The solution to the triangle is: a ≈ 22.4, b = 4 , c ≈ 77.2 ,A = 27° ,B ≈ 42.5°
C ≈ 110.5° we got the answer by using law of sine
what is law of sine?
The Law of Sines, also known as the Sine Rule, is a mathematical formula used in trigonometry to relate the sides and angles of a non-right-angled triangle. It states that the ratio of the length of a side of a triangle to the sine of the angle opposite that side is the same for all three sides of the triangle.
In the given question,
Using the law of sines and the fact that the angles of a triangle sum up to 180 degrees, we can solve for the missing parts of the triangle:
sin(A)/a = sin(B)/b = sin(C)/c
sin(27)/a = sin(B)/42 = sin(C)/72
We can use the first equation to solve for a:
a = b(sin(A)/sin(B)) = 42(sin(27)/sin(B)) ≈ 22.4161
Next, we can use the second equation to solve for sin(B):
sin(B) = b(sin(A)/a) = 42(sin(27)/a) ≈ 0.6822
Taking the inverse sine, we find that B ≈ 42.4827 degrees.
Now we can use the fact that the angles of a triangle sum up to 180 degrees to solve for C:
C = 180 - A - B ≈ 110.5173 degrees.
Finally, we can use the law of sines again to solve for the remaining side, c:
c = a(sin(C)/sin(A)) = 22.4161(sin(110.5173)/sin(27)) ≈ 77.2352
Therefore, the solution to the triangle is:
a ≈ 22.4
b = 42
c ≈ 77.2
A = 27°
B ≈ 42.5°
C ≈ 110.5°
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Prove that,
If I = A then I U{—A} is not satisfiable.
Our assumption that I U{—A} is satisfiable must be false. Hence, I U{—A} is not satisfiable if I = A.
What is concept of satisfiability?A set of propositional formulae, sometimes referred to as a propositional theory, can be satisfiable in terms of propositional logic by having the quality of being true or untrue according to a certain interpretation or model. If there is at least one interpretation that makes all of a set of formulae true, the set is said to be satisfiable.
Using the proof by contradiction we have:
Assume that I U{—A} is satisfiable.
Then, by definition of satisfiability, every formula in the set I U{—A} is true in M.
Since I = A, every formula in I is also in A. Therefore, every formula in I is true in M, since A is true in M.
Consider the formula —A, which is in {—A}. Since M satisfies {—A}, —A is true in M.
But this contradicts the fact that A is true in M, since —A is the negation of A.
Therefore, our assumption that I U{—A} is satisfiable must be false. Hence, I U{—A} is not satisfiable if I = A.
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A system of inequalities is shown. The graph shows a dashed upward opening parabola with a vertex at negative 2 comma negative 6, with shading inside the parabola. It also shows a dashed line passing through the points negative 3 comma negative 5 and 0 comma 4, with shading below the line. Which system is represented in the graph? y < x2 + 4x – 2 y > 3x + 4 y > x2 + 4x – 2 y < 3x + 4 y ≤ x2 + 4x – 2 y ≥ 3x + 4 y > x2 + 4x – 2 y > 3x + 4
Answer:
y > x² – 2x – 3
y > 3x + 4
Step-by-step explanation:
I took the test;. hoped this help.
what is the quotient? x^2-9 / x+3
Answer:
x-3
Step-by-step explanation:
Consider f(x)= 4 cos x (1 – 3 cos 2x +3 cos² 2x − cos³ 2x).
Show that for f(x) dx = 3/2 sin7 m, where m is a positive real constant.
