Answer:
he correct answer is D. 12 adult tickets, 4 child ticket
Step-by-step explanation:
An equilateral triangle with side lengths of 8. 7 centimeters is shown. An apothem has a length of a and the radius has a length of 5 centimeters. The apothem and radius form a triangle with a base length of b. Which statements about finding the area of the equilateral triangle are true? Select three options. The apothem can be found using the Pythagorean theorem. The apothem can be found using the tangent ratio. The perimeter of the equilateral triangle is 15 cm. The length of the apothem is approximately 2. 5 cm. The area of the equilateral triangle is approximately 65 cm2.
The image of the triangle is missing, so i have attached it.
Also, the options are;
A) The apothem can be found using the Pythagorean theorem.
B) The apothem can be found using the tangent ratio.
C) The perimeter of the equilateral triangle is 15 cm.
D) The length of the apothem is approximately 2.5 cm.
E) The area of the equilateral triangle is approximately 65 cm².
Answer:
Options A, B & D are true
Step-by-step explanation:
A) We are told that the triangle is an equilateral triangle.
Thus, the 3 sides equal 8.7 cm.
Now from the image, b is half of one of the sides.
Thus, b = 8.7/2 = 4.35 cm
Now, we want to find the apothem "a".
Using Pythagoras theorem, we have;
a² + 4.35² = 5²
a² = 25 - 18.9225
a² = 6.0775
a = √6.0775
a ≈ 2.5 cm.
Thus, option A is true as Pythagoras theorem was able to calculate the apothem "a"
B) since the main triangle is equilateral, it means each angle is 60°.
Now, the radius line from one corner point to the center will divide the 60° angle into 2 equal parts.
Thus, the angle made by the radius line with the base of the triangle is 60/2 = 30°
Now, from tangent ratios, we know that;
Opposite/Adjacent = tan θ
In the small triangle, opposite is apothem "a" while adjacent is b = 4.35 cm
Thus;
a/4.35 = tan 30
a = 4.35 tan 30
a ≈ 2.5 cm.
Thus, option B is correct as Tangent ratio can be used to find the apothem
C) The perimeter of equilateral triangle = 3x
Where x is length of one side.
One side is 8.7 cm
Thus, perimeter = 3 × 8.7 = 26.1 cm
Thus option C is not correct.
D) From calculations above, we saw that in both options A & B, the apothem is approximately 2.5 cm.
Thus, option D is true.
E) Area of triangle is;
A = ½ × base × height
Base = 8.7 cm
To get height, we will use trigonometric ratio. Thus;
h/8.7 = sin 60°
h = 8.7 sin 60°
Thus;
A = ½ × 8.7 × 8.7 sin 60°
A = 32.77 cm²
Thus is not equal to 65 cm². Thus, option E is not correct.
The statements that are true for the considered equilateral triangle are:
Option A: The apothem can be found using the Pythagorean theorem.Option B: The apothem can be found using the tangent ratio.Option D: The length of the apothem is approximately 2. 5 cm.For a regular polygon, the apothem is the line segment from the center of the polygon to the mid of one of the sides of the considered polygon.
For this case, referring to the figure attached below, we have:
Length of the apothem = x (assume)The triangle ABC is equilateralLength of line segment from vertex to center (radius) = 5 cmLength of each side of the triangle = 8.7 cmSince the triangle is equilateral, there can be 6 congruent triangles like BOD.
Thus, Area of triangle ABC = 6 × Area of triangle BOD
Area of BOD = [tex]\dfrac{1}{2} \times x \times 4.35 = 2.175x \: \rm cm^2[/tex]
Area of ABC = [tex]6 \times 2.175x = 13.05x \: \rm cm^2[/tex]
The length of the apothem is x cm, and can be obtained by using Pythagoras theorem.
We can also use the tangent ratio as the line segment BO is bisecting the internal angle B (each internal angle is of 60 degrees in an equilateral triangle), so angle OBD is of 60/2 = 30 degrees. So using angle and the fact that tangent ratio is ratio of side opposite to angle and the remaining adjacent side(not hypotenuse).
