, or 360 degrees) its angle is 90. Since one part of it is 45 degrees. A=90-45=45
What's 2/3 times 3/4?
Answers
Answer:
0.5
Step-by-step explanation:
Answer: 1/2 or 0.5
Step-by-step explanation:
attached the solution below for better understanding...
Hope that helps...
An object was launched from the ground. The graph below shows the path that the object took. Use the graph to answer questions 9-10. What is the domain and range?
Answers
Using the concepts of domain and range, it is found that for the function given in the graph:
The domain is [0, 4].The range is [0,64].What are the domain and the range of a function?The domain of a function is the set that contains all the values of the input. In a graph, it is the set that contains the values of the horizontal axis.The range of a function is the set that contains all the values of the output. In a graph, it is the set that contains the values of the vertical axis.The graph in this problem gives the height of a projectile after t seconds, hence:
The domain is [0, 4].The range is [0,64].More can be learned about the domain and range of a function at https://brainly.com/question/10891721
You and your younger sister (who weighs half as much you do) are at a skating rink. You are both wearing roller skates and are facing each other. What will happen to your and your sister's motion if you push against each other
You move forward and your sister moves backward at a faster rate.
You both move forward, but you accelerate at a greater rate.
You move backward and your sister moves forward at a faster rate.
You both move backward but your sister accelerates at a greater rate
Answers
What will happen to you and your sister's motion if you push against each other Is; ( A ) You move forward and your sister moves backward at a faster rate.
Meaning of Force and MotionForce is the product of a mass and an acceleration due to gravity while Motion is a change in position with respect to time.Because you are bigger you will alter her movement by making her go in your direction. you impose more force on here which will make her go faster. But because of that collision, your force will reduce, thereby reucing your speed.
In conclusion the one with the higher mass have the greater force. Therefore What will happen to you and your sister's motion Is that You move forward and your sister moves backward at a faster rate.
Learn more about motion: https://brainly.com/question/453639
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The cost of a taxi ride is $2 per mile plus an initial charge of $2.75. Sean spent $26.75. Write an equation that represents the situation l. Solve to find the number of miles that Sean traveled.
Answers
x= 12
24+2.75 = 26.75
A bee colony produced 0.21 pounds of honey, but bears ate 0.01 pounds of it. How much honey remains?
Answers
Answer:0.20 pounds remain .0.21 minus 0.01 = 0.20
Answer:
0.20
Step-by-step explanation:
Choose all sequences of transformations that produce the same image of a given figure.
a reflection across the y-axis followed by a clockwise rotation 90° about the origin
a reflection across the y-axis followed by a counter-clockwise rotation 90° about the origin
a clockwise rotation 90° about the origin followed by a reflection across the x-axis
a counter-clockwise rotation 90° about the origin followed by a reflection across the y-axis
a reflection across the x-axis followed by a counter-clockwise rotation 90° about the origin
Answers
Answer:
a b
Step-by-step explanation:
Answer:
All of these transformations are equivalent to reflection across the line y=x:
A. a reflection across the y-axis followed by a clockwise rotation 90° about the origin
C. a clockwise rotation 90° about the origin followed by a reflection across the x-axis
D. a counter-clockwise rotation 90° about the origin followed by a reflection across the y-axis
E. a reflection across the x-axis followed by a counter-clockwise rotation 90° about the origin
Step-by-step explanation:
EDGE
10000 POINTS AND BRAINLIEST SHOW YOUR WORK!!!!!!!!!!
Answers
A) = 23.0 miles
B) 14.4 Miles
Step-by-step explanation:A) [tex]distance\ AD= x+y.\\ First\ find\ the\ value\ of\ x\ and\ z,\ then\ use\ the\ value\\ \\ yz\ to\ get\ the\ value\ of\ y\\ cos60\textdegree\ =\frac{21}{hy}=\frac{x}{10}[/tex][tex]sin60\textdegree\ =\frac{opp}{hyp}=\frac{z}{10}[/tex]
[tex]z=10\times sin60\textdegree =10\times 0.8660=8.66\ miles[/tex]
[tex]use\ pythagores\ theorem\ to\ get\ the\ value\ of\ y.\ l,e[/tex]
[tex]y=\sqrt{{20}^2-z^2}=\sqrt{{20}^2-{8.66}^2}=\sqrt{325.0044}[/tex]
[tex]=18.03\ miles[/tex]
[tex]\therefore\ distance\ AD=5+18.03[/tex]
[tex]=23.03\\ 23.0\ miles[/tex]
B) [tex]Ansween\ 14.4\ Miles[/tex][tex]< ABN=\varphi=30\textdegree\ \{Beary\ 4A\ from\ B=360\textdegree\ -60\textdegree\ =300\textdegree\}[/tex]
[tex]AB=y.[/tex]
[tex]\cos{\theta=\frac{ads}{h}p}\\ cos\ G\begin{matrix}0\\0\\\end{matrix}=\frac{x}{25}[/tex]
[tex]x=25\times cos\ 60\textdegree[/tex]
[tex]=12.5\ mle[/tex]
[tex]cos\ 30\textdegree=\frac{xe}{y}=\frac{12.5}{y}[/tex]
[tex]\because\ y=\frac{12.5}{cos\ 30\textdegree}[/tex]
[tex]=14.Fmm'_\mathcal{i}(es[/tex]
I hope this helps you
:)
Find the degree you of this polynomial
-8x 4 squared
Answers
Simplify
x + x + y * y
Answers
Answer:
2x+y²
Step-by-step explanation:
add the similar terms. since x and x is similar so it'd be
2x + y * y
notice that y and y is also similar so y times y would become
2x+y^2 will be the final answer
I need number 2 answered ASAP please!!!
