for the given points p(0;1; 3), q(2; 2; 1), r(2; 2; 4). find each angle of the triangle pqr. round your answers to the nearest degrees if needed.
Answers
The angles of triangle PQR are approximately 94°, 80°, and 80°.
To find the angles of triangle PQR with points P(0, 1, 3), Q(2, 2, 1), and R(2, 2, 4), you first need to find the length of each side using the distance formula:
PQ = √((2-0)² + (2-1)² + (1-3)²) = √(6)
PR = √((2-0)² + (2-1)²+ (4-3)²) = √(6)
QR = √((2-2)² + (2-2)² + (4-1)²) = √9)
Now, use the cosine rule to find the angles:
cos(∠P) = (PQ² + PR² - QR²) / (2 * PQ * PR) = (-1) / 12 ∠P ≈ acos(-1/12) ≈ 94° cos(∠Q) = (PQ² + QR² - PR²) / (2 * PQ * QR) = (3) / 18 ∠Q ≈ acos(1/6) ≈ 80° cos(∠R) = (PR² + QR² - PQ²) / (2 * PR * QR) = (3) / 18 ∠R ≈ acos(1/6) ≈ 80°Learn more about triangle at https://brainly.com/question/17354158
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Related Questions
Find all values of k, if any, that satisfy the equation.
[1 1 0] [k] [k 1 1] [1 0 2] [1] = 0
[0 2 -3] [1]
Answers
Expanding the matrix multiplication, we have k + 1 + 0 = 0, k + 2 = 2, 3 = -3, and k + 5 = 0. However, the equation 3 = -3 has no solution.
Let's calculate the matrix multiplication on the left-hand side of the equation. Expanding the multiplication, we obtain:
[k + 1 + 0] [k + 0 + 2] [1] = [0 2 -3]
[1 + 0 + 2] [k + 1 + 4] [1]
Simplifying, we have:
[k + 1] [k + 2] [1] = [0 2 -3]
[3] [k + 5] [1]
To determine if there are values of k that satisfy the equation, we compare the corresponding entries on both sides. From the first row, we have k + 1 = 0 and k + 2 = 2. Solving these equations gives k = -1 and k = 0, respectively.
However, when we consider the second row, we have 3 = -3, which has no solution. Therefore, there are no values of k that satisfy the given equation. This means that the equation [1 1 0] [k] [k 1 1] [1 0 2] [1] = 0 [0 2 -3] [1] has no solution.
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Let A = {1, 2, 3, 6, 7, 8) and for a, b € A define a < b if and only if b/a is an integer. Show that is a partial order on A, draw the Hasse diagram, and find all maximum, maximal, minimum, and mini
Answers
To show that "<" is a partial order on set A = {1, 2, 3, 6, 7, 8}, we need to verify three properties: reflexivity, antisymmetry, and transitivity.1. Reflexivity: For any element a ∈ A, a < a must hold. Since a/a = 1, which is an integer, reflexivity is satisfied for all elements in A.2. Antisymmetry: If a < b and b < a, then a = b. Let's consider all possible pairs of elements in A:
- For (1, 2): 2/1 = 2, which is an integer. However, 1/2 = 0.5, which is not an integer. Thus, 1 < 2, but not 2 < 1.
- For (1, 3): 3/1 = 3 and 1/3 = 0.33, so 1 < 3, but not 3 < 1.
- For (1, 6): 6/1 = 6 and 1/6 = 0.17, so 1 < 6, but not 6 < 1.
- For (1, 7): 7/1 = 7 and 1/7 = 0.14, so 1 < 7, but not 7 < 1.
- For (1, 8): 8/1 = 8 and 1/8 = 0.125, so 1 < 8, but not 8 < 1.
- For (2, 3): Both 3/2 = 1.5 and 2/3 = 0.67 are not integers, so neither 2 < 3 nor 3 < 2.
- For (2, 6): 6/2 = 3 and 2/6 = 0.33, so 2 < 6, but not 6 < 2.
- For (2, 7): 7/2 = 3.5 and 2/7 = 0.29, so 2 < 7, but not 7 < 2.
- For (2, 8): 8/2 = 4 and 2/8 = 0.25, so 2 < 8, but not 8 < 2.
