This figure shows three identical spherical billiard balls of diameter 6 cm inside an equilateral triangular frame.
Work out the perimeter of the frame, leaving your answer
in surd form.
Answers
Answer:
Perimeter = 18(1 + √3 ) cm
Step-by-step explanation:
The radius of each ball = 1/2 * 6 = 3 cm.
Lines drawn from the 2 points of contact for one billiard ball to the center of the ball are at right angles to the sides of the triangle ( Tangent/radius theorem).
If we now draw a line from the vertex of the big triangle to the center of the ball we get 2 right triangles, and they are 30-60-90 triangles.
If the adjacent side of a triangle ( which is part of the side of the big triangle) = x:
tan 30 = 3 / x
x = 3 / tan 30
= 3 / 1/√3
= 3√3 cm.
There are 6 of these sides in the big triangle so their total length =
18√3 cm.
The three 'middle' sides joining 2 billiard balls each have a length of 2 radii = 6 cms ( as they form a rectangle with the radii of 2 billiard balls).
So the perimeter of the triangle = 18√3 + 3(6)
= 18(1 + √3 ) cm
I would have liked to transfer a diagram but I can't get to copy it to this site.
Related Questions
pls help me find all missing sides and angles. ;-;
Answers
Answer:
see explanation
Step-by-step explanation:
the sum of the 3 angles in the triangle = 180° , then
∠ BAC + 51° + 90° = 180°
∠ BAC + 141° = 180° ( subtract 141° from both sides )
∠ BAC = 39°
using the tangent ratio in the right triangle
tan51° = [tex]\frac{opposite}{adjacent }[/tex] = [tex]\frac{AC}{BC}[/tex] = [tex]\frac{AC}{12.8}[/tex] ( multiply both sides by 12.8 )
12.8 × tan51° = AC , then
AC ≈ 15.8 ( to 1 dec. place )
using the cosine ratio in the right triangle
cos51° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{BC}{AB}[/tex] = [tex]\frac{12.8}{AB}[/tex] ( multiply both sides by AB )
AB × cos51° = 12.8 ( divide both sides by cos51° )
AB = [tex]\frac{12.8}{cos51}[/tex] ≈ 20.3 ( to 1 dec. place )
Graph the function g(x)=−[tex]\frac{1}{3}[/tex](x+2)(x+8)
Answers
Answer:
Step-by-step explanation:
Comment
If you do not have a graphing calculator the best thing to use is Desmos. Desmos is free -- anyone can use it and and the graphs can be used here on Brainly. I've downloaded the graph for you.
There are a couple of things you should notice.
The most downward point is (-5,-3)
The largest root is x = -2
The smallest root is x = - 8
Notice the roots are the opposite of what you are given. You will eventually learn how to do all of these things.
HELP! need help ASAP, 50 points and brainiest will be given to whoever helps.
Solve for x:
Answers
Answer:
12
Step-by-step explanation
Which of these tables does NOT represent a function?
Answers
Helpppp meeeeee pleaseeeee
Answers
Answer:
C. 54 tens
Step-by-step explanation:
54×10=540
54tens=540
Answer:
54 tens
Step-by-step explanation:
This is like regular multiplication, sort of.
54 x 10= 540
540=54
A meteorologist predicts that there is a 42% chance of rain on Saturday and a 54% chance of rain on Sunday.
Use the meteorologist's predictions to enter the probability that it will not rain on both Saturday and Sunday. Write your answer as a percent and round it to the nearest whole number.
Answers
Pleaseeee helplpppppp
Answers
Answer:
Step-by-step explanation:
PLEASE HELP NEED TO PASS
Answers
Answer:
The second answer
Step-by-step explanation:
Answer:
-3 ± √41
Step-by-step explanation:
Numerator of Quadratic Formula
-b ± √b² - 4aca = 2b = 3c = -4⇒ -3 ± √(-3)² + 4(2)(-4)
⇒ -3 ± √9 + 32
⇒ -3 ± √41
Give the following number
in Base 10.
E16 = [?]10
Enter the number that belongs in the green box.
Answers
Answer:
14
Step-by-step explanation:
A hexadecimal (base 16) number can have any of 16 digits. Conventionally, digits 0–9 are used, along with letters A–F. The letters are assigned the values ...
A = 10
B = 11
C = 12
D = 13
E = 14
F = 15
Find the surface area of the cylinder. Use 3.14 for $\pi$ .
a can with a radius of 60 millimeters and a height of 160 millimeters
Answers
A can with a radius of 60 mm and a height of 160 mm. Then the surface area of the cylinder will be 1808640 mm³.
