1.62,16.2,15/20 greatest to least
Answer
The order of the number from greatest to least is 1.62, 15/20, 16.2%
Step-by-step explanation
Given: 1.62 16.2% 15/20
To order these data in descending order (i.e. from highest to least), follow the steps below
1. Convert all numbers to decimals
1.62
16.2% = 16.2/100
16.2% = 0.162
15/20 = 0.75
So, the number are 1.62, 0.162, 0.75
2. Compare the three decimals and arrange in descending order
1.62 > 0.75 > 0.162
This means that 1.62 is greater than 0.75 and 0.75 is greater than 0.162
By substituting 16.2% for 0.162 and 15/20 for 0.75, the order of the number from greatest to least is
1.62, 15/20, 16.2%
what are the answers to these questions
1) 4x=24
2) x3=11
3) 8=n÷3
4) 5x÷6=20
5) 3a=12
6) 5⋅z=35
7) 40=4y
8) 42=7k
9) 7x=105
10) 75=6⋅w
Answer:
X=6Step-by-step explanation:
X=6X=3.7n=24X=24a=4Z=7y=10k=6x=15w=12.5The data set represents the number of miles Mary jogger each day for the past nine days.
Answer: 0
Step-by-step explanation: It is furthest away from the other numbers with a difference of at least 5. If plotted in a table it would visually be seen to be further away from the general trend.
3. It took an average of 20 days for a car dealership to sell a new car. Due to the current shortage in the new car market, you believe it is now quicker to sell a car. You take a sample of 30 recently sold cars and find that it took an average of 15 days to sell. You know the population standard deviation is 12 days and it is fairly stable. Test your hypotheses at the 5% significance level using the p-value approach. Follow the 4-step procedure and show your work.
Answer to the given Hypotheses is : The current shortage in the new car market has made it quicker to sell a car.
In this scenario, we have to determine if the current shortage in the new car market has affected the time it takes a car dealership to sell a new car. To answer this question, we will use the p-value approach.
First, we will determine the null and alternative hypotheses. The null hypothesis (H₀) is that the average time it takes to sell a car has not changed, while the alternative hypothesis (H₁) is that the current shortage in the new car market has made it quicker to sell a car.
H₀: μ = 20
H₁: μ < 20
Second, we will choose the appropriate test statistic and determine the level of significance. In this case, we will use a one-sample t-test, as the population standard deviation is known, and you will use a 5% level of significance (α = 0.05).
Third, we will calculate the test statistic and the p-value. The test statistic is calculated by dividing the difference between the sample mean and the hypothesized population mean by the standard error of the mean.
t = (x' - μ) / (σ / √n)
t = (15 - 20) / (12 / √30)
t = -2.89
Using a t-distribution table with 29 degrees of freedom, the p-value is 0.004.
Since the p-value is less than the level of significance, we reject the null hypothesis and conclude that the current shortage in the new car market has made it quicker to sell a car.
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Given 1 || m ||
|| n, find the value of x.
(x-6)⁰
60⁰
1
m
n
The value of x in the lines is 126 degree
We are given that;
Three parallel line and one intersecting line
Angles= (x-6) and 60
Now,
By supplementary angles property
Angle 1 + Angle 2 = 180 degree
Substituting the values of angles
x-6 + 60 = 180
x + 54 = 180
x = 180-54
x = 126
Therefore by supplementary angles answer will be 126 degree.
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Help me with this question no explanation needed or just give it to me
Answer:
Step-by-step explanation:
No explanation is needed because there is no question.
