Lines I and P can be considered parallel if they have the same slope, and ABC and CEF can be considered similar if they have the same size, but not necessarily the same shape.
What is angle?Angle is a two-dimensional figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle. An angle is measured in degrees, which are represented by the symbol °. The size of an angle is determined by the amount of rotation between the two rays, with the vertex being the point of rotation. Angles can be described as acute, obtuse, right, reflex, straight and full.
A) The slope of line I is equal to the slope of line P. - True. If two lines have the same slope, they are parallel.
B) ABC is congruent to CEF - False. Congruent shapes have the same size and same shape. ABC and CEF are not necessarily the same size or shape.
C) Lines I and P are parallel - True. If two lines have the same slope, they are parallel.
D) ABC is similar to CEF - True. Similar shapes have the same size, but not necessarily the same shape.
E) Sin (A) = Sin (C) - False. The sine of an angle is only equal to the sine of another angle if they are the same angle.
F) Sin (B) = cos (F) - False. The sine of an angle is not equal to the cosine of another angle.
In conclusion, lines I and P can be considered parallel if they have the same slope, and ABC and CEF can be considered similar if they have the same size, but not necessarily the same shape. However, the sine of an angle is only equal to the sine of another angle if they are the same angle, and the sine of an angle is not equal to the cosine of another angle.
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1.
2y = -2x + 6
x- 5y = -15
2.
5x + y = 2
20x + 3y = -4
please include a solution thank you.
Step-by-step explanation:
To solve the system of equations:
2y = -2x + 6 ----(1)
x - 5y = -15 ----(2)
We can use substitution method or elimination method. Here, we will use elimination method to eliminate y.
Multiplying equation (1) by -5, we get:
-10y = 10x - 30 ----(3)
Adding equations (2) and (3), we get:
-15y = -45
Dividing by -15 on both sides, we get:
y = 3
Substituting y = 3 in equation (2), we get:
x - 5(3) = -15
x - 15 = -15
Adding 15 on both sides, we get:
x = 0
Therefore, the solution of the system of equations is (x, y) = (0, 3).
To solve the system of equations:
5x + y = 2 ----(1)
20x + 3y = -4 ----(2)
We can use substitution method or elimination method. Here, we will use elimination method to eliminate y.
Multiplying equation (1) by -3, we get:
-15x - 3y = -6 ----(3)
Adding equations (2) and (3), we get:
5x = -10
Dividing by 5 on both sides, we get:
x = -2
Substituting x = -2 in equation (1), we get:
5(-2) + y = 2
-10 + y = 2
Adding 10 on both sides, we get:
y = 12
Therefore, the solution of the system of equations is (x, y) = (-2, 12).
Answer:
1) (0, 3)
2) (-2, 12)
Step-by-step explanation:
1)
2y = -2x + 6 → y = -x + 3
x - 5y = -15
Substitute the simplified first equation into the second equation and solve for x.
x - 5( -x + 3 ) = -15
x + 5x - 15 = -15
6x = 0
x = 0
Substitute into first equation to get y.
y = -(0) + 3
y = 3
The solution to the system is the coordinate (0, 3).
2)
5x + y = 2
20x + 3y = -4
Solve the first equation for y.
y = -5x + 2
Substitute this into the second equation and solve for x.
20x + 3 ( -5x + 2 ) = -4
20x - 15x + 6 = -4
5x = -10
x = -2
Substitute this value on the first equation to get y.
y = -5( -2 ) + 2
y = 10 + 2
y = 12
The solution to the system is the coordinate (-2, 12).
51. For which of the following values of L will the lines whose equations are 2x+3y=8
and 8x+12y = L be parallel?
I. L = 0
II. L = 8
III. L = −8
A. I only
B. II only
C. III only
D. I and II only
E. I, II, and III
Two cars leave towns 320 kilometers apart at the same time and travel toward eachother. One car's rate is 12 kilometers per hour less than the other's. If they meet in 2 hours, what is the rate of the slower car?
