Answer:
Lateral surface area of cone is 1580 feet²Surface area of cone is 2287 feet²[tex]\\[/tex]
Step-by-step explanation:
Given that Height of cone shaped roof is 30 ft and radius is 15 ft.
To calculate the lateral surface area and Surface area of the cone we will use the formula given below:
[tex]\\[/tex]
[tex]\star \: { \underline { \boxed { \purple{ \pmb { \sf{Lateral \: surface \: Area _{(cone)} = \pi rl}}}}}}[/tex]
[tex]\\[/tex]
[tex]\star{\underline{ \boxed{ \purple{ \pmb { \sf{Surface \: area _{(cone)} = \pi rl + \pi {r}^{2} }}}}}}[/tex]
[tex]\\[/tex]
Finding the Slant height of the cone:
[tex]\dashrightarrow \: \:L = \sqrt{ {(r)}^{2} + {(h)}^{2} } \\ [/tex]
[tex] \dashrightarrow \: \: L = \sqrt{225 +900 } \\ [/tex]
[tex] \dashrightarrow \: \: L = \sqrt{1125 } \\ [/tex]
[tex]{ \dashrightarrow \: \: { \pink{ \boxed { \: L = 33.541 }}}}\\ [/tex]
Hence, Slant height of cone is 33.54 feet.Substituting values in above formula:
[tex]\dashrightarrow \: \: LSA = \pi rl \\ [/tex]
[tex]\dashrightarrow \: \: LSA = \dfrac{22}{7} \times 15 \times 33.54 \\ [/tex]
[tex]\dashrightarrow \: \: LSA = \dfrac{22 \times 15 \times 33054}{7} \\ [/tex]
[tex]\dashrightarrow \: \: LSA = \dfrac{11068.2}{7} \\ [/tex]
[tex]\dashrightarrow \: \:{ \boxed { \pmb{ \sf {\pink{ LSA \: \approx1580 \: {ft}^{2}}}} }} \\ [/tex]
[tex]\\[/tex]
Hence, Lateral surface area of cone is 1580 feet²
Now, Calculating surface area:
[tex]\dashrightarrow \: \:SA = \pi rl + \pi {r}^{2} \\ [/tex]
[tex]\dashrightarrow \: \:SA = \pi (15)(33.54) + \pi {(15)}^{2} \\ [/tex]
[tex]\dashrightarrow \: \:SA = \pi(503.1) + 22 5 \pi \\ [/tex]
[tex]\dashrightarrow \: \: SA = 728.1 \pi \\ [/tex]
[tex]\dashrightarrow \: \:SA = 728.1 \times 3.14 \\ [/tex]
[tex]\dashrightarrow \: \:{ \boxed{ \pmb{ \pink{ \sf{SA \approx2287 \: {ft}^{2} }}}}} [/tex]
[tex]\\[/tex]
Hence, surface area of cone is 2287 feet²Find the highest common factor (HCF) of 270 and 450.
Answer:
HCF = 90
Step-by-step explanation:
Hope it Helps!!!
l need help with this pls
Answer:
50°
Step-by-step explanation:
In a parallelogram opposite angles have the same measure. Angle ABC has then the same measure of angle ADC, which is 38°+12°=50°
Fatima has 3 packs of batteries. Each pack contains 4 batteries. She gives her brother 8 batteries to put in his toy robot.
Let b represent the number of batteries Fatima has left.
Which equation could be used to find the value of b?
3×4−8=b
3+4−8=b
3 × 4 + 8 = b
3 + 4 + 8 = b
Using a system of equations, it is found that the equation that could be used to find the value of b is given by:
3×4−8=b
What is a system of equations?A system of equations is when two or more variables are related, and equations are built to find the values of each variable.
Fatima has 3 packs of batteries. Each pack contains 4 batteries, hence:
b = 3 x 4
She gives her brother 8 batteries to put in his toy robot, hence:
b = 3 x 4 - 8
Which means that the first expression is correct.
More can be learned about a system of equations at https://brainly.com/question/24342899
Please help me to answer this
Pls help pls pls help me pls pls help pls
Answer:
D should be the answer because the rate of Mason and Evan is 3 pages per a minute because three goes into both like so 30÷10=3 and 12÷4=3. Which is why D is your answer.
What is the definition of a Pythagorean triple?
Answer:
a set of numbers that are used to find the hypotenuse
Step-by-step explanation:
brainliest
The integer solutions to the Pythagorean theorem, are called Pythagoras triples.
Definition of Pythagorean Triples:
The integer solutions to the Pythagorean theorem, [tex]a^{2} +b^{2} =c^{2}[/tex] are called Pythagorean triples which contains three positive integers a, b and c.