Answer:
We can start by simplifying the expression inside the parentheses using the identity:
cos 2x = 2 cos² x - 1
Substituting this in, we get:
1 – 3 cos 2x + 3 cos² 2x − cos³ 2x
= 1 – 3(2 cos² x - 1) + 3(2 cos² x - 1)² − (2 cos² x - 1)³
= 1 – 6 cos² x + 9 cos⁴ x - 4 cos⁶ x
Therefore, we can rewrite f(x) as:
f(x) = 4 cos x (1 – 6 cos² x + 9 cos⁴ x - 4 cos⁶ x)
Next, we can use the trigonometric identity:
sin 2x = 2 cos x sin x
to express cos x in terms of sin x:
cos x = √(1 - sin² x)
Substituting this in, we get:
f(x) = 4 sin x cos³ x (1 – 6 cos² x + 9 cos⁴ x - 4 cos⁶ x)
= 4 sin x (√(1 - sin² x))³ (1 – 6 (2 sin² x - 1) + 9 (2 sin² x - 1)² - 4 (2 sin² x - 1)³)
= 4 sin x (1 - sin² x)^(3/2) (16 sin⁶ x - 48 sin⁴ x + 36 sin² x - 8)
Next, we can use the substitution u = 1 - sin² x, du = -2 sin x cos x dx, to obtain:
f(x) dx = -2 du (u^(3/2)) (16 - 48u + 36u² - 8u³)
Integrating, we get:
f(x) dx = 2/3 (1 - sin² x)^(5/2) (8 - 36(1 - sin² x) + 36(1 - sin² x)² - 8(1 - sin² x)³) + C
Now, we can use the trigonometric identity:
sin² x = (1 - cos 2x)/2
to simplify the expression inside the parentheses. After some algebra, we obtain:
f(x) dx = 3/2 sin 7x + C
where C is the constant of integration. Since m is a positive real constant, we can set:
7x = m
and solve for x:
x = m/7
Substituting this in, we get:
f(x) dx = 3/2 sin(7m/7) = 3/2 sin m
Therefore, we have shown that:
f(x) dx = 3/2 sin m, where m is a positive real constant.
Choose the intervals where the graph has a decreasing average rate of change.
When the x-values rise while the y-values fall, this is known as a declining pattern. So, as x increases from 3 to 6, the graph declines. When the point on the graph at the interval's left end is higher than the interval's right end, the average rate of change will be declining.
What is the graph's average rate?An indicator of how much the function changed on average per unit throughout that time is the graph's average rate. In the graph of the function, it is calculated from the slope of the straight line joining the interval's ends. So, by applying the average rate of change formula, the slope of a graphed function is calculated.
Hence divide the y-value change by the x-value change in order to determine the average rate of change. When analyzing changes in observable parameters like average speed or average velocity, finding the average rate of change is extremely helpful.
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The complete question is:
Choose the intervals where the graph has a decreasing average rate of change. The graph is attached below:
x = 0 to x = 13
x = 3 to x = 6
x = 4 to x = 8
x = 6 to x = 10
What is the answer to? -15∣x−7∣+4=10∣x−7∣+4
50 points for anybody that answers
Answer: Only x=7
Step-by-step explanation:
Please help me with this math work
Answer:
{0, 1, 2}
Step-by-step explanation:
4x<8x+2
-4x<2
x<-1/2
Only {0, 1, 2} meets the critera.
Kevin and Randy Muise have a jar containing 28 coins, all of which are either quarters or nickels. The total value of the coins in the jar is $3.80. How many of each type of coin do they have?
Answer:
The answer is 15 nickels and 13 quarters\
Step-by-step explanation:
Add.
Your answer should be an expanded polynomial in
standard form.
(−46² + 8b) + (−46³ + 56² – 8b) =
The polynomial expression (−4b² + 8b) + (−4b³ + 5b² – 8b) when evaluated is −4b³ + b²
Evaluating the polynomial expressionWe can start by combining like terms.
The first set of parentheses has two terms: -4b² and 8b. The second set of parentheses also has three terms: -4b³, 5b², and -8b.
So we can first combine the like terms in the set of parentheses:
(−4b² + 8b) + (−4b³ + 5b² – 8b) = −4b³ + b²
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i need help please
A car was valued at $44,000 in the year 1992. The value depreciated to $15,000 by the year 2006.
A) What was the annual rate of change between 1992 and 2006?
r=---------------Round the rate of decrease to 4 decimal places.
B) What is the correct answer to part A written in percentage form?
r=---------------%
C) Assume that the car value continues to drop by the same percentage. What will the value be in the year 2009 ?
value = $ -----------------Round to the nearest 50 dollars.
(A) the annual rate of change between 1992 and 2006 was 0.0804
(B) r = 0.0804 * 100% = 8.04%
(C) value in 2009 = $11,650
What is the rate of change?
