Answers
The measurements that are correct for the given triangle are
sin C = 9/15
B ≈ 53.13°
Trigonometrical ratiosFrom the question, we are to determine which of the given trigonometrical ratios for the given triangle are correct
The given triangle is a right angle triangle
Using SOH CAH TOA
sin C = 9/15
∴ The option sin C = 9/15 is correct
Also,
Using SOH CAH CAH
tan B = 12/9
∴ The option tan B = 9/12 is NOT correct
To determine the measure of angle B (m ∠B)
From tan B = 12/9
Then,
tan B = 1.33333
B = tan⁻¹(1.33333)
∴ B ≈ 53.13°
Thus, the option B ≈ 53.13° is correct
Hence, the measurements that are correct for the given triangle are
sin C = 9/15
B ≈ 53.13°
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Related Questions
A bus moves away from a bus stop in a straight line. it moves 10 meters by the end of the 1st second, 20 meters by the end of the 2nd second, and 30 meters by the end of the 3rd second. how many meters away is the bus from the bus stop after 10 seconds? a. 100 c. 120 b. 110 d. 190 please select the best answer from the choices provided a b c d
Answers
10 meters away is the bus from the bus stop after 10 seconds.
What is arithmetic sequence?A series of integers in which the difference between succeeding words is always the same is referred to as an arithmetic sequence or arithmetic progression. For instance, the difference in the arithmetic series 1, 5, 9, 13, 17,... is always 4. The common difference is what we refer to as.
According to the given information:A bus moves away from bus stop in a straight line. After 1 second it was 10 meters away, after 2 seconds it was 20 meters and after 3 seconds it was 30 meters away.
In this way bus forms an arithmetic sequence
10, 20, 30, 40........up to 10 terms.
nth term of an arithmetic sequence is represented by
[tex]T_{n}[/tex] = a+ (n - 1)d
Here a = 10 and d = common difference = 10
Therefore 10th term = 10 + (10-1)10
= 10 + 90
= 100
Therefore after 10 seconds bus will be 10 meters away from the bus stop.
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A boat sails on a bearing of 63 for 124 miles and then turns and sails 201 miles on a bearing of 192. Find the distance of the boat from its starting point.
Answers
The distance of the boat from its starting point is 156.226 .
According to the question
A boat sails on a bearing of 63 degree for 124 miles
i.e
By making 63 degree covers 124 miles
therefore ,
In figure below
AC = 124 miles
Then turns and sails 201 miles on a bearing of 192 degree
therefore ,
In figure below
CD = 201 miles
Now,
According to the sum of triangle
∠ACB + ∠ABC + ∠BAC = 180°
∠ACB + 90° + 63° = 180°
∠ACB = 27°
CE = 180° (Straight line )
therefore,
∠DCE = 192° - 180°
= 12°
As ∠C = 90°
therefore
∠ACD = ∠C - ∠DCE - ∠ACB
= 90° - 12°- 27 °
= 51°
Now,
The distance of the boat from its starting point = AD
By using Law of Cosines
As
The Law of Cosines can be used to find the unknown parts of an oblique triangle(non-right triangle), such that either the lengths of two sides and the measure of the included angle is known (SAS) or the lengths of the three sides (SSS) are given.
The Law of Cosines (also called the Cosine Rule) says:
c² = a² + b² − 2ab cos(C)
As we have 2 sides and one angle available we can use Law of Cosines
Therefore,
by substituting the value
(AD)² = (AC)² + (CD)² − 2(AC)(CD) cos(∠ACD)
(AD)² = (124)² + (201)² − 2*124*201 cos(51)
AD = 156.226
Hence, the distance of the boat from its starting point is 156.226 .
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A ladder resting against a wall makes an
angle of 63° with the ground. The foot of
the ladder is 4.7 m from the wall.