For example:
(3, 4, 5)
By evaluating we get
[tex]3^{2} +4^{2} =5^{2}[/tex]
⇒ 9 + 16 = 25
Hence, 3, 4 and 5 are Pythagorean triples.
Learn more about Pythagorean Triples here:
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Need help with his geometry question. Find the value of x
Answer: 15
Step-by-step explanation:
Tadeo is a beekeeper. The table shows the weekly number of bees producing honey in a new hive. Which expression gives the number of bees in week 12?
The exponential equation that gives the number of bees in week 12 is of:
[tex]y = 4(3)^{11} = 708588[/tex]
What is an exponential function?It is modeled by:
[tex]y = ab^x[/tex]
In which:
a is the initial value.b is the rate of change.In this problem, considering that the initial week is the first, and the value triples every week, the expression for the number of bees after x weeks is given by:
[tex]y = 4(3)^{x - 1}[/tex]
Hence, after 12 weeks, the expression is:
[tex]y = 4(3)^{11} = 708588[/tex]
More can be learned about exponential equations at https://brainly.com/question/25537936
Answer:
4 • 3^11
Step-by-step explanation:
For each of the following, draw a diagram or use words to explain your answer.
A. How many 2/3 are in 2?
B. How many 1/10 are in 3?
Answer:
A. 3. B. 20
Step-by-step explanation:
2 divided by 2/3 is 2/ 2/3 or 6/2 which is 3.
3 divided by 1/10 is 3/ 1/10 or 30.
If the circle has a diameter of 6 feet about how long is the chalk outline
Answer:
Find the circumference,
C = 2πr
Where 'π' is pi (3.14 or 22/70, and 'r' is the radius.
To find the radius of a diameter, you must the half of the diameter:
Diameter/2 = radius
6/2 = 3 is the radius.
Plug this into our formula;
C = 2πr
C = 2 x 3.14 x 3
C = 6.28 x 3
C = 18.84 feet.
NO LINKS!!!
Part 3: Figure A is a dilated image of Figure B. Find the scale factor. #5 and 6
Answer:
Step-by-step explanation:
Scale:- 1box=1units
So
Take one side of each
B=6unitsA=10unitsScale factor(A to B)
[tex]\\ \rm\rightarrowtail \dfrac{6}{10}=\dfrac{3}{5}[/tex]
Scale factor (B to A) is 5/3#6
B=12A=6Scale factor (A to B)
[tex]\\ \rm\rightarrowtail \dfrac{12}{6}=2[/tex]
Scale factor (B to A)
[tex]\\ \rm\rightarrowtail \dfrac{6}{12}=0.5[/tex]
C
X
A parabola has a focus at ( 1.5, 0) and a directrix of x= -1.5. Which of the following equations represent the parabola?
Step-by-step explanation:
Since the focus lies on the x axis, and the diretcrtirx is a vertical line, we have a sideways parabola so we have the equation
[tex](y - k) {}^{2} = 4p(x - h)[/tex]
where h,k is the vertex and
p is the distance from the vertex to the focus or the distance fromcthe vertex to the directrix.
Since the focus is 1.5, and the directrix is -1.5 the vertex is (0,0) so we have
[tex]y {}^{2} = 4px[/tex]
We know p is 1.5 so we have
[tex] {y}^{2} = 6x[/tex]
[tex] \frac{1}{6 } {y}^{2} = x[/tex]
The number 9 is a common factor of _________.
A) 6 and 9
B) 9 and 36
C) 16 and 27
Answer:
Step-by-step explanation:
B) 9 and 36
================================================
9 is a common factor of
9 and 36.
Here's why:
6 is not evenly divisible by 9
16 is not divisible evenly by 9 (it is divisible by 8)
All the other numbers are divisible by 9.
=============================================
note:-Hope everything is clear; if you need any more explanation/clarification, kindly let me know, and I will comment and/or edit my answer. :)
Estimate the amount of the tip by rounding the bill to the nearest dollar before calculating 20% tip on a bill of $46.69, the amount of the tip is approximately $_____
Answer:
9 doller
Step-by-step explanation:
we will find 20 percent of 46.69
is=pxw divided by 100
=9.338
or 9 doller
The table below shows part of the operating budget of a small dairy farm for last year. The only expense not listed in the table is maintenance. Food = 1/3 housing = 1/3 medical care = 1/4 .This year,the managers of the farm will change the fraction of the budget for housing to 1/8 but will leave the fraction of the budget for food and medical care the same.Again,the remaining portion of the budget will be for maintenance expenses.What is the difference between the fraction of the budget for maintenance this year and last year?
The difference between the fraction of the budget for maintenance this year and last year is 5/24.
What is the difference?The first step is to determine the fraction of the budget used for maintenance last year.
Fraction of the budget used for maintenance = 1 - (1/3 + 1/3 + 1/4)
1 - 11/12 = 1/12
The second is to determine the fraction of the budget used for maintenance this year.