[tex]tan(30^\circ) = x/4.35 \implies x = 4.35 \times \tan(30^\circ) \approx 2.5 \: \rm cm[/tex]
Using Pythagoras theorem too, we can get the value of x as:
[tex]5^2 = 4.35^2 + x^2\\x = \sqrt{25 - 18.9225} \approx 2.465 \: \rm cm \approx 2.5 cm[/tex]
Thus, area of the equilateral triangle ≈ [tex]13.05 \times x \approx 13.05 \times 2.5 = 32.575 \: \rm cm^2[/tex]
This isn't 65 sq. cm.
Thus, the statements that are true for the considered equilateral triangle are:
Option A: The apothem can be found using the Pythagorean theorem.Option B: The apothem can be found using the tangent ratio.Option D: The length of the apothem is approximately 2. 5 cm.Learn more about tangent ratio here:
https://brainly.com/question/14169279
PLS HELP WILL GIVE BRAINLIEST
Answer:
y = 1/2x - 1
Step-by-step explanation:
The x value is divided by 2 and then has 1 subtracted from it.
also for future posts, put the question in the title that way people know what you need and can click if they know the answer.
What is the area of this quadrilateral(Please show a step by step process)
Answer:
40ft
Step-by-step explanation:
What you need to know is the formula for the air of a rectangle:
the long side * the short side.
First calculate the area of the rectangle in the middle: 3*8=24ft
Then we are left with two right-angled triangles, one on the left and one on the right. If we juxtapose them, we realize that it forms a rectangle whose large side measures 8 and the small 2 so 2*8=16ft.
Finally, just add the area of the middle rectangle with the area of our rectangle formed by the two triangles on the right and on the left. So 16+24=40ft
Harold got home from school at 3:50 P.M. and played video games for 1 hour and 5 minutes. Then, it took him 1 hour and 40 minutes to finish his homework. What time was it when Harold finished his homework?
Answer:
6:35.
Step-by-step explanation:
I start by adding the hours spent to the time leaving me with 5:50, I then add the 40 which brings it to 6:30 and the additional 5 minutes bringing the final answer to 6:35.
Answer:
6:35 PM
Step-by-step explanation:
When Harold got home, it was already 3:50 PM. Then he played games for an hour and five minutes. Adding on an hour, it made the time 4:50 PM, and then adding on the five minutes, made the time 4:55 PM. When he finished playing games, he took an hour and forty minutes to do his homework. 4:55 PM, adding on the hour makes it 5:55 PM, then adding the 40 minutes, makes it 6:45 PM.
- Educationist
A plane traveling with the wind travels 900 miles in 5 hours. the return trip is against the wind and takes 9 hours. find the rate of the plane in still air and the rate of the wind.
Using the relation between velocity, distance and time, it is found that:
The rate of the plane in still air is of 140 mph.The rate of the wind is of 40 mph.What is the relation between velocity, distance and time?Velocity is distance divided by time, that is:
[tex]v = \frac{d}{t}[/tex]
A plane traveling with the wind travels 900 miles in 5 hours, hence:
[tex]v_a + v_w = \frac{900}{5}[/tex]
[tex]v_a + v_w = 180[/tex]
The return trip is against the wind and takes 9 hours, hence:
[tex]v_a - v_w = \frac{900}{9}[/tex]
[tex]v_a - v_w = 100[/tex]
From the first equation, we have that:
[tex]v_w = 180 - v_a{/tex]
Replacing on the second:
[tex]v_a - v_w = 100[/tex]
[tex]v_a - 180 + v_a = 100[/tex]
[tex]2v_a = 280[/tex]
[tex]v_a = 140[/tex]
[tex]v_w = 180 - 140 = 40{/tex]
Hence:
The rate of the plane in still air is of 140 mph.The rate of the wind is of 40 mph.More can be learned about the relation between velocity, distance and time at https://brainly.com/question/24316569
A town has a population of 141,300 and grows at a rate of 5% every year. Which equation represents the town’s population after 6 years?
Answer:
P=141,300(1+0.05)^6
Step-by-step explanation:
r = rate = 5/100 = 0.05
a = starting amount = 141,300
t = time = 6 years
% growth formula:
a(1+r)^t
141,300(1.05)^6
Answer:
P=141,300(1+0.05)^6
Step-by-step explanation:
r = rate = 5/100 = 0.05
a = starting amount = 141,300
t = time = 6 years
% growth formula:
a(1+r)^t
141,300(1.05)^6
Please help ASAP
Dave is 8 years younger than 4 times Julia's age. If Dave is 16, how old is Julia?
