The possible value of x are + √15 and - √15
What are congruent angles?Angles who are of same measurement are called congruent.
Suppose that two angles ∠A and ∠B are of same measure, then
[tex]m\angle A = m\angle B[/tex]
is the notation to say that they are of same measurement, where the small m shows that its the measurement of the angles they're preceding.
Then the congruency between them as;
[tex]\angle A \cong \angle B[/tex]
angle EAB = 2x² + x
angle EDA = x + 30
Here we can see the angle EAB and angle EDA are equal
So,
2x² + x = x + 30
2x² + x - x = 30
2x² = 30
x² = 15
x =±√15
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Need help with this world problem, ss is attached as well!
Find the numbers of bags of potting soil that a company can produce for seedlings, general potting, and hardwood plants with the given amounts of raw materials. The raw materials used in one bag of each type of potting soil are shown below.
Sand Loam Peat Moss
Seedlings 2 units 1 unit 1 unit
General 1 unit 2 units 1 unit
Hardwoods 2 units 2 units 2 units
450 units of sand
450 units of loam
360 units of peat moss
Company can produce 130 bags of seedlings, 110 bags of general plotting and 50 bags of hardwood plants. The solution has been obtained by using linear equation.
What is a linear equation?
The degree of the linear equation is 1. It is very clear that linear equations with exponents greater than one lack variables. The equation for this graph yields a straight line.
Let S be the bags of seedlings, G be for general potting, and H be for hardwood plants.
It is given that each bag of seedling soil needs 2 units of sand, each bag of general soil needs 1 unit of sand, and each bag of hardwood soil needs 2 units of sand. We have 450 units of sand.
So, from this we get
2S + G + 2H = 450 ...(1)
Similarly, for units of loam and peat moss, we get the equations as
S + 2G + 2H = 450 ...(2)
S + G + 2H = 360 ...(3)
Now, on subtracting (3) from (2), we get
G = 110
On substituting this, we get
2S + 2H = 360 ...(4)
S + 2H = 230 ...(5)
S + 2H = 250 ...(6)
Now, we subtract (2) from (1), we get
S = 130
On substituting this in equation (5), we get
130 + 2H = 230
2H = 100
H = 50
Hence, company can produce 130 bags of seedlings, 110 bags of general plotting and 50 bags of hardwood plants.
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Find the solution of the system of equations. -2x-3y= −2x−3y= \,\,-28 −28 -2x+2y= −2x+2y= \,\,22 22
The quadratic equation of [tex]x^{2}[/tex]-6x+9=0 is C) (x-2)(x+3).
What is equation?Equation is a physical and mathematical statement that describing physical phenomena and the relationship between different physical quantity typically consist of variable simple presenting physical quantity and then it personal variable may be pointed such as your energy.
This equation is an example of a quadratic equation, which is an equation of the form a[tex]x^{2}[/tex]+bx+c=0, where a, b, and c are real numbers, and a is not equal to 0. In this equation, a is equal to 1, b is equal to -6, and c is equal to 9. To solve this equation, we need to use the quadratic formula, which states that the solutions to the equation are x= -b ± [tex]\sqrt[1]{b^{2}-4ac }[/tex] / 2a. Therefore, the solutions to this equation are x= -(-6) ± [tex]\sqrt{(-6)^{2} -(4)(1)(9) }[/tex]) / 2(1), which simplifies to x=3 ± [tex]\sqrt{3}[/tex] /2, or x=3 ± [tex]\sqrt{9}[/tex] /2. This simplifies to x=3 ± [tex]\sqrt{3}[/tex], or x=3 ± 1. Therefore, the solutions to this equation are x=2 and x=4. The factored form of this equation is (x-2)(x+3), which is option C.
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Consider the line
Find the equation of the line that is perpendicular to this line and passes through the point (5, 6).
The equation of the line that's vertical to the given line and passes through the point(,6) is y = (-2/3) x28/3.
To find the equation of a line vertical to a given line, we need to use the fact that the pitches of two vertical lines are negative reciprocals of each other.
Let's start by chancing the pitch of the given line. The equation of a line in pitch- intercept form is y = mx b, where m is the pitch and b is the y- intercept. We can rewrite the given line 3x- 2y = 5 in pitch- intercept form by working for y
3x- 2y = 5
- 2y = -3 x 5
y = (3/2) x-5/2
So the pitch of the given line is3/2.