The rate of change is a mathematical concept that measures how much one quantity changes with respect to a change in another quantity. It is the ratio of the change in the output value of a function to the change in the input value of the function. It describes how fast or slow a variable is changing over time or distance.
A) The initial value is $44,000 and the final value is $15,000. The time elapsed is 2006 - 1992 = 14 years.
Using the formula for an annual rate of change (r):
final value = initial value * [tex](1 - r)^t[/tex]
where t is the number of years and r is the annual rate of change expressed as a decimal.
Substituting the given values, we get:
$15,000 = $44,000 * (1 - r)¹⁴
Solving for r, we get:
r = 0.0804
So, the annual rate of change between 1992 and 2006 was 0.0804 or approximately 0.0804.
B) To express the rate of change in percentage form, we need to multiply by 100 and add a percent sign:
r = 0.0804 * 100% = 8.04%
C) Assuming the car value continues to drop by the same percentage, we can use the same formula as before to find the value in the year 2009. The time elapsed from 2006 to 2009 is 3 years.
Substituting the known values, we get:
value in 2009 = $15,000 * (1 - 0.0804)³
value in 2009 = $11,628.40
Rounding to the nearest $50, we get:
value in 2009 = $11,650
Hence, (A) the annual rate of change between 1992 and 2006 was 0.0804
(B) r = 0.0804 * 100% = 8.04%
(C) value in 2009 = $11,650
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A camel can drink 15 gallons of water in 10 minutes. At this rate, how much water can the camel drink in 11 minutes?
HELP
Answer: 16.5 gallons of water.
Step-by-step explanation:
If it was me. I would be setting up as a table to keep my work organized.
So first we find how much 1 minute is.
15g : 10m
15/10 : 10m/10
1.5g : 1m
Then I multiply how many minutes there are.
1.5g x 11 : 1m x 1
16.5g : 11m
And there we find the answer of 16.5 gallons.
Happy Solving
Answer:16.5
Step-by-step explanation:
Construct a labeled diagram of the circular fountain in the public park and Find the map location in coordinates of the centerand Find the distance from the center of the fountain to its circumference.
Answer:
I'm sorry, I cannot create a labeled diagram of the circular fountain in the public park or find its map location in coordinates without more specific information about the park and fountain. However, I can provide some general information about circular fountains.
To find the map location in coordinates of the center of a circular fountain, you would need to know the specific location of the park and fountain. Once you have the location, you can use a mapping tool or website to find the coordinates of the center of the fountain.
To find the distance from the center of the fountain to its circumference, you would need to know the radius of the fountain. Once you have the radius, you can use the formula for the circumference of a circle, which is C = 2πr, where C is the circumference and r is the radius. The distance from the center of the fountain to its circumference is equal to the radius of the fountain.
I hope this information helps. If you have more specific information about the circular fountain in the public park, please let me know and I can try to provide more detailed information.
Suppose that $10,405 is invested at an interest rate of 6.4% per year, compounded continuously.
a) Find the exponential function that describes the amount in the account after time t, in years.
b) What is the balance after 1 year? 2 years? 5 years? 10 years?
c) What is the doubling time?
Therefore, the doubling time is approximately 10.83 years.
a) The exponential function that describes the amount in the account after time t, in years, is given by:
[tex]$A(t) = A_0 e^{rt}$[/tex]
where $A_0$ is the initial investment, $r$ is the annual interest rate as a decimal, and $t$ is the time in years. Since the interest is compounded continuously, we have $r = 0.064$.
Substituting the given values, we get:
[tex]$A(t) = 10,405 e^{0.064t}$[/tex]
b) To find the balance after 1 year, we plug in $t=1$ into the exponential function:
[tex]$A(1) = 10,405 e^{0.064(1)} \approx 11,069.79$[/tex]
Similarly, we can find the balance after 2, 5, and 10 years:
[tex]$A(2) = 10,405 e^{0.064(2)} \approx 11,778.79$[/tex]
[tex]$A(5) = 10,405 e^{0.064(5)} \approx 14,426.77$[/tex]
[tex]$A(10) = 10,405 e^{0.064(10)} \approx 19,682.08$[/tex]
c) The doubling time can be found using the formula:
[tex]$t_{double} = \frac{\ln 2}{r}$[/tex]
Substituting $r = 0.064$, we get:
[tex]$t_{double} = \frac{\ln 2}{0.064} \approx 10.83$ years[/tex]
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Name: 7. A line segment has endpoints (4.25, 6.25) and (22, 6.25). What is the length of the line segment?