Fraction of the budget used for maintenance = 1 - (1/8 + 1/3 + 1/4)
1 - 17/24 = 7/24
The difference = 7/24 - 1/12
= 5/24
To learn more about subtraction of fractions, please check: https://brainly.com/question/915789
Prove that:-
[tex] \sqrt{ \frac{1 + cos30 {}^{ \circ} }{1 - cos {30}^{ \circ} } } = sec \: {60}^{ \circ} + tan \: {60}^{ \circ} [/tex]
Answer:
[tex] \displaystyle{ \sqrt{ \frac{1 + cos \: {30}^{ \circ} }{1 - cos \: {30}^{ \circ} } } = sec \: {60}^{ \circ} + tan \: {60}^{ \circ} }[/tex]
[tex]LHS = \displaystyle{ \sqrt{ \frac{1 + cos \: {30}^{ \circ} }{1 - cos \: {30}^{ \circ} } } }[/tex]
[tex] \displaystyle{ \sqrt{ \frac{1 + \frac{ \sqrt{3} }{2} }{1 - \frac{ \sqrt{3} }{2} } } }[/tex]
[tex] \displaystyle{ \sqrt{ \frac{ \frac{2 + \sqrt{3} }{2} }{ \frac{2 - \sqrt{3} }{2} } } }[/tex]
[tex] \displaystyle{ \sqrt{ \frac{2 + \sqrt{3} }{2 - \sqrt{3} } \times \frac{2 + \sqrt{3} }{2 + \sqrt{3} } } }[/tex]
[tex] \displaystyle{ \sqrt{ \frac{(2 + \sqrt{3} {)}^{2} }{4 - 3} } }[/tex]
[tex] \displaystyle{2 + \sqrt{3} }[/tex]
[tex]RHS = sec \: {60}^{ \circ} + tan \: {60}^{ \circ} [/tex]
[tex] = 2 + \sqrt{3} [/tex]
[tex] \rm\therefore{LHS=RHS,proved. }[/tex]
18 - [5 + 1 + (4 - 2 + 2)}] please solve
Answer:
8
Step-by-step explanation:
[tex]\hookrightarrow 18 - [5 + 1 + (4 - 2 + 2)]\\\\\hookrightarrow 18-[5+1+(6-2)]\\\\\hookrightarrow 18-[5+1+4]\\\\\hookrightarrow 18-10\\\\\hookrightarrow 8[/tex]
Riley has completed 6 of the 30 pages she was assigned for homework. What percentage of her homework does Riley have left to complete?
Answer:
80 Percent
Step-by-step explanation:
Since she has done 6/30 pages, she has 24/30 more pages to complete. Convert 24/30 to a decimal by dividing 24 by 30 to get the percentage, which is 80 percent
Hopefully this helps - let me know if you have any questions!
PLEASE HELP WILL GIVE BRANLIEST
Write as a square of a binomial:
4.8xy+36y^2+0.16x^2
Answer:
(0.4x + 6y)²
Step-by-step explanation:
rsm sucks. i have a 5 hour class tomorrow and i hate it but here you go this is the right answer
What is a Semicircle?
Answer:
half a circle
All changes saved 16. The Abdul family is comparing the costs of two different high-speed Internet services. With plan A, equipment installation is $199, and the monthly fee is $50. With plan B, the installation is $50, with a $90 monthly fee. The cost of Part A is given by f(x) = 50x + 199 and the cost of Part B is given by g(x) = 90x + 50, where x is the number of months of service.
Part A: Make two tables that you could use to graph the functions. Let x = 0, 1, 2, 3, 4, 5, and 6.
Part B: Graph both functions.
Part C: The Abduls plan on using the Internet service for one year. Based on cost, which plan would you recommend? Explain.
For one year, plan B would be recommended, because it would be cheaper.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
The cost of plan A is given by f(x) = 50x + 199 and the cost of plan B is given by g(x) = 90x + 50
For one year, plan B would be recommended, because it would be cheaper.
Find out more on equation at: https://brainly.com/question/2972832
Answer: Plan A
Step-by-step explanation:
f(x) = 50x + 199 = A
g(x) = 90x + 50 = B
Plan A = (1,249) (2, 299) (3,349) (4,399) (5,449) (6,499)
Plan B = (1, 140) (2, 230) (3, 320) (4,410) (5, 500) (6, 590)
Plan A would be recommended because plan A you pay the least amount = 499 dollars over 6 months versus 590 dollars over 6 months with plan B.
