An equilateral triangle has an apothem measuring 2.16 cm and a perimeter of 22.45 cm.
What is the area of the triangle, rounded to the nearest tenth?
2.7 cm2
4.1 cm2
16.2 cm2
24.2 cm2
Answers
we know that
An equilateral triangle is a regular polygon, because all sides are equal
In a regular polygon the area is equal to
[tex]A=\frac{1}{2}*apothem*perimeter[/tex]
in this problem we have
[tex]apothem=2.16\ cm\\ perimeter=22.45\ cm[/tex]
substitute in the formula
[tex]A=\frac{1}{2}*2.16*22.45[/tex]
[tex]A=24.2\ cm^{2}[/tex]
therefore
the answer is
the area of the triangle is [tex]24.2\ cm^{2}[/tex]
The area of an equilateral triangle rounded to the nearest tenth is 24.2 [tex]cm^2[/tex].
Given the following data:
Apothem of triangle = 2.16 cm.Perimeter of triangle = 22.45 cm.What is an equilateral triangle?An equilateral triangle can be defined as a type of triangle or regular polygon that has equal length of sides.
Mathematically, the area of an equilateral triangle is given by this formula:
[tex]Area = \frac{1}{2} \times apothem \times perimeter[/tex]
Substituting the given parameters into the formula, we have;
[tex]Area = \frac{1}{2} \times 2.16 \times 22.45\\\\Area = \frac{1}{2} \times 48.492[/tex]
Area = 24.246 ≈ 24.2 [tex]cm^2[/tex].
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Related Questions
A public pool charges a membership fee of $50 and a fee for each visit. Every time you go to the pool, it costs $2.50.
a. Write an equation to represent your total cost c for v visits.
b. How much will it cost if you go to the pool 22 times? *PLEASE SHOW YOUR WORK*
Answers
Answer:
A. C=2.50v
B. C=2.50x22
C=55
Step-by-step explanation:
A student had to multiply 328 x 41. The student’s answer was 4,598. Use estimation to explain why this answer is not reasonable
Answers
Grab a sheet of paper and follow along, write 328 x 41 and put 328 on top of 41.
multiply 8 x 1
multiply 2 x 1
multiply 3 x 1
multiply 8 x 4 which is 32
multiply 2 x 4 which is 8
multiply 3 x 4 which is 12
bring down the carry digit of 1
add 328 + 13120 which is 13448
or multiply 328 x 41 and u get 13448
The answer is not reasonable because its not the correct solution.
Which phrase could be represented by this expression?
k/5 + 8
or
k over 5 + 8
eight more than a fifth of a number
five times a number plus eight
eight more than five times a number
one-fifth of the sum of a number and eight
Answers
Eliza earns $400 per week plus $15 for each new customer she signs up. Let c represent the number of new customers Eliza signs up. Write an expression that shows how much she earns in a week. Then find how much Eliza earns in a week in which she signs up 18 customers.
Answers
She made $400 one week plus $165 for 18 new customers
Answer:
400+ (15c)
$670
Step-by-step explanation:
Eliza earns per week = $400
She earns for each new customer's signs up = $15
Let the number of new customers Eliza signs up = c
The expression that shows her earning in a week will be
400+ (15c)
If the number of customers that signs up = 18
The weekly earning of Eliza will be = 400+(15 × 18)
= 400 + 270
= $670
Eliza's earning in a week would be $670.
Purple paint is made with a 16:3:1 ratio of white paint:blue paint:red paint. How much white paint, in gallons, is needed in order to make one gallon of purple paint? Express your answer as a common fraction.
Answers
Answer:
4/5
Step-by-step explanation:
The purple paint is split into 16+3+1=20 parts: 16 parts of white, 3 parts of blue, and 1 part of red. Thus, in one gallon of purple paint, 16 out of the total 20 parts are white paint, so there are 16/20 x 1 gallon = 4/5 gallons of white paint in one gallon of purple paint.
The amount of white paint that is needed in order to make a gallon of purple paint would be 4 / 5 gallons.
How to find the number of gallons ?The ratio of white:blue:red paint is given as 16:3:1. The sum of these ratio components gives the total parts for one 'unit' of paint.
So, 16 (for white) + 3 (for blue) + 1 (for red) = 20 total parts.
This implies that the 20 parts in this ratio make up 1 gallon of purple paint (as per the question). To find the quantity of white paint needed, we simply need to convert the 'parts' of white paint into gallons.
Since 20 parts is equivalent to 1 gallon, 1 part would be equivalent to 1/20 of a gallon. Therefore, 16 parts of white paint would be equivalent to :
= 16 * (1/20)
= 16/20
= 4/5 gallons
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How can the difference 13-(-24)be rewritten as a sum with the correct solution? Explain?