- For (3, 6): 6/3 = 2, which is an integer. However, 3/6 = 0.5, which is not an integer. Thus, 3 < 6, but not 6 < 3.
- For (3, 7): 7/3 = 2.33 and 3/7 = 0.43, so neither 3 < 7 nor 7 < 3.
- For (3, 8): 8/3 = 2.67 and 3/8 = 0.38, so neither 3 < 8 nor 8 < 3.
- For (6, 7): Both 7/6 = 1.17 and 6/7 = 0.86 are not integers, so neither 6 < 7 nor 7 < 6.
- For (6, 8): Both 8/6 = 1.33 and 6/8 = 0.75 are not integers, so neither 6 < 8 nor 8 < 6.
- For (7, 8): Both 8/
The Hasse diagram for the given partial order "<" on set A is as follows:
8
/
6
/ \
2 3
\ /
1
|
7
In this diagram, each element of set A is represented as a node, and an upward arrow indicates that one element is greater than another. The element 8 is the maximum element in A since it is greater than all other elements. There are no maximal elements, which are elements that have no elements greater than them. The element 1 is the minimum element since it is smaller than all other elements.
To show that "<" is a partial order, we need to verify the three properties. The first property, reflexivity, is satisfied because for every element a in A, a/a = 1, which is an integer. The second property, antisymmetry, holds because if a < b and b < a, then a/b and b/a are integers, implying a/b = b/a = 1. Therefore, a = b. The third property, transitivity, is also satisfied because if a < b and b < c, then a/b and b/c are integers, so (a/b) * (b/c) = a/c is an integer as well. Hence, "<" is a partial order on set A.
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Use the first five terms of the exponential series of e^x ands calculator to approximate e^0.6 to the nearest hundredth
Answers
e^0.6 to the nearest hundredth using the first five terms of the exponential series of eˣ is; e^(0.6) = 1 + 0.6 + 0.6²/2! + 0.6³/3! + 0.6⁴/4....
How to solve Maclaurin Series?We want to use the first 5 terms of the exponential series of eˣ to approximate e^(0.6)
The type of exponential series we will utilize is called the Maclaurin Series for. Thus, for eˣ, we have;
eˣ = 1 + x + x²/2! + x³/3! + x⁴/4.....
Thus;
e^(0.6) = 1 + 0.6 + 0.6²/2! + 0.6³/3! + 0.6⁴/4....
e^(0.6) = 1 + 0.6 + 0.18 + 0.072 + 0.0324
e^(0.6) = 1.88 to the nearest hundredth
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Find the sum of the first 50 terms of the sequence below. Please Help!
Answers
Answer:
in 1st sequence put 1 instead of n
i.e
a1=3×1+2
=3+2
=5
Step-by-step explanation:
now do all the 50 terms by placing 1 to 50 instead of n
A limited-edition poster increases in value each year with an initial value of $18. After 1 year and an increase of 15% per year, the poster is worth $20.70. Which equation can be used to find the value, y, after x years? (Round money values to the nearest penny.)
y = 18(1.15)x
y = 18(0.15)x
y = 20.7(1.15)x
y = 20.7(0.15)x
Answers
Answer: A) 18(1.15)x
Step-by-step explanation:
18 was the original cost, so the price will always be determined with this starting point. Sice there is an increasing value, that makes it 1.15 instead of .15. And it goes up by 15%, making it the coefficient.
Answer:
A) y = 18(1.15)x
Step-by-step explanation:
Four dice are tossed. Two dice have 20 sides, and two dice have six sides.
How many different ways can the dice land so that the two 20-sided dice show different numbers from each other and the two 6-sided dice show different numbers from each other?
So I am having a bit of a hard time figuring out whether or not this question is making the two results independent. I assume if you treat the two dice as separate entities, the answer is obviously 410 as (20 x 19) + (6 x 5) would result in 410.
However, I have seen others answer this question treating their probabilities as mutually dependent, resulting in (20 x 19) x (6 x 5) = 11, 400.
The possible answers are 11,400, 410, 14,400, and 436.
Answers
The number of different ways the dice can land so that the two 20-sided dice show different numbers from each other and the two 6-sided dice show different numbers from each other is 11,400.