Calculate the height of the top of the
ladder above the ground
Answers
Answer:
9.224
Step-by-step explanation:
Which of the following is NOT a monomial? -11x
x - 4
3
22xy
Answers
Answer:
x - 4
Step-by-step explanation:
monomial is one term
-11x is only one term
x-4 isn't
3 is one term
22xy is only one term
only x-4 isn't a monomial
because there is a minus
Here is the histogram of a data distribution. What is the shape of this distribution?
Answers
Considering it's histogram, the shape of the distribution is given by:
D. Bimodal.
What is an histogram?An histogram of a data-set is a graph that shows the number of times each element of x was observed.
In this problem, elements 1 and 10 were each observed 5 times, meaning that there are two modes in the data-set, hence the data-set is bimodal and option D is correct.
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Michael is constructing a circle circumscribed about a triangle. he has partially completed the construction. what should be his next step in the construction?
Answers
Answer:
Connect the arcs to make a perpendicular bisector
HL=
Help me asap!! Thanks so much I appreciate it :)
Answers
The value of length HL is 8.
How to find HL when two secant intersect outside a circle?A secant is a line that intersects a circle in exactly two points
When two secants intersect outside a circle, the circle divides the secants into segments that are proportional with each other.
Therefore,
(EF + FL)FL = HL(GH + HL)
(10 + 14)10 = (HL + 30 - HL)HL
240 = 30(HL)
divide both sides by 30
Hence,
240 / 30 = 30HL / 30
8 = HL
Therefore,
HL = 8
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REALLY HARD QUESTION HELPPPP
Drag the tiles to the correct boxes to complete the pairs.
∆ABC and ∆PQR are similar. ∆ABC is dilated by a scale factor of 1.25 and rotated 45° counterclockwise about point B to form ∆PQR. The side lengths of ∆ABC are AB, 5 units; BC, 4.2 units; and AC, 4 units. Match each side of ∆PQR to its length.
Answers
Answer:
Step-by-step explanation: I did the test and the answer should be A
hope this helps :)
What is the probability that 2 precedes 1 when we randomly select a permutation of {1, 2,. ,n} where n ≥ 4?
Answers
The probability is 1/3.
Probability is sincerely how likely something is to show up. whenever we're unsure about the final results of an event, we will communicate about the probabilities of positive consequences—how probably they're. The evaluation of events governed by way of possibility is called information.
Probability is the branch of mathematics concerning numerical descriptions of ways likely an occasion is to arise, or how in all likelihood it's far that a proposition is actual. The opportunity of an event is more than a few among 0 and 1, wherein, kind of talking, zero suggests impossibility of the occasion and 1 shows the truth.
Chance = the wide variety of approaches to achieving achievement. the whole range of viable consequences. as an example, the opportunity of flipping a coin and its being heads are ½ because there may be 1 manner of getting a head and the overall wide variety of feasible results is two (a head or tail). We write P(heads) = ½.
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Howard buys 6 plants if same price from a flower shop for $640 including the shipping fee. If the shipping fee is $100, find the price of each plant.
Answers
640 - 100 = 540 / 6 =90
What is 11% of 15?
1.65
1.56
2.5
Answers
A positive five-digit integer is in the form ; where , and are each distinct digits. What is the greatest possible value of that is divisible by eleven
Answers
The the biggest 5 digit number based on the computation will be 87,978.
How to compute the value?The difference between the sum of the odd-numbered digits (1st, 3rd, 5th...) and the sum of the even-numbered digits (2nd, 4th...) is divisible by 11.
An example is that 34871903 is divisible by 11
3+8+1+0=12
4+7+9+3=23
23-12=11
Here, we want (b + b) - (a + c + a) to be divisible by 11.