Answers
Answer:
125 kg
Step-by-step explanation:
500 kg * 25 % =
500 * .25 = 125 kg
Answer:
125 kg
Step-by-step explanation:
500/100 × 25 = 125
..........
Factor x3 – 7x2 – 5x 35 by grouping. what is the resulting expression? (x2 – 7)(x – 5) (x2 – 7)(x 5) (x2 – 5)(x – 7) (x2 5)(x – 7)
Answers
The factored expression ofx^3 - 7x^2 -5x +35 is (x^2 - 5)(x - 7)
What is an expression?An expression is an algebraic term used for a mathematical statement that includes addition subtraction multiplication and division
x^3 – 7x^2 – 5x + 35
factor the given equation
x^2(x – 7) – 5(x - 7)
Factor out x - 7
(x^2 - 5)(x - 7)
Therefore, the factored expression is (x^2 - 5)(x - 7)
To learn more about the factored expression visit:
https://brainly.com/question/723406
Answer:
c. (x^2 - 5)(x - 7)
Step-by-step explanation:
c. (x^2 - 5)(x - 7)
Which linear function has the greatest rate of change?
Answers
Answer:
D
Step-by-step explanation:
The rate of chnage is the same as the slope.
Slope is x/y. How many y increases/decreases per increase of 1 x
slope for A is
2/500 every 2 x increase, y goes up by 500.
slope for B is
2/500 every 2 x increase, y goes up by 600-100 = 500
slope for C is
1/250
slope for D is
756/3
The greatest one out of these options is D, 756/3
WORTH A LOT OF POINTS. PLEASE HELP THANKSSSSSS!!!!!!!!!!
There is an error in the solution. Identify the error, then solve the problem correctly.
Answers
Problem 1
The error happens on the third step. The result should be 47 degrees (approximately). Refer to the steps below to see how I got that value.
[tex]\frac{\sin x}{7} = \frac{\sin 110^{\circ}}{9}\\\\\sin x = \frac{7*\sin 110^{\circ}}{9}\\\\\sin x \approx 0.73087203838903\\\\x \approx \sin^{-1}(0.73087203838903)\\\\x \approx 46.9595500055922^{\circ}\\\\x \approx 47^{\circ}\\\\[/tex]
Make sure your calculator is in degree mode.
If I had to guess where the [tex]m\angle \text{x} = 73^{\circ}[/tex] mistakenly came from, it's probably from the 0.73 shown on step 3, but the student somehow lost the decimal point out front.
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Problem 2
The error happens on step 1. The sin(120) should be over top the 35 because the 120 degree angle is opposite the side length of 35.
Similarly, the sin(50) should be over the x
Each fraction involves the angle with its paired opposite side, and vice versa.
Here's one way to write the correct steps to find x.
[tex]\frac{\sin(120)}{35} = \frac{\sin(50)}{x}\\\\x\sin(120) = 35\sin(50)\\\\x = \frac{35\sin(50)}{\sin(120)}\\\\x \approx 30.9593175812171\\\\x \approx 30.96\\\\[/tex]
What is the summation notation for the geometric series 5 10 20 40 80?
Answers
The summation notation for the geometric series will be expressed as [tex]\sum5(-2)^{n-1}\\[/tex]
Series and sequencesSeries are sum of sequences
Given the following alternating series as shown:
5 - 10 + 20 - 40 + 80
The series is geometrc series with the following parameters
First term "a" =5
ratio= -10/5 = 20/-10 = -2
Since the nth term of geometric sequence is expressed as:
Tn = ar^n-1
Tn =5(-2)^n-1
Hence the summation notation for the geometric series will be expressed as [tex]\sum5(-2)^{n-1}\\[/tex]
Learn more on geometric series here: https://brainly.com/question/24643676
Answer:
A
Step-by-step explanation:
Can someone help me I don’t understand how to do this
Answers
Step-by-step explanation:
how is water used in this place write a brief explanation of the answer sheet
Answer:
1: x = 93, verticle, congruent
2: x=135 or 85, same side exterior
3: x=103, alternate interior
4: x=108
5: m<1=m<5, m<3=m<7, m<4=m<12, m<11=m<15, m<7, m<16=m<12
What is the completely factored form of x4 + 8x2 – 9?
(x + 1)(x – 1)(x + 3)(x + 3)
(x + 1) (x minus 1) (x squared + 9)
(x2 – 1)(x + 3)(x – 3)
(x + 1)(x + 1)(x + 3)(x + 3)
Answers
Answer:
Hope that the payment picture will help you.Please mark me brilliant
Answer:
Its B
Step-by-step explanation: on edg 2022
If in total I have 166 students and 32 of them surf, what is their percentage?
Answers
32/166 = 16/83
Converting into a decimal, we get:
0.19, which is 19%. Hope this helps