Do not do any rounding.
Answer:
74 kilometers per hour.
Step-by-step explanation:
Let's call the speed of the faster car "x" (in kilometers per hour). Then, according to the problem, the speed of the slower car is "x - 12" (in kilometers per hour).
The two cars are traveling towards each other, so the distance between them decreases at a rate equal to the sum of their speeds. In other words, the relative speed between the two cars is:
x + (x - 12) = 2x - 12
According to the problem, they meet after 2 hours of travel, so the total distance they cover is:
distance = speed × time
For the faster car, the distance it covers is:
distance = x × 2
For the slower car, the distance it covers is:
distance = (x - 12) × 2
Since they are both traveling towards each other, the sum of the distances covered by both cars should be equal to the total distance between them at the start of the trip (320 kilometers):
x × 2 + (x - 12) × 2 = 320
Simplifying this equation:
2x + 2x - 24 = 320
4x = 344
x = 86
Therefore, the speed of the faster car is 86 kilometers per hour.
To find the speed of the slower car, we can use the expression we found earlier:
x - 12 = 86 - 12 = 74
Therefore, the speed of the slower car is 74 kilometers per hour.
Help, solve this pls
Which set has an average of 8?
A) A
B) B
C) A and B
D) none of the above
Answer:
IT IS B hope this helped
Step-by-step explanation:
Solve the expression 7 + (one-fifth x 18 – 3) using the order of operations.
The solution to the expression 7 + (one-fifth x 18 – 3) using the order of operations is 7.6 .
What is order of operations?The order of operations is:
Perform any calculations inside parentheses first.
Exponents (ie powers and square roots, etc.)
Multiplication and Division (from left to right)
Addition and Subtraction (from left to right)
To solve the expression 7 + (one-fifth x 18 – 3), we need to apply the order of operations, which is a set of rules that determines the sequence in which we perform mathematical operations.
Using the order of operations simplifies the expression as follows:
Calculate what's inside the parentheses:
one-fifth x 18 – 3 = (1/5) x 18 – 3
= 3.6 - 3
= 0.6
Add 7 to the result:
7 + 0.6 = 7.6
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How much do we need to invest each month at a rate of 8% compounded monthly so that we have a total of $600,000 saved in 25 years?
Will mark brainliest
we need to invest $1,410.91 each month at a rate of 8% compounded monthly to have a total of $600,000 saved in 25 years.
define rate of interestThe rate of interest is the percentage amount charged by a lender or financial institution for borrowing money or the percentage amount paid to an investor or saver for lending money. It represents the cost of borrowing or the return on investment over a period of time.
To calculate the monthly investment required, we can use the formula for future value of an annuity, which is:
FV = PMT x ((1 + r)ⁿ⁻¹) / r
where:
FV is the future value of the annuity
PMT is the monthly payment or investment
r is the monthly interest rate
n is the total number of periods (months)
In this case, we want to save $600,000 in 25 years, which is equivalent to 300 monthly payments (25 years x 12 months/year). The monthly interest rate is 8% / 12 = 0.00667.
Plugging in the values, we get:
$600,000 = PMT x ((1 + 0.00667)³⁰⁰⁻¹) / 0.00667
Solving for PMT, we get:
PMT = $600,000 x 0.00667 / ((1 + 0.00667)³⁰⁰⁻¹)
= $1,410.91 (rounded to the nearest cent)
Therefore, we need to invest approximately $1,410.91 each month at a rate of 8% compounded monthly to have a total of $600,000 saved in 25 years.