How do find the lateral surface area of a cylinder?The lateral surface area of a cylinder is also called the curved surface area of the cylinder.
Suppose that:
Radius of the considered cylinder = 'r' units
Height of the considered cylinder = 'h' units
Then, the lateral surface area of that cylinder is:
SA = πr²h
A can with a radius of 60 mm and a height of 160 mm. Then the surface area of the cylinder will be
SA = π x (60)² x 160
SA = 3.14 x 3600 x 160
SA = 1808640 mm³
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please solve this problem using the pythagorean theorem, and give me the right answer and I will give you brainliest. :)
Answers
Answer:
6.5
Step-by-step explanation:
9.1^2-6.4^2 is 41.85
square root of that is 6.469...
Kyle buys a car for $58,000. His car immediately starts depreciating, losing 23% of its value every year. How much will the car be worth in 12 years?
Answers
The depreciated value of the car after 12 years that Kyle buys for $58,000 today, which declines 23% annually, will be $2,520.
What is depreciation?Depreciation is the reduction or decrease in the value of an asset over time.
Depreciation occurs because an asset is put to use, and undergoes wear and tear.
The current price of the car = $58,000
The annual depreciation rate = 23%
The depreciated value after one year = 0.77 (1 - 23%)
Let the number of years of depreciation = x
The worth of the car after 12 years = 58,000 x 0.77^x
= 58,000 x 0.77^12
= 58,000 x 0.04344
= $2,519.52
= $2,520
The car's depreciated value can be modeled by the exponential function (decay) abˣ, which yields $2,520 in this situation.
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Freida has 12 red apples and 15 green apples. She is going to share the apples equally among 8 people and keep any extra apples for herself. How many apples will Freida keep for herself?
Answers
Answer: 3 apples
Step-by-step explanation:
Given:
12 red apples
15 green apples
8 people
Freida
..............................................................................................................................................
12 + 15 = 27
Since she is going to give the apples equally among 8 people,
27 / 8 = 3 remainder 3
Each of the 8 people will get 3 apples each.
Freida will get the remaining 3 apples.
(A-5)² + (B- 3)² = 18 B=A-2 A = ?, B = ?
Answers
Answer:
A = 8 and B = 6
Step-by-step explanation:
Since (B = A - 2), we can substitute (A - 2) in for the "B" variable in the first equation to isolate "A".
(A - 5)² + (B - 3)² = 18 -----> Original equation
(A - 5)² + ((A - 2) - 3)² = 18 -----> Plug in B = A - 2
(A - 5)² + (A - 5)² = 18 -----> Subtract
(A² - 10A + 25) + (A² - 10A + 25) = 18 -----> Expand parentheses
2A² - 20A + 50 = 18 ------> Add like terms
2A² - 20A + 32 = 0 -----> Subtract 18 from both sides
2(A² - 10A + 16) = 0 -----> Remove common factor
2(A - 2)(A - 8) = 0 -----> Factor within parentheses
A = 2 -----> Find A - 2 = 0
A = 8 -----> Find A - 8 = 0
Since "A" gave two possible values, we need to plug them into both equations to see which value gives reasonable "B" values.
When A = 2:
B = A - 2 -----> Original equation
B = 2 - 2 -----> Plug in A = 2
B = 0 -----> Subtract
(A - 5)² + (B - 3)² = 18 -----> Original equation
(2 - 5)² + (B - 3)² = 18 ------> Plug in A = 2
(-3)² + (B - 3)² = 18 -----> Subtract within first parentheses
9 + (B - 3)² = 18 -----> Square value within first parentheses
(B - 3)² = 9 -----> Subtract 9 from both sides
B - 3 = 3 -----> Take square root of both sides
B = 6 -----> Add 3 to both sides
When A = 8:
B = A - 2 -----> Original equation
B = 8 - 2 -----> Plug in A = 8
B = 6 -----> Subtract
(A - 5)² + (B - 3)² = 18 -----> Original equation
(8 - 5)² + (B - 3)² = 18 ------> Plug in A = 8
(3)² + (B - 3)² = 18 -----> Subtract within first parentheses
9 + (B - 3)² = 18 -----> Square value within first parentheses
(B - 3)² = 9 -----> Subtract 9 from both sides
B - 3 = 3 -----> Take square root of both sides
B = 6 -----> Add 3 to both sides
As you can see, when A = 2, there are two possible values of "B" depending on the equation. However, when A = 8, both equations give a "B" value of B = 6. Therefore, A = 8 and B = 6 are the answers.
