A triangle has sides with lengths 5, 12, and 13. Verify this is a Pythagorean triple. Approximate the acute angles in this triangle.
Answers
A triangle with lengths 5, 12, and 13 is a Pythagorean triple
The approximate acute angles are 22.6° and 67.4°
Pythagorean triple
Pythagorean triple consist of positive number(a, b, c) such that it obeys the rule:
c² = a² + b²A triangle whose sides form a Pythagorean triple is called a right angle triangle.
The longest side is the hypotenuse side.
Therefore,
5² + 12² 25 + 144 = 169√169 = 13Therefore,
5² + 12² = 13²
This means the triangle is a Pythagorean triple.
Acute angles
Acute angles are angles that are less than 90 degrees. This means the other two angles are acute angle.
Therefore, let's find them
tan ∅ = opposite / adjacent = tan ∅ = 5 / 12 = ∅ = 22.6198649155 = 22.6°180 - 22.6 - 90 = 67.4°learn more on Pythagorean triple here: https://brainly.com/question/2293263?referrer=searchResults
The given numbers (can be taken as) the length of the three sides of a
(right) triangle.
Correct response:
13² = 5² + 12², therefore, 5, 12, and 13 are a Pythagorean tripleThe acute angles are; θ₁ ≈ 67.38°, and θ₂ ≈ 22.62°Method of analysis to verify a Pythagorean tripleA Pythagorean triple are three positive integers, a, b, and c that are
related as follows;
c² = a² + b²
Therefore;
\(c = \mathbf{\sqrt{a^2 + b^2}}\)
Where;
a = 5, b = 12, we have;
\(\mathbf{\sqrt{5^2 + 12^2} } = 13 = c\)
Therefore;
The three numbers form a Pythagorean triple, the hypotenuse side (longest side = c = 13)The acute angles are found as follows;
From trigonometric ratio, we have;
\(An \ tangent \ of \ acute \ angle \ \theta_1, \ \tan(\theta_1) = \dfrac{12}{5} = \mathbf{ 2.4}\)
Which gives;
An acute angle of the right triangle, θ₁ = arctan(2.4) ≈ 67.38°The acute angles of a right triangle are complimentary.
Therefore;
The other acute angle is therefore, θ₂ ≈ 90° - 67.38° = 22.62°Learn more about the Pythagorean theorem here:
https://brainly.com/question/18929869
Related Questions
Suppose a Hospitality Management student is picked at random. What is the probability that the student has not visited between 21 and 30 states
Answers
The probability that the student has not visited between 21 and 30 states is 0.4772 or approximately 48%.
Suppose a Hospitality Management student is picked at random.
We need to calculate the probability that the student has not visited between 21 and 30 states.
To calculate the probability, we can use the formula:
Probability = Number of favorable outcomes / Total number of possible outcomes
Let X be the number of states visited by the student.
Given that X follows a normal distribution with mean μ = 25 and standard deviation σ = 7.
So, the z-score for X = 21 and X = 30 can be calculated as follows:
z1 = (21 - 25) / 7 = -0.57,
z2 = (30 - 25) / 7 = 0.71
Now, we can find the probability of the student not visiting between 21 and 30 states using the standard normal distribution table:
P(21 < X < 30) = P(z < 0.71) - P(z < -0.57)= 0.7611 - 0.2839= 0.4772
Therefore, the probability that the student has not visited between 21 and 30 states is 0.4772 or approximately 48%.Note: The answer is 48% approximately.
Learn more about standard normal distribution here https://brainly.com/question/30390016
#SPJ11
The vertices of ABC are A (0, 0), B (6, 0), and C (3, 7). What type of triangle is ABC?
A. acute isosceles triangle
B. acute scalene triangle
C. right isosceles triangle
D. right scalene triangle
Answers
Two sides of triangle are equal triangle ABC acute scalene triangle. Option B right choice.
The type of triangle ABC can use the Pythagorean to check if it is a right triangle and the distance formula to check if it is an isosceles or scalene triangle.
Using the distance formula can find the lengths of the three sides of triangle ABC:
AB = √((6-0)² + (0-0)²) = 6
BC = √((3-6)² + (7-0)²) = √(58)
AC = √((3-0)² + (7-0)²) = √(58)
BC=AC ≠AB , and the triangle is a acute scalene triangle.