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i need help to do spiral review 5 on lesson 9.7 pls help
Answer: wheres the page/diagram
Step-by-step explanation:
helo I don't understand show work please
Answer:
a = 4.5 , b = 7.5
Step-by-step explanation:
using Pythagoras' identity in the two right triangle
outer right triangle
b² + 10² = (8 + a)² = 64 + 16a + a² → (1)
inner right triangle
a² + 6² = b² → (2)
substitute b² = a² + 6² = a² + 36 into (1)
a² + 36 + 100 = 64 + 16a + a² ( subtract a² from both sides )
136 = 64 + 16a ( subtract 64 from both sides )
72 = 16a ( divide both sides by 16 )
4.5 = a
----------------------------------------
substitute a = 4.5 into (2)
4.5² + 6² = b² , that is
20.25 + 36 = b²
56.25 = b² ( take square root of both sides )
[tex]\sqrt{56.25}[/tex] = b , then
b = 7.5
lodine-131, a radioactive substance that is effective in locating brain tumors, has a half-life of only eight days. A
hospital purchased 16 grams of the substance but had to wait six days before it could be used. How much of the
substance was left after six days?
...
The amount of substance left after six days was
9.
(Round the final answer to three decimal places as needed. Round all intermediate values to seven decimal places as
needed.)
The mass of substance left after 6 days is 9 g
The mass of substance left, N is given by
N = N₀exp(-λt) where λ = decay constant and N₀ = initial mass of substance present = 24 g and t = time
Also, λ = 0.693/t' where t' = half-life of iodine = 8 days
So, λ = 0.693/t'
λ = 0.693/8
λ = 0.086625/day
Since the mass of substance left is N = N₀exp(-λt) and we require the mass of substance after t = 6 days,
N = N₀exp(-λt)
N = 16 gexp(-0.086625/day × 7 days)
N = 16 gexp(-0.606375)
N = 16 g × 0.5453
N = 8.72 g
N = 8.72 → 9 g
So, the mass of substance left after 7 days is 9 g
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I have a queston can you answer it pls
Answer:
0.1 gallons per second or 6 gallons per minute
Step-by-step explanation:
Unit rate =measurement/time
Measurement=
42
gallons
Time=
7
42/7=6
Or if you want in seconds, change the mins to seconds. There are 60 seconds in a minute
7
×
60
=
420
seconds
Unit rate =
42
420
=
0.1
gallons per second
21. समूह 'घ' (Group 'D') [4x5=20] रामले 3 वर्षको लागि 12% प्रतिवर्ष साधारण ब्याजदरले रु. 50000 लगानी गर्यो र श्यामले 10% प्रतिवर्ष वार्षिक चक्रीय ब्याजदरले त्यति नै समयका लागि त्यति नै रकम लगानी गर्यो भने पत्ता लगाउनुहोस् । Ram invested Rs. 50000 for 3 years at the rate of 12% simple interest per annum and Shyam invested same amount for the same time at the rate of 10% annual compound Interest, calculate. . X रामले प्राप्त गरेको ब्याज (The interest received by Ram) श्यामले प्राप्त गरेको ब्याज (The interest received by Shyam) समय र ब्याजदरलाई यथावत् राखेर बराबर ब्याज प्राप्त गर्न रामले कति बढी वा घटी रकम लगानी गर्नुपर्ला ? Without altering time and rate of interest, how much more or less amount should Ram have to invest for equal interest? (Ans: L. Rs.18000, ii, 16550, ill.