There are two 20-sided dice and two 6-sided dice. The 20-sided dice can produce 20 x 20 = 400 outcomes, and the 6-sided dice can produce 6 x 6 = 36 outcomes.
The number of ways the two 20-sided dice can show different numbers from each other is equal to the number of permutations of 20 things taken two at a time, which is ²°P2 = 380.
Similarly, the number of ways the two 6-sided dice can show different numbers from each other is equal to the number of permutations of 6 things taken two at a time, which is 6P2 = 30.To obtain the number of different ways the dice can land so that the two 20-sided dice show different numbers from each other and the two 6-sided dice show different numbers from each other, we need to multiply these three numbers: 380 x 30 x 1 = 11,400.
Therefore, the correct answer is 11,400.
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What is the slope of this line?
Answers
Answer:
slope = 15
Step-by-step explanation:
the slope of the line is how much it goes up in the span of one x
when it goes to the right one it goes up 15
this means that the slope is 15
Two cars start from the same point and move in a straight line, one east at a speed of 60 km per hour and the other west at a speed of 80 km per hour. After what time will they live at a distance of 770 km?
Answers
Answer: At 5.5 hours they will be 770 km apart.
Step-by-step explanation: Divide the distance by the total speed at which they are moving apart.
60 km/h + 80km/ = 140 km/h
770 km ÷140 km/h = 5.5 hours
In a sample of 300 skittles taken from this 54 oz bag, 72 of the skittles were observed to be purple. What is the value of p-hat (the sample proportion)?.
Answers
The value of p-hat (the sample proportion) is 0.24, or 24% if total number of skittles in a sample is 300 out of which 72 skittles are purple.
The sample proportion, denoted by p-hat, is the proportion of purple skittles in the sample. We can calculate p-hat by dividing the number of purple skittles by the total number of skittles in the sample
p-hat = number of purple skittles / total number of skittles in sample
In this case, we have
Number of purple skittles = 72
Total number of skittles in sample = 300
Therefore,
p-hat = 72/300 = 0.24
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which of the following is the standard equation of a circle with center (-1,-6) and radius 5?
Answers
Answer:
(x + 1)^2 + (y + 6)^2 = 25.
Step-by-step explanation:
The standard equation of a circle with center (h, k) and radius r is given by:(x - h)^2 + (y - k)^2 = r^2In this case, the center of the circle is (-1, -6) and the radius is 5. Substituting these values into the equation, we get:(x - (-1))^2 + (y - (-6))^2 = 5^2Simplifying and rearranging terms, we get:(x + 1)^2 + (y + 6)^2 = 25Therefore, the standard equation of the circle with center (-1, -6) and radius 5 is (x + 1)^2 + (y + 6)^2 = 25.PLS GET ME DA ANSWER ASAP AHHHHHHHHHHH!!!!!!!!!!!!!!!!!!!!!!!
Answers
Answer:
C
Step-by-step explanation:
You can use process of elimination. In D and A all the y numbers are staying the same. In B, the numbers are decreasing. So the only possible answer is C.
Hope this helped!! :D
evaluate the indefinite integral. (use c for the constant of integration.) eu (2 − eu)2 du
Answers
The indefinite integral of eu(2 − eu)² du is 2u² - 4u³/3 + u⁴/4 + C
To evaluate the indefinite integral of eu(2 − eu)² du, we can use substitution. Let's make the substitution v = eu, then dv = e du:
∫ (eu(2 − eu)²) du
Let v = eu, then dv = e du
∫ (v(2 - v)²) (1/e) dv
∫ (v(2 - v)²) / e dv
Expanding the expression inside the integral:
∫ (v(4 - 4v + v²)) / e dv
∫ (4v - 4v² + v³) / e dv
Now we can integrate each term separately:
∫ (4v - 4v² + v³) / e dv
= ∫ (4v/e - 4v²/e + v³/e) dv
= (4/e) ∫ v dv - (4/e) ∫ v² dv + (1/e) ∫ v³ dv
Integrating each term:
= (4/e) * (v²/2) - (4/e) * (v³/3) + (1/e) * (v⁴/4) + C
Substituting back v = eu:
= (4/e) * (eu)²/2 - (4/e) * (eu)³/3 + (1/e) * (eu)⁴/4 + C
= 2eu²/e - 4eu³/3e + eu⁴/4e + C
Simplifying further:
= 2u² - 4u³/3 + u⁴/4 + C
Therefore, the indefinite integral of eu(2 − eu)² du is 2u² - 4u³/3 + u⁴/4 + C, where C is the constant of integration.