Solve:-
[tex] \frac{x + 4}{x - 4} + \frac{x - 4}{x + 4} = 3 \frac{1}{3} [/tex]
help mmmm
Answer:
[tex] \displaystyle{ \frac{x + 4}{x - 4} + \frac{x - 4}{x + 4} = 3 \frac{1}{3} }[/tex]
[tex]\displaystyle{ \frac{ {(x + 4) }^{2} + {(x - 4)}^{2} }{(x + 4)(x - 4)} = \frac{10}{3} }[/tex]
[tex]\displaystyle{ \frac{ {x}^{2} + 8x + {4}^{2} + {x}^{2} - 8x + {4}^{2} }{ {x}^{2} - {4}^{2} } = \frac{10}{3} }[/tex]
[tex]\displaystyle{ \frac{ {2x}^{2} + 16 + 16 }{ {x}^{2} - 16 } = \frac{10}{3} }[/tex]
[tex]\displaystyle{3( {2x}^{2} + 32) = 10( {x}^{2} - 16) }[/tex]
[tex]\displaystyle{ {6x}^{2} + 96 = {10x}^{2} - 160 }[/tex]
[tex]\displaystyle{ {10x}^{2} - 160 = {6x}^{2} + 96 }[/tex]
[tex]\displaystyle{ {10x}^{2} - {6x}^{2} - 160 - 96 = 0 }[/tex]
[tex]\displaystyle{ {4x}^{2} - 256 = 0}[/tex]
[tex]\displaystyle{4( {x}^{2} - 64) = 0}[/tex]
[tex] {x}^{2} - {8}^{2} = \displaystyle{ \frac{0}{4} }[/tex]
[tex]\displaystyle{(x + 8)(x - 8) = 0}[/tex]
[tex]\displaystyle{ \rm{either, \: x + 8 = 0............(1) }}[/tex]
[tex] \rm{or ,\: x - 8 = 0...............(2)}[/tex]
From equation (1)
[tex]x + 8 = 0[/tex]
[tex]x = - 8[/tex]
From equation (2)
[tex]x - 8 = 0[/tex]
[tex]\displaystyle{x = 8}[/tex]
[tex] \therefore{x=±8}[/tex]
2) Jose bought a magazine for $10 and some erasers for $2 per eraser. He spent a total of $26. How many erasers
he buy?
I can solve it i just need to know the equation with X
If 2 cups = 1 pint, how many cups of liquid are in a 11-pint container?
Group of answer choices
John multiplies one side of the equation 20 + 48 = 68 by a number s. What does he need to do balance the equation?
In order to balance the equation, John should multiply the second side of the equation by s.
Why?
Remember the Golden Rule of Algebra:-
[tex]\bigstar{\boxed{\sf{Whatever~you~do~to~one~side,~you~do~to~the~other.}}[/tex]
So if you multiply 1 side of the equation by s, you multiply the second side by s.
Please tell John about the Golden Rule of Algebra ;)
note:-Hope everything is clear; if you need any explanation/clarification, kindly let me know, and I will comment and/or edit my answer :)
Pam’s monthly food budget is equal to 40% of her monthly rent payment. If her food budget is $200 a month, how much is her rent payment each month?
so we know that 40% for the rent payment is for food, and we also know that those 40% are really 200 bucks, so what would it be for the 100%?
[tex]\begin{array}{ccll} \%&amount\\ \cline{1-2} 40 & 200\\ 100& x \end{array} \implies \cfrac{40}{100}=\cfrac{200}{x}\implies \cfrac{2}{5}=\cfrac{200}{x} \\\\\\ 2x=1000\implies x=\cfrac{1000}{2}\implies x=500[/tex]
calvin and susie baked some cookies in the ratio of 3 : 7. calvin baked 60 fewer cookies than susie. how many cookies did they bake altogether?
Answer:
Acc to ques
7x-3x = 60
x = 15
so they made total of 10x = 150
use the equality below to answer the question
0.08g+0.2<5
Answer:
g< 0.0153
Step-by-step explanation:
0.08g +0.2 < 5
0.08g < 5 + 0.2
0.08g < 5.2
g< 0.0153
Given the data presented in the bar graph, which age group represents 25% of the people at the family reunion?
A) 10-19
B) 20-29
C) 30-39
D) 50-59
The age group that represents 25% of the people at the family reunion as displayed by the bar graph is: B. 20 - 29.
What is a Bar Graph?A bar graph can be described as a graphical representation of a data distribution usin bars/bins to display the frequency of a group or data points.
First, find the total number of people at the family reunion:
Total number of people = 8 + 10 + 19 + 15 + 5 + 13 + 3 + 5 = 78 people.
25% of 79 = 25/100 × 78 = 19.5
19.5 is closer to 19.
People in the age group 20 - 29 from the bar graph represents 19 people, therefore, the age group that represents 25% of the people at the family reunion as displayed by the bar graph is: B. 20 - 29.
Learn more about bar graph on:
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Answer: B
Step-by-step explanation: I took the test in K12