Answer:
you got it
Step-by-step explanation:
no explanation needed
Side panel MF Open course index Open block drawer Learnership Pre-Assessment and Evaluation v1 Figure Classification Assessment  QUIZ Figure Classification Assessment Back Time left 0:59:33 Question 1 Not yet answered Not graded Flag question Question text This test consists of several different items. Each item of the test appears in a separate question. The form of an item - item 25, say, is as follows:  You will notice that there are six boxes: 1 box in the first row 2 boxes in the second row, and 3 boxes in the third row In the top left-hand corner of each box, there is a letter labelling each box. For example, the letter ‚"A" labels the box in the first row. The number, which appears to the left of the box ‚"A" is the number of the item. In this example, it is item 25. Every item of the test will have this form, with each box containing a drawing of shapes or patterns. The following is an example of an item:  You must group the 6 drawings into two groups of 3 drawings each. The drawings of each group must be similar to one another in some way - they must belong together. In the example - item 25 - drawings A, B and F belong together because they are shaded the same way, and drawing C, D and E belong together because their shadings are the same. Now turn to your answer sheet and look at it carefully. At the top of the page is 2 rows of 6 boxes. The first row of the boxes refers to the item "Example (i)" and the second row of the boxes refer to the item "Example (ii)." Below these two rows are 24 rows of 6 boxes. Each row refers to a particular item of the test. The number which appears to the left of each row of boxes refers to the item number in the test. Each row of 6 boxes is divided into 2 groups of 3 boxes. The first box of each row contains the letter "A". In the following two empty boxes, you insert the letters of the two drawings which belongs to the same group as that to which drawing A belongs. In the second group of 3 empty boxes you must insert the letters of the other 3 drawings which belong together. Here is another example of an item - item 26.  In this item, drawings A, D and E belong together because their outlines consist of single lines. Drawings B, C and F belong together because their outlines consist of double lines. The answer to this practice item should be filled in as follows:  Please note the following: 1. It is NOT correct to find a reason for grouping together 3 drawings of an item, and assume that the other 3 drawings belong together. For example, when solving item 26 (Previous page), it would be incorrect to group together drawings A, E and F on the basis that each of these is a 4-sided figure, and drawings B, C and D on the basis that they do not have 4 sides. You must be able to find something common to the 3 drawings of each group. 2. A drawing may NOT belong to both groups. For example, the response-  would be incorrect since the drawing "D" is common to both groups. Select one: a. Continue b. Ask for assistance Clear my choice Question 2 Not yet answered Not graded Flag question Question text You must now do two example items on your own. These examples are on the next two pages. Please fill in the answers to the two examples in the first two rows of the answer sheet. These two rows are labelled “Example (i)" and “Example (ii)". Group the 6 drawings into two groups of 3 drawings each. The drawings of each group must be similar to one another in some way - they must belong together. Hint: Type the answer as one word e.g. ABC  Answeris the first group. Answeris the second group.
The solution is: the dimensions of the flag in inches is:
40 inches by 55 inches.
The flag is rectangular in nature and the formula for calculating the perimeter of a rectangle is P = 2(L+W) where;
L is the length of the flag
W is the width of the flag
From the diagram, L = y and W = 11y/8
Since the perimeter = 190 inches, we will substitute the given parameters into the formula and firs calculate the value of y.
190 = 2(y+11y/8)
190 = 2y + 11y/4
multiply through by 4
760 = 8y+11y
760 = 19y
y = 760/19
y = 40
The length of the flag is 40 inches and the Width of the flag is 11(40)/8 = 55inches.
Hence, the dimensions of the flag in inches is 40 inches by 55 inches.
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complete question:
Item 15 Question 1 Write and solve an equation to answer the question. The perimeter of the Norwegian flag is 190 inches. What are the dimensions of the flag? Equation: =190 y= Question 2 Label the dimensions of the flag in inches.
Answer:
Step-by-step explanation:
Which term describes the distribution of this graph?
A. Uniform
B. Skewed Right
C. Normal
D. Skewed Left
(Reward, 50 Points.)
HELP ME PLS ASAP………….
Answer:
=
Step-by-step explanation:
0.67 is the same as 0.670
Please solve this question
Answer:2x-14
Step-by-step explanation:
Find the length of the three missing sides in the rhombus below.
y
Z
X
82
As all sides of a Rhombus are of equal length, the length of the missing sides are 82
Property of a RhombusThe property of a Rhombus required for answering this question is associated with the length of it's sides. A Rhombus has four sides with the length of all these sides being equal.
This means that with the length of one of it's sides being 82 , the length of the remaining 3 sides would be 82 as well.
The length of sides x = y = z = 82. Hence, x, y and z are 82
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Your ability to borrow money at lower rates improves as
OA. you save more
OB. you earn more
OC. your debt ratio increases
OD. your credit score increases
Your ability to borrow money at lower rates improves as your credit score increases. Option D.