A mining company has identified a mineral layer below ground.
The mining company wishes to drill down to reach the mineral layer and mode
situation as follows.
With respect to a fixed origin O,
• the ground is modelled as a horizontal plane with equation z = 0
• the mineral layer is modelled as part of the plane containing the points
A(10, 5, -50), B(15, 30, -45) and C(-5, 20, -60), where the units are in
(a) Determine an equation for the plane containing A, B and C, giving your ans
the form r.n=d
Answers
Answer:
90
bc i don't care about this
The equation of plane containing the points ABC is 13x+y-18z = 1035.
What is equation of plane?A plane in 3D coordinate space is determined by a point and a vector that is perpendicular to the plane. The equation of plane is defined as the position vectors and the Cartesian product of the vector perpendicular to the plane.
For the given situation,
The plane containing the points
A(10, 5, -50), B(15, 30, -45) and C(-5, 20, -60).
The equation of the plane in the form r.n=d can be represented as
[tex](r-a).[(b-a)[/tex] × [tex](c-a)]=0[/tex] ------ (1)
Let r = xi + yj +zk
a = 10i + 5j - 50k
b = 15i + 30j - 45k
c = -5i + 20j - 60k
[tex](r-a)=(x-10)i+(y-5)j+(z+50)k[/tex] ------- (2)
[tex](b-a)=(15-10)i+(30-5)j+(-45-(50))k[/tex]
⇒ [tex](b-a)=5i+25j+5k[/tex]
[tex](c-a)=(-5-10)i+(20-5)j+(-60-(50))k[/tex]
⇒ [tex](c-a)=-15i+15j-10k[/tex]
Now, [tex](b-a)[/tex] × [tex](c-a)[/tex]
⇒ [tex](5i+25j+5k)[/tex] × [tex](-15i+15j-10k)[/tex]
⇒ [tex]\begin{vmatrix}i&j&k\\5&25&5\\-15&15&-10\end{vmatrix}[/tex]
⇒ [tex]i(-250-75)-j(-50+75)+k(75+375)[/tex]
⇒ [tex]-325i-25j+450k[/tex] -------- (3)
Substitute all values in equation 1,
⇒ [tex][(x-10)i+(y-5)j+(z+50)k].[(-325i-25j+450k)]=0[/tex]
⇒ [tex]-325(x-10)-25(y-5)+450(z+50)=0[/tex]
⇒ [tex]-325x+3250-25y+125+450z+22500=0[/tex]
⇒ [tex]-325x-25y+450z=-22500-3250-125[/tex]
⇒ [tex]-325x-25y+450z=-25875[/tex]
On dividing by 25 and multiply with negative sign on both sides,
⇒ [tex]13x+y-18z=1035[/tex]
Hence we can conclude that the equation of plane containing the points ABC is 13x+y-18z = 1035.
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A bakery produces eight different kinds of pastry, one of which is eclairs. Assume there are at least twenty five pastries of each kind. Suppose the bakery has only ten eclairs but has at least twenty five of each of the other kinds of pastry. Suppose in addition to having only ten eclairs, the bakery has only eight napoleon slices. How many different selections of twenty five pastries are there
Answers
There are 142506 different selections of twenty-five pastries
How to determine the number of different selections?The given parameters are:
Pastry, n = 6Pastries to select, r = 25The number of different selections is calculated using:
[tex]C(n + r - 1,r) = \frac{(n + r - 1)!}{r!(n - 1)!}[/tex]
The above formula is used because repetitions are allowed.
So, we have:
[tex]C(6 + 25 - 1,25) = \frac{(6 + 25 - 1)!}{25!(6 - 1)!}[/tex]
Evaluate the sum and difference
[tex]C(30,25) = \frac{30!}{25!5!}[/tex]
Evaluate the expression
C(30,25) = 142506
Hence, there are 142506 different selections of twenty-five pastries
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In this figure, AB || CD and m/1 = 110°
A
1/2 B
4 3
What is mZ5?
5/6
8 7
Answers
Answer is 105 degrees.
Explanation:
Given two parallel lines AB and CD and a transversal cutting the two lines.
We know that when a transversal cuts two parallel line,
i) corresponding angles would be equal
ii) Interior angles total to 180
iii) alternate angles are equal.