6 years
24 years
32 years
O
56 years
Step-by-step explanation:
Age of dave = y
Age of Julia = x
y = 4x - 8
if y = 16
then
4x - 8 = 16
4x = 16 + 8
4x = 24
x = 24/4
x = 6
Julia is 6 years old
Answer:
Julia is 6 years old.
Step-by-step explanation:
Dave + 8 = 4 Julia
16 + 8 = 4 Julia
24 = 4 Julia
6 = Julia
Julia is 6 years old
Molly bought a large basket of 60 apples.
When she got home, she found 6 rotten
ones. If she goes back and buys 200 more
apples, how many rotten apples would she
expect there to be?
Answer:
approximately 14
Step-by-step explanation:
first find out how many sets of 60 there are
200/60=3.3
3.3 sets of 4 apples
but you can't have 2/3 of a rotten apple
so 3.5 sets of 4 rotten apples
4x3.5=14
i need help on this question
Answer:
1st question
Sry if its wrong xx
An angle measuring (870n)° is in standard position. for which value of n will the terminal side fall on the y-axis? n = 3 n = 4 n = 5 n = 6
The value of n will the terminal side fall on the y-axis at n=3
The terminal side of an angle fall along the positive portion of the y-axis,
If it can written in the form of [tex](90^0)a[/tex]
Where a = positive odd integer,
We hyave given the given angle is,
[tex](870n)^0,[/tex]
What is terminal side?The terminal side of an angle theta drawn in angle standard position is the side which isn't the initial side
Now for n=3
[tex](870(3))^0=2610^0[/tex]
The angle will be 2610°
Its terminal side fall along the positive portion of the y-axis,
[tex]2610^0 = (90^0)a \implies a = 29[/tex]......( Positive odd integer )
Therefore for n = 3, the terminal side of the angle (870n)° falls along the positive portion of the y-axis,
For n = 4,
Our angle will be 3480°
Its terminal side fall along the positive portion of the y-axis,
[tex]3480^0 = (90^0)a \implies a = 38.6667 ( Not possible )[/tex]
Therefore for n = 4, the terminal side of the angle (870n)° does not fall along the positive portion of the y-axis
Next is for n = 5,
Our angle will be 4350°
Its terminal side fall along the positive portion of the y-axis,
[tex]4350^0 = (90^0)a \implies a = 48.333.. ( Not possible )[/tex]
Thus, for n = 5, the terminal side of the angle (870n)° does not fall along the positive portion of the y-axis,
For n = 6,
Our angle will be 5220°
Its terminal side fall along the positive portion of the y-axis,
[tex]5220^0 = (90^0)a \implies a = 58..... ( Not possible )[/tex]
Thus, for n = 6, the terminal side of the angle (870n)° does not fall along the positive portion of the y-axis.
Therefore,the value of n will the terminal side fall on the y-axis at n=3.
To learn more about the terminal side visit:
https://brainly.com/question/24680641
Answer:
a
Step-by-step explanation:
x=3 on edge
Please help thank you
Answer:
Q = mCpΔT where Q is the energy in heat (joules), m is the mass (grams), Cp is the specific heat capacity (J/g/°C), and ΔT is the change in temperature (T2 - T1) in °C.
Step-by-step explanation:
So, since Q = mCpΔT then m = Q/(CpΔT) or (45.0)/(0.780•2.00) = 45/1.56 = 28.846 grams. Since there are 3 sig figs, we round to:
m = 28.8 g
Which is the algebraic representative for a rotation 180 degrees clockwise?
Answer:
algebraic expression for 180 degree clockwise rotation about the origin (x,y) → (-y, x) algebraic expression for 270 degree clockwise rotation about the origin equals a 270 degree counterclockwise rotation 90 degree clockwise rotation equals a 90 degree counterclockwise rotation
Step-by-step explanation:
hope this helps
have an awesome day -TJ
Write the expression. Then, check all that apply.
a number cubed increased by four
Answer: C and B
Step-by-step explanation: because its rational.
-LearnWithBrainly
A bag contains 16 blue marbles, 12 red marbles, and 12 green marbles.
If Malik randomly draws a marble from the bag (and puts it back) 25 times, how many times should he expect to pull a blue marble?
