let H be the altitude from vertex C. Which proves the first equality in the law of sines
Answers
The sine law of triangles can be proved by dividing the triangle into right-triangles.
Option (c) proves the first equality in the law of sines
From the question, we have:
h equals to the distance from point C to segment AB
The sine of angle is:
[tex]\mathbf{sin(\theta) = \frac{Opposite}{Hypotenuse}}[/tex]
For angle at A, we have:
[tex]\mathbe{\theta = A}[/tex]
[tex]\mathbf{Hypotenuse = b}\\\mathbf{Opposite = h}[/tex]
So, we have:
[tex]\mathbf{sin(\theta) = \frac{Opposite}{Hypotenuse}}[/tex]
Substitute values for Opposite, Hypotenuse and theta
[tex]\mathbf{sin A = \frac{h}{b}}[/tex]
Similarly
[tex]\mathbf{sin B = \frac{h}{a}}[/tex]
Make h the subject
[tex]\mathbf{h = a\ sinB}[/tex]
Substitute [tex]\mathbf{h = a\ sinB}[/tex] in [tex]\mathbf{sin A = \frac{h}{b}}[/tex]
[tex]\mathbf{sin A = \frac{a\ sinB}{b}}[/tex]
Divide both sides by a
[tex]\mathbf{\frac{sin A}{a} = \frac{sinB}{b}}[/tex]
Hence, the correct option is (c).
Read more about proof of sine law at:
https://brainly.com/question/4637169
Related Questions
This question in algebraic expression and number form : the difference between 20 and x
Answers
Answer: Let the numbers be x and y.
x+y = 20 …(1)
x-y = 10 …(2)
Add (1) and (2)
2x = 30, or x = 15, and so y = 5.
The product of the two numbers = xy = 15*5 = 75.
Step-by-step explanation:
The regular price of a skateboard is $74.99.
Find the sale price when the skateboard is reduced by:
a) 30% b) 25% c) 60% d) 50%
Calculate each sale price, including taxes of 13%.
Answers
Answer:
a)$62.2417
b)$65.9912
c)$39.7447
d)$47.2437
Step-by-step explanation:
a)100%-30%=70%
70%+13%=83%
83/100x74.99=62.2417
b)100%-25%=75%
75%+13%=88%
88/100x74.99=65.9912
c)100%-60%=40%
40+13=53
53/100x74.99=39.7447
d)100%-50%=50%
50+13=63%
63/100X74.99=47.2437
Hope this helps! Thanks.
Which of the following are remote interior angles of angle 1? Check all that apply
A. <5
B. <2
C. <3
D. <1
E. <4
F. <6
Answers
Answer:
The answer would be 6 and 4.
Step-by-step explanation:
Because when they mean remote interior, they are hinting that the interior angles that are not close to 1. We cannot choose 3 in this situation because it is adjacent to angle 1.
Zahid and nasir had 7350 game cards. Zahid gave 520 cards to nasir. Now zahid had 4 times as many games cards as nasir. How many game cards did zahid bave at first?
Answers
Answer:
Zahid had/has 31480 cards
7350 + 520= 7870
7870 times 4 = 31480
Step-by-step explanation:
Hope this helps
can i get braineist
Answer:
Step-by-step explanation:
Zahid and nasir had game cards= 7350
Zahid gave cards =520
Total cards left= 7350 - 520= 6830
Let
Zahid =x
Nasir = 4x
x+4x=6830
5x=6830
x=6830/5=1366
Zahid=1366
Nasir=4x=4(1366)=5464
Check
Zahid=1366+520=1886
Nasir=5464
Zahid+Nasir=1886+5464=7350
Please Help!
1. If you take a Uber and they charge $5 just to show up and $1.57 per mile, how much will it cost you to go 12 miles? (Assume no tip.)
a. Create an equation from the information above.
b. Identify the slope in the equation?
c. Calculate the total cost of the ride?
2. With the same charges as #1, how many miles could you go with $50, if you also gave a $7.50 tip? (Challenge Question! Hint, you only have a $50, exactly, with you.)