The triangle is a right triangle can use the Pythagorean:
If the triangle is a right triangle, then one of the sides must be the hypotenuse and the other two sides must be the legs.
Let's assume that AC is the hypotenuse and AB and BC are the legs. Then, we have:
(AC)² = (AB)² + (BC)²
Substituting the values we found earlier, we have:
(√58)² = 6² + (BC)²
58 = 36 + (BC)²
(BC)² = 22
22 is not a perfect square so (BC)² cannot be equal to the difference between two perfect squares.
Triangle ABC is not a right triangle.
Option B right choice.
For similar questions on acute scalene triangle
https://brainly.com/question/24057388
#SPJ11
How do you use the distributive property to write the expression without parentheses: 6(a-2)?
Answers
Answer:
\(6(a - 2) = 6a - 12\)
Help please (Image attached)
Answers
The value of the infinite series as n tends to 0 is: 0
How to estimate infinite series?Infinite series is defined as the sum of infinitely many numbers related in a given way and listed in a given order. Infinite series are important in mathematics and in such disciplines as physics, chemistry, biology, and engineering.
From the infinite series, we want to find the value of the series as n tends to 0.
We are given the series as:
x/2ˣ
At x = 0, we have:
0/2⁰ = 0/1 = 0
Read more about infinite series at: https://brainly.com/question/30221799
#SPJ1
2041 to 3sf
Anyone help??
Answers
Answer:
2040
Step-by-step explanation:
hope this helps
which function in vertex form is equivalent to f(x) = x2 8 – 16x?f(x) = (x – 8)2 – 56f(x) = (x – 4)2 0f(x) = (x 8)2 – 72f(x) = (x 4)2 – 32
Answers
The given function f(x) = x² - 8x can be rewritten in vertex form using the process of completing the square. The vertex form of a quadratic function is f(x) = a(x - h)² + k, where (h, k) is the vertex of the parabola. The process of completing the square involves adding and subtracting a constant term to the expression in such a way that it becomes a perfect square trinomial.
So, f(x) = x² - 8x = (x² - 8x + 16) - 16 = (x - 4)² - 16. Therefore, the function f(x) = x² - 8x is equivalent to f(x) = (x - 4)² - 16 in vertex form. Now, we need to check which function in vertex form is equivalent to f(x) = x² - 8x from the given options:Option A: f(x) = (x - 8)² - 56Comparing it with the vertex form f(x) = a(x - h)² + k, we can see that h = 8, which is not equal to -4. So, this function is not equivalent to f(x) = x² - 8x.
Option B: f(x) = (x - 4)² + 0Comparing it with the vertex form f(x) = a(x - h)² + k, we can see that h = 4, which is equal to -(-4). So, this function is equivalent to f(x) = x² - 8x.Option C: f(x) = (x + 8)² - 72Comparing it with the vertex form f(x) = a(x - h)² + k, we can see that h = -8, which is not equal to -4. So, this function is not equivalent to f(x) = x² - 8x.Option D: f(x) = (x + 4)² - 32Comparing it with the vertex form f(x) = a(x - h)² + k, we can see that h = -4, which is equal to -(-4). So, this function is equivalent to f(x) = x² - 8x.Therefore, the function in vertex form equivalent to f(x) = x² - 8x is f(x) = (x - 4)² - 16.
To know more about parabola visit:
https://brainly.com/question/11911877
#SPJ11
30
35
40
45
50
55
60
A teacher kept track of how much money each of her students raised for the fundraiser. She put the data in th
How many students raised $50 or more?
A)
2
B)
3
)
4
Answers
Answer:
4 because when you count all the x students who got $50 I could see that there where four
solve for x on both
1. -1-3x+7x=17
2. 4x-5+7x=-10
(please show your work if possible:)
Answers
Step-by-step explanation:
1. -3x+7x=18
x(-3+7)=18
x=\(\frac{18}{(-3+7)}\)
2. 4x+7x=-5
x(4+7)=-5
x=\(\frac{-5}{(4+7)}\)
I hope this helped, may be wrong but ive done it my way
The fish population in a lake decreases by 2% each year. What is the common ratio? –0. 02 –0. 98 0. 02 0. 98.
Answers
The common ratio when the fish population is decreasing by 2% will be 0.98
What will be the Common ratio?
It is given that the fish population in the lake is decreasing by 2% every year.