Step-by-step explanation:
रामले 3 वर्षको लागि 12% प्रतिवर्ष साधारण ब्याजदरले रु. 50000 लगानी गरेको थियो। यसको आधारमा उनले प्राप्त गरेको ब्याज हो:
Simple Interest (S.I.) = (P × R × T) / 100
यहाँ, P = रु. 50000 हो, R = 12% = 12/100 = 0.12 हो, र T = 3 वर्ष हो।
S.I. = (50000 × 0.12 × 3) / 100 = रु. 18000
त्यसैपछि, श्यामले चक्रीय ब्याजदरले रु. 50000 लगाएर 3 वर्षमा त्यति रकम लिन्छन्। चक्रीय ब्याजदरले ब्याज प्राप्त गर्नको लागि प्रत्येक वर्षको अन्तिम रकममा पूर्ववत ब्याज पनि जोडिन्छ। त्यसको आधारमा उनले प्राप्त गरेको ब्याज हो:
Compound Interest (C.I.) = P × [(1 + R/100)ᵀ - 1]
यहाँ, P = रु. 50000 हो, R = 10% = 10/100 = 0.10 हो, र T = 3 वर्ष हो।
C.I. = 50000 × [(1 + 0.10)³ - 1] = रु. 16532.10
त्यस्तै ब्याजदर र समयको आधारमा रामले पनि रकम लगाएर बराबर ब्याज प्राप्त गर्न चाहनुहुन्छ। यसलाई गणना गर्न प्रयोग गरिएको समान ब्याज तथा समय भएको सिस्टमको नाम "Compound Interest with annual installments" हो। यसक
The circumference of a circle is 15.25 feet. What is the diameter when 3.14 is used for pi?
Answer:
4.85423
Step-by-step explanation:
D equals C/PI
Where D=Diameter and C=Circumference and PI=PI(3.14)
50pts!!!!!!!!!!!!!!!!!
she has a gross income of $105500
. If she pays $26982
in income tax and $2110
for the Medicare levy, what is her net income?
Answer:
Step-by-step explanation:
Claro que sí. El ingreso neto es el ingreso que queda después de restar los impuestos y otros gastos del ingreso bruto. La fórmula del ingreso neto es:
Ingreso neto = Ingreso bruto – Impuestos – Comisiones – Intereses – Créditos – Otros Gastos
En tu caso, el ingreso bruto es $105500 y los impuestos son $26982 por el impuesto sobre la renta y $2110 por el impuesto de Medicare. No sé si tienes otros gastos que debas restar, pero si no los tienes, entonces el ingreso neto sería:
Ingreso neto = $105500 - $26982 - $2110 Ingreso neto = $77408
Espero que te haya servido de ayuda.
Could someone help answer Number 22 please
Area of the first triangle is 582.86 square units
Area of the second triangle is 694 square units
How to find the area of the trianglesThe formula for area of a triangle is solved by
= 1/2 * b * h
For the first figure, we solve for h first using trigonometry
tan 68 = 48 / h
h = 48 / tan 68
h = 19.39
The other side of the base is solved using tan 58
tan 58 = 43.22 / b
b = 43.22 / tan 58
b = 12.12
base of the triangle = 48 + 12.12 = 60.12
Area of the first triangle = 0.5 * 60.12 * 19.39 = 582.86 square units
22. Solving for h
cos 64 = h / 50
h = 50 * cos 64 = 21.92
the other part of the base
sin 64 = b / 50
b1 = 50 * sin 64 = 44.94
tan 50 = h / b2 = 21.92 / b2
b2 = 21.90 / tan 50 = 18.38
base = b1 + b2 = 44.94 + 18.38 = 63.32
Area of the second triangle = 0.5 * 21.92 * 63.32 = 693.99 square units
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If 4x-3=5, what is the value of x
Answer: the answer is two :)
Step-by-step explanation:
4x=5+3
4x=8
x= 8/4
x=2
A, B, C and D are 4 towns
B is 30km due east of A.
C is 30km due North of A.
D is 45km due South of A.
Calculate the bearing of D to B
The bearing of D to B is approximately 33.7°, measured in a clockwise direction from the north-south axis.
We can start by drawing a diagram to represent the positions of the four towns. Let A be the origin of the coordinate system, B be located 30 km due east of A, C be located 30 km due north of A, and D be located 45 km due south of A. The diagram would look like this:
C (30 km)
|
|
|
A (0,0)---+---B (30 km)
|
|
|
|
D (45 km)
To calculate the bearing of D to B, we need to determine the angle that DB makes with the north-south axis (i.e., the y-axis) in a clockwise direction.
