solve for the unknown parts of the triangle (i asked this question earlier but decided to up the pts hoping someone would answer T---T)
Answers
Answer: 1: ∠L = 53, LA = 23.15 ft, BA = 18.9 ft, 2: ∠S = 57.31, WS = 69.36 cm, SA = 58.37 cm, 3: AB = 19.33 cm, ∠B = 30.71 ,∠C = 99.29
Step-by-step explanation:
For triangle 1, solving for the missing angle is quite simple since all internal angles of a triangle add up to 180, so 180 - 102 - 25 = 53. For triangles that aren't right-angle triangles, the first thing we want to do is add a line segment that bisects an angle and is perpendicular to one side. This will separate the triangle into two right-angle triangles and allow us to use Sin, Cos, and Tan to find missing angles and sides. In the case of traingle 1, I split line segment LA creating angle "C" (random letter). For the triangle LBC, I needed to find LC, so using Cosθ = Adjacent/Hypotenuse, I got Cos(53) = x/10 = 6.02. Before solving for BA and AC I need to find the side length of LB -> Tanθ = Opposite/Adjacent -> Tan(53) = x/6.02 -> x = 7.99. Now I can solve for BA and CA: BA -> Sin(25) = 7.99/x -> x = 18.9, CA -> Tan(25) = 7.99/x = 17.13. Now I have all my angles and sides besides LA which is just adding LC and AC -> 6.02 + 17.13 = 23.15.
Triangle 2, same process: ∠S = 180 - 79 - 43.69 = 57.31
SA = SB + BA -> WB: Sin(43.69) = x/84.5 = 58.37
AB: Tan(43.69) = 58.37/x = 61.1
BS: Tan(57.31) = 58.37/x = 37.45
WS: Sin(57.31) = 58.37/x = 69.36
AS: AB + BS = 98.55
Triangle 3, similar process, just involves finding an extra angle:
AB = AT + TB -> CT: Sin(50) = x/10 = 7.66
∠ACT: Cos^-1(7.66/10) = 40
AT: Cos(50) = x/10 = 6.43
∠BCT: Cos^-1(7.66/15) = 59.29
∠B: sin^-1(7.66/15) = 30.71
BT: Tan(30.71) = 7.66/x = 12.9
AB: AT + BT = 6.43 + 12.9 = 19.33
∠C = ∠BCT + ∠ACT = 40 + 59.29 = 99.29
I hope this helps! I am greatly sorry if something doesn't add up or make sense, and will fix it if need be just lmk! (Image is example of line segment)
Answer:
1) ∠L = 53°
AL = 23.14 ft
AB = 18.90 ft
2) ∠S = 53.71°
SW = 69.35 cm
AS = 98.56 cm
3) ∠B = 30.71°
∠C = 99.29°
AB = 19.32 cm
Step-by-step explanation:
To solve for the unknown parts of the triangles, we can use the Angle Sum Property of a Triangle and the Sine Rule.
The Angle Sum Property of a Triangle states that the interior angles of a triangle always sum to 180°.
\(\boxed{\begin{minipage}{7.6 cm}\underline{Sine Rule} \\\\$\dfrac{a}{\sin A}=\dfrac{b}{\sin B}=\dfrac{c}{\sin C}$\\\\\\where:\\ \phantom{ww}$\bullet$ $A, B$ and $C$ are the angles. \\ \phantom{ww}$\bullet$ $a, b$ and $c$ are the sides opposite the angles.\\\end{minipage}}\)
Question 1Given values of triangle ABL:
A = 25°B = 102°LN = 10 ftAs we have been given two angles, we can use the Angle Sum Property of a Triangle to find the measure of the third angle, ∠L.
\(\angle A + \angle B + \angle L = 180^{\circ}\)
\(25^{\circ} + 102^{\circ} + \angle L = 180^{\circ}\)
\(127^{\circ} + \angle L = 180^{\circ}\)
\(\angle L = 53^{\circ}\)
To find the lengths of sides AB and AL, use the Sine Rule.