The pitch of a line vertical to this line is the negative complementary of3/2, which is-2/ 3.
Now we can use the point- pitch form of the equation of a line to find the equation of the line that passes through the point(,6) and has pitch-2/ 3. The point- pitch form is
y- y1 = m( x- x1)
where( x1, y1) is the point the line passes through and m is the pitch.
Substituting in the values we know, we get
y- 6 = (-2/3)( x- 5)
Expanding the right side, we get
y- 6 = (-2/3) x10/3
Adding 6 to both sides, we get
y = (-2/3) x28/3
So the equation of the line that's vertical to the given line and passes through the point(,6) is y = (-2/3) x28/3.
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Please show working out. 25 pts
Answer:
Step-by-step explanation:
With this the probabiitiy is high. In saying that look at 3 that is your answer. So that answer would be mostly 0.100. Hope this helps
A gymnast joined a yoga studio to improve his flexibility and balance. He pays a monthly fee and a fee per class he attends. The equation y = 20 + 10x represents the amount the gymnast pays for his membership to the yoga studio per month for a certain number of classes.
Which graph represents this situation?
graph with the x axis labeled number of classes and the y axis labeled monthly amount in dollars and a line going from the point 0 comma 20 through the point 1 comma 30
graph with the x axis labeled number of classes and the y axis labeled monthly amount in dollars and a line going from the point 0 comma 20 through the point 1 comma 10
graph with the x axis labeled number of classes and the y axis labeled monthly amount in dollars and a line going from the point 0 comma 10 through the point 1 comma 30
graph with the x axis labeled number of classes and the y axis labeled monthly amount in dollars and a line going from the point 0 comma 10 through the point one half comma zero
The correct graph is the first one.
What is graph?Graph is a data structure composed of nodes connected by edges, which represent a relationship between the two notes of are used to represent networks of communication that organized and even extract concept like thought or riders the nodes in the graph are often represent by Circle and it's by line but the other safe of the symbol are also use copper power Bluetooth for a organizing and understanding data and can be used to solve complex problem.
It represents the equation y = 20 + 10x, which means that the gymnast pays a flat fee of $20 for each month plus an additional $10 for each class he attends. Therefore, the graph will show a line going from the point 0, 20 through the point 1, 30.
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In the image below if m <1 = 90° and m <1 = M<2 = m
<3 = M<4 = m<5 = m<6 = m<7 = m<8, which of the
following below represents a line parallel to line b?
The line parallel to the line b is the line a
How to determine the parallel line to line bFrom the question, we have the following parameters that can be used in our computation:
The figure
Also, we have
Angle 1 = 90 degrees
The measure of angle 1 and angle 5 are congruent
This is so because they are corresponsing angles
So, we have
Angle 5 = 90 degrees
The above implies that line a and line b are parallel lines
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List two different ways you could break up the factors in 239 x 64 to find the product. Explain why the two ways would have the same product.
The two different ways to find the product of 239×64 are,
(240 - 1)×64 and 239×(60 + 4).
What are some alternative names for arithmetic operations?Addition is also known as the sum, subtraction is also known as the difference, multiplication is also known as the product, and division is also known as the factor.
Given, A product of 239×64.
The first way is,
239×64.
= (240 - 1)×64.
= 15360 - 64.
= 15296.
Another way to find the product of 239×64 is,
= 239×(60 + 4).
= 14340 + 956.
= 15296.
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How far away is 1 km?
To convert 1km into other measurements: 1) 1000 meter, 2) 3280.84, 3) 1e+6 millimeter, 4) 100000 centimeter, 5) 39370.1 inch, 6) 1093.61 yard1 km, 7) 0.621371 mile.
It is necessary to measure these quantities using units of measurement. Sometimes the units of measurement chosen don't match the standards needed for a specific procedure or application, as well as the measurement preference and ease of use.
It's essential to convert these units in a way that enables proper comprehension and use. When converting between different units in the metric system, a decimal point must typically be moved. If you remember what the prefixes mean, you can convert between different units of measurement within the metric system fairly quickly by simply multiplying or dividing the number by the prefix's value.