2b - (2a + c) to be divisible by 11
ab,cba (using 7 and 8 and 9 since they biggest)
78 987 --> 2*8 - (2*7 + 9) = 16 - (14 + 9) = 16 - 23 = -7 NO
87 978 --> 2*7 - (2*8 + 9) = 14 - (16 + 9) = 14 - 25 = -11 YES
79 897 --> 2*9 - (2*7 + 8) = 18 - (14 + 8) = 18 - 22 = -4 NO
97 879 --> 2*7 - (2*9 + 8) = 14 - (18 + 8) = 14 - 26 = -12 NO
89 798 --> 2*9 - (2*8 + 7) = 18 - (16 + 7) = 18 - 23 = -5 NO
98 789 --> 2*8 - (2*9 + 7) = 16 - (18 + 7) = 16 - 25 = -9 NO
Therefore, the biggest 5 digit number is 87,978.
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Determine which of the following graphs does not represent a function
Answers
Explanation:
Assuming there are four answer choices, we can eliminate choices A through C because they are functions. This is because they pass the vertical line test.
The vertical line test is where we try to draw a single vertical line through more than one point on the curve. If such a task is possible, then it is said to "fail the vertical line test" and it's not a function.
For choice A, we cannot draw a single vertical line through more than one point on the parabola. Choice A passes the vertical line test. Hence, it is a function. The same goes for choices B and C.
Unfortunately choice D is not shown, but if it's the only thing left, then I'm assuming that it's some curve that fails the vertical line test.
Consider this quadratic equation. x2 3 = 4x which expression correctly sets up the quadratic formula to solve the equation?
Answers
The expression which correctly sets up the quadratic formula to solve the equation is (A) [tex]\frac{-(-4)+-\sqrt[]{-4^{2}-4(1)(3) } }{2(1)}[/tex].
What is an expression?
In mathematics, an expression is a combination of numbers, variables, and functions (such as addition, subtraction, multiplication or division, etc.) Expressions are similar to phrases. A phrase in language may comprise an action on its own, but it does not constitute a complete sentence.To find which expression correctly sets up the quadratic formula to solve the equation:
Theory of quadratic equation - A quadratic equation is defined as any equation containing one term in which the unknown is squared and no term in which it is raised to a higher power.
An example of a quadratic equation in x is [tex]-4x^{2} +4=9x[/tex].
How to solve any quadratic equation using the Sridharacharya formula?
Let us represent a general quadratic equation in x, [tex]ax^{2} +bx+c=0[/tex] where a, b and c are coefficients of the terms.
According to the Sridharacharya formula, the value of x or the roots of the quadratic equation is -
[tex]x=\frac{-b+-\sqrt{(b)^{2}-4(a)(c) } }{2a}[/tex]
The given equation is [tex]x^{2} -4x+3=0[/tex]
Comparing with the general equation of quadratic equation, we get a = 1, b = -4 , c = 3.
Putting the values of coefficients in the Sridharacharya formula,
[tex]\frac{-(-4)+-\sqrt[]{-4^{2}-4(1)(3) } }{2(1)}[/tex] which is (A).
Therefore, the expression which correctly sets up the quadratic formula to solve the equation is (A) [tex]\frac{-(-4)+-\sqrt[]{-4^{2}-4(1)(3) } }{2(1)}[/tex].
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The complete question is shown below:
Consider this quadratic equation. x^2+3=4x. Which expression correctly sets up the quadratic formula to solve the equation?
A con is tossed n times. How many difference sequences of head and tails can you get?
Answers
Answer:
2^n
Step-by-step explanation:
So whenever you flip a coin, you can see it as 2 nodes branching off of each existing node. so for example when you flip a coin once you're going to have 2 sequences initially H and T, now when you flip a coin again for each of those 2 sequences 2 are going to branch off of that, making the total sequences 4, and the next flip 2 sequences are going to branch off each of the 4 sequences and so on. this can generally be described as: 2^n
I attached an image describing this a bit better but the bottom line is that for each 'end node'/sequence you're going to have 2 branch off of it, thus for each coin flip the number of sequences multiplies by 2
Answer:
2^n
Step-by-step explanation:
dont worry bout it ur welcome
A.22
B.183
C.246
D.213
Answers
Answer:
B. 183
Step-by-step explanation:
m<L = (1/2)[m(arc)KN - m(arc)KM)]
35 = (1/2)(177x - 107x)
70 = 70x
x = 1
m(arc)KN = 177x = 177
m(arc)NMK = 360 - m(arc)KN
m(arc)MNK = 360 - 177
m(arc)MNK = 183
The exponential model A = 999.8 0.002t describes the population, A, of a country' in millions, t years after 2003. Use
the model to determine when the population of the country will be 1051 million?