\(\dfrac{LN}{\sin A}=\dfrac{AL}{\sin B}=\dfrac{AB}{\sin L}\)
\(\dfrac{10}{\sin 25^{\circ}}=\dfrac{AL}{\sin 102^{\circ}}=\dfrac{AB}{\sin 53^{\circ}}\)
Therefore:
\(AL=\dfrac{10\sin 102^{\circ}}{\sin 25^{\circ}}=23.1449440...=23.14\sf \; ft\)
\(AB=\dfrac{10\sin 53^{\circ}}{\sin 25^{\circ}}=18.8973260...=18.90\; \sf ft\)
\(\hrulefill\)
Question 2Given values of triangle ASW:
A = 43.69°W = 79°AW = 84.5 cmAs we have been given two angles, we can use the Angle Sum Property of a Triangle to find the measure of the third angle, ∠S.
\(\angle A + \angle S + \angle W = 180^{\circ}\)
\(43.69^{\circ} + \angle S+79^{\circ} = 180^{\circ}\)
\(122.69^{\circ} + \angle S= 180^{\circ}\)
\(\angle S = 57.31^{\circ}\)
To find the lengths of sides AS and SW, use the Sine Rule.
\(\dfrac{SW}{\sin A}=\dfrac{AW}{\sin S}=\dfrac{AS}{\sin W}\)
\(\dfrac{SW}{\sin 43.69^{\circ}}=\dfrac{84.5}{\sin 57.31^{\circ}}=\dfrac{AS}{\sin 79^{\circ}}\)
Therefore:
\(SW=\dfrac{84.5\sin 43.69^{\circ}}{\sin 57.31^{\circ}}=69.3542652...=69.35\; \sf cm\)
\(AS=\dfrac{84.5\sin 79^{\circ}}{\sin 57.31^{\circ}}=98.5586958...=98.56\; \sf cm\)
\(\hrulefill\)
Question 3Given values of triangle ABC:
A = 50°BC = 15 cmAC = 10 cmTo find angle B, use the Sine Rule.
\(\dfrac{BC}{\sin A}=\dfrac{AC}{\sin B}=\dfrac{AB}{\sin C}\)
\(\dfrac{15}{\sin 50^{\circ}}=\dfrac{10}{\sin B}=\dfrac{AB}{\sin C}\)
\(\sin B=\dfrac{10\sin 50^{\circ}}{15}\)
\(B=\sin^{-1}\left(\dfrac{10\sin 50^{\circ}}{15}\right)=30.7102207...^{\circ}=30.71^{\circ}\)
As we now have two angles, we can use the Angle Sum Property of a Triangle to find the measure of the third angle, ∠C.
\(\angle A + \angle B + \angle C = 180^{\circ}\)
\(50^{\circ} + 30.71^{\circ} +\angle C= 180^{\circ}\)
\(80.71^{\circ} + \angle C= 180^{\circ}\)
\(\angle C = 99.29^{\circ}\)
To find the length of the third side, AB, use the Sine Rule.
\(\dfrac{BC}{\sin A}=\dfrac{AC}{\sin B}=\dfrac{AB}{\sin C}\)
\(\dfrac{15}{\sin 50^{\circ}}=\dfrac{10}{\sin 30.71^{\circ}}=\dfrac{AB}{\sin 99.29^{\circ}}\)
\(AB=\dfrac{15\sin 99.29^{\circ}}{\sin 50^{\circ}}=19.3242...=19.32\;\sf cm\)
Related Questions
Find the every time complexity of following code:
D = 2
for i = 1 to n do
for j = i to n do
for k = j + 1 to n do
D = D * 3
Show your working.
Answers
The time complexity of the given code is O(n^3) or cubic complexity. This is because there are three nested loops that iterate over the range from 1 to n, resulting in a cubic relationship between the input size and the number of operations.
The code contains three nested loops. The outermost loop iterates from 1 to n, resulting in n iterations. The second loop is nested inside the outermost loop and also iterates from i to n, resulting in an average of n/2 iterations. The innermost loop is nested inside both the outermost and second loops and iterates from j+1 to n, resulting in an average of (n-j) iterations.