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solubility of a hypothetical compound, A2B, is 0.131 mol/L A2B (s) <==> 2 A+ (aq) + B-2 (aq) Calculate the Ksp of this compound
What is the pH of a solution prepared by adding 97.42 mL of 0.100 M sodium hydroxide to 60.18 mL of 0.503 M benzoic acid (Kg = 6.14 x 10-5)?
Answers
The Ksp of compound A2B can be calculated using the given solubility expression: A2B (s) <==> 2 A+ (aq) + B-2 (aq). The solubility of A2B is given as 0.131 mol/L. Since there are 2 A+ ions and 1 B-2 ion produced for every A2B molecule that dissolves, the concentration of A+ ions and B-2 ions will both be twice the solubility of A2B. Therefore, the concentration of A+ ions and B-2 ions will be 2 * 0.131 = 0.262 mol/L. The Ksp of A2B can be calculated by multiplying the concentrations of the ions raised to their stoichiometric coefficients: Ksp = [A+]^2 * [B-2] = (0.262)^2 * 0.262 = 0.018 mol^3/L^3.
The solubility product constant (Ksp) of compound A2B is calculated by multiplying the concentrations of the ions raised to their stoichiometric coefficients. In this case, since there are 2 A+ ions and 1 B-2 ion produced for every A2B molecule that dissolves, the concentration of A+ ions and B-2 ions will both be twice the solubility of A2B. Therefore, the concentration of A+ ions and B-2 ions will be 0.262 mol/L. By plugging in these values into the Ksp expression, we can calculate the Ksp of A2B: Ksp = (0.262)^2 * 0.262 = 0.018 mol^3/L^3.
In this case, the main answer is the calculation of the Ksp of compound A2B, which is 0.018 mol^3/L^3. The supporting explanation provides the step-by-step process of how to calculate the Ksp using the given solubility expression and the stoichiometry of the compound.
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If two out of every fifteen trick or treaters that came to your house last halloween were dressed as spider-man, what proportion of trick or treaters were not dressed as spider-man?
Answers
Given:
The fraction of treaters dressed up us halloween, x=2/15.
Let the total trickers be taken as 1.
Now, the proportion of treakers that were not dressed up as spiderman is,
\(\begin{gathered} y=1-x \\ =1-\frac{2}{15} \\ =\frac{15-2}{15} \\ =\frac{13}{15} \end{gathered}\)put each shape through this classification flow chart
Answers
Step-by-step explanation:
what huh?????? i dont understand
John wanted to estimate the average literacy rate for all countries. He randomly selected 35 countries and researched the literacy rate for the 35 countries. The statistical unit for John's study is:
A. the 35 countries
B. a literacy rate. C. a country O
D. an individual
Answers
The statistical unit for John's study is A. the 35 countries. John is trying to estimate the average literacy rate across all countries, and he randomly selected 35 countries to research their literacy rates. The statistical unit in this case is the individual country, as each country's literacy rate is being used to calculate the average.
The statistical unit for John's study is A. the 35 countries. This is because John's study is based on a sample of 35 countries that he randomly selected. The sample is used to estimate the average literacy rate for all countries. The sample size of 35 countries is large enough to provide a representative sample of the population of countries. If John had selected only a few countries or individuals, his estimate of the average literacy rate would not have been reliable. However, by selecting a sample of 35 countries, John can make a more accurate estimation of the average literacy rate for all countries. In conclusion, the statistical unit for John's study is the sample of 35 countries that he researched to estimate the average literacy rate for all countries.
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on december 1, 2021, your company borrowed $46,500, a portion of which is to be repaid each year on november 30. specifically, your company will make the following principal payments: 2022, $6,200; 2023, $9,300; 2024, $12,400; and 2025, $18,600. show how this loan will be reported in the december 31, 2022 and 2021 balance sheets, assuming principal payments will be made when required.