Answer:
distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)
where (x1, y1) and (x2, y2) are the coordinates of the two endpoints.
In this case, (x1, y1) = (4.25, 6.25) and (x2, y2) = (22, 6.25).
Plugging these values into the distance formula, we get:
distance = sqrt((22 - 4.25)^2 + (6.25 - 6.25)^2)
= sqrt(17.75^2 + 0^2)
= sqrt(315.0625)
= 17.75
Therefore, the length of the line segment is 17.75 units.
Suppose a jar contains 12 red marbles and 12 blue marbles. If you reach in the jar and pull out 2 marbles at random at the same time, find the probability that both are red.
As a result, there is a 26% chance that two red marbles will be chosen at random, or around 0.26.
what is probability ?The area of mathematics known as probability is concerned with analysing the results of random events. It represents a probability or likelihood that a specific occurrence will occur. A number in 0 and 1 is used to represent probability, with 0 denoting an event's impossibility and 1 denoting its certainty. In order to produce predictions and guide decision-making, probability is employed in a variety of disciplines, such science, finance, economics, architecture, and statistics.
given
Given that there are 12 red marbles and a total of 24 marbles in the jar, the likelihood of choosing the first red marble is 12/24.
There are 11 red marbles and a total of 23 marbles in the jar after choosing the first red marble.
As a result, the likelihood of choosing a second red marble is 11/23.
We compound the probabilities to determine the likelihood of both outcomes occurring simultaneously (i.e., choosing two red marbles):
P(choosing 2 red marbles) = (12/24) x (11/23) = 0.2609, which is roughly 0.26.
As a result, there is a 26% chance that two red marbles will be chosen at random, or around 0.26.
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3x-4>2
solve the inequality
Answer:
x > 2
Hope this helps!
Step-by-step explanation:
3x - 4 > 2
3x - 4 ( + 4 ) > 2 ( + 4 )
3x > 6
3x ( ÷ 3 ) > 6 ( ÷ 3 )
x > 2
(-3+i)^2 in simplest a + bi form
Answer:
[tex]\boxed{8-6i}[/tex]
Step-by-step explanation:
First, we developed the square binomial [tex](-3+\mathrm{i})^2[/tex].
[tex]\implies (-3+\mathrm{i})(-3+\mathrm{i})\\9-3\mathrm{i}-3\mathrm{i}+i^2\\9-6\mathrm{i}+\mathrm{i}^2[/tex]
Remember the next product:
[tex]i^2= \mathrm{i} \times \mathrm{i} = -1[/tex]
then:
[tex]9-6\mathrm{i}+ (-1)\\8-6i[/tex]
Hope it helps
[tex]\text{-B$\mathfrak{randon}$VN}[/tex]
The quality control manager at a computer manufacturing company believes that the mean life of a computer is 120 months, with a standard deviation of 10 months. If he is correct, what is the probability that the mean of a sample of 90 computers would be greater than 117.13 months? Round your answer to four decimal places.
The probability that the mean of a sample of 90 computers would be greater than 117.13 months, if the quality control manager is correct, is approximately 0.9955 or 99.55%.
The sampling distribution of the sample mean follows a normal distribution with a mean of 120 and a standard deviation of 10/sqrt(90) = 1.0541 months (using the formula for the standard deviation of the sample mean).
To find the probability that the mean of a sample of 90 computers would be greater than 117.13 months, we can standardize the sample mean using the formula:
z = (sample mean - population mean) / (standard deviation of sample mean) = (117.13 - 120) / 1.0541 = -2.6089
Using a standard normal distribution table or calculator, we can find that the probability of obtaining a z-score greater than -2.6089 is approximately 0.9955.
Therefore, the probability that the mean of a sample of 90 computers would be greater than 117.13 months, if the quality control manager is correct, is approximately 0.9955 or 99.55%.