A: (-13) + (-24) = -37
B: 13 + (-24) = -11
C: (-13) + 24 = 11
D: 13 + 24 = 37
Answers
Remember the rule:
Subtracting a negative is the same as adding a positive.
Due to fire laws, no more than 720 people may attend a performance at Metro Auditorium. The balcony holds 120 people. There are 32 rows in the ground floor each for the same number of seats write an inequality to find the numbers of people that can sit in a ground floor row if the balcony is full. Identify what your variable represents.
Answers
s=seats
r=rows
There are 32 rows with x amount of seats but only p amount of people can be in the auditorium due to fire laws.
32r=x>p
Which equivalent fraction would you have to use in order to add 3/5 to 21/25
Answers
5x5 is 25
3 x 5 is 15
21/25+ 15/25= 36/25
58 1/3 ÷ 6 2/3 equals what?
Answers
175/3 / 20/3
175/3 x 3/20
525/60
8 3/4
______________________________________________
Explanation:
_________________________________________________
Given: 58 ⅓ ÷ 6 ⅔ = ? ;
_________________________________________________
Note: 58 ⅓ = [ (3*58) + 1 ] / 3 = (174 + 1) / 3 = 175 / 3 ;
6 ⅔ = [ (3*6) + 2 ] / 3 = (18 + 2) / 3 = 20/3 ;
_________________________________________________
So; Rewrite: "58 ⅓ ÷ 6 ⅔ " ; as:
_________________________________________________
"(175/3) ÷ (20/3) = ??
_____________________________________
Note: "(175/3) ÷ (20/3) = (175/3) * (3/20) = ?
→ The "3's cancel out to "1" ; since "(3÷3 = 1)" ;
________________________________________
and we have: "175 * (1/20) = 175/20 ;
= 35/4; or; " 8 ¾ " ; or, " 8.75 " .
________________________________________
Alternate method:
________________________________________
Given: 58 ⅓ ÷ 6 ⅔ = ? ;
________________________________________
→ Using calculator:
"58 ⅓ = 58.3333333333333333.... = 175/3 " ;
"6 ⅔ =6.6666666666666667 = 20/3 ;
_________________________________________
58 ⅓ ÷ 6 ⅔ = (58.3333333333333333) (58.3333333333333333) ÷ (6.6666666666666667) (6.6666666666666667) = 8.75 ;
or; better (using a calculator): (175 ÷ 3) ÷ (20 ÷ 3) = 8.75 .
{or: " (175 / 3) / (20 / 3) = 8.75 " .
_________________________________________
Evaluate the expression 3(7 + 4)2 − 14 ÷ 7. 50 361 363 586
Answers
The first step for solving this is to add the numbers in the parenthesis.
3 × 11 × 2 - 14 ÷ 7
Divide -14 by 7.
3 × 11 × 2 - 2
Divide the first 3 numbers together.
66 - 2
Subtract the numbers together to get your final answer.
64
Let me know if you have any further questions.
:)
to rent a car,the fast company charges $75 per day plus $0.05 per mile. how many miles did mrs.kline drive if the cost of renting the car was $ 92.40?
Answers
0.05m=92.4-75
0.05m=17.4
m=348
mrs. kline drove 348 miles
The three seventh grade classes at Sunview Middle School collected the most boxtops for a school fundraiser. They won a $600 prize to share among them. Mr. Aceves’ class collected 3,760 box tops, Mrs. Baca’s class collected 2,301, and Mr. Canyon’s class collected 1,855. How should they divide the money so that each class gets the same fraction of the prize money as the fraction of the box tops that they collected? Explain your reasoning.
Answers
Answer: The share would be approximately $285, $175, $141 respectively.
Step-by-step explanation:
Since we have given that
Number of box tops collected by Mr. Aceves's class = 3760
Number of box tops collected by Mrs. Baca's class = 2301
Number of box tops collected by Mr, Canyon's class = 1855
We first find the ration of box tops of Mr. Aceves, Mrs. Baca and Mr. Canyon respectively:
3760:2301:1855
Total = 3760+2301+1855=7916
Total amount to be share among them as a prize = $600
Mr. Aceves's share is given by
[tex]\dfrac{3760}{7916}\times 600\\\\=284.99\\\\\approx 285[/tex]
Mrs. Baca's share is given by
[tex]\dfrac{2301}{7916}\times 600\\\\=175.08\\\\\approx 175[/tex]
Mr. Canyon's share is given by
[tex]\dfrac{1855}{7916}\times 600\\\\=140.60\\\\\approx 141[/tex]
Hence, the share would be approximately $285, $175, $141 respectively.
You buy a movie for 19.99 and a set of earphones for 12.49 how much is the bill before taxes
Answers
19.99 for the movie and 12.49 for the earphones together they make 32.48
Answer:32.39
Step-by-step explanation: cost of movie is 19.9
Cost of earphone is 12.49
Adding both cost is 19.9+12.49
=32.39
The cost before tax deduction is 32.39
Graph y=−56x−4 .