Answers
The December 31, 2022 and 2021 balance sheets
Dec. 2021 $0 $46,500
Nov. 2022, $6200 $37200
Nov. 2023, $9300 $34100
Nov. 2024, $12400 $18600
Nov. 2025, $18600 $0
Balance Sheet
A balance sheet summarizes a company's assets, liabilities and shareholders' equity at a specific point in time (as indicated at the top of the statement). It is one of the fundamental documents that make up a company's financial statements.
The following the loan will be reported in Company's Balance Sheets:
Company Balance Sheets As of December 31
2022 2021
Current Liabilities:
Loan Payable $9,300 $6,200
Long-term Liabilities:
Loan Payable $34,100 $37,200
Data and Calculations:
Dec. 1, 2021, Loan = $46,500
Repayment of Loan:
Date Repayment Dec. 31 Balance
Dec. 2021 $0 $46,500
Nov. 2022, $6200 $37200
Nov. 2023, $9300 $34100
Nov. 2024, $12400 $18600
Nov. 2025, $18600 $0
Thus, the loan payable in 2022 and 2023 will be shown under current liabilities in 2021 and 2022, respectively. The remaining portion will appear under long-term liabilities.
The December 31, 2022 and 2021 balance sheets
Dec. 2021 $0 $46,500
Nov. 2022, $6200 $37200
Nov. 2023, $9300 $34100
Nov. 2024, $12400 $18600
Nov. 2025, $18600 $0
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Put the times in chronological order
Answers
Answer:
b,c,e,d,a,f
Step-by-step explanation:
What is the type? f(x)=-1/5x³-5+10x²
Answers
f(x) = -1.5x^3 + 10x^2 - 5
The capacity of a fih tank i 492 pint. What i the capacity of the tank in quart?
Answers
The capacity of fish tank in quarts is 246.
Therefore the answer is 246.
A pint is a unit of volume in the US customary system of measurement and is equal to 16 fluid ounces. A quart is also a unit of volume in the US customary system of measurement and is equal to 32 fluid ounces or 2 pints.
There are 2 pints in 1 quart, so to convert from pints to quarts, we need to divide by 2.
The capacity of the fish tank in pints is 492.
Therefore, the capacity of the fish tank in quarts is
= 492 pints / 2 pints per quart
= 246 quarts
So, the capacity of the tank in quarts is 246 quarts.
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i don’t understand how to find x to solve.
Answers
Answer:
X + 3
Step-by-step explanation:
There is no definite working. The first container is what I call the base because everything is a little above the first container, X. They are basically asking you what is the total of the four jars bigger than X. In other words how many steps more to climb before the top floor while you are on the first step. So then you add the other numbers like 0.5 etc which will give you X +3. Hope it helps.
Can anyone help ??????
Answers
Answer:
32
Step-by-step explanation:
i went through the answer choices and did .75x each one
and the one that worked was 32
Answer:
I think b
Step-by-step explanation:
Solve and graph the solution of this inequality 4/9×-10>×/3-12
Answers
Step-by-step explanation:
4/9x-10>x/3-12
3 4/9x-3 10>x/3-12
4/3x-10>x-12
3 4/3x-3(10>x)-3(12)
4x-30x<-36
26x<-36
Please help with this!!! 8 points!!!
Answers
Answer:
d
Step-by-step explanation:
Please help me with this question as well!
Answers
Sheila made 3, 3-point shots.
The correct answer to the given question is option G.
To find the number of 3-point shots Sheila made, we can use algebraic equations to represent the situation.
Let's assume Sheila made x shots worth 2 points and y shots worth 3 points. We know that the total number of shots made is 9, so we have the equation:
x + y = 9 -- Equation (1)
We also know that the total points Sheila scored is 21. Since each 2-point shot contributes 2 points and each 3-point shot contributes 3 points, we have another equation:
2x + 3y = 21 -- Equation (2)
To solve this system of equations, we can multiply Equation (1) by 2 and subtract it from Equation (2):
2x + 3y - 2x - 2y = 21 - 2(9)
y = 3
Therefore, the number of 3-point shots Sheila made is 3.
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Enter the correct answer in each box.
Complete the statement. In your answer, rationalize the denominator and write it in simplest form.