In the picture given we have corresponding angles as
(2,6) . Hence angle 2 = angle 6.
Angle 6 = 75 (given)
Hence angle 2 =75.
Angles 1 and 2 are supplementary because they form a linear pair.
Hence angle 1 = 180-75
Angle 1 =105
The majority of Americans spend most of their income on:
housing.
A.food.
B.health care.
C.entertainment.
Answers
Please help with 6 and 7
Answers
Answer:
6. The number is [tex]-5[/tex]
7. The two numbers are [tex]10[/tex] and [tex]11[/tex]
Step-by-step explanation:
Question six can be re-worded to create the following expression:
[tex]-2=\frac{4x+10}{5}[/tex]
Solve for x to find the number:
[tex]-2=\frac{4x+10}{5}\\-10=4x+10\\-20=4x\\\frac{-20}{4} = x\\-5 = x[/tex]
Question seven can be solved by first listing the constraints (assuming x is smaller than y):
x and y are less than 20[tex]x + 1 = y[/tex][tex]3x - 8 = 2y[/tex]To get the numbers, we can create a system of linear equations. First, solve for [tex]y[/tex] in each expression:
[tex]y = x+1[/tex]
[tex]2y = 3x-8\\y = \frac{3}{2}x - 4[/tex]
Solve for [tex]x[/tex]:
[tex]x+ 1 = \frac{3}{2}x - 4\\x + 5 = \frac{3}{2}x\\5 = \frac{3}{2}x - x\\5 = \frac{1}{2}x\\10 = x[/tex]
Solve for [tex]y[/tex]:
[tex]y = x + 1\\y = 10 + 1\\y= 11[/tex]
Answer:
see explanation
Step-by-step explanation:
(6)
let n be the number then the sum of 4 times the number and 10 is 4n + 10
so
[tex]\frac{4n+10}{5}[/tex] = - 2 ( multiply both sides by 5 to clear the fraction )
4n + 10 = - 10 ( subtract 10 from both sides )
4n = - 20 ( divide both sides by 4 )
n = - 5
(7)
let the consecutive integers be n and n + 1 , then
3n = 2(n + 1) - 8 ← distribute parenthesis and simplify right side
3n = 2n + 2 - 8
3n = 2n - 6 ( subtract 2n from both sides )
n = - 6 and n + 1 = - 6 + 1 = - 5
the 2 integers are - 6 and - 5
If 25% of the people in a small town are voters and there are 2360 voters, what is the population of the town?
Answers
Answer:
x=11800
Step-by-step explanation:
make a proportion:
2360/.2=X/1
2360(1)=.2x
x=11800
I need help finding the value of x which is the base of a triangle.
Answers
Answer:
sqrt(13)
Step-by-step explanation:
The entire base is 4, so 1/2 of the base is 2
We can use the pythagorean theorem
a^2 = b^2 = c^2
2^2 + 3^2 = x^2
4+9 = x^2
13 = x^2
Taking the square root of each side
sqrt(13) = x
Check the picture below.
GIVE A GOOD DETAILED AND ORIGINAL ANSWER FOR BRAINLIEST
Question 3(Multiple Choice Worth 5 points)
(08.03 MC)
The two dot plots below compare the forearm lengths of two groups of schoolchildren:
Two dot plots are shown one below the other. The title for the top dot plot is Forearm Length, Group A and the title for the bottom plot is Forearm Length, Group B. Below the line for each dot plot is written Length followed by inches in parentheses. There are markings from 11 to 14 on each line at intervals of one. For the top line there are 3 dots above the second mark, 4 dots above the third mark, and 3 dots above the fourth mark. For the bottom line there are 3 dots above the first mark, 5 dots above the second mark, and 2 dots above the third mark.
Based on visual inspection of the dot plots, which group appears to have the longer average forearm length?
Group B, because three children in the group have the least forearm length of 11 inches
Group A, because three children in the group have the least forearm length of 11 inches
Group A, because seven children have a forearm length longer than 12 inches
Group B, because two children have a forearm length longer than 12 inches
Answers
Using the dot plot, the correct option regarding the group that appears to have the longer average forearm length is:
Group A, because seven children have a forearm length longer than 12 inches
What does a dot plot show?A dot plot shows the number of times each measure appears in the data-set.
In this problem, Group A has 3 students with forearm length of 14 inches, while group B have none. Group A also has more students with forearm length of 13 inches, and less of 11 and 12(lower values). Hence the correct option is given by:
Group A, because seven children have a forearm length longer than 12 inches.