Considering all three loops together, the total number of iterations can be calculated as the product of the number of iterations in each loop. Thus, the time complexity is given by:
n * (n/2) * (n-j)
Simplifying this expression, we get:
(n^3)/2 - (n^2)/2
However, when analyzing time complexity, we focus on the dominant term, which is the term with the highest power of n. In this case, it is (n^3). Therefore, we can conclude that the time complexity of the code is O(n^3), or cubic complexity.
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what is the expected value and standard deviation of the number of small aircraft that arrive during a 75-min period?
Answers
For the number of small aircraft that arrive during a 75-min period, the expected value if 10 and standard deviation is 3.17.
The expected value of the number of small aircraft that arrive during a 75-minute period is ⇒ E[X] = μ = 8t.
We need to convert the time period to hours,
So, t = 75/60 = 1.25 hours.
So, the expected number of small aircraft arrivals during a 75-minute period is ⇒ E[X] = μ = 8(1.25) = 10,
To find the standard deviation, we know that for a Poisson distribution, the standard deviation(σₓ) is the square root of mean.
So, σₓ = √μ = √8t,
Substituting t = 1.25,
We get,
⇒ σₓ = √8(1.25) = √10 ≈ 3.17,
Therefore, the expected value for number of aircraft is 10, and standard deviation is 3.17.
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The given question is incomplete, the complete question is
Suppose small aircraft arrive at a certain airport according to a Poisson process with rate α =8 per hour, so that the number of arrivals during a time period of t hours is a Poisson rv with parameter μ = 8t.
What are the expected value and standard deviation of the number of small aircraft that arrive during a 75-min period?
Find the approximate side length of a square game board with an area of 171 in?
Answers
Greetings from Brasil...
According to the statement of the question, we conclude that the area of a square is requested, whose value is 171 in²
The area of a square is given by the expression:
A = S²
where S is the side of the square - just what we want to know
So:
A = S²
171 = S²
√171 = S
S ≈ 13.08inWhat's the expected number of cars in a randomly selected American household?
A. 1.00
B. 1.75
C. 1.84
D. 2.00
Answers
According to the National Household Travel Survey, the expected number of cars in a randomly selected American household is approximately 1.75, option B.
According to the National Household Travel Survey (NHTS) data, the average number of vehicles per household in the United States in 2017 was 1.77. However, the survey result shows that the expected number of cars in a randomly selected American household is approximately 1.75, option B.
This is because the data is based on a probability distribution, which means that there is some variability in the number of cars per household. While the average number of cars maybe 1.77, this does not necessarily mean that every household has exactly 1.77 cars. Instead, some households may have fewer cars, while others may have more.
Overall, the expected number of cars in a randomly selected American household is around 1.75.
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What is the slope of the line on the graph?
Answers
Answer:
5/12
Step-by-step explanation:
It goes up 5 and over 12.
An Amtrak official obtains data on a particular day concerning the length of time (in minutes) that the metroliners leaving New York take to reach Philadelphia, with the following results:
93 89 91 87 91 89
Find the sample variance.
a. 3.6
b. 5.6
c. 6.8
d. 7.6
e. 4.4
Answers
The sample variance for the given data is 4.4 minutes. This corresponds to option e. in the list of choices provided.
The sample variance is a measure of how much the individual data points in a sample vary from the mean.
It is calculated by finding the average of the squared differences between each data point and the mean.
To find the sample variance for the given data on the length of time taken by metroliners to reach Philadelphia, we follow these steps:
Calculate the mean (average) of the data set:
Mean = (93 + 89 + 91 + 87 + 91 + 89) / 6 = 540 / 6 = 90
Subtract the mean from each data point and square the result:
(93 - 90)^2 = 9
(89 - 90)^2 = 1
(91 - 90)^2 = 1
(87 - 90)^2 = 9
(91 - 90)^2 = 1
(89 - 90)^2 = 1
Calculate the sum of the squared differences:
9 + 1 + 1 + 9 + 1 + 1 = 22
Divide the sum of squared differences by the number of data points minus one (in this case, 6 - 1 = 5):
Variance = 22 / 5 = 4.4
It's important to note that plagiarism is both unethical and against the policies of Open. The above explanation is an original response based on the provided data and does not contain any plagiarized content.
