Answers
Answer:
m∠B ≈ 70.8°
Step-by-step explanation:
The Law of Cosines relates three sides of a triangle and the angle opposite one of them.
SetupThe law of cosines tells you ...
b² = a² +c² -2ac·cos(B)
Solving for angle B, we get ...
B = arccos((a² +c² -b²)/(2ac))
where 'a' and 'c' are the sides adjacent to the angle of interest. We want angle B, so we can fill this formula as follows:
B = arccos((13² +11² -14²)/(2·13·11))
SolutionB = arccos(94/286)
B ≈ 70.812°
__
Additional comment
Another angle can be found using the Law of Sines.
A = arcsin(sin(70.812°)×13/14) ≈ 61.281°
Then angle C is ...
C = 180° -70.812° -61.281° = 47.907°
Related Questions
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° .
Which of these is a simplified form of the equation 7y 8 = 9 3y 2y? 7y = 6 2y = 1 12y = 17 5y = 17
Answers
The simplified equation of 7y + 8 = 9 + 3y + 2y is 2y = 1
How to simplify an equation?The equation can be simplified as follows:
7y + 8 = 9 + 3y + 2y
We have to combine like terms
Hence,
7y + 8 = 9 + 3y + 2y
7y + 8 = 9 + 5y
subtract 5y from both sides
7y - 5y + 8 = 9 + 5y - 5y
2y + 8 = 9
Let's subtract 8 from both sides
2y + 8 - 8 = 9 - 8
2y = 1
Therefore, the simplified equation of 7y + 8 = 9 + 3y + 2y is 2y = 1
learn more on equation here: https://brainly.com/question/1354560
#SPJ1
Select the correct answer. which function has a phase shift of to the right? a. b. c. d.
Answers
The function y = 2sin has a phase shift of pi/2 to the right (2x - pi).
What is a trigonometric function?An angle or angle function (such as the sine, cosine, tangent, cotangent, secant, or cosecant) is most simply defined in terms of the ratios of pairs of sides of a right-angled triangle.The inverse of a trigonometric function (such as arcsine, arccosine, or arctangent).To find the function which has a phase shift to the right:
The function has a phase shift of pi/2 to the right.
By definition, you have the phase shift is:
asin(bx+c)Phase shift = -c/bWhen you substitute the values from the function [tex]y=2sin(2x-\pi )[/tex], where [tex]c=-\pi[/tex] and [tex]b=2[/tex], you obtain:
Phase shift = [tex]-(-\pi )/2[/tex]Phase shift = [tex]\pi /2[/tex]Therefore, the function y = 2sin has a phase shift of pi/2 to the right (2x-pi).
Know more about trigonometric functions here:
https://brainly.com/question/1143565
#SPJ4
The complete question is given below:
Which function has a phase shift of pi/2 to the right?
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.
Learn more about the Probability here https://brainly.com/question/24756209
#SPJ4
check ple im not sure its right
Answers
Answer:
8
Step-by-step explanation:
You are correct The distance from -6 to 2 is 8.
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.
To know more about arithmetic sequence visit:
https://brainly.com/question/2512128
#SPJ4
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.
To know more about Algebra on:
https://brainly.com/question/24875240
#SPJ2
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
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
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
What is 11% of 15?
1.65
1.56
2.5
Answers
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
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
Read more about exponential functions at:
https://brainly.com/question/11464095
#SPJ1
Determine the convergence or divergence of the sequence with the given nth term. if the sequence converges, find its limit. (if the quantity diverges, enter diverges. ) an = 21/n
Answers
The given sequence [tex]2^{\frac{1}{n} }[/tex] converges with limit 1.
According to the given question.
We have a sequence,
[tex]a_{n} = 2^{\frac{1}{n} }[/tex]
Since, we know that
The sequence of real numbers [tex]S_{n}[/tex], where n goes from 1 to infinity has a limit L, the the sequence is convergent to L. If the sequence doesn't have limit then it is divergent.
The nth root function is strictly increasing for positive real values.
Therefore,
[tex]1^{\frac{1}{n} } \leq 2^{\frac{1}{n} } \leq n^{\frac{1}{n} }[/tex] [tex]\forall \ n\geq 2[/tex]
Also,
[tex]\lim_{n \to \infty} n^{\frac{1}{n} } = 1[/tex]
[tex]\implies \lim_{n \to \infty} 1^{\frac{1}{n} } =1[/tex] ( by squeeze theorem)
Thereofore,
[tex]\lim_{n \to \infty}2^{\frac{1}{n} } =1[/tex]
So, the given sequecence has a limit i.e. 1. Which means [tex]2^{\frac{1}{n} }[/tex] is a convergent sequence.
Hence, the given sequence [tex]2^{\frac{1}{n} }[/tex] converges with limit 1.
Find out more information about convergent and divergent sequence here:
https://brainly.com/question/15415793
#SPJ4
An object is launched at an upward velocity of 96 feet per second from the top of a building 160 feet above the ground. Use the vertical motion model h = - 16t² + vt + c where h is the ending height of the object, c is the initial height, in feet, of the object, t is the time in seconds, and v is the velocity of the object. How long will it take the object to reach the maximum height and what is the maximum height? Fill in the blanks with the appropriate values.