Use the line tool and select two points on the line.
Answers
and -4 is the y intercept
so you first graph 0,-4
then use the slope and move 5 units up and 6 to the right
The two points on the line y = − 56x − 4 will be (1, −60) and (−1, 52).
What is the solution to the equation?The distribution of weights to the variables involved that establishes the equilibrium in the calculation is referred to as a result.
y = − 56x − 4
Let x = 1, the value of y will be
y = − 56 (1) − 4
y = − 56 − 4
y = − 60
Let x = − 1, the value of y will be
y = − 56(−1) − 4
y = 56 − 4
y = 52
The two points on the line y = − 56x − 4 will be (1, −60) and (−1, 52). Then the diagram of the line is given below.
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Three times the smaller of two consecutive EVEN integers IS four less than twice the larger. What are the two integers?
PLEASE HELP ME WITH THIS
Answers
The two consecutive even integers are 8 and 10.
Given that, three times the smaller of two consecutive even integers is four less than twice the larger.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
Let two consecutive even integers be x and x+2.
Now, 3x-4=2(x+2)
⇒ 3x-4=2x+4
⇒ 3x-2x=4+4
⇒ x=8
So, x+2=10
Therefore, the two consecutive even integers are 8 and 10.
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A baseball weighs 5 ounces and the NY Yankees ordered 3,200 baseballs. How many tons do the baseballs weigh?
Answers
3200
x 5
16000 ounces
Then you need to convert that into pounds. Since there are 16 ounces in a pound, you need to divide by 16.
16000
÷ 16
1000 pounds
Since the question asks you how many TONS the baseballs weigh, you need to convert pounds to tons. There are 2000 pounds in a ton, so you divide by 2000.
1000
÷2000
0.5 tons
0.5 tons is your answer.
Answer:
dont come at me if im wrong but im pretty sure the answer is 1/2 or .5
Step-by-step explanation:
The value of -4 2 is _____. pls help
Answers
The value of -4 squared (-4^2) is -16 because the exponent only applies to 4, not the negative sign. To include the negative in the exponent, use parentheses like (-4)^2 = 16.
Explanation:The value of -4^2 is -16. This is because the exponent applies only to the number 4 and not the negative sign in front of the 4. In other words, -4^2 means -(4*4) which is -16. To make the negative part of the base, the operation should be placed in parentheses like (-4)^2 = 16.
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The complete question is given below:
The value of -4^2 is _____.
It costs $2.55 to make a sandwich at the local deli shop. To make a profit, the deli sells it at a price that is 140% of the cost. The sandwich sells for $___.
Answers
-0.3,0.5,0.55,-0.35 in least to greatest
Answers
is your answer
hope this helps
What is the answer to this? I don’t
Answers
Can we divide 11 by 1? yes. can we divide the other digit of 11 by 1? yes. Thus, 11 satisfies the criterion "they are divisible by each of their digits."
What about 12: is 12 divisible by 1? YES. Is 12 divisible by 2? YES.
And so on.
list all the possible numbers:
10 - cant be divisible by 0
11 - can be divided by 1 and 1
12 - can be divided by 1 and 2
13 - cant be divided by 3
14 - cant be divided by 4
15 - can be divided by 1 and 5
16 - cant be divided by 6
17 - cant be divided by 7
18 - cant be divided by 8
19 - cant be divided by 9
20 - cant be divided by 0
21 - cant be divided by 2
22 can be divided by 2 and 2
23 - cant be divided by 3
24 - can be divided by 2 and 4
the numbers are 11, 12, 15, 22 and 24
Solve the following system of equations algebraically for all values of x,y and z
x+3y+5z=45
6x-3y+2z=-10
-2x+3y+8z=72
Answers
6x - 3y + 2z = - 10
------------------------add
7x + 7z = 35
6x - 3y + 2z = -10
-2x + 3y + 8z = 72
----------------------add
4x + 10z = 62
7x + 7z = 35....multiply by 4
4x + 10z = 62...multiply by -7
---------------------
28x + 28z = 140 (result of multiplying by 4)
-28x - 70z = - 434 (result of multiplying by -7)
--------------------add
- 42z = - 294
z = -294/-42
z = 7
4x + 10z = 62
4x + 10(7) = 62
4x + 70 = 62
4x = 62 - 70
4x = - 8
x = -8/4
x = -2
x + 3y + 5z = 45
-2 + 3y + 5(7) = 45
-2 + 3y + 35 = 45
3y + 33 = 45
3y = 45 - 33
3y = 12
y = 12/3
y = 4
solution is (-2,4,7) <==
The system of equations x+3y+5z=45, 6x-3y+2z=-10, -2x+3y+8z=72 can be solved algebraically to get the values x=6, y=12, z=-1.