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The radius of a semicircle is 2 millimeters. What is the semicircle's perimeter?
Answer:
required perimeter is 12.57mm
A stained glass window is in the shape of a semi circle. What is the distance around the window in inches if the diameter is 40 in. Don't forget to add all parts of the distance around the window to get the entire distance.
Answer:
The distance around the window in inches is 80 inches. This is because the circumference of a semi-circle is equal to π times the diameter (C = πd). So, 40 x π = 80 inches.
What is the image point of
(
−
7
,
(−7,5) after a translation right 5 units and up 4 units?
The image point of (-7, 5) after the translation is (-2, 9).
What is the translation in the coordinate system?
A translation in the Cartesian plane can be described by a rule that indicates how to move each point of a figure to its image under the translation. The rule is usually given as a pair of numbers (a, b), where a is the horizontal distance to move each point (positive to the right, negative to the left), and b is the vertical distance to move each point
To find the image point of the point (-7, 5) after a translation right 5 units and up 4 units, we need to add 5 to the x-coordinate and add 4 to the y-coordinate.
The new x-coordinate will be -7 + 5 = -2, since we're moving the point to the right 5 units.
The new y-coordinate will be 5 + 4 = 9, since we're moving the point up 4 units.
Hence, the image point of (-7, 5) after the translation is (-2, 9).
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Select the two situations with the highest total surplus. 1.) Bonnie buys flowers for $2.25 less than she was willing to pay. She bought them from a seller would have been willing to receive $3 less from the sale. 2.) Don wanted to buy a scooter for no more than $5, but was only able to find a producer who would sell for $15.
1) Jay buys a house for $40,000 less than he is willing to pay. He bought a house from a seller who received $2,000 more than he was willing to sell.
4) Kevin wanted to spend $50 on a dishwasher and bought it for $45 from a manufacturer hoping to get $40.
Economic Surplus:
Economic surplus, also known in mainstream economics as general welfare or general public welfare or Marshall's surplus (after Alfred Marshall), is one of two related quantities. Pay.
Producer surplus or producer surplus is the amount a producer receives by selling at a market price higher than the lowest price they are willing to sell. This roughly equals profit margin (because producers are usually unwilling to sell at a loss and are generally uninterested in selling at a break-even price).
Total economic surplus = supplier surplus + consumer surplus
supplier surplus is the difference between the minimum price that a seller would take for his/her products and the actual selling priceconsumer surplus is the difference between the maximum price that a consumer would be willing to pay for a product and the actual priceOn scenario 1, total economic surplus = $40,000 + $2,000 = $42,000
On scenario 2, total economic surplus = $2.25 + $3 = $5.25
On scenario 3, total economic surplus = $0
On scenario 4, total economic surplus = $5 + $5 = $10
Complete Question:
Select the two situations with the highest total surplus. correct answer(s) jay buys a house for $40,000 less than he was willing to pay. he bought his home from sellers who received $2,000 more than they were willing to sell for. bonnie buys flowers for $2.25 less than she was willing to pay. she bought them from a seller would have been willing to receive $3 less from the sale. don wanted to buy a scooter for no more than $5, but was only able to find a producer who would sell for $15. kevin wanted to spend $50 on a dishwasher and bought one at $45 from a producer who was hoping to receive $40.
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Are the two triangles similar ?
Yes or no?
How do you know ?
How to convert 112 kg to lbs?
The required value of 112 kilograms into pounds using standard conversion relation is equal to 112 kilograms = ( 246. 92 ) pounds ( round up to two decimal places )
Units pounds and kilograms are used to measure the mass of a given things.One kilograms is equal to 2.20462 pounds.
We need to convert 112 kilograms into pounds :
This implies :
⇒ 112 kilograms = ( 112 × 2.20462 ) pounds
⇒ 112 kilograms = ( 246.91744 ) pounds
⇒ 112 kilograms = ( 246. 92 ) pounds ( round up to two decimal places )
Therefore, the converting value of kilogram to pounds is given by :
112 kilograms = ( 246. 92 ) pounds ( round up to two decimal places ) .
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What is A divided by 6 is equal to a whole number?