Answers
The population of the country will be 1051 million in 2014
How to model the population of the country?The exponential model that describes the population of a country' in millions, t years after 2003 is given as:
A = 999.8 e0.002t
Rewrite the function properly as:
A = 999.8 * e^(0.002t)
When the population of the country is 1051 million, it means that:
A = 1051
Substitute the known values in the above equation
So, we have:
1051 = 999.8 * e^(0.002t)
Divide both sides by 999.8
1.0512 = e^(0.002t)
Take the natural logarithm of both sides of the equation
ln(1.0512) = ln(e^(0.002t)
Rewrite the equation as:
ln(e^(0.002t) = log(1.0512)
This gives
0.002t = log(1.0512)
Evaluate the logarithmic expression
0.002t = 0.0216
Divide both sides of the equation by 0.002
t = 0.0216/0.002
Evaluate the quotient
t = 10.8
Approximate 10.8 as 11
t = 11
11 years from 2003 is 2014
Hence, the population of the country will be 1051 million in 2014
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On a coordinate plane, a circle has a center at (0, 0). Point (0, negative 10) lies on the circle.
A circle centered at the origin contains the point
(0, –9). Does (8, StartRoot 17 EndRoot) also lie on the circle? Explain.
No, the distance from the center to the point
(8, StartRoot 17 EndRoot) is not the same as the radius.
No, the radius of 10 units is different from the distance from the center to the point
(8, StartRoot 17 EndRoot).
Yes, the distance from the origin to the point
(8, StartRoot 17 EndRoot) is 9 units.
Yes, the distance from the point (0, –9) to the point (8, StartRoot 17 EndRoot) is 9 units.
Answers
The distance between point [tex](8, \sqrt{17})[/tex] and the center (0,0) is of 9 units, which is less than the radius, hence the correct option is:
Yes, the distance from the origin to the point [tex](8, \sqrt{17})[/tex] is of 9 units.
What is the distance between two points?Suppose that we have two points, [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]. The distance between them is given by:
[tex]D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
In this problem, we have a circle with center at (0,0) and radius 10. Hence, every point that is less than 10 units of distance from point (0,0) will be on the circle.
The distance of [tex](8, \sqrt{17})[/tex] is:
[tex]D = \sqrt{(8 - 0)^2+(\sqrt{17} - 0)^2}[/tex]
[tex]D = \sqrt{81}[/tex]
D = 9 units.
9 < 10, hence the correct option is:
Yes, the distance from the origin to the point [tex](8, \sqrt{17})[/tex] is of 9 units.
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Tim has a bag containing only red, yellow and green jelly beans.
- the number of red jellybeans is 25
- the number of yellow jelly beans is a third of red jelly beans
- a half of his jelly beans are green.
How many of Tim's jellybeans are green?
Answers
Answer:
green=100 jellybeans
Step-by-step explanation:
let the bag be (B)
red jellybeans (R)
yellow jellybeans (Y)
green jellybeans (G)
R=25
Y=3R............(1)
½ of B=G ..........(2)
from equation (1)
Y=3(25)
Y=75
since 1/2 0f the bag are G that means R+Y is equal to the remaining bag
R+Y=75+25=100 which is half of the bag
G that's half of the bag =100
Which equation could represent a linear combination of the system?
Answers
The equation that could represent a linear combination of the system 2/3x + 5/2y = 15 and 4x + 15y = 12 is 0 = 26
What are linear equations?Linear equations are equations that have constant average rates of change, slope or gradient
How to determine the linear combination to the system?A system of linear equations is a collection of at least two linear equations.