First, we can use the Pythagorean theorem to find the distance between B and D:
BD² = AB² + AD²
BD² = 30² + 45²
BD² = 2025
BD = √2025
BD = 45 km
Next, we can use trigonometry to find the angle that DB makes with the north-south axis. Let θ be the angle we are looking for. Then:
tan θ = (opposite / adjacent) = (AB / AD) = (30 / 45) = 2/3
Taking the arctangent of both sides, we get:
θ = tan⁻¹(2/3) ≈ 33.7°
Therefore, the bearing of D to B is approximately 33.7°, measured in a clockwise direction from the north-south axis.
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18 students decide they don't want to be rescued and want to continue to live in the jungle if this represents 40 of the students how many students want to be rescued. The answer is 45 right?
A set of ten cards were labeled as E, X, P, R, E, S, S, I, O, N. What is the sample space for choosing one card? S = {E, P, X} S = {S, I, O, N} S = {E, X, P, R, E, S, I, O, N} S = {E, E, I, N, O, P, R, S, S, X}
QUICK
The sample space for chosing one card is S = {E, X, P, R, E, S, I, O, N}.
What is sample space?Sample space refers to the set of all possible outcomes of a random experiment or a probability event. In the context of your card example, the sample space is the set of all possible cards that could be chosen from the labeled set.
In this case, the sample space would be {E, X, P, R, S, I, O, N}, as these are the possible outcomes when selecting one card from the set.
Therefore the sample space for chosing one card is S = {E, X, P, R, E, S, I, O, N}.
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y = 3x + 1
y = 8x - 4
with solution pls, i would rlly appreciate it
Answer:
si y = a 55 es 5.7
Step-by-step explanation:
la otra es 3.9
Consider the Ricardian model of international trade with two countries, China and India, and two
goods, rich (R) and automobiles (A). The table below displays unit labour requirements (how
many units of labour are required to produce one unit of output) for the two countries. China
has 1,260 labour units and India has 60 labour units.
The unit of labor required to produce one unit of output for the two countries are 2 and 1/3.
The world automobiles-to-rice relative supply curve slopes upward, indicating that as the world price ratio of rice to automobiles rises, so will the relative supply of automobiles to rice.
How to calculate supply curve?To draw the world automobiles-to-rice relative supply curve, calculate the relative supply of automobiles to rice for each country. The relative supply is the ratio of the quantity of automobiles produced to the quantity of rice produced, multiplied by the ratio of the world price of rice to the world price of automobiles. Express this mathematically as:
Relative supply of automobiles to rice = (QA/RA)/(QR/RR) x (PR/PA)
where QA and RA are the quantities of automobiles and rice produced by a country, QR and RR are the quantities of rice produced by a country, and PR and PA are the world prices of rice and automobiles, respectively.
Using the unit labor requirements given in the table, calculate the relative supply of automobiles to rice for China and India as follows:
Relative supply of automobiles to rice for China = (1/4)/(1/2) x (2/1) = 2
Relative supply of automobiles to rice for India = (1/12)/(1/2) x (2/1) = 1/3
We can then plot these points on a graph, where the x-axis represents the relative supply of automobiles to rice and the y-axis represents the world price ratio of rice to automobiles. Assume that the world price ratio of rice to automobiles is initially set at 1, which means that the price of rice is equal to the price of automobiles. We can then draw a line connecting the two points, which represents the world automobiles-to-rice relative supply curve.
The kink point of the relative supply curve occurs when the relative supply of automobiles to rice is equal to 2, which is the point where China switches from being a net exporter of automobiles to a net importer of automobiles. At this point, the world price ratio of rice to automobiles increases, which means that the price of rice increases relative to the price of automobiles. As a result, China reduces its production of automobiles and increases its production of rice, which reduces its relative supply of automobiles to rice.