What is a credit score?Your ability to borrow money at lower rates improves as your credit score increases.
A higher credit score indicates to lenders that you have a strong credit history, responsible financial behavior, and a lower risk of defaulting on loans.
Lenders view borrowers with higher credit scores as more reliable and trustworthy, making them more likely to offer lower interest rates and better loan terms.
While saving more and earning more can indirectly contribute to improving your credit score by positively impacting your financial stability and ability to manage debt, they are not direct factors that lenders consider when determining interest rates.
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Help Me please!!!!!!!!!!!
The triangles are similar and
Yes , ΔPSQ ≅ ΔRST because ∠S ≅ ∠S and PS / RS = QS / TS . Thus the triangles are similar by the SAS theorem
Given data ,
Let the first triangle be ΔPSQ
Let the second triangle be ΔRST
Now , the corresponding sides are
PS / RS = QS / TS
where the corresponding sides of similar triangles are in the same ratio
And , the common angle to both the triangles is m∠S
So , ∠S ≅ ∠S and PS / RS = QS / TS
Two sides are equal and the angle between the two sides is equal (SAS: side, angle, side)
Hence , the triangles are similar
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Find the length of side x to the nearest tenth.
Answer: x=6.6
Step-by-step explanation:
The is a 30-60-90 triangle, which means it falls into the special right triangles category
That means that the hypotenuse (x) is the smaller leg (sqrt11) multiplied by 2.
Sqrt11 times 2 is 6.6332495807108
Rounded to the nearest tenth would turn out to be 6.6
PLEASE HELP LOL
What is the value of x in this triangle?
Enter your answer in the box.
x =
The solution is: the value of x in this triangle is x = 83°.
Here, we have,
given that,
the angles of a triangle are:
44, 53 and x
now, we have to find the value of x in this triangle.
we know that,
Angle sum property of triangle states that the sum of interior angles of a triangle is 180°.
so, we have,
44 + 53 + x = 180°
or, x= 83
Hence, The solution is: the value of x in this triangle is x = 83°.
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If someone walks along the outside of the garden from point A to point B, what percent of the garden's border would they have walked around? Round your answer to the nearest whole percent. Type the correct answer in the box. Use numerals instead of words. They would have walked around approximately % of the outside border of the garden.
The outside border of the garden would have walked around approximately 58%.
Without more information about the shape and dimensions of the garden, it's impossible to give an exact answer. However, if we assume that the garden is a rectangle, we can use the formula for the perimeter of a rectangle to estimate the percentage of the garden's border that would be walked around.
Let's say that the length of the garden is L and the width of the garden is W. The perimeter of the rectangle is then:
P = 2L + 2W
If the person walks from point A to point B along the outside of the garden, they are essentially walking along two sides of the rectangle. Let's call these sides S1 and S2. Depending on the location of A and B, S1 and S2 may be two adjacent sides, two opposite sides, or one side and one diagonal.
To estimate the percentage of the garden's border that the person would walk around, we can calculate the length of S1 and S2 and divide by the total perimeter of the rectangle:
Percentage walked = (S1 + S2) / P * 100%
Again, without more information about the shape and dimensions of the garden, we can't give an exact answer. However, if we assume that the person walks along two adjacent sides of the rectangle, the percentage of the garden's border that they would walk around would be:
Percentage walked = (2L + W) / (2L + 2W) * 100%
Simplifying this expression, we get:
Percentage walked = (2L + W) / (2(L + W)) * 100%
Assuming that L and W are measured in the same units (e.g. meters), we can simplify further:
Percentage walked = (2 + W/L) / (2 + 2W/L) * 100%
For example, if the length of the garden is 10 meters and the width of the garden is 5 meters, then the percentage of the garden's border that the person would walk around if they walked along two adjacent sides would be:
Percentage walked = (2 + 5/10) / (2 + 2*5/10) * 100%
= 7/12 * 100%
= 58.3%
So the outside border of the garden would have walked around approximately 58%.
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Elijah wraps a gift box in the shape of a right rectangular prism. The figure below shows a net for the gift box.How much wrapping paper did he use, in square meters?
The amount of wrapping paper which Elijah used is equal to 812 m².