In this case, the system of equations is given as
2/3x + 5/2y = 15
4x + 15y = 12
Multiply the first equation by 6, to eliminate the fractions.
6 * (2/3x + 5/2y = 15)
This gives
4x + 15y = 90
Subtract the equation 4x + 15y = 90 from 4x + 15y = 12
4x - 4x + 15y - 15y = 12 - 90
Evaluate the difference
0 + 0 = -78
Evaluate the sum
0 = -78
The above equation is the same equation as option (b) 0 = 26
This is so because they both represent that the system of equations have no solution
Hence, the equation that could represent a linear combination of the system is 0 = 26
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Complete question
The system of equations below has no solution.
2/3x + 5/2y = 15
4x + 15y = 12
Which equation could represent a linear combination of the system?
what all can you tell me about this shape?
Answers
Answer: It is an equilateral square
Step-by-step explanation: it has 4 tick marks
evaluate:25 divided by 5+2 multiplied by 3
Answers
Answer:
11
Step-by-step explanation:
25 than you divided 5 + 2 than you multiply 3 and you get
Answer:
11
Step-by-step explanation:
Each sales associate at an electronics store has a choice of the two salary options shown below:
$115 per week plus 9.5% commission on the associate’s total sales
$450 per week with no commission
The average of the total sales amount for each associate last year was $125,000. Based on this average, what is the difference between the two salary options each year? (1 year = 52 weeks)
Answers
Using proportions, it is found that the difference between the two salary options each year is of $5,545.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.
For the first option, $115 per week plus 9.5% commission on the associate’s total sales, the yearly salary is:
115 x 52 + 0.095 x 125000 = $17,855.
For the second option, $450 per week with no commission, the yearly salary is:
450 x 52 = $23,400.
Hence the difference is given as follows:
23400 - 17855 = $5,545.
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Lesson 1.6 Multiply by 1-digit numbers.
estimate then find the product
(only the circled ones)
Answers
The multiplication shows that the answers will be:
1. 3744
2. 8244
3. 3630
4. 2616
5. 20772
6. 7820
7. 3916
8. 3521
9. 21285
10. 54162
11. 4548
12. 2091
13. 17128
14. 55692
15. $895
16. 4300 miles
How to calculate the value?1. 416 × 9 = 3744
2. 1374 × 6 = 8244
3. 726 × 5 = 3630
4. 872 × 3 = 2616
5. 2308 × 9 = 20772
6. 1564 × 5 = 7820
7. 4 × 979 = 3916
8. 503 × 7 = 3521
9. 5 × 4257 = 21285
10. 6018 × 9 = 54162
11. 758 × 6 = 4548
12. 3 × 697 = 2091
13. 2141 × 8 = 17128
14. 7 × 7956 = 55692
15. From the information given, the cost of each ticket is $179. Also, there are 5 people that are flying.
Therefore, the total cost will be:
= $179 × 5
= $895
16. Also, for the second question, since the distance between the two cities is 2150 miles. The exact distance will be:
= 2150 × 2
= 4300 miles.
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The total cost charged for a day of fun at Aussie World consists of an entry fee of $15 and a rate of $3 per ride. Write the rule for the total cost, C, where r rides are taken.
Answers
C = 3r + 15 is the rule for the total cost, C, where r rides are taken given that the total cost charged for a day of fun at Aussie World consists of an entry fee of $15 and a rate of $3 per ride. This can be obtained by converting the statements to algebraic equation with variables and constants.
Find the rule for the total cost:Here in the question it is given that,
The total cost charged for a day of fun at Aussie World consists of
an entry fee of $15 a rate of one ride is $3We have to find a rule for the total cost, C, where r rides are taken.