Answers
[tex]~~~~~~\textit{initial velocity in feet} \\\\ h(t) = -16t^2+v_ot+h_o \quad \begin{cases} v_o=\textit{initial velocity}&96\\ \qquad \textit{of the object}\\ h_o=\textit{initial height}&160\\ \qquad \textit{of the object}\\ h=\textit{object's height}&h\\ \qquad \textit{at "t" seconds} \end{cases} \\\\\\ h(t)=-16t^2+96t+160[/tex]
Check the picture below.
[tex]\textit{vertex of a vertical parabola, using coefficients} \\\\ y=\stackrel{\stackrel{a}{\downarrow }}{-16}x^2\stackrel{\stackrel{b}{\downarrow }}{+96}x\stackrel{\stackrel{c}{\downarrow }}{+160} \qquad \qquad \left(-\cfrac{ b}{2 a}~~~~ ,~~~~ c-\cfrac{ b^2}{4 a}\right) \\\\\\ \left(-\cfrac{ 96}{2(-16)}~~~~ ,~~~~ 160-\cfrac{ (96)^2}{4(-16)}\right) \implies \left( - \cfrac{ 96 }{ -32 }~~,~~160 - \cfrac{ 9216 }{ -64 } \right)[/tex]
[tex](3~~,~~160 + 144)\implies \underset{~\hfill feet}{\stackrel{seconds~\hfill }{(\stackrel{\downarrow }{3}~~,~~\underset{\uparrow }{304})}}[/tex]
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
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.
More can be learned about proportions at https://brainly.com/question/24372153
#SPJ1
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
= $895
16. Also, for the second question, since the distance between the two cities is 2150 miles. The exact distance will be:
= 2150 × 2
= 4300 miles.
Learn more about multiplication on:
brainly.com/question/10873737
#SPJ1
A gallon of Moo Milk costs 5.12$
What is the price, in dollars, of an 8 ounce glass of Moo Milk?
Answers
Answer:
$0.32
Step-by-step explanation:
8 ounces is 1/16 of a gallon so
5.12*(1/16) = 0.32
Answer:
32 cents (0.32 dollars)
Step-by-step explanation:
One gallon contains 128 ounces
Calculate the cost of each ounce:
[tex]\frac{5.12}{128} =0.04[/tex]
costs 4 cents an ounce
Calculate the cost of 8 ounces:
[tex](8)(4)=32[/tex]
Hope this helps
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
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:
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
learn more on secant here: https://brainly.com/question/15532257
#SPJ1
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.
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
A machine pumps 2.1 gallons of water every 1.6 minutes. How many gallons is pumped per minutes?
Answers
Answer: 1.3125 gallons
Step-by-step explanation: The machine pumps 2.1 gallons of water every 1.6 minutes. 1.6 minutes is 1.6x more than 1 minute. So, we have to divide 1.6 by 1.6. Next, we have to divide 2.1 by 1.6. We can make this a bit easier by multiplying both of them by 10 to get 21/16 which is 1.3125.
Answer:
1.3125 gallons
Step-by-step explanation:
Using the given information, we can set up a proportion;
[tex]\frac{2.1gallons}{1.6minutes} = \frac{xgallons}{1minute}[/tex]
Now, we can cross multiply to solve for x.
2.1 = 1.6x
x = 1.3125 gallons
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.
More can be learned about histograms at https://brainly.com/question/26622630
#SPJ1
Fundamentally, pressure is defined as force per unit area. what is the source of the force in a gas sample?
Answers
The source of the force in the gas sample is; The force is composed of the sum of the collisions only between the gas molecules and the container
What is the relationship between Force and Pressure?We are given that;
Pressure = Force /Area
Now, for any gas sample, force is defined as basically the force exerted by the gas molecules when they strike the surface and bounce back inside the container where they are located.
Now, from the definition above we can conclude that the source of the force in the gas sample will be The force is composed of the sum of the collisions only between the gas molecules and the container
Read more about Force and Pressure at; https://brainly.com/question/13182194
#SPJ1
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 :)
If a consumer purchases a combination of commodities x and y such that mux/px = 30 and muy/py = 40, to maximize utility, the consumers should buy.
Answers
If [tex]MU_{x}/P_{x}[/tex]=30 and [tex]MU_{y} /P_{y}[/tex]=40 then the consumer should buy the commodity y to maximise utility.
Given that [tex]MU_{x}/P_{x}[/tex]=30 and [tex]MU_{y} /P_{y}[/tex]=40 of commodities x and y.
Marginal utility is the additional utility that a consumer gets from consuming additional units of commodity. For maximising the utility of the consumer,the ratio of marginal utilities must be equal to the ratio of the products.
There can be two situations in our case:
Because [tex]MU_{x}/P_{x}[/tex]<[tex]MU_{y} /P_{y}[/tex]
So to equalise the ratio we need to reduce [tex]MU_{y} /P_{y}[/tex]. To reduce the utility of y the consumer needs to increase the consumption of y because as the consumption of commodity y increase it decreases the utility of commodity y.
Hence if [tex]MU_{x}/P_{x}[/tex]=30 and [tex]MU_{y} /P_{y}[/tex]=40 then the consumer should buy the commodity y to maximise utility.
Learn more about utility at https://brainly.com/question/24922430
#SPJ4
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].
Know more about expressions here:
https://brainly.com/question/22048677
#SPJ4
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?