The random selection of a blue marble is an illustration of probability
You should expected to pull a blue marble 10 times
How to determine the expected blue marble?The given parameters are:
Blue = 16
Red = 12
Green = 12
The total number of marbles is:
Total = 16 + 12 + 12
So we have:
Total = 40
The probability of selecting a blue marble is:
[tex]P(Blue) = \frac{16}{40}[/tex]
When 25 marbles are selected, the expected number of blue is:
[tex]Blue = n * P(Blue)[/tex]
So, we have:
[tex]Blue = 25 * 16/40[/tex]
[tex]Blue = 10[/tex]
Hence, the expected number of blue marbles is 10
Read more about expected values at:
https://brainly.com/question/15858152
√2 x √27 use the properties of radicals to simplify
Answer: look at the image
Step-by-step explanation:
1 yards equals 3 feet in one mile equals 5280 feet how many yards are in 5 MI
Answer:
A conversion calculator gave me 8800
What is the area of this trapezoid?
Answer:
(b1+b2)h divided by 2 is the formula for a trapezoid
Step-by-step explanation:
ANSWER: 468 ft (squared?)
Billy invested $18 of savings in two major business enterprises which paid interest at the rate of 3% and 6%, respectively. If his annual income for these two enterprises was equivalent to a return of 5% on the entire investment, find how much he invested at 3%.
Answer:
$6
Step-by-step explanation:
System of equations
x+y = 18
0.03x+0.06y = 5% of 18 = 0.9
(0.03x+0.06y=0.9)*100 = 3x+6y=90
(3x+6y=90)÷3 = x+2y=30
Substract (1)-(2)
x+2y=30 ... (1)
x+y=18 ... (2)
y=12
x+12=18
x=6
Thanks.
1. What is the volume, in cubic feet, of a rectangular solid with a length of 12 feet, a width of
3 feet, and a height of 4 feet?
Answer: 144 Cubic Feet
Explanation: Multiply all of your numbers together to get your volume.
Numbers : Length(12) x Width(3) x Height(4) = 144 cubic feet.
I hope this helps you! :)
The area of a rectangular garden is 3927cm . If the width of the garden is 51 m , what is its length?
Answer:
77
Step-by-step explanation:
The area of a rectangle is A = lw. 'A', the area, is 3927, and 'w', the width, is 51. By substituting the values in, we get that 3927 = 51L. Dividing both sides by 51, we get that L, the length, is 77.
HELP ASAP I GIVE BIG BRAIN
Give one example of a relationship that IS a function and explain how you know (explain it as if you are talking to someone who has never heard of a function before). In ur own words please...
A function is a relation where there is only one output for every input. In other words for every x value, there is only one y value.
Example : Multiply by 3 is a very simple function.
Input : 0 Output : 0
Input : 1 Output : 3
Input : 2 Output : 6
Input : 3 Output :9
And so on!
Hope this helps!
Today only, a table is being sold for 134.40 . This is 32% of its regular price. What was the price yesterday?
Answer:
$177.41
Step-by-step explanation:
when it says 32% OF , of always means multiply in word problems so we multiple 132% (1.32) times 134.40
$177.41
Answer:
420
Step-by-step explanation:
32% of its original price
32%=134.40
100%=?
cross multiply
100/100 x 134.40 × 100/32
1×134.40×3.125
=420
hey, i'm kinda confused on how you do this again factories 3n+12
Answer:
we should take common first
3n+12
taking 3 common
3(n+4)
A company produces circular drink coasters. the equation x2 y2 = 18.0625, with units in inches, represents the size of a coaster. each coaster is cut from a square piece of cardboard. what is the minimum possible area of each cardboard piece? 4.25 in2 8.5 in2 18.0625 in2 72.25 in2
The minimum possible area of each square cardboard piece which is used to produce circular drink coasters is 72.25 in².
What is the equation of circle?The equation of the circle is the equation which is used to represent the circle in the algebraic equation form with the value of center point in the coordinate plane and measure of radius.
The standard form of the equation of the circle can be given as,
[tex](x-h)^2+(y-k)^2=r^2[/tex]
Here (h,k) is the center of the circle and (r) is the radius of the circle.