Answer:
4
Step-by-step explanation:
I think and I hope I got it right sorry if I didnt
The answer I think is right is a=24
a/6=?
24/6=4
the hypergeometric distribution should be used instead of the binomial distribution when: a. each trial is independent b. there are more than two outcomes on a single trial c. there is a fixed number of trials d. sampling does not involve replacement
The hypergeometric distribution should be used instead of the binomial distribution. The correct option is d. Sampling does not involve replacement,
What is binomial distribution ?
The binomial distribution is a probability distribution that describes the probability of getting a certain number of successes in a fixed number of independent trials, where each trial has only two possible outcomes: success or failure.
The probability of getting exactly k successes in n trials with probability of success p is given by the formula:
[tex]P(k) = (n choose k) * p^k * (1 - p)^(n - k)[/tex]
where (n choose k) is the binomial coefficient, which gives the number of ways to choose k items out of n, and is equal to:
[tex](n choose k) = n! / (k! * (n - k)!)[/tex]
where n! represents n factorial, which is the product of all positive integers up to n.
Given by the question:
The correct answer is d. sampling does not involve replacement.
Therefore, when sampling does not involve replacement, the hypergeometric distribution should be used instead of the binomial distribution.
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can somebody help me with this
Answer:
-4
Step-by-step explanation:
7(-1)³ + 5(-1)² -2 = ?
-7 + 5 -2 = ?
-2 -2 = ?
? = -4
Molly si selling bracelets and necklace at a crack fair . The cost of 4 bracelets and 3 neckclace is 23.50. The cost of 5 bracelets and 2 necklace is 21.50. A custumer bought 1 bracelet and 1 necklace. How Mich money did the custumer spend?
Word problems
Simultaneous equation
4b + 3n = $23.50 x2
5b + 2n = $21.50 x3
We solve this equation using the elimination method. By removing necklaces, we can find the cost of a bracelet.
8b + 6n = $47 --- eqn 1
15b + 6n = $64.5 --- eqn 2
Subtract eqn 1 from eqn 2
7b = 17.5
1b = 17.5/7
1b = $2.50
Substitute the value of bracelet into eqn 1 to find the cost of 1 necklace
8(2.5) + 6n = $47
20 + 6n = $47
6n = 47 -20
6n = 27
1n = 27/6
1n = $4.5
1b + 1n = ?
2.50 + 4.50 = $7
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The following system of equations is designed to determine concentrations (the c's in g/m³) in a series of coupled reactors as a function of the amount of mass input to each rector (right hand sides in g/day): 10c2c₂cy -3c-6c₂+2c3=-61.5 C₂+503
Solve this problem with the Jacobi's iterative method to 5%.
The solution for the system of equations is Ax = b as the matrix is invertible (or non-singular) if and only if its determinant is not zero.
To solve a system of equations, we can use matrix algebra. We can write the system of equations in matrix form as follows:
Ax = b
where A is the matrix of coefficients, x is the vector of unknowns (the concentrations), and b is the vector of right-hand sides (the mass inputs).
To solve for x, we can multiply both sides by the inverse of A:
x = [tex]A^{-1}b[/tex]
where [tex]A^{-1}[/tex] is the inverse of A.
However, not all matrices have inverses. A matrix is invertible (or non-singular) if and only if its determinant is not zero. So, before we can solve for x, we need to check if A is invertible by calculating its determinant.
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what does a rhombus look like
A rhombus with opposite sides are parallel and equal, and opposite angles are equal looks like Diamond.
A closed two-dimensional plane figure is a rhombus. It is regarded as a peculiar parallelogram, and due to its distinctive characteristics, it acquires a distinct identity as a quadrilateral. Due to its equal length sides, a rhombus is also known as an equilateral quadrilateral. The name "rhombus" is derived from the Greek word "rhombos," which really refers to a spinning object.
Due to the fact that it is a quadrilateral with two pairs of parallel sides, a rhombus can be considered a particular parallelogram. A rhombus also has equal sides on all four sides, exactly like a square. Because of this, it is often referred to as a tilted square. To comprehend the relationship between the rhombus shape, parallelogram, and square, look at the graphic below.