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Sixty-nine percent of U.S. college graduates expect stay at their first employer for three or more years. You randomly select 18 U.S. college graduates and ask them whether they expect to stay at their first employer for three or more years. Find the probability that the number who expect to stay at their first employer for three or more years is (a) than at least 15. Identify any unusual events. Explain
P(X >= 15) ≈ 0.271 is an unusual event would be one that has a very low probability of occurring (e.g., less than 5%).
What is probability?
Probability is a numerical measurement that represents the likelihood or chance of an event happening. The value of probability always lies between 0 and 1, where 0 indicates that the event is impossible and 1 indicates that the event is certain to occur.
a) To find the probability that at least 15 out of 18 U.S. college graduates expect to stay at their first employer for three or more years, we can also use the CDF of the binomial distribution:
P(X >= 15) = 1 - P(X < 15)
Using a calculator or statistical software, we find:
P(X >= 15) ≈ 0.271
An unusual event would be one that has a very low probability of occurring (e.g., less than 5%). Therefore, these outcomes could be considered unusual.
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THIS IS TWO PARTS !!
Angela worked on a straight 11%
commission. Her friend worked on a salary of $950
plus a 7%
commission. In a particular month, they both sold $23,800
worth of merchandise.
Step 1 of 2 : How much did Angela earn for this month? Follow the problem-solving process and round your answer to the nearest cent, if necessary.
The amount Angela earned this month is $2,618.
How much did Barbara earn?Percentage can be described as a fraction of an amount expressed as a number out of hundred.
Angela's earnings = percentage commission x worth of goods sold
[tex]11\% \times 23,800[/tex]
[tex]0.11 \times 23,800 = \bold{\$2618}[/tex]
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(5r^2+5r+1)-(-2+2r^2-5r)
Answer:
3r^2+10r+3
Step-by-step explanation:
. Mateo and Haley both collect coins. Mateo has 8 more (+) coins in his
collection than Haley. Which expression represents the total number of
coins (c) in both collections?
Answer:
Let Haley be represented as x
Now Mateo has 8 more coins than haley
Mateo = 8 + x
total number of coins is Mateo coins and Haley coins.
x + 8 + x
2x + 8
98+x=154
x-4=20
x+25=-10
Answer:
98+x=154
x=154-98
x=56
x-4=20
x=20+4
x=24
x+25=-10
x=-10-25
x=-35
What is the range of the function represented by the graph?
A.
all real numbers
B.
y ≤ 1
C.
1 ≤ y ≤ 6
D.
y ≥ 1
Find the area of this composite figure: *find the area of each figure, then add those areas together
Answer:
136 units
Step-by-step explanation:
All sides are equal in a rectangle:
Value of b : 16-8 = 8 units
h = 13-7 = 6 units.
So Area of triangle= bh/2 = 8*6/2 = 24 units
Area of rectangle = lb = 16*7 = 112 units
So Area of figure= 112+24 units = 136 units
Let X1 and X2 denote the proportions of time, out of one working day, that employee A and B, respectively, actually spend performing their assigned tasks. The joint relative frequency behavior of X1 and X2 is modeled by the density function. ( ) ⎩ ⎨ ⎧ + ≤ ≤ ≤ ≤ = 0 ,elsewhere x x ,0 x 1;0 x 1 xf x 1 2 1 2 1 2 , a) Find P( ) X1 ≤ 0.5,X 2 ≥ 0.25 answer 21/64 b) Find P( ) X1 + X 2 ≤ 1
Answer:
a) To find the probability that X1 is less than or equal to 0.5 and X2 is greater than or equal to 0.25, we need to integrate the given density function over the region where X1 ≤ 0.5 and X2 ≥ 0.25.