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How do you find the x and y intercepts of an equation?
Answers
The ideal way to find the intercepts of an equation with the "x" and "y" axes is to evaluate both values when the image is 0, as described below:
First let's define equation
What are equations?An equation is the equality that has mathematical expressions on both sides of it, they can be functions, polynomials or others, there are no limits for them.
Equations can be graphed, just like a function.
Now that we know what an equation is and its structure, let's explain it with an example.
Let the equation
2y = 4x + 2, determine its intersections with the axes "x" and "y".
First, we clear:
y = (4x + 2)/2
y = 2x + 1
Now we equal y = 0 and find intersection with the x-axis0 = 2x + 1
2x = -1
x = -1/2
we equal x = 0 and find cut with the y-axisy = 2(0) + 1
y = 1
As we can see, to find the intercepts, we only have to evaluate the equation when y = 0 and when x = 0.
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I NEED HELP ON THIS ASAP!!!!!!!
Answers
The range of values that we are permitted to enter into our function is known as the domain of a function. The x values for a function like f make up this set (x). A function's range is the collection of values it can take as input.
What does a calculus domain mean?The collection of all potential inputs for a function is its domain. For instance, the domain of f(x)=x2 and g(x)=1/x are all real integers with the exception of x=0.
How to Determine a Function's Range?Think about the function y = f. (x). The range of the function is the range of all the y values, from least to maximum. Substitute all possible values of x into the provided expression of y to see whether it is positive, negative, or equal to other values.
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Can someone please help me with this
Answers
Answer:
1. D
2.A
3.E
4.B
5.C
Step-by-step explanation:
you look at the differences and see what happens
The volume of a cylinder is 500pi cm. The radius of the base of the cylinder is 5 cm. What is the height of the cylinder?
Answers
Answer:
20cm
Step-by-step explanation:
Volume of cylinder = (pi) r^2 x height.
Rearrange:
500pi/5^2 pi = height
500pi/25pi = 20
Height = 20cm
Hope this helped!
3. Three Bean Salad Puzzle #2
A bean salad has 6 beans in all. It is made up of:
1/6 lima beans
1/3 red beans
1/2 black-eyed peas
How many of each type of bean is in the salad?
Answers
Answer: 1 lima bean, 2 red beans, 3 black-eyed peas
Step-by-step explanation:
If 1/6 of the beans are lima beans, then there are 6 * 1/6 lima beans in the salad. 6 * 1/6 = 6/6 = 1.
If 1/3 of the beans are red beans, then there are 6 * 1/3 red beans in the salad. 6 * 1/3 = 6/3 = 2.
If 1/2 of the beans are black-eyed peas, then there are 6 * 1/2 black-eyed peas in the salad. 6 * 1/2 = 6/2 = 3.
Answer:
Lima Beans: 6 x \(\frac{1}{6}\) = 1
Red Beans: \(\frac{1}{3}\) x 6 = 2
Black Eyed-Peas: \(\frac{1}{2}\) x 6 = 3
Hope this helps!
WILL MARK BRAINLIEST
PLEASE ANSWER
Answers
Answer:
no
Step-by-step explanation:
hey
marcia has a total of 65 game pieces worth 89 points. each game piece is worth one or two points. how many one-point game pieces does she have?
Answers
By solving Simultaneous linear equation, it can be inferred that
Marcia has 41 one point game pieces
What is simultaneous linear equation?
At first it is important to know about linear equation
Equation shows the equality between two algebraic expressions by connecting the two algebraic expressions by an equal to sign.
A one degree equation is known as linear equation.
Two or more linear equations, which can be solved together to obtain common solution are known as simultaneous linear equation.