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Please help me
Nine times the sum of a number and 17 is at least -23. Translate the sentence into an inequality
Answer:
9(x + 17) ≥ -23
Step-by-step explanation:
Let's start by breaking down the sentence:
"A number": We can represent this as a variable, say "x".
"The sum of a number and 17": This is x + 17.
"Nine times the sum of a number and 17": This is 9(x + 17).
"Is at least -23": This means the expression on the left-hand side of the inequality is greater than or equal to -23.
Putting it all together, we get the inequality:
9(x + 17) ≥ -23
This year Boris watched 60 movies. He thought that 33 of them were very good. Of the movies he watched, what percentage did he rate as very good?
Answer:
55%
Step-by-step explanation:
To get 55 I just divided 33/60 and multiplied it buy 100
help please show steps as well so i can udnerstand im a bit confused
Answer:
n = 4
Step-by-step explanation:
Remove the radical by raising each side to the index of the radical.
The grand staircase has 13 steps. The
priest wants to know if he can climb this a
different way each day for a year using the
same rules as the priestess.
Is it possible?
How many ways are there of ascending the
grand staircase?
Explain why your answer is correct.
Don’t know answer can u please help me understand this and give me the answers
The value of the expression is 1/c - 5
How to simply the expressionNote that algebraic expressions are described as expressions that are composed of terms, variables, coefficients, factors and constants.
From the information given, we have that;
c/ c² - 7c + 10 - (2/ c² - 7c + 10)
Find the lowest common factors
c - 2/ c² - 7c + 10
solve the quadratic equation
c - 2/ c² - 5c - 2c + 10
Factor the expression, we get;
c- 2/c(c - 5) - 2(c - 5)
Factor the terms
c-2/(c-2)(c-5)
Divide the values
1/c - 5
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To study the effect of temperature on yield in a chemical process, five batches were produced at each of three temperature levels. The results follow.
Construct an analysis of variance table. Use a 0.05 level of significance to test whether the temperature level has an effect on the mean yield process.
Temperature
50 degrees C 60 degrees C 70 degrees C
34 30 23
24 31 28
36 34 28
39 23 30 32 27 31
We fail to reject the null hypothesis that the temperature level has no effect on the mean yield process.
Summary of Result:
Source | SS | df | MS | F | p-value
Treatment | 118.2 | 2 | 59.1 | 2.94 | 0.095
Error | 241.0 | 12 | 20.1 | |
Total | 359.2 | 14 | | |
To construct an analysis of variance (ANOVA) table and test whether the temperature level has an effect on the mean yield process, we need to perform the following steps:
Step 1: Calculate the total sum of squares (SST), the treatment sum of squares (SSTR), and the error sum of squares (SSE).
SST = ΣΣ(yij - ȳ)^2 = 359.2
where yij is the yield of the ith batch at the jth temperature level and ȳ is the overall mean yield.
SSTR = Σ(nj(ȳj - ȳ)^2) = 118.2
where nj is the number of batches produced at the jth temperature level, ȳj is the mean yield at the jth temperature level, and ȳ is the overall mean yield.
SSE = SST - SSTR = 241.0
Step 2: Calculate the degrees of freedom (df) for SST, SSTR, and SSE.
df(Total) = N - 1 = 14
where N is the total number of observations.
df(Treatment) = k - 1 = 2
where k is the number of treatment levels.
df(Error) = df(Total) - df(Treatment) = 12
Step 3: Calculate the mean square (MS) for SSTR and SSE.
MS(Treatment) = SSTR / df(Treatment) = 59.1
MS(Error) = SSE / df(Error) = 20.1
Step 4: Calculate the F-statistic.
F = MS(Treatment) / MS(Error) = 2.94
Step 5: Determine the critical value of F for a 0.05 level of significance with df(Treatment) = 2 and df(Error) = 12.
From a table of F-distributions, the critical value of F is 3.89.
Step 6: Compare the F-statistic to the critical value of F and make a decision.
Since 2.94 < 3.89, we fail to reject the null hypothesis that the temperature level has no effect on the mean yield process. In other words, we do not have sufficient evidence to conclude that there is a difference in mean yield among the three temperature levels.
Step 7: Summarize the results in an ANOVA table.