Answers
Answer:
1. 23.84
a. Let x = Each mile
5 + 1.57x
b. Let Y = graph position
y = 5 + 1.57x
c. 23.84
2. 27 Miles
Step-by-step explanation:
which is equivalent to 2 5/6?
A. 5/3
B. 12/5
C. 7/6
D. 17/6
(IF YOU ARE ABLE TO, PLEASE PROVIDE AN EXPLANATION FOR THE ANSWER)
Answers
7. Trading volume on the New York Stock Exchange is heaviest during the first half hour (early morning) and last half hour (late afternoon) of the trading day. The early morning trading volumes (millions of shares) for 13 days in January and February are shown here (Barron’s, January 23, 2006; February 13, 2006; and February 27, 2006). 214 163 265 194 180 202 198 212 201 174 171 211 211 The probability distribution of trading volume is approximately normal. a) Compute the mean and standard deviation to use as estimates of the population mean and standard deviation. b) What is the probability that, on a randomly selected day, the early morning trading volume will be less than 180 million shares? c) What is the probability that, on a randomly selected day, the early morning trading volume will exceed 230 million shares?
Answers
In this problem, first we find the sample mean and the standard deviation, and then, we use the normal distribution. Then, we get that:
a) The mean is of 199.69 and the standard deviation is of 25.02.
b) 0.2148 = 21.48% probability that, on a randomly selected day, the early morning trading volume will be less than 180 million shares.
c) 0.1131 = 11.31% probability that, on a randomly selected day, the early morning trading volume will exceed 230 million shares.
In a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
It measures how many standard deviations the measure is from the mean. After finding the z-score, we look at the z-score table and find the p-value associated with this z-score, which is the percentile of X.Item a:
The mean is the sum of all observations divided by the number of observations, thus:
[tex]\mu = \frac{214 + 163 + 265 + 194 + 180 + 202 + 198 + 212 + 201 + 174 + 171 + 211 + 211}{13} = 199.69[/tex]
The standard deviation is given by the square root of the sum of the difference squared between each observation and the mean, divided by the number of values. Thus:
[tex]\sigma = \sqrt{\frac{(214-199.69)^2 + (163-199.69)^2 + (265-199.69)^2 + (194-199.69)^2 + ... + (211-199.69)^2}{13}} = 25.02[/tex]
The mean is of 199.69 and the standard deviation is of 25.02.
Item b:
This probability is the p-value of Z when X = 180, thus:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{180 - 199.69}{25.02}[/tex]
[tex]Z = -0.79[/tex]
[tex]Z = -0.79[/tex] has a p-value of 0.2148.
0.2148 = 21.48% probability that, on a randomly selected day, the early morning trading volume will be less than 180 million shares.
Item c:
This probability is 1 subtracted by the p-value of Z when X = 230, thus:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{230 - 199.69}{25.02}[/tex]
[tex]Z = 1.21[/tex]
[tex]Z = 1.21[/tex] has a p-value of 0.8869.
1 - 0.8869 = 0.1131
0.1131 = 11.31% probability that, on a randomly selected day, the early morning trading volume will exceed 230 million shares.
A similar problem is given at https://brainly.com/question/24663213
4. As Jody dives below the water, its temperature decreases by 0.3 degrees Fahrenheit per foot that he dives. If
Jody is diving at a rate of 2.5 feet per second and the water at the surface is at a temperature of 68 degrees
Fahrenheit then what is the temperature of the water Jody is in after diving for 20 seconds?
(1) 48
(3) 57
(2) 53
(4) 83
Answers
Answer:
83
Step-by-step explanation:
The temperature of the water Jody is in after diving for 20 seconds is 53.
Given that,
The temperature should be decreased by 0.3 degrees.The rate should be 2.5 feet per second and the temperature of 68 degrees.And, the time taken is 20 seconds.Based on the above information, the calculation is as follows:
[tex]= 68 - (2.5\times 20\times 0.3)[/tex]
= 68 - 15
= 53
Therefore we can conclude that the temperature of the water Jody is in after diving for 20 seconds is 53.