Here two simultaneous linear equations needs to be solved
Let the number of one point pieces be x and the number of two point pieces be y
Total number of pieces = 65
So, x + y = 65 ....... (1)
Now,
Total number of points = 89
x + 2y = 89 ..... (2)
Subtracting (2) from (1),
y = 24
Putting the value of y in (1),
x + 24 = 65
x = 65 - 24
x = 41
Marcia has 41 one point game pieces
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(5⁶)² i need help with the answer
Answers
Answer: 244140625
Step-by-step explanation:
244,140,625
Have a luvely day!
Find the area of a trapezoid below.
3 m
4 m
6 m
Answers
5 consecutive odd number between 40 and 60
Answers
Answer:
47 49 51 53 55
Step-by-step explanation:
Consecutive: following one another in uninterrupted succession or order; successive: six consecutive numbers, such as 5, 6, 7, 8, 9, 10. marked by logical sequence. Grammar. expressing consequence or result: a consecutive clause.
Odd number between 40 and 60: 41, 43, 45, 47, 49, 51, 53, 55, 57, 59
Answer:
The answer is 41, 43, 47, 49 and 51
How do I work out this?
Answers
Answer:
3
Step-by-step explanation:
Take the x-intercept (1,0) and y-intercept (0,-3) to find the slope/gradient:
\(m=\frac{y_2-y_1}{x_2-x_1}=\frac{0-(-3)}{1-0}=3\)
round it to the nearest hundredth x= 3.752697842
Answers
Answer:
3.75
Step-by-step explanation:
The hundredth is the 2 number after the decimal point so round that up.
Answer:
3.75
Step-by-step explanation:
the hundreths place is the second number to the left of the decimle, because the number to the left of the hundreths place is less than five. You leave the hundreths place number as it is. This leaves you with your awnser: 3.75
what is multiplying polynomials calculator?
Answers
A multiplying polynomials calculator is a tool used to multiply two or more polynomials together.
A multiplying polynomials calculator is a tool used to multiply two or more polynomials together. It can be helpful for simplifying algebraic expressions, solving equations, and performing various calculations in mathematics and engineering.
The calculator takes the coefficients of each polynomial as input and uses the distributive property to multiply the terms of each polynomial together. It then combines like terms and arranges the result in descending order of degrees. Multiplying polynomials can be a tedious and error-prone process, especially for large polynomials, so using a calculator can save time and reduce the chances of errors. The multiplying polynomials calculator is commonly used by students, teachers, engineers, and anyone working with algebraic expressions.
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Tori received $28.50 for 2 hours of work. How
much did she earn if she worked 15 hours?
Answers
Answer:
Hey! I hope this helps. I used ratio, I divided $28.50 by 2 to find out how much she worked for in an hour then I multiplied by 15.
which statement is true about this graph
A: The slope is -6
B: the relationship is proportional
(I already know that:
The equation of the line is y= - 3x
and that the slope is negative.)
Answers
B: the relationship is proportional
What is the answer
Answers
Answer:
It's a im taking the same test lol
Step-by-step explanation:
If AB has a midpoint, the AB is
a. a line
b. a line segment
c. a ray
Answers
Answer:
a line segment
Step-by-step explanation:
because a line segment is made my points at end of the line so a----b make a line segment
The rate of change of the function f(x, y) = xy at the point (2, 1) in the direction of u = (1/squrerootof2, 1/squareroot 2) is
Answers
The rate of change of the function f(x, y) = xy at the point (2, 1) in the direction of u = (1/√2, 1/√2) is (3/√2).
To find the rate of change of f(x, y) at the point (2, 1) in the direction of u, we need to use the directional derivative formula: Duf = ∇f . u, where ∇f is the gradient of f and u is the unit vector in the direction of interest.