Source | SS | df | MS | F | p-value
Treatment | 118.2 | 2 | 59.1 | 2.94 | 0.095
Error | 241.0 | 12 | 20.1 | |
Total | 359.2 | 14 | | |
Note: The p-value is calculated as P(F > 2.94) = 0.095, which is greater than the significance level of 0.05. Therefore, we do not reject the null hypothesis.
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Find the area of the shaded region. Round to the nearest square unit when applicable. Show appropriate work. formules, and substitutions.
The areas of the composite figures are listed below:
516 55π cm² 96 m² (29.5π + 77) m² 58 ft² 588 cm²How to determine the areas of composite figures
In this problem we need to determine the areas of composite figures, which are the result of adding and subtracting geometric figures, whose area formulas are listed below:
Rectangle
A = b · h
Triangle
A = 0.5 · b · h
Circle
A = π · r²
Semicircle
A = 0.5π · r²
Quarter of a circle
A = 0.25π · r²
Square
A = l²
Where:
b - Baseh - Heightl - Side lengthr - RadiusA - AreaNow we proceed to determine the area of each figure:
Area 1
A = 30 · 20 - 6 · 14
A = 600 - 84
A = 516
Area 2
A = π · (8 cm)² - π · (3 cm)²
A = (64 - 9) · π cm²
A = 55π cm²
Area 3
A = (14 m)² - 4 · (5 m)²
A = 196 m² - 100 m²
A = 96 m²
Area 4
A = 0.5π · (7 m)² + 0.5 · (14 m) · (11 m)
A = 29.5π m² + 77 m²
A = (29.5π + 77) m²
Area 5
A = (7 ft) · (10 ft) + (3 ft) · (4 ft)
A = 70 ft² - 12 ft²
A = 58 ft²
Area 6
A = (28 cm)² - 4 · 0.25π · (14 cm)²
A = 784 cm² - 196π cm²
A = 588 cm²
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A carpet in Frank’s house has a length of 2 1/4 meters and a width of 1 1/5 meters. What is the area of the carpet? 6 9/10 meters 2 1/20 square meters 2 7/10 square meters 2 7/20 meters
The area of the carpet is [tex]2 7/20[/tex] square meters.
The size of a patch on a surface is determined by its area. Surface area refers to the area of an open surface or the boundary of a three-dimensional object, whereas the area of a plane region or plane area refers to the area of a form or planar lamina.
To find the area of the carpet, we need to multiply its length by its width.
The mixed numbers must first be transformed into improper fractions:
Length: 21/4 = 9/4
Width: 11/5 = 6/5
Then we can multiply:
Area = length x width
Area = (9/4) x (6/5)
Area = 54/20 or 27/20 square meters
Therefore, the area of the carpet is 27/20 square meters.
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In ΔABC, a = 6 inches, mm∠A=121° and mm∠B=36°. Find the length of b, to the nearest 10th of an inch.
Using a calculator, we find that b ≈ 3.9 inches (rounded to the nearest 10th of an inch).
What is the Law of Sines?
The Law of Sines, also known as the sine rule, is a trigonometric formula used to find unknown sides or angles in a triangle.
To solve this problem, we can use the Law of Sines, which states that for any triangle ABC,
a/sin(A) = b/sin(B) = c/sin(C)
where a, b, and c are the side lengths opposite the corresponding angles A, B, and C, respectively.
Using this formula, we can set up the following proportion:
b/sin(B) = a/sin(A)
Plugging in the values we know, we get:
b/sin(36°) = 6/sin(121°)
Solving for b, we get:
b = (6 sin(36°))/sin(121°)
Using a calculator, we find that b ≈ 3.9 inches (rounded to the nearest 10th of an inch).
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what is 1 8 in decimal
1/8 in a decimal, divide the denominator by the numerator to get 1/8 as a decimal 1/8 is 0.125.
We divide the numerator by the denominator to convert a fraction to a decimal number. This results in a decimal value because, when dividing, we add the decimal place and then add the necessary number of zeros to finish the division.
1/8
1/2 x 1/2 x 1/2
0.5 x 0.5 x 0.5
0.125
To convert a fraction to a decimal, all you have to do is divide the numerator by the denominator. We position the number over its place value when converting a decimal to a fraction.
Just dividing the numerator by the denominator is all that is required to convert a fraction to a decimal.
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