How to calculate the surface area of a rectangular prism?In Mathematics and Geometry, the surface area of a rectangular prism can be calculated and determined by using this mathematical equation or formula:
Surface area of a rectangular prism = 2(LH + LW + WH)
Where:
SA represents the surface area of a rectangular prism.L represents the length of a rectangular prism.W represents the width of a rectangular prism.H represents the height of a rectangular prism.By substituting the given side lengths into the formula for the surface area of a right rectangular prism, we have the following;
Surface area of a right rectangular prism = 2[3 × 10 + (10 × 12 × 2) + (13 × 12 × 2)]
Surface area of a right rectangular prism = 812 m².
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Missing information:
The question is incomplete and the complete question is shown in the attached picture.
pls help marking as brainlist
Answer:
138ft^2
Step-by-step explanation:
9x2=18
10x12=120
18+120=138ft^2
If y varies directly as x, and y = 2 when x = 3, find y when x = 1.
a. y = 2x; y(1) =2
4
y = x; y(1) = 4
3
b.
3
2-x; 9(1) = 1/2
Y = 2 x; }
y
-
C.
d.
2
Y = 3 X; y(1) = ²
3
Answer:
2/3
Hope this helps
prove that: (cosec A- sec A) (cot A-tan A) = (cosec A + sec A) (sec A cosec A-2)
Answer: To prove the given identity:
(cosec A - sec A)(cot A - tan A) = (cosec A + sec A)(sec A cosec A - 2)
We will start by simplifying both sides of the equation.
Left-hand side (LHS):
(cosec A - sec A)(cot A - tan A)
Using trigonometric identities, we can rewrite cosec A, sec A, cot A, and tan A in terms of sin A and cos A:
cosec A = 1/sin Asec A = 1/cos Acot A = cos A / sin Atan A = sin A / cos A
Substituting these values into the LHS:
(cosec A - sec A)(cot A - tan A)
= (1/sin A - 1/cos A)(cos A / sin A - sin A / cos A)
= ((cos A - sin A) / (sin A * cos A)) * ((cos A^2 - sin A^2) / (sin A * cos A))
= (cos^2 A - sin^2 A) / (sin^2 A * cos^2 A) [Using the difference of squares identity: a^2 - b^2 = (a + b)(a - b)]
= ((cos A + sin A)(cos A - sin A)) / (sin^2 A * cos^2 A)
Right-hand side (RHS):
(cosec A + sec A)(sec A cosec A - 2)
Again, using the same trigonometric identities:
(cosec A + sec A)(sec A cosec A - 2)= (1/sin A + 1/cos A)((1/cos A)(1/sin A) - 2)= ((cos A + sin A) / (sin A * cos A)) * (1 / (sin A * cos A) - 2)= (cos A + sin A) / (sin^2 A * cos^2 A) * (1 - 2sin^2 A * cos^2 A)
Now, we need to show that the LHS is equal to the RHS:
((cos A + sin A)(cos A - sin A)) / (sin^2 A * cos^2 A) = (cos A + sin A) / (sin^2 A * cos^2 A) * (1 - 2sin^2 A * cos^2 A)
To prove this, we can cancel out the common factors in the numerator and denominator of the LHS:
(cos A - sin A) = 1 - 2sin^2 A * cos^2 A
Next, we'll simplify both sides individually:
1 - 2sin^2 A * cos^2 A= 1 - 2(sin A * cos A)^2= 1 - 2(sin A * cos A)(sin A * cos A)= 1 - 2sin A * cos A * sin A * cos A= 1 - 2sin^2 A * cos^2 A
Therefore, the LHS is equal to the RHS, and the given identity has been proven.
Brennan knew his parents had set up their will some years ago. Neither he nor his sister, Maureen, had ever discussed the will with their parents. When both parents passed away, they met with the family lawyer about the will. What they found was that the money their parents had been giving them over the last few years was a gift and part of their estate planning. The gifts reduced the size of the estate to ensure the value of the estate upon their passing would be under the tax-free limit.
Their parents had not really talked with Brennan or Maureen about how the “gift” money they had been receiving would affect their final inheritance. As they listened to
the estate lawyer give them details of their inheritance, they were shocked to learn there was less than what they had thought.