A company produces circular drink coasters. the equation which represents the size of a coaster is,
[tex]x^2+ y^2 = 18.0625[/tex]
The units are in the inches. This equation can be written as,
[tex]x^2+ y^2 = \dfrac{289}{16}\\x^2+ y^2 =\left( \dfrac{17}{4}\right)^2[/tex]
Compare it with the equation of the circle, we get,
[tex]h=0\\k=0\\r=\dfrac{17}{4}\rm\; in[/tex]
The radius of the circular coaster is 17/4. The diameter of it is,
[tex]d=2\times\dfrac{17}{4}\\d=\dfrac{17}{2}\rm \; in[/tex]
Now, each coaster is cut from a square piece of cardboard. The diameter of the circular coaster will be equal to the side of the square piece of cardboard.
[tex]a=d=\dfrac{17}{2}\rm\; in[/tex]
The area of the square is the square of its side. Thus, the area of a square piece of cardboard is,
[tex]A=a^2\\A=\left(\dfrac{17}{2}\right)^2\\A=72.25\rm\; in^2[/tex]
Thus, the minimum possible area of each square cardboard piece which is used to produce circular drink coasters is 72.25 in².
Learn more about the equation of circle here;
https://brainly.com/question/1506955
A surveyor determines that the angle of elevation between herself and the top of an observation tower is 60^o. She determines that the distance between her position and the base of the tower is 20 meters. Approximately how tall is the tower?
I NEED HELP ASAP!!!!!!!!!!!!!!!
Answer:
The one on the very top left corner is the right one.
Step-by-step explanation:
It shows the exact data that you were looking for: ten small apples were green and 3 out of the 12 large apples were red.
In a trapezoid the sum of the bases is 28 and the area is 84.
What is the altitude or height of the trapezoid?
Answer: If you sketch this out, you should be able to convince yourself that if you drew a line parallel to the bases and halfway between them, and a vertical at the end of that line, there would be an extra triangle on the longer base that would just fit into the space at the end of the shorter base, if you cut and pasted it.
You should also be able to convince yourself by what you know about similarity that the length of that parallel halfway line is just halfway between the lengths of the bases (you can add them and divide by two).
So your trapezoid (trapezium, we call ’em this side of the pond) has the same area as a rectangle with an altitude equal to the trapezoid’s and a width equal to the sum of those bases divided by two. And since you know about rectangles, you’re home and dry. I suggest you do the sketch, fill in the numbers, and then you’ve completed a model piece of homework that should earn full marks and the teacher’s approval.
Step-by-step explanation:
What is the value of x?
Answer:
I would say 30
Reasoning:
Because that thing your looking at is 180% degree angle and the other side is 90%. x is small it seems to be acute and I think 2x is about 60%.
If im incorrect im terribly sorry but at least my answer wasnt bad like the 1st guys
A rectangular red sticker has a perimeter of 40 millimeters and an area of 64 square
millimeters. What are the dimensions of the sticker?
millimeters by millimeters
Submit
Answer:
16 x 4.
Step-by-step explanation:
What multiplies into 64?
could be 16 and 4?
16 x 2 = 32
4 x 2 = 8
32 + 8 = 40, therefore, this is correct.
Determine if the following system of equations has no solutions 4x+3y= -8 -8x-6y= 16
[tex]\begin{cases} 4x+3y=-8\\\\ -8x-6y=16 \end{cases}~\hspace{10em} \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array} \\\\[-0.35em] ~\dotfill[/tex]
[tex]4x+3y=-8\implies 3y=-4x-8\implies y=\cfrac{-4x-8}{3}\implies y=\stackrel{\stackrel{m}{\downarrow }}{-\cfrac{4}{3}} x-\cfrac{8}{3} \\\\[-0.35em] ~\dotfill\\\\ -8x-6y=16\implies -6y=8x+16\implies y=\cfrac{8x+16}{-6} \\\\\\ y=\cfrac{8}{-6}x+\cfrac{16}{-6}\implies y=\stackrel{\stackrel{m}{\downarrow }}{-\cfrac{4}{3}} x-\cfrac{8}{3}[/tex]
one simple way to tell if both equations do ever meet or have a solution is by checking their slope, notice in this case the slopes are the same for both, meaning the lines are parallel lines, however, notice both equations are really the same, namely the 2nd equation is really the 1st one in disguise.
since both equations are equal, their graph will be of one line pancaked on top of the other, and the solutions is where they meet, hell, they meet everywhere since one is on top of the other, so infinitely many solutions.