Explanation:First, we can combine the first and the second equations and the first and third equations to cancel out y.
Doing so, we get: x+3y+5z+6x-3y+2z=45-10 and x+3y+5z-2x+3y+8z=45+72
The new equations simplify to 7x+7z=35 and -x+13z=117
Next, we can divide the first new equation by 7 to get x+z=5. Subtract x from both sides to get z=5-x.
Substitute z=5-x into the second equation to find the value of x.
Performing these substitutions gives x=6. Substituting x=6 back into the equation z=5-x gives z=-1.
Finally, we substitute x=6 and z=-1 back into the original equations to solve for y: y=(45-6-5(-1))/3 = 12
So, x=6, y=12, z=-1 are the solutions to the system of equations.
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If 45 cookies will serve 15 students, how many collies are needed for 30 students?
Answers
3 x 30 = 90 cookies
you need 90 cookies for 30 students
hope this helps
Help me please 2. You learn from your science teacher that water expands when you freeze it. The next time that you freeze your water bottle, you leave room for the water to expand so that the bottle does not crack. What kind of reasoning did you use? inductive reasoning deductive reasoning algebraic reasoning direct reasoning I think the answer is b
Answers
Liz earns a salary of $2,100 per month, plus a commission of 5% of her sales. She wants to earn at least $2,400 this month. Write an inequality to find the amount of sales that will meet her goal. Identify what your variable represents.
Answers
(greater than or equal to)
X represents her sales
The scale on a map is 2cm = 15miles. Dave measures the distance to the next town at 7cm. How many miles away is the next town?
Answers
Answer:
[tex]52.5\ miles[/tex]
Step-by-step explanation:
we know that
The scale on the map is equal to
[tex]\frac{2}{15}\frac{cm}{miles}[/tex]
so
by proportion
Find how many miles are [tex]7\ cm[/tex] on the map
[tex]\frac{2}{15}\frac{cm}{miles}=\frac{7}{x}\frac{cm}{miles}\\ \\x=15*7/2\\ \\x=52.5\ miles[/tex]
3. For ΔFHG, find the measure of the smallest angle, ∠HFG, if m∠ GHF = 92° and m∠HGF =
72°
Answers
hope this helps,,
Answer: The Answer is 16
could someone help please thx
Answers
42-24 divide 6 ; value 3
Answers
The result of the expression 42-24 divided by 6, calculated using the 'Order of Operations' rule, is 38.
Explanation:You've asked to solve this mathematical expression: 42-24 divided by 6. To do this correctly, we must follow the 'Order of Operations,' often remembered by the acronym PEMDAS, which stands for Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right).
In your problem, the operations are Subtraction and Division. Following the PEMDAS rule, we perform Division before Subtraction. Therefore, first perform 24 divided by 6, which is 4. Then, subtract that result from 42. In the end, 42 minus 4 gives us 38 as the final answer.
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A used-car dealer has a vehicle on the lot with a sticker price of $5999. if the dealer markup on used vehicles is 20%, how much did the dealer pay for the car?
Answers
Answer:
the correct APEX answer is $4999.17
The cost of car is $4,999.16.
What is Percentage?To determine the quantity or percentage of something in terms of 100, use the percentage formula. Per cent simply means one in a hundred. Using the percentage formula, a number between 0 and 1 can be expressed. A number that is expressed as a fraction of 100 is what it is. It is mostly used to compare and determine ratios and is represented by the symbol %.
Given:
A used-car dealer has a vehicle on the lot with a sticker price of $5999.
Mark up = 20%
let the cost of Car be x.
So, x+ 20% of x = 5999
x + 20/100 x = 5999
x + 0.20 x = 5999
1.2 x= 5999
x = 5999/ 1.2
x = $4,999.16
Hence, the cost of car is $4,999.16.
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WILL GIVE BRAINLIEST!!!!!!!!!!!!!!!!!!
describe the relationship between: the domain, relation, and range
Answers
Relations are subsets of products A×BA×B where AA is the domain and BB the codomain of the relation.
A function ff is a relation with a special property: for each a∈Aa∈A there is a unique b∈Bb∈B s.t. ⟨a,b⟩∈f⟨a,b⟩∈f.
This unique bb is denoted as f(a)f(a) and the 'range' of function ff is the set {f(a)∣a∈A}⊆B{f(a)∣a∈A}⊆B.
You could also use the notation {b∈B∣∃a∈A[⟨a,b⟩∈f]}{b∈B∣∃a∈A[⟨a,b⟩∈f]}
Applying that on a relation RR it becomes {b∈B∣∃a∈A[⟨a,b⟩∈R]}{b∈B∣∃a∈A[⟨a,b⟩∈R]}
That set can be labeled as the range of relation RR.