1. Discuss your thoughts on how Brennan’s and Maureen’s parents handled the informationin the will prior to their passing. Should the parents have explained more clearly about the “gift” money and how it affected their inheritance?
2. What responsibility did Brennan and Maureen have to discuss the will with their parents?
3. What experience do you have with a family member’s will? How would you approach
the topic of writing a will with a family member?
1.It is generally considered best practice for parents to discuss their intentions with their children and heirs to avoid confusion or misunderstandings.
2.As potential heirs, Brennan and Maureen had a responsibility to communicate with their parents about their estate planning and express any concerns or questions they had.
3.I have personally not had experience with a family member's will. However, I believe it is important to approach the topic of writing a will with sensitivity and empathy.
1. While it is understandable that Brennan and Maureen's parents may have wanted to keep their financial affairs private, their lack of communication may have caused confusion and disappointment for their children. Ideally, the parents should have discussed their estate planning with their children and explained the impact of the gifts on their final inheritance.
2. As potential heirs, Brennan and Maureen had a responsibility to communicate with their parents about their estate planning and express any concerns or questions they had. While it can be difficult to broach sensitive topics like death and inheritance, it is important for family members to have open and honest communication to prevent misunderstandings or disputes down the line.
3. It can be a difficult and emotional topic to discuss, but it is important to have open communication to ensure that everyone's wishes are respected and honored. It may be helpful to consult with a lawyer or financial advisor to ensure that the will is properly drafted and that everyone's needs are addressed.
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Write a sin function that has a midline of y=3, and amplitude of 2, and a period of 3/4.
The required sine function is
y = 2 sin (3π/4 (x) + 3
For given function,
A sine function that has a midline of 3, an amplitude of 2 and a period of 3pi/4
A = 2
T = 3π/4
Since we know
The values of all trigonometric functions depending on the ratio of sides in a right-angled triangle are defined as trigonometric ratios. The trigonometric ratios of any acute angle are the ratios of the sides of a right-angled triangle with respect to that acute angle.
In this case, the midline is 3
⇒ D = 3
Using the generalized equation of sine function,
y = A sin (B (x + C)) + D
y = 2 sin (3π/4 (x + 0) + 3
y = 2 sin (3π/4 (x) + 3
Therefore, the required sine function is
y = 2 sin (3π/4 (x) + 3
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13. Find mzYZU.
(10x +9)
(6x-13)
34°
Right angle
Pls help ASAP
Given is a circle with center Z, we need to find the measure of the angle YZU,
We know that,
In a circle, the length of an arc and the length of the corresponding central angle are inextricably linked and equal.
Also,
The whole circle measures 360°.
So,
arc YU + arc UV + arc VX + arc YX = 360°.
10x+9 + 90° + 34° + 6x-13 = 360°
16x = 240°
x = 15
So, arc YU = 10(15) + 9
arc YU = 159°
Since arc YU = ∠ YZU
Therefore the measure of the angle YZU is 159°
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sin 78° find the value
Answer:
Approx. 0.2079
Step-by-step explanation:
To find the value of sin 78°, we can use a scientific calculator or a trigonometric table. However, I can provide an approximate value using the trigonometric identity:
sin(90° - θ) = cos(θ)
In this case, we can use the identity sin(90° - 78°) = cos(78°). Since the cosine of 78° can be determined more easily, we can calculate that instead.
cos 78° ≈ 0.2079
Therefore, sin 78° is approximately equal to 0.2079.
Find the area of the shape
The area of the given figure is 27.5 square centimeter which has a rectangle and triangles
The given figure has a rectangle and triangles
The area of rectangle is length times width
Area of rectangle =5×4
=20 square centimeter
Area of triangle =1/2×base×height
=1/2×2.5×3
=7.5/2
=3.75 square centimeter
As there are two triangle = 2(3.75)
=7.5 square centimeter
Total area = 7.5+ 20
=27.5 square centimeter
Hence, the area of the given figure is 27.5 square centimeter
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4Test 33 points possible 8/20 answered Question 6 < A B 0 Total 7 9 6 13 16 12 Total 20 25 18 Male Female A test was given to a group of students. The grades and gender are summarized below P(female B) > 22 41 63 1hr45mins X Progress saved Submit and End Blake If one student is chosen at random from those who took the test, find the probability that the student female GIVEN they got a 'B'. Write your answer as a reduced fraction.