Learn more: brainly.com/question/20459283
DO NOT ANSWER WITH A LINK
The sum of three consecutive integers is 42. Which of the equations could represent this relationship? Select the two correct answers.
x + (x + 1) + (x + 2) = 42
x + (x + 2) + (x + 4) = 42
(x minus 1) + x + (x + 1) = 42
(x minus 2) + x + (x + 2) = 42
x + 2 x + 3 x = 42
Answers
Answer:
x+(x+1)+(x+2)=42
(x minus 1)+x +(x+1)=42
Step-by-step explanation:
to find the smaller number and to find the middle number
I hope this help you
A rectangular picture frame has a length that is 6 cm greater than the width. The total perimeter is 36
cm. What are the dimensions for the frame? Write an equation, solve and then fully answer the
question.
Answers
Answer:
Step-by-step explanation:
width= x
length= x+6
perimter = 2x+ 2(x+6)
36= 2x+ 2x+ 12
36= 4x + 12
36-12= 4x
4x= 24
x= 6
therefore width= 6cm
length= 6+6 = 12
Show your work!!
Solve for missing angle
Answers
So, you do 80 + 35 + x = 180
115 + x = 180
180-115= 65
the answer is 65 degrees
Who ever answers first will be marked brainliest
Answers
Answer:
The answer is x≥9.
Step-by-step explanation:
Answer:
x≥9
Step-by-step explanation:
this is the answer all you have to do is solve it
What is the system of measurement used most often in the United States?
customary
converted
metric
similar
Answers
Answer:
metric po
Step-by-step explanation:
measurements and metric units of measure
solve pls brainliest
Answers
Answer:
y = 1.28
Step-by-step explanation:
Hi there!
[tex]10.24=8y[/tex]
To solve for y, divide both sides by 8:
[tex]\displaystyle \frac{10.24}{8} =\displaystyle \frac{8y}{8} \\\\1.28=y[/tex]
Therefore, y = 1.28.
I hope this helps!
Answer:
= 1 . 2 8
Step-by-step explanation:
10.24 =8y
10.24 = 8y
8 8
Please help me I only have 10 points left so ten points I’ll give please help thank you I’ll give brainless to the first person
Answers
Answer:
It would be g(x) = 2^-x
Step-by-step explanation:
Help or no if so thanks<3
Answers
4/21 of a spool
Step-by-step explanation:
2/7 * 2/3 = 4/21
Solve for n.
ples help me solv for n
Answers
Answer: 50 miles per hour
Step-by-step explanation: It is that because when the line passes on the one hour mark it is 50.
Find f-1(x), if f(x) = 3x – 6. Justify your
reasoning with math calculations and/or a written
explanation.
Answers
Explanation: given f(x) = 3x - 6.
Let y = f(x) and so y = 3x - 6.
Trade places between x and y.
x = 3y - 6
Solve for y
x + 6 = 3y
y = x + 6/3
Now the new y is the inverse and so y = f-1(x)
f-1(x) = 1/3(x + 6)
whats nine plus 10 ;)
Answers
Answer:
19
Step-by-step explanation:
9+10=19
please mark me brainliest
Answer:
21 ^^
jk jk lol 19 >->
but reality... i believe it's 2356486513
A quality control engineer inspects a random sample of 3 batteries from each lot of 24 car batteries that is ready to be shipped. If such a lot contains six batteries with slight defects, what is the probability that the inspector's sample will contain none of the batteries with defects
Answers
Answer:
10
Step-by-step explanation:
The probability of getting a sample without any defect is 1 / 6.
What is probability?Probability is defined as the ratio of the number of favourable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.
Probability = Number of favourable outcomes / Number of sample
Given that a quality control engineer inspects a random sample of 3 batteries from each lot of 24 car batteries that are ready to be shipped.
Total batteries = 24
Total non-defective batteries = 24 - 6 = 18
Probability = Number of favourable outcomes / Number of sample
Probability = 3 / 18
Probability = 1 / 6
Therefore, the probability of getting a sample without any defect is 1 / 6.
To know more about probability follow
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Which expression is equivalent to -0.25(16m + 12)?