If tan(x) = 3/5, and x is an angle in quadrant I, what is the value of cos(x)
Answers
The value of the cosine angle will be \(\rm cos(x) = \dfrac{5}{\sqrt{34}}\).
Trigonometric ratios are mathematical functions that connect the angles of a right triangle to the ratios of its sides. They are also referred to as trigonometric functions.
There are six fundamental trigonometric ratios: secant, cosecant, cotangent, sine, and cosine. To analyse and resolve issues involving angles and distances, these ratios are often employed in mathematics, physics, engineering, and other disciplines.
Given that:
\(\rm tan(x) = \dfrac{3}{5}\)
From the given angle the two values perpendicularly are 3 and the base is 5. The value of the hypotenuse is calculated as,
\(\rm H^2 = P^2+B^2\\H \ = \sqrt{3^2+5^2}\\H \ = \sqrt{34}\)
The value cos(x) is calculated as,
\(\rm cos(x) = \dfrac{Base}{Hypotneuse}\\cos(x) = \dfrac{5}{\sqrt{34}}\)
Hence, the value cos(x) is \(\dfrac{5}{\sqrt{34}}\).
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What is 67 kg in stones and pounds?
Answers
Kilograms (kg) is a unit of mass that is commonly used in the metric system. However, in some countries, such as the United Kingdom and the United States, the customary unit of measurement for weight is stone and pounds.
67 kg in stones is equivalent to approximately 147.71 pounds.
It's important to note that while the conversion from kilograms to stone and pounds is straightforward, the conversion is not exact due to rounding. However, this difference is generally small and can be ignored for most practical purposes.
Overall, understanding the conversion from kilograms to stone and pounds can be useful for students who are studying or traveling between countries that use different units of measurement for weight. Additionally, the process of converting from one unit of measurement to another can help reinforce important mathematical skills, such as division and rounding.
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Find the value of x and y.
Answers
Answer:
x= 73
y= 13
Step-by-step explanation:
The sum of the angles opposite the exterior angle = the exterior angle so
x= 141-68
x= 73
The angle sum of a triangle= 180.
180-68-73= 39
since there are 3 "y"s we need to divide 39 by 3
39/3= 13
1. in 2009, 33% of americans felt that one parent should stay home to raise the children instead of using day care. in a poll conducted in 2011, 416 out of 1015 americans believed that one parent should stay home. at a 99% level of confidence, is there sufficient evidence to conclude that the percentage has increased from its 2009 value?
Answers
Answer: Yes
Step-by-step explanation: To show that the percentage has increased we would need to prove that 416/1015 with a 99% level of confidence or a 1% margin of error to do this we divide 416 by 1015
This equals 0.40985221674
Which can be rounded to 0.41 or 41% since there is a one percent margin of error we can assume that this is enough evidence, because if 1% of the poll's recipients mistakenly voted for a option they did not really think was true it would not be enough to change 41% to 33%
Hope this helps!
Find the coordinate of the given point.
The point Y between X(1,-2) and Z(11, 3) such that the ratio of XY to YZ is 3:2
Answers
\(\textit{internal division of a line segment using ratios} \\\\\\ X(1,-2)\qquad Z(11,3)\qquad \qquad \stackrel{\textit{ratio from X to Z}}{3:2} \\\\\\ \cfrac{X\underline{Y}}{\underline{Y} Z} = \cfrac{3}{2}\implies \cfrac{X}{Z} = \cfrac{3}{2}\implies 2X=3Z\implies 2(1,-2)=3(11,3)\)
\((\stackrel{x}{2}~~,~~ \stackrel{y}{-4})=(\stackrel{x}{33}~~,~~ \stackrel{y}{9}) \implies Y=\underset{\textit{sum of the ratios}}{\left( \cfrac{\stackrel{\textit{sum of x's}}{2 +33}}{3+2}~~,~~\cfrac{\stackrel{\textit{sum of y's}}{-4 +9}}{3+2} \right)} \\\\\\ Y=\left( \cfrac{ 35 }{ 5 }~~,~~\cfrac{ 5}{ 5 } \right)\implies {\Large \begin{array}{llll} Y=(7~~,~~1) \end{array}}\)