The second segment of the relative supply curve occurs when the relative supply of automobiles to rice is less than 1/3, which is the point where India switches from being a net exporter of automobiles to a net importer of automobiles. At this point, the world price ratio of rice to automobiles decreases, which means that the price of automobiles increases relative to the price of rice. As a result, India reduces its production of rice and increases its production of automobiles, which increases its relative supply of automobiles to rice.
The world automobiles-to-rice relative supply curve is upward sloping, which means that as the world price ratio of rice to automobiles increases, the relative supply of automobiles to rice also increases. This reflects the fact that countries specialize in the production of goods for which they have a comparative advantage, and trade with other countries to obtain goods for which they do not have a comparative advantage.
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Suppose the probability of an IRS audit is 1.5 percent for U.S. taxpayers who file form 1040 and who earned $100,000 or more.
(a) What are the odds that such a taxpayer will be audited? (Round your answers to the nearest whole number.)
(b) What are the odds against such a taxpayer being audited? (Round your answers to the nearest whole number.)
(a) For every 100 taxpayers who file form 1040 and who earned $100,000 or more, about 2 of them will be audited. (b) for every 100 taxpayers who file form 1040 and who earned $100,000 or more, about 66 of them will not be audited.
(a) To calculate the odds that a taxpayer will be audited, we need to divide the probability of being audited by the probability of not being audited. The probability of being audited is given as 1.5 percent or 0.015. The probability of not being audited is the complement of the probability of being audited, which is 1 - 0.015 = 0.985. Therefore, the odds that a taxpayer will be audited are:
0.015/0.985 = 0.0152284264
To convert this to odds notation, we divide the probability of being audited by the probability of not being audited:
0.015/0.985 = 0.0152284264 = 0.0152 (rounded to four decimal places)
This means that for every 100 taxpayers who file form 1040 and who earned $100,000 or more, about 2 of them will be audited.
(b) The odds against a taxpayer being audited is the ratio of the probability of not being audited to the probability of being audited. We have already calculated the probability of not being audited to be 0.985, and the probability of being audited to be 0.015. Therefore, the odds against a taxpayer being audited are:
0.985/0.015 = 65.66666667
To convert this to odds notation, we divide the probability of not being audited by the probability of being audited:
0.985/0.015 = 65.66666667 = 66 (rounded to the nearest whole number)
This means that for every 100 taxpayers who file form 1040 and who earned $100,000 or more, about 66 of them will not be audited.
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QUESTION 5..... [1.5 marks]
The following data set represents the score distribution for the Final Exam in MATH 146:
55, 56, 57, 58, 59, 60, 60, 61, 63, 65, 69, 71, 78, 78, 79, 79, 82, 82, 83, 83
Find the 85th percentile.
Solution. Please write your detailed solution here:
answer
82
steps
put data in numerical order
55, 56, 57, 58, 59, 60, 60, 61, 63, 65, 69, 71, 78, 78, 79, 79, 82, 82, 83, 83
there are 20 numbers = 20
85 is the percentile = p
percentile rank formula
PR = (p/100) * (n + 1)
PR = (85/100) * (20 + 1) = 17.85
round up 17.85 to 18
it's the 18th number which is
82
chatgpt
Using function notation, write the formula for the function g(x) whose graph is obtained by
morizontally stretching the graph of f(x) by a factor of 2.
The function notation formula is given as g(x) = f(x/2)
Function notation explained.
Function notation is a way of representing a mathematical function using symbols and variables. It is a shorthand way of writing the rule or formula for a function, which specifies how the input values (usually denoted by x) are transformed into output values (usually denoted by y or f(x)).
In function notation, a function is typically represented by a letter (usually f, g, or h) followed by parentheses that enclose the input value or variable, such as f(x), g(t), or h(y). This notation indicates that the function takes an input value (x, t, or y) and produces a corresponding output value (f(x), g(t), or h(y)).