Now to find the common ratio we will calculate next year's population
The next year's population will be given as
\(100-2=98\)
Here the population of the fish will be 98% for the next year or we can convert it
98 % = \(\dfrac{98}{100} =0.98\)
Thus the common ratio when the fish population is decreasing by 2% will be 0.98
To know more about common ratio follow
https://brainly.com/question/1509142
6x - y = -35
5x - 2y = -35
Answers
Answer:
x=-5 y=5 (-5,5)
Step-by-step explanation:
(6x-y=-35)-2
5x-2y=-35
-12x+2y=70
5x-2y=-35
-7x=35
x=-5
5(-5)-2y=-35
-25-2y=-35
-2y=-10
y=5
17.
Denise graphed the points AC-3, 5) and B(1, -9) on a coordinate plane and
connected the two points to form AB.
-
To the nearest tenth, what is the length of AB?
A.
6.4 units
B.
14.6 units
C.
52.7 units
D.
212.0 units
Answers
find the equation of the tangent line to the curve at the given point. y = 9x − 6 x , (1, 3)
Answers
To find the equation of the tangent line to the curve y = 9x - (6/x) at the given point (1, 3), follow these steps: 1. Find the derivative of the function: dy/dx r,
Represents the slope of the tangent line at any point (x, y) on the curve.
y = 9x - (6/x)
dy/dx = d(9x)/dx - d(6/x)/dx
Using the power rule for the first term and the quotient rule for the second term:
dy/dx = 9 - (-6/x^2)
dy/dx = 9 + 6/x^2
2. Find the slope of the tangent line at the given point (1, 3) by plugging x = 1 into the derivative:
m = 9 + 6/1^2
m = 9 + 6
m = 15
3. Use the point-slope form of a linear equation to find the equation of the tangent line:
y - y1 = m(x - x1)
where (x1, y1) is the given point (1, 3) and m is the slope:
y - 3 = 15(x - 1)
4. Solve for y to get the equation of the tangent line:
y = 15(x - 1) + 3
y = 15x - 15 + 3
y = 15x - 12
The equation of the tangent line to the curve y = 9x - (6/x) at the given point (1, 3) is y = 15x - 12.
To know more about derivative click here
brainly.com/question/29096174
#SPJ11
Consider the system of linear equations 2x + 3y = 8 and 3x + y = –2. Which statement is correct?
The point (1, 2) is not a solution to the system of equations because it satisfies neither equation.
The point (1, 2) is not a solution to the system of equations because it does not satisfy the equation 3x + y = –2.
The point (1, 2) is a solution to the system of equations because it satisfies the equation 2x + 3y = 8.
The point (1, 2) is a solution to the system of equations because it satisfies both equations.
Answers
Answer:
Answer: The point (1, 2) is not a solution to the system of equations because it does not satisfy the equation 3x + y = –2.
Step-by-step explanation:
System of Equations
Consider the following system of equations
2x + 3y = 8 [1]
3x + y = -2 [2]
And the point (1,2). Substituting in both equations:
For equation [1]:
2*1 + 3*2 = 8
2 + 6 = 8
8 = 8
Since the equation is true, point (1,2) satisfies the equation 2x + 3y = 8
Now for equation [2]:
3*1 + 2 = -2
3 + 2 = -2
5 = -2
Since this equation is false, point (1,2) does not satisfy the equation 3x + y = -2
Answer: The point (1, 2) is not a solution to the system of equations because it does not satisfy the equation 3x + y = –2.
Answer:
B: The point (1, 2) is not a solution to the system of equations because it does not satisfy the equation 3x + y = –2.
Step-by-step explanation:
i got it right on my quiz!
Which expression represents the area of the base of the cone? A cone with diameter 12 inches, height 8 inches, and slant height 10 inches. B = pi r squared (pi) (5 squared) (pi) (6 squared) (pi) (10 squared) (pi) (12 squared)
Answers
Answer: (pi) (6 squared)
Step-by-step explanation:
Hi, the base area of a cone is a circle, so, to answer this question we have to apply the next formula:
Area of a circle: (pi) radius^2
The diameter (d) of a circle is equal to: 2 radius
So:
D = 2r
Replacing with the value given:
12 =2r
12/2=r
radius= 6 inches
Back with the Area formula:
A = (pi) 6^2
Feel free to ask for more if needed or if you did not understand something.