PLEASE HELP
Answers
Answer:
-4m-3
Step-by-step explanation:
Step-by-step explanation:
→ -0.25(16m+12)
→ (-0.25×16m)+(-0.25×12)
→ (-4m)+(-3)
→ -4m-3. Answer
hey guys pls help me i need to submit this before 1hr .graphing an inverse function.y = 4x + 12 using the x values (-2,-1, 0, 1 and 2).
Answers
Answer:
4, 8, 12, 16, 24
Step-by-step explanation:
Replace the x with the x values starting at -2 and use the equation with the new x value.
E.g.
x = -2
y = 4 * -2 + 12
y = 4
Sorry if my explanation isn't the best.
a. Complete the table to chart his calorie expenditure for different amounts of time.
Time (minutes)
to
5
45
30
120
20
80
75
15
Calories Burned
to
20
9
b. Plot the table of values on the graph.
X/
x9
400f%
300
Calories Burned
200
100
20
10 20 30 40 50 60 70 80 90 100
Time (minutes)
Answers
Answer:
you are missing the values; 25, 50, 90, and 105
Solved by using - Guv=8piG(Tuv+P^Guv)
50 points need awnserd asap
A store manager wishes to investigate whether there is a relationship between the type of promotion offered and the number of customers who spend more than $30 on a purchase. Data will be gathered and placed into the two-way table below. Customer Spending by Promotion Run Customers Spending More than $30 Customers Spending $30 or Less $10 off $50 15% off $5 off $25 Buy-1-Get-1 Half Off Which statement best describes how the manager can check if there is an association between the two variables? The manager must check relative frequencies by row because there are more than two different promotions. The manager must check relative frequencies by column because there are more than two different promotions. The manager cannot use relative frequencies to look for an association because there are more than two different promotions. The manager should check both relative frequencies by row and by column to look for an association.
Answers
Write 1000 as a power of 10
Answers
a line passes through the point of (4,2) and has a slope of -5/4
Answers
Answer:
y = -5/4x + 7
Step-by-step explanation:
y = -5/4x + b
2 = -5/4(4) + b
2 = -5 + b
7 = b
wich of the following 7/18 closest to
Answers
Answer:
1/2
hope this helps
Answer:
1/2
Step-by-step explanation:
7/18 is close to 1/2
I’m a little lost on this
Answers
Which is the label of the ordered pair (1,3)?
1. V
2.W
3.X
4. Y
5. Z
Answers
Answer:
dude. its 4.Y
Question 7
Maya, Tom, and Greg sent a total of 153 text messages over their cell phones during the weekend, Greg sent 9 fewer messages than Maya,
Tom sent 4 times as many messages as Greg, How many messages did they each send?
Answers
[tex]▪▪▪▪▪▪▪▪▪▪▪▪▪ {\huge\mathfrak{Answer}}▪▪▪▪▪▪▪▪▪▪▪▪▪▪[/tex]
The messages sent by them are ~
Maya = 33 messages Greg = 24 messages Tom = 96 messages[tex] \large \boxed{ \mathfrak{Step\:\: By\:\:Step\:\:Explanation}}[/tex]
Let the number of messages sent by Maya be x,
messages sent by Greg = x - 9
messages sent by Tom = 4(x - 9)
and, total number of messages sent by them all together is equal to ~ 153
that is ~
[tex]x + x - 9 + 4(x - 9) = 153[/tex][tex]2x - 9 + 4x - 36 = 153[/tex][tex]6x - 45 = 153[/tex][tex]6x = 153 + 45[/tex][tex]6x = 198[/tex][tex]x = 198 \div 6[/tex][tex]x = 3 3[/tex]Hence, the messages sent by them are ~
Maya = x = 33Greg = x - 9 = 33 - 9 = 24Tom = 4(x - 9) = 4 × 24 = 96Let Maya send m
Greg send m-9
Tom sent 4(m-9)
ATQ
m+m-9+4(m-9)=1532m-9+4m-36=1536m-45=1536m=153+456m=198m=33Greg=33-9=24
Tom=4(24)=96