Assuming we want to horizontally stretch the graph of f(x) by a factor of 2 to obtain the graph of g(x), the function notation for g(x) can be written as:
g(x) = f(x/2)
In other words, we plug in x/2 instead of x in the formula for f(x) to get the corresponding value of g(x) that is horizontally stretched by a factor of 2. This is because when we substitute x/2 in f(x), it effectively multiplies the input (x) by 2, which horizontally stretches the graph by a factor of 2.
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How many total Sophomores were surveyed?
Answer: 22 sophomores were surveyed
Step-by-step explanation:
Find the centre and radius of 364+28y+y^2+x^2=-26x
Step-by-step explanation:
hope it will help you , and give some clue to do typical qno..
Bill's father can paint a room in 3 hours less than Bill can paint it. Working together they cam
complete the job in 2 hours. How much time would each require working alone?
Answer: Bob 3 Hours Jack 2 Hours
Step-by-step explanation:
Mel's cat eats 3/4 of a bag of cat food each month. How many
bags of cat food does Mel's cat eat in 10 months? Show your
work
Step-by-step explanation:
3/4 bag / months * 10 month = 30/ 4 bags = 7 1/2 bags
Standard Deviation. Find the Standard Deviation of the following set of data. You must fill out the table and show the ending calculations in order to get full credit here.
7.2, 8.9, 2.7, 11.6, 5.8, 10.2
show ALL steps
The standard deviation of the data set is 1.03.
What is the standard deviation?
The standard deviation is a measure of the amount of variation or dispersion of a set of data values. It measures how spread out the data is from the mean or average value.
To find the standard deviation, we first need to find the mean of the data set:
Mean = (7.2 + 8.9 + 2.7 + 11.6 + 5.8 + 10.2) / 6 = 7.4
Next, we calculate the deviations from the mean for each data point:
| x - mean | (x - mean)²
0.2 0.04
1.5 2.25
4.7 22.09
4.2 17.64
1.6 2.56
2.8 7.84
To find the variance, we add up the (x - mean)² values and divide by the number of data points:
Variance = (0.04 + 2.25 + 22.09 + 17.64 + 2.56 + 7.84) / 6 = 6.36/6 = 1.06
Finally, we take the square root of the variance to get the standard deviation:
Standard deviation = √(1.06) = 1.03 (rounded to two decimal places)
Therefore, the standard deviation of the data set is 1.03.
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please help me on this question
Answer:
x = 30 cm
Perimeter = 72 cm
Step-by-step explanation:
By Pythagoras theorem,
x² = 18² + 24²
x² = 324 + 576
x² = 900
x² = 30²
x = 30 cm
Perimeter of a triangle is just the sum of its sides,
Perimeter = 18 + 24 + 30
Perimeter = 72 cm
Answer:
30cm, 72cm
Step-by-step explanation:
c²=a²+b²
x²=18²+24²=900
x=√900
x=30cm
p=a+b+c
p=18+24+30
p=72cm
The diameter of a cone's circular base is 12 inches. The height of the cone is 12 inches.
What is the exact volume of the cone?
Enter your answer in the box.
in³
Answer: It is 144 but add pi symbol
Step-by-step explanation:
In conclusion the exact volume of the cone is 144π cubic inches.
How to solve and what does volume mean?
The radius of the circular base is half the diameter, which is 12/2 = 6 inches.
The volume of a cone can be found using the formula V = (1/3)πr²2h, where r is the radius and h is the height.
Substituting the given values, we get:
V = (1/3)π(6²2)(12)
V = (1/3)π(36)(12)
V = (1/3)(432π)
V = 144π
Therefore, the exact volume of the cone is 144π cubic inches.
Volume is a measure of the amount of space occupied by a three-dimensional object, such as a solid, liquid, or gas. It is typically measured in cubic units, such as cubic meters (m³) or cubic centimeters (cm³). The volume of an object can be determined by measuring its dimensions, such as length, width, and height, and applying the appropriate formula for the shape of the object.
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