Answer:
B
Step-by-step explanation:
B is correct
Find the Quotient what is 6,589 ÷8
Answers
6,589 divide 8 is 823
A computer company will sell its new tablet
computer for six hundred forty dollars and
sixty-five cents. How is this number written in
expanded notation?
Answers
Explanation: J is equivalent to $640.65
hope that helps if you have any questions let me know and if you could mark this as brainliest i would really appreciate it!!
t=1. I need as soon as possible 1. [30 MARKS] Let t be the 7th digit of your Student ID. Answer each of the following questions:
(a) [5 MARKS] Find the limit of the following sequence:
Xn =
etn3 t2 + 3n+ (t + 1)n3
en [In(1)-In(t+2)] and qn = (Yn)2.
Define the sequences yn = =en
(b) [4 MARKS] If yn converges to I, where does a converge to? Write your answer in terms of I.
(c) [5 MARKS] Define a subsequence a, by choosing every second element of yn (i.e. ak = Y2k). Write down the first 4 elements of an. Where does this subsequence converge to if yn converges to I? Write your answer in terms of 1.
(d) [8 MARKS] Prove the following statement: A sequence can have at-most one limit.
(e) [8 MARKS] Argue whether a and q can converge to two different limits. Using your conclusion, calculate the value of the limit ..
Answers
In this question, we are provided with a sequence Xn and a related sequence Yn. We need to find the limit of Xn, determine the limit of a given subsequence yn, prove a statement regarding limits of sequences, and discuss the possibility of different limits for sequences a and q. Finally, we calculate the value of a specific limit.
(a) We are asked to find the limit of the sequence Xn. By simplifying the expression and applying limit properties, we can evaluate the limit of Xn as n approaches infinity.
(b) We need to determine where sequence a converges to if sequence yn converges to I. By understanding the relationship between the sequences and the given convergence, we can express the limit of a in terms of I.
(c) A subsequence an is defined by choosing every second element of yn. We are asked to write down the first four elements of an and identify the convergence point of this subsequence. By considering the pattern of the chosen elements, we can express the limit of an in terms of 1, based on the convergence of yn.
(d) We are required to prove the statement that a sequence can have at most one limit. By utilizing the definition of convergence and assuming two different limits, we can arrive at a contradiction, demonstrating that a sequence cannot have more than one limit.
(e) We are asked to argue whether sequences a and q can converge to different limits. By analyzing the given information and using the conclusion from part (d), we can determine whether it is possible for a and q to have distinct limits. Based on this conclusion, we then calculate the value of the specified limit.
To learn more about limit: -brainly.com/question/12211820
#SPJ11
HURRY WILL MARK YOU BRAINLIEST RIGHT ANSWER ONLY
Answers
Answer:a)EF congruent to QR
Step-by-step explanation:
10% of 240 is what number?
Answers
The answer is 24
what is the purpose of statistical inferences? to estimate mean, median, mode, variance, and skewness of large sample data to make generalizations about population characteristics from sample results to study characteristics of binomial or poisson random variables to fully describe the characteristics of the population
Answers
The main purpose of statistical inferences is to make generalizations about a population from a small sample result.
What is the meaning of statistical inference?Whenever we chart graphs, we try to represent raw data in tabular form. This data is mainly collected by us through surveys conducted on a small group of people, maybe our friends, family or anyone random. Through the data we receive, we can evaluate it to know results of out particular survey topic. Now, if we use this result to draw generalized conclusions about the whole population, then it is known as "inference" statistics. In inference statistics we donot limit the data to our sample size but rather use it to make predictions about the population.
For example: if we want to know the effictivity of a particular drug, we test it on a group of let's say, 100 people. The results show that about 75 treated got cured of the disease for which the drug was made to combat. Using statistical inference, we can conclude that in a population, the drug has an effictivity of 75%.
Further hypothesis can be conducted on the data using inferential statistics.
For more information on Statistical Inferences, clcik on link: https://brainly.com/question/28352023
#SPJ4
Plot 213, −56, and −312 on the number line.
Answers
Answer:
Step-by-step explanation:
Plot 213, −56, and −312 on the number line.
What is
3 times 6 tenths =
Answers
Answer:
1.8
Step-by-step explanation:
Roger bought a pair of leather gloves that originally cost $30.00 on sale at a 30% discount.
How much money did Roger save?
A.
$21.00
B.
$3.00
C.