For one ride the rate is 3 ⇒ therefore for r rides the rate is 3r
We can convert the statements to algebraic equation so that we get the required rule,
⇒ The total cost consists of entry fee and rate of rides
⇒ The total cost = entry fee + rate of rides
⇒ C = 15 + 3r (from the given information)
⇒ C = 3r + 15
Hence C = 3r + 15 is the rule for the total cost, C, where r rides are taken given that the total cost charged for a day of fun at Aussie World consists of an entry fee of $15 and a rate of $3 per ride.
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HELP If there are 79 people in a hip-hip dance group and 14 are girls,
what is the probability that a person chosen at random will be a boy?
State your answer as a fraction.
Answers
Answer:
you better give me brainliest
65/79
Step-by-step explanation:
number if boys =79-14 = 65
p of selecting a boy >> 65/79
can't cancel out so leave your answer like that
Rearrange the formula to highlight the height
Answers
Answer:
[tex]h = \frac{2A}{b+c}[/tex]
Step-by-step explanation:
Original Equation:
[tex]A = \frac{1}{2} (b+c)h[/tex]
Divide both sides by height
[tex]\frac{A}{h} = \frac{1}{2}(b+c)[/tex]
Raise both sides to the exponent -1 :
[tex](\frac{A}{h})^{-1} = (\frac{1}{2}(b+c))^{-1}[/tex]
Rewrite using the definition of a negative exponent: [tex](\frac{a}{b})^{-x} = (\frac{b}{a})^{x}[/tex]
[tex]\frac{h}{A} = \frac{1}{\frac{1}{2}(b+c)}\\[/tex]
Multiply 1/2 by (b+c)
[tex]\frac{h}{A} = \frac{1}{\frac{b+c}{2}}\\[/tex]
Keep, change, flip
[tex]\frac{h}{A} = \frac{1}{1} * \frac{2}{b+c} = \frac{2}{b+c}[/tex]
Multiply both sides by A
[tex]h = \frac{2A}{b+c}[/tex]
Also I forgot to mention but the exponent (-1) can be ignored after you flip it, since: [tex](\frac{a}{b})^x = \frac{a^x}{b^x}[/tex], but since in our case the exponent is 1, and [tex]a^1 = a[/tex], so there's really no need to write out the distribution part, since we just get the same fraction, after flipping it.
Point M is the midpoint of AB. Find BM.
Answers
since we know that M is the midpoint of the AB segment, that simply means that the two halves it makes are congruent, namely AM = BM.
[tex]\stackrel{AM}{4x+13}~~ = ~~\stackrel{BM}{3x+17}\implies x+13=17\implies x=4~\hfill \stackrel{3(4)~~ + ~~17}{BM=29}[/tex]
The required length of the side BM is 29.
What is algebra?Algebra is a study of mathematical expressions, in which numbers and quantities are represented in formulas and equations by letters and other universal symbols.
In the given question,
Point M is the midpoint of line AB.
AM = 4x + 13,
and BM = 3x + 17
To find the length of MB, use midpoint property.
Since, Point M is the midpoint of AB,
Therefore, AM = MB
4x + 13 = 3x + 17
4x - 3x = 17 - 13
x = 4
The length of MB = 3x + 17 = 3 × 4 + 17 = 12 + 17 = 29.
The length of MB, where M is midpoint of AB, is 29.
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I am a 2-dimensional shape with all my sides of equal length.
I have an angle sum of 180 degrees.
What am I?
Answers
Answer:
=> Equilateral Triangle
Step-by-step explanation:
Equilateral Triangle is having 2-d shape with all equal sides and the sum of angles of any triangle is 180° .
A scientist uses a submarine to study ocean life. She begins 88 feet below sea level. • After traveling down for 6 seconds, she's 182 feet below sea level. Find the rate of change in the submarine's elevation in feet per second. Round your answer to the nearest tenth.
Answers
Answer:
original ft below sea level =88 feet
In six seconds goes to 182 feet
Amount of feet covered in 6 seconds=182-88=94 ft
Step-by-step explanation:
rate in feet per second = 94/6=15.66
rounding to nearest tenth=15.7ft/s