The probability of a student being female given that they got a 'B' is 87/315.
We can use Bayes' theorem to find the probability of a student being female given that they got a 'B'. Let's first find the total number of students who got a 'B':
Total number of students who got a 'B'
= 7 + 9 + 6 + 13 + 16 + 12
= 63
Out of these 63 students, the number of females who got a 'B' is:
Number of females who got a 'B' = 13 + 16 = 29
So, the probability of a student being female given that they got a 'B' is:
P(Female | B) = P(B | Female) x P(Female) / P(B)
From the given data, we can calculate these probabilities as follows:
P(B | Female) = 29/25
P(Female) = 25/63
P(B) = 63/175
Plugging in these values, we get:
P(Female | B)
= (29/25) x (25/63) / (63/175)
= 87/315
Therefore, the probability of a student being female given that they got a 'B' is 87/315.
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Which of the following equations are equivalent? Select three options. 2 + x = 5 x + 1 = 4 9 + x = 6 x + (negative 4) = 7 Negative 5 + x = negative 2
The three equivalent equations are 2 + x = 5, x + 1 = 4 and -5 + x = -2. So, correct options are A, B and E.
Two equations are considered equivalent if they have the same solution set. In other words, if we solve both equations, we should get the same value for the variable.
To determine which of the given equations are equivalent, we need to solve them for x and see if they have the same solution.
Let's start with the first equation:
2 + x = 5
Subtract 2 from both sides:
x = 3
Now let's move on to the second equation:
x + 1 = 4
Subtract 1 from both sides:
x = 3
Notice that we got the same value of x for both equations, so they are equivalent.
Next, let's look at the third equation:
9 + x = 6
Subtract 9 from both sides:
x = -3
Since this value of x is different from the previous two equations, we can conclude that it is not equivalent to them.
Now, let's move on to the fourth equation:
x + (-4) = 7
Add 4 to both sides:
x = 11
This value of x is also different from the first two equations, so it is not equivalent to them.
Finally, let's look at the fifth equation:
-5 + x = -2
Add 5 to both sides:
x = 3
Notice that we got the same value of x as the first two equations, so this equation is also equivalent to them.
So, correct options are A, B and E.
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Complete question is:
Which of the following equations are equivalent? Select three options.
2 + x = 5
x + 1 = 4
9 + x = 6
x + (- 4) = 7
- 5 + x = - 2
�
=
# correct
X=# correctX, equals, start text, \#, space, c, o, r, r, e, c, t, end text
0
00
1
11
2
22
3
33
�
(
�
)
P(X)P, left parenthesis, X, right parenthesis
0.05
0.050, point, 05
0.20
0.200, point, 20
0.50
0.500, point, 50
0.25
0.250, point, 25
Mean:
�
�
=
1.95
μ
X
=1.95mu, start subscript, X, end subscript, equals, 1, point, 95
Standard deviation:
�
�
≈
0.8
σ
X
≈0.8sigma, start subscript, X, end subscript, approximately equals, 0, point, 8
Mr. Gupta decides to score the tests by giving
10
1010 points for each correct question. He also plans to give every student
5
55 additional bonus points. Let
�
YY represent a random student's score.
What are the mean and standard deviation of
�
YY?
�
�
=
Answer:
is every whole number a natural number
What is the probability that either event will occur? 3 A 18 B 15 P(A or B) = P(A) + P(B) P(A or B) = [?] Enter as a decimal rounded to the nearest hundredth.
Answer:
the probability that either event will occur is 0.92
Step-by-step explanation:
the probability that either event will occur is 0.92
What is the probability that either event will occur?
From the question, we have the following parameters that can be used in our computation:
Event A = 18
Event B = 15
Other Events = 3
Using the above as a guide, we have the following:
Total = A + B + C
So, we have
Total = 18 + 15 + 3
Evaluate
Total = 36
So, we have
P(A) = 18/36
P(B) = 15/36
For either events, we have
P(A or B) = 33/36 = 0.91666
Hence, the probability that either event will occur is 0.92 (rounded to nearest hundreth)
NO LINKS!!!! URGENT HELP PLEASE!!!!!