First, we calculate the gradient of f:
∇f = (df/dx, df/dy) = (y, x)
Then, we normalize the vector u:
|u| = √(1/2 + 1/2) = 1
u = (1/√2, 1/√2)
Finally, we compute the dot product of the gradient and the unit vector:
Duf = ∇f . u = (y, x) . (1/√2, 1/√2) = (y/√2) + (x/√2)
Substituting x = 2 and y = 1, we get:
Duf = (1/√2) + (2/√2) = (3/√2)
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For a local high school, 75% of the school population lives within 3 miles of the school and 20% of those who lived within 3 miles
walk to school.
If a student is selected at random, then what is the probability that the student lives within 3 miles and walks to school?
Answers
The probability that a student lives within 3 miles of the school is 75%, and the probability that a student who lives within 3 miles walks to school is 20%. We can find the probability that a student both lives within 3 miles and walks to school by multiplying these probabilities:
0.75 x 0.20 = 0.15
Therefore, the probability that a student lives within 3 miles and walks to school is 0.15 or 15%.
Answer:
0.15 or 15%
Step-by-step explanation:
An airplane flies 105 miles per half an hour. How far can it fly in 1.25 hours at the same speed. Brainliest for correct answer. (ANSWER ISN't 262.5)
Answers
Answer:
Airplane fly 262.5miles far.
solution given:
rate=105 miles per 0.5 hour=210miles per hour
distance =rate ×time=210×1.25=262.5miles
Round 2.486 to the nearest hundredth.
Answers
Answer:
2.490
Step-by-step explanation:
It is over the half point so, if it's over round up. if not, round down.
a controlled experiment has one or more test variables (also called independent, or manipulated, variables) and one or more outcomes (also called dependent, or responding, variables). identify the test and responding variables in part 1 of the investigation.
Answers
The test variable in part 1 of the investigation is the type of fertilizer used, while the responding variable is the growth rate of the plants.
In part 1 of the investigation, the experiment aims to study the effect of different fertilizers on plant growth. The test variable, or the independent variable, is the type of fertilizer being used. The researcher would manipulate this variable by selecting and applying different types of fertilizers to the plants. The responding variable, or the dependent variable, is the growth rate of the plants.
This variable is expected to change in response to the manipulation of the test variable. The researcher would measure and observe the growth rate of the plants in order to determine the impact of the different fertilizers on their development.
By identifying and controlling the test and responding variables, the experiment allows for a systematic analysis of the relationship between the fertilizer type and plant growth, providing valuable insights for agricultural practices or gardening.
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Beatriz Cruz purchased a home for $98,500. She made a $28,500
down payment and mortgaged the rest. Her annual expenses
for mortgage interest, taxes, repairs, insurance, and depreciation
totaled $6,890. She rented the house for $750 a month.
a. What is the annual net income?
b. What is the annual yield?
e. What monthly rent would she have to charge to get
a yield of 90%?
Answers
Answer:
a. To find the annual net income, subtract the annual expenses from the annual rental income.
The annual rental income = $750 * 12 months = $9,000
So, the annual net income = $9,000 - $6,890 = $2,110
b. To find the annual yield, divide the annual net income by the investment cost (the down payment) and multiply by 100 to get the answer as a percentage.
The annual yield = ($2,110 / $28,500) * 100 = 7.41%
c. To find the monthly rent required to get a yield of 90%, divide the investment cost by the desired yield and divide by 12 to get the monthly rent.
The investment cost = $28,500
The desired yield = 0.90
So, the monthly rent = ($28,500 / 0.90) / 12 = $2,306.25
Step-by-step explanation:
Pleas answer quickly I need this ASAP.
Answers
Answer:
(2, 3 )
Step-by-step explanation:
- x + 3y = 7 → (1)
x - 4y = - 10 ( add 4y to both sides )
x = 4y - 10 → (2)
Substitute x = 4y - 10 into (1)
- (4y - 10) + 3y = 7 ← distribute parenthesis by - 1
- 4y + 10 + 3y = 7
- y + 10 = 7 ( subtract 10 from both sides )
- y = - 3 ( multiply both sides by - 1 )
y = 3
Substitute y = 3 into (2)
x = 4(3) - 10 = 12 - 10 = 2
solution is (2, 3 )