$9.00
D.
$6.00
Answers
Answer:
C, my friend. Trust the BlueDragon
Step-by-step explanation:
30% of $30 is 9, $30-$9 is $21.00
He saved $9.00
just get the cost and multiple by the percentage so put 30.00 x .30
$9
Sarah works as a nanny and charges different rates for working during the week and the weekend. One week, she earned 902.50 working 45 hours, of which 5 hours were during the weekend. The following week she earned 1045 working 50 hours, of which 10 hours were during the weekend. What does Sarah charge per hour, in dollars, for working during the week?
Answers
Sarah's charges per hour for working during the week will be $9.5.
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.
Sarah is a nanny who bills clients at various prices depending on whether she is working during the week or on the weekend. She worked 45 hours in a single week for a salary of $902.50, of which 5 hours were on the weekend. She worked 50 hours the next week, 10 of which were on the weekend, and made 1045 dollars.
Let x be the charge per working hour and y be the number of charges per hour during the weekend. Then the equation will be
45x + 5y = 902.5 ...1
50x + 10y = 1045
25x + 5y = 522.5 ...2
Subtract equation 2 from equation 1, then we have
45x - 25x = 902.5 - 522.5
20x = 380
x = 19
And the value of y will be
25 (19) + 5y = 522.5
475 + 5y = 522.5
5y = 47.5
y = 9.5
Sarah's charges per hour for working during the week will be $9.5.
More about the solution of the equation link is given below.
https://brainly.com/question/545403
#SPJ1
m∠A
m∠B
m∠ACB
what are the answers
Answers
A rectangular dog cage has a length of 4 1/2 feet and a width of 3 3/7 feet. What is the area of the cage?
(Help please)
Answers
Step-by-step explanation:
Area of rectangle =height×base
4 1/2×3 3/7=9/2×24/7=216/14=15 6/14=15 3/7
Which proportion is a representation of “The number x is 25% of 70”
Answers
Answer:
25/100 = x/70
Step-by-step explanation:
Hope this helps!
Work out the area of this semicircle with radius 3cm give your answer in terms of pie
Answers
Answer:
A=4.5π
The formula for finding a circle is A=πr² so just plug in the value for the radius. Don't forget to divide the entire thing by 2 when you finish, cos it's a semi circle (which is a half circle)
Step-by-step explanation:
Cos Milky Said it.
Answer:
Answer=4.5π
Step-by-step explanation:
you square 3 and then divide it by 2 and then just add pi
A building has a height of 125 meters and a length of 80 meters. on a scale drawing of the building, the height is 25 centimeters
Answers
Based on the provided information, on a scale drawing the length of the building on the scale drawing is 16 centimeters.
To find the length of the building on the scale drawing in centimeters, we need to use the concept of scale factor. Scale factor is the ratio of the length of a drawing or model to the length of the actual object.
In this case, the scale factor is 25 cm / 125 m = 0.2 cm/m.
Now, we can use the scale factor to find the length of the building on the scale drawing. We just need to multiply the actual length of the building by the scale factor:
Length on scale drawing = Actual length × Scale factor
Length on scale drawing = 80 m × 0.2 cm/m
Length on scale drawing = 16 cm
Therefore, the length of the building on the scale drawing is 16 centimeters.
Note: The question is incomplete. The complete question probably is: A building has a height of 125 meters and a length of 80 meters. On a scale drawing of the building, the height is 25 centimeters. What is the length of the building on the scale drawing in centimeters?
Learn more about Scale drawing:
https://brainly.com/question/25324744
#SPJ11
Kelsey wants to compare the number of blouses that she owns a total of 30 blouses. 20% of them are blue. Five of them are red. 30% of them are white. The rest are pink. How many blouses are pink?
Answers
Number of blue blouses = 20% of 30 = 0.2 x 30 = 6
Number of red blouses = 5
Number of white blouses = 30% of 30 = 0.3 x 30 = 9
Now we can find the total number of blue, red, and white blouses:
Total number of blue, red, and white blouses = 6 + 5 + 9 = 20
Finally, we can find the number of pink blouses by subtracting the total number of blue, red, and white blouses from the total number of blouses:
Number of pink blouses = Total number of blouses - Total number of blue, red, and white blouses
Number of pink blouses = 30 - 20
Number of pink blouses = 10
Therefore, Kelsey has 10 pink blouses.