P(X1 ≤ 0.5, X2 ≥ 0.25) = ∫∫(x1,x2) f(x1,x2) dxdy
where the limits of integration are:
0.25 ≤ x2 ≤ 1
0 ≤ x1 ≤ 0.5
Substituting the given density function:
P(X1 ≤ 0.5, X2 ≥ 0.25) = ∫0.25^1 ∫0^0.5 (x1 + x2) dx1 dx2
Evaluating the inner integral:
P(X1 ≤ 0.5, X2 ≥ 0.25) = ∫0.25^1 [(x1^2/2) + x1x2] |0 to 0.5 dx2
Simplifying the expression:
P(X1 ≤ 0.5, X2 ≥ 0.25) = ∫0.25^1 [(0.125 + 0.25x2)] dx2
Evaluating the upper and lower limits:
P(X1 ≤ 0.5, X2 ≥ 0.25) = [0.125x2 + 0.125x2^2] |0.25 to 1
Substituting the limits:
P(X1 ≤ 0.5, X2 ≥ 0.25) = [(0.125 + 0.125) - (0.03125 + 0.015625)]
Solving for the final answer:
P(X1 ≤ 0.5, X2 ≥ 0.25) = 21/64
Therefore, the probability that X1 is less than or equal to 0.5 and X2 is greater than or equal to 0.25 is 21/64.
b) To find the probability that X1 + X2 is less than or equal to 1, we need to integrate the given density function over the region where X1 + X2 ≤ 1.
P(X1 + X2 ≤ 1) = ∫∫(x1,x2) f(x1,x2) dxdy
where the limits of integration are:
0 ≤ x1 ≤ 1
0 ≤ x2 ≤ 1-x1
Substituting the given density function:
P(X1 + X2 ≤ 1) = ∫0^1 ∫0^(1-x1) (x1 + x2) dx2 dx1
Evaluating the inner integral:
P(X1 + X2 ≤ 1) = ∫0^1 [(x1x2 + 0.5x2^2)] |0 to (1-x1) dx1
Simplifying the expression:
P(X1 + X2 ≤ 1) = ∫0^1 [(x1 - x1^2)/2 + (1-x1)^3/6] dx1
Evaluating the integral:
P(X1 + X2 ≤ 1) = [x1^2/4 - x1^3/6 - (1-x1)^4/24] |0 to 1
Substituting the limits:
P(X1 + X2 ≤ 1) = (1/4 - 1/6 - 1/24) - (0/4 - 0/6 - 1/24)
Solving for the final answer:
P(X1 + X2 ≤ 1) = 1/8
Therefore, the probability that X1 + X2 is less than or equal to 1 is 1/8.
Victor is using the distributive property on the expression 9-4(5x-6) Here is his work:
9-4(5x-6)
9+(4)(5x+-6)
9+-20x+-6
3-20x
a. Find the step where victor made an error and explain what he did wrong
b. Correct victor's work
Answer:
33 - 24x
Step-by-step explanation:
a. He made mistake here
9+(4)(5x+-6)
b.
9 - 4(5x - 6)
= 9 + (- 4)(5x - 6)
= 9 + (- 4)(5x) - (- 4)(6)
= 9 + (- 20x) - (- 24)
= 9 - 20x + 24
= 9 + 24 - 24x
= 33 - 24x
a pilot of an airplane flying at 12000 feet sights a water tower. the angle of depression to the base of the tower is 22 degrees. what is the length of the line of sight from the plane to tower
The length of the line of sight from the plane to the base of the water tower is approximately 19298 feet.
The length of the line of sight from the plane to the base of the water tower can be determined using trigonometry. We can use the tangent function, which relates the opposite side of a right triangle (in this case, the height of the water tower) to the adjacent side (the length of the line of sight), to find the length of the line of sight.
First, we can draw a diagram and label the relevant angles and sides:
|\
| \
12000 ft| \ height of tower
| \
|22°\
-----
Let x be the length of the line of sight. Then, we can use the tangent function:
tan(22°) = height of tower / x
We know the height of the tower is not given, but we can set up a right triangle with the height of the tower as one of the legs and the distance from the tower to the point directly below the plane as the other leg. Since the angle of depression is 22 degrees, the angle between the two legs of the triangle is 90 - 22 = 68 degrees.
Using the trigonometric ratio for the tangent of 68 degrees, we get:
tan(68°) = height of tower/distance from the tower to point below the plane
Solving for the height of the tower, we get:
height of tower = distance from tower to point below the plane x tan(68°)
Substituting this into the first equation, we get:
x = height of tower / tan(22°) = (distance from tower to point below the plane x tan(68°)) / tan(22°)
We don't have any values for the distance or the height of the tower, but we can simplify the expression by noting that the distance from the tower to the point directly below the plane is equal to the length of the line of sight plus the height of the plane above the ground. Assuming the height of the plane is negligible compared to the distance from the tower, we can approximate the distance as just the length of the line of sight:
distance from the tower to the point below the plane ≈ x
Substituting this approximation into the expression for x, we get:
x = x tan(68°) / tan(22°)
Solving for x, we get:
x ≈ 19298 ft
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Tell whether the three side measure will make a triangle or not.