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Solve -3(x - 4) > -2x + 5
Answers
Answer:
x<7
Step-by-step explanation:
-3(x - 4) > -2x + 5 Distribute
-3x+12>-2x+5 Subtract 12 from both sides
-3x>-2x-7 Add 2 to both sides
-5x>-7 Simplify
x<7
Answer:
x < 7.
Step-by-step explanation:
-3(x - 4) > -2x + 5
-3x + 12 > -2x + 5
-3x + 2x > 5 - 12
-x > -7 Note: we divide by -1 so the sign flips:
x < 7.
List all of the factors of 78. (Type the factors in numeric order from smallest to largest. Separate each factor with a comma and a space after the comma.)
Answers
Answer:
1, 2, 3, 6, 13, 26, 39, 78
Step-by-step explanation:
The factors of a number are the numbers that "go into" 78 "evenly" that is, without a remainder. You can make a factor tree or divide to find the prime factors. Any combination "goes into" 78. That's why we'll include 6 and 26 on this list.
1×78
2×39
3×26
6×13
all make 78!
Find the area of the kite
Answers
Answer:
180
Step-by-step explanation:
(10×11)+(10×7)=110+70
The area of the kite is expressed as 1/2 × (Product of its diagonals)
In this case, we have;
Diagonal₁ - 10 + 10 feet = 20 feetDiagonal₂ - 7 + 11 feet = 18 feetTherefore, when we substitute the diagonals in the formula, we get;
⇒ 1/2 × (Product of its diagonals)⇒ 1/2 × (20 × 18)When simplified, we get;
⇒ 1/2 × (20 × 18)⇒ 1/2 × (360)⇒ 360/2 = 180 ft²Therefore, the area of the kite is 180 ft².
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Please belpppp don’t understand
Answers
Answer:
[tex]\huge 3w^2\sqrt[4]{2\:w^{3}}[/tex]
Step-by-step explanation:
[tex]\huge\sqrt[4]{162\:w^{11}}[/tex][tex]=\huge\sqrt[4]{81*2\:w^{8}*w^{3}}[/tex][tex]=\huge\sqrt[4]{3^4*2\:(w^{2})^4*w^{3}}[/tex][tex]=\huge 3w^2\sqrt[4]{2\:w^{3}}[/tex] (Elements with power 4 within the radical will come out and the rest will be within the radical sign)which is closer to 12? 11.96 or 12.0321
Answers
Answer:The answer is 12.0321
Step-by-step explanation:
This is the answer because I’m order to get to 12 from 11.96, you would have to go up .4 and to go back to 12 from 12.321 it would be less then .4
An animal shelter had 45 animals adopted over one week. The ratio of dogs to ferrets was 5:1. The ratio of cats to dogs was 9:5.
Select the diagrams that would represent the types of animals adopted.
How many of each type of animals were adopted?
Answers
There are total 15 dogs, 27 cats, and 3 ferrets were adopted if the ratio of dogs to ferrets was 5:1. The ratio of cats to dogs was 9:5.
What is the ratio?It is described as the comparison of two quantities to determine how many times one obtains the other. The proportion can be expressed as a fraction or as a sign: between two integers.
We have:
An animal shelter had 45 animals adopted over one week. The ratio of dogs to ferrets was 5:1. The ratio of cats to dogs was 9:5.
Combine ratio dogs:ferrets:cats = 5:1:9
Let's suppose the number of ferrets is x then:
5x + x + 9x = 45
15x = 45
x = 3
Ferrets x = 3
Dogs = 5x = 5(3) = 15
Cats = 9x = 9(3) = 27
Thus, there are total 15 dogs, 27 cats, and 3 ferrets were adopted if the ratio of dogs to ferrets was 5:1. The ratio of cats to dogs was 9:5.
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The rule is "Star, Circle, Heart."What is the
17th shape?
Answers
Answer:
Circle
Step-by-step explanation:
I'm a bit stuck, I need help
Answers
Let's consider all the trig identities, to help us with the problem:
⇒ (look at the attached image for help with that)
After looking at all the trig identity, let's look at the problem given to us:
⇒ cos(θ) = [tex]\frac{5}{13}[/tex]
⇒ we know that sec(θ) = 1 / cos(θ) = 1 / (5/13) = 13/5
Thus: sec(θ) = 13/5, which just so happens to be Choice (D)
Answer: sec(θ) = 13/5 or Choice (D)
Hope that helps!