Solve ΔABC using the Law of Sines Part 1
3. A = 110°, a= 14, b= 9
4. B = 110°, c = 13, b = 21
Answer:
3) B = 37.2°, C = 32.8°, c = 8.1
4) A = 34.4°, C = 35.6°, a = 12.6
Step-by-step explanation:
To solve for the remaining sides and angles of the triangle, given two sides and an adjacent angle, use the Law of Sines formula:
[tex]\boxed{\begin{minipage}{7.6 cm}\underline{Law of Sines} \\\\$\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}}[/tex]
Question 3Given values:
a = 14b = 9A = 110°Substitute the given values into the formula and solve for angle B:
[tex]\implies \dfrac{a}{\sin A}=\dfrac{b}{\sin B}[/tex]
[tex]\implies \dfrac{14}{\sin 110^{\circ}}=\dfrac{9}{\sin B}[/tex]
[tex]\implies 14\sin B=9\sin 110^{\circ}[/tex]
[tex]\implies \sin B=\dfrac{9\sin 110^{\circ}}{14}[/tex]
[tex]\implies B=\sin^{-1}\left(\dfrac{9\sin 110^{\circ}}{14}\right)[/tex]
[tex]\implies B=37.1632517...^{\circ}[/tex]
[tex]\implies B=37.2^{\circ}[/tex]
As the interior angles of a triangle sum to 180°:
[tex]\implies A+B+C=180^{\circ}[/tex]
[tex]\implies C=180^{\circ}-A-B[/tex]
[tex]\implies C=180^{\circ}-110^{\circ}-37.1632517...^{\circ}[/tex]
[tex]\implies C=32.8367482...^{\circ}[/tex]
[tex]\implies C=32.8^{\circ}[/tex]
Finally, substitute the values of a, A, and C into the Law of Sines formula and solve for side c:
[tex]\implies \dfrac{a}{\sin A}=\dfrac{c}{\sin C}[/tex]
[tex]\implies \dfrac{14}{\sin 110^{\circ}}=\dfrac{c}{\sin 32.8367482...^{\circ}}[/tex]
[tex]\implies c=\dfrac{14\sin 32.8367482...^{\circ}}{\sin 110^{\circ}}[/tex]
[tex]\implies c=8.07866414...[/tex]
[tex]\implies c=8.1[/tex]
[tex]\hrulefill[/tex]
Question 4Given values:
b = 21c = 13B = 110°Substitute the given values into the formula and solve for angle C:
[tex]\implies \dfrac{b}{\sin B}=\dfrac{c}{\sin C}[/tex]
[tex]\implies \dfrac{21}{\sin 110^{\circ}}=\dfrac{13}{\sin C}[/tex]
[tex]\implies 21 \sin C=13\sin 110^{\circ}[/tex]
[tex]\implies \sin C=\dfrac{13\sin 110^{\circ}}{21}[/tex]
[tex]\implies C=\sin^{-1}\left(\dfrac{13\sin 110^{\circ}}{21}\right)[/tex]
[tex]\implies C=35.5712205...^{\circ}[/tex]
[tex]\implies C=35.6^{\circ}[/tex]
As the interior angles of a triangle sum to 180°:
[tex]\implies A+B+C=180^{\circ}[/tex]
[tex]\implies A=180^{\circ}-B-C[/tex]
[tex]\implies A=180^{\circ}-110^{\circ}-35.5712205...^{\circ}[/tex]
[tex]\implies A=34.4287794...^{\circ}[/tex]
[tex]\implies A=34.4^{\circ}[/tex]
Finally, substitute the values of b, B, and A into the Law of Sines formula and solve for side a:
[tex]\implies \dfrac{a}{\sin A}=\dfrac{b}{\sin B}[/tex]
[tex]\implies \dfrac{a}{\sin 34.4287794...^{\circ}}=\dfrac{21}{\sin 110^{\circ}}[/tex]
[tex]\implies a=\dfrac{21\sin 34.4287794...^{\circ}}{\sin 110^{\circ}}[/tex]
[tex]\implies a=12.6349923...[/tex]
[tex]\implies a=12.6[/tex]