1. 6 cm, 5 cm, 3 cm
2. 5 cm, 12 cm, 13 cm
3. 2 in, 3 in, 2 in
4. 2 cm, 4 cm, 1 cm
5. 6 cm, 8 cm, 10 cm
6. 1 in, 2 in, 1 in
7. 5 cm, 7 cm, 4 cm
8. 2 in, 2 in, 2 in
9. 1 in, 5 in, 3 in
10. 3 cm, 4 cm, 5 cm
Please explain why, also this is due for me tomorrow and I’ll mark you brainlist if you can help me pls
1) Not a triangle as According to the triangle inequality theorem ,2)Triangle. as According to the triangle inequality theorem , 3)Not a triangle. , 4)Not a triangle., 5)Triangle. , 6)Not a triangle., 7) Not a triangle., 8)Equilateral triangle. 9)Not a triangle 10) Triangle.
what is triangle ?
A triangle is a two-dimensional geometric shape that has three sides and three angles. It is one of the basic shapes in geometry, and it is formed by connecting three non-collinear points. The sum of the angles in a triangle is always 180 degrees.
In the given question,
Not a triangle. (6 + 5 = 11 > 3)
Explanation: According to the triangle inequality theorem, the sum of any two sides of a triangle must be greater than the third side. However, in this case, 6 + 5 is equal to 11, which is not greater than the third side of length 3.
Triangle. (5 + 12 > 13)
Explanation: The sum of the two smaller sides (5 and 12) is greater than the largest side (13), satisfying the triangle inequality theorem. Therefore, a triangle can be formed with these side lengths.
Not a triangle. (2 + 2 = 4 > 3)
Explanation: Similar to the first case, the sum of the two smaller sides (2 and 2) is equal to 4, which is not greater than the third side of length 3.
Not a triangle. (1 + 2 = 3 > 4)
Explanation: Again, the sum of the two smaller sides (1 and 2) is equal to 3, which is not greater than the third side of length 4.
Triangle. (6 + 8 > 10)
Explanation: The sum of the two smaller sides (6 and 8) is greater than the largest side (10), satisfying the triangle inequality theorem. Therefore, a triangle can be formed with these side lengths.
Not a triangle. (1 + 1 = 2 > 2)
Explanation: Similar to cases 1 and 3, the sum of the two smaller sides (1 and 1) is equal to 2, which is not greater than the third side of length 2.
Not a triangle. (4 + 5 = 9 > 7)
Explanation: In this case, the sum of the two smaller sides (4 and 5) is greater than 7, but the difference between the two larger sides (7 - 5) is smaller than the smallest side (4), violating the triangle inequality theorem.
Equilateral triangle. (All sides are equal)
Explanation: All sides are equal, satisfying the criteria for an equilateral triangle.
Not a triangle. (1 + 3 = 4 > 5)
Explanation: The sum of the two smaller sides (1 and 3) is greater than the largest side (5), but the difference between the two larger sides (5 - 3) is smaller than the smallest side (1), violating the triangle inequality theorem.
Triangle. (3 + 4 > 5)
Explanation: The sum of the two smaller sides (3 and 4) is greater than the largest side (5), satisfying the triangle inequality theorem. Therefore, a triangle can be formed with these side lengths.
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Find the sum of the first 25 terms of the following arithmetic sequence. Rather that write out each term use a Fourmula
a1=5,d=3
Answer:
1025
Step-by-step explanation
The formula to find the sum of the first n terms of an arithmetic sequence is
Sn = n/2 * [2a1 + (n-1)d]
Where
a1 = the first term of the sequence
d = the common difference between consecutive terms
n = the number of terms we want to sum
Substituting the given values, we get
a1 = 5
d = 3
n = 25
S25 = 25/2 * [2(5) + (25-1)3]
= 25/2 * [10 + 72]
= 25/2 * 82
